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(3] An alloy is to contain copper and
zinc in the ratio 9 : 4. The zinc
required to melt with 24 kg of copper
is :
2
(a) 10 kg
{
(c)
3
9 kg
3
(d) 9kg
(4) 7 log (
(a) a:
) + 5 log
(!!) + 3
log :
CHAPTER 1
•.
.
•.
Ratio and Proportion, Indices and Logarithm
( :) is equal to :
1
(a) O
(b) 1
(C) log 2
(d) log 3
j 2007 - February
2006-- November
I
(1) Two numbers are in the ratio 2 : 3
and the difference of their squares is
320. The numbers are :
(a) 12, 18
{b) 16, 24.
(c) 14, 21
{d) None.
(2) If p : q is the sub-duplicate ratio of p
(5) Two numbers are in he ratio 7 : 8. If
3 is added to each of them, their
ratio becomes 8 : 9..The numbers
are :
- x2 :q - x2, then x2 is : ·
la) 14,16
(a)
P
(c) 21,24
(d) 16,18
(b)
p q
q
(b) 24,27
(c) ..9e...
p-q
(d) None.
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#2
I 2007 -August
I
2001 -May
(10] Eight people are planning to share
equally the cost of a rental car. If
one person withdraws from the
arrangement and the others share
equally entire cost of the car, then
the share of each of the remaining
persons increased by :
(a)
(c) 1!7
(d) 7/8
each type of coins :
(a) 102, 136, 170
(b) 136, 102, 170
(c) 170, 102, 136
(d) None.
m+3n
4m-9n
x .-_x •.
is :
(13] If log (2a - 3b) = log a - log b, then
(a)
2b-1
3b
(b)
(c)
{d)
-- --+
+ -----
1 + z•·b+:zB· C 1 + z b· C +,zb· I 1 + zC· l +zC·b
reduces to :·
1
(a)
(18] Number of digits in the numeral for
264• [Given log 2 = 0.30103] :
[22]
· )!Vl (
(a) 1
(b) 19 digits
(b)
(c) 20 digits
(d) 21 digit$ .
(c) . 3
(d)
-]
)7/2 x 9 is equal to :
3
(a) 18digits
j 2007 - November
z 2(a• b•q
/3
9./3
·
log 8
3
1
[19] f 407 are to be divided among A, B
and C so that their shares are inthe
If the earnings of A increase by 50%
and those of B decrease by 25%,
the new ratio of. their earning
becomes 8 :7.What is A's earning ?
(a) f 21,000
(b) f 26,000
(c) f 28,000
(d) Data inadequate.
[16) P, Q and R are three cities. The ratio
(a)
(b)
(c)
(d)
22 : 27
27 : 22
32 :33
1
equal to :
2b+1
3b2
(b) 1
(c) 2
o
1
: 5 :6
1
1
. Tha
rspeet1•ve
shares of A, B, C are :
(a) f 165, t 132, ,110
(b) . 165, f 110, f 132
(c) f 132, f 110, ,165
(d)
n 10, , 132, ,165
[20] The incomes of A and B are in the
ratio 3 : 2 and their expenditures in
the ratio 5 :3. If each saves f 1,500,
then B's income is :
(a) f 6,000
(b) f 4,500
(c) f 3,000
(d) ,7,500
[21] If 4• = SY = 2oz then z is equal to :·
. (a) xy
(b)
1
[17] log111(abc) + log11c(abc) + '°9c.(abc) is
(a)
4
rati.o 1
None.
2b-1
b2
2b+1
1
of average temperature between P
and Q is 11 : 12 and that between P
and R is 9 :8. The ratio between the
average temperature of Q and R is :
(a) x m
(b) x· m
(c) x n
(d) X""
3b2
1
. (d) 0
[15] Ratio of earnings of A and B is 4 :7.
(11]A bag contains t 187 inthe form oj1
rupee, 50 paise and 1O paise coins
in the ratio 3:4:5. Find the number of
a =:
(14] On simplification
(b) z(S • b•q
(c) 1
1/9
(b) 1/8
(12] Simplification of
J
(c)
xy
1
-
xy
(d)
xy
x +y
(d) -1
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From www.castudynotes.com
l 2008 - February
· •
I
[24] In 40 litres mixture of glycerine and
water, the, ratio of glycerine and
· water is 3:1. The quantity of water
added in the ·mixture in order to.
make this ratio 2:1 is:
(a) 15 litres
(b) 10 litres
(c) 8 litres
(d) 5 litres.
[25] The third proportional between
(a2 - b2) and (a+b)2 is :
(a) a+b
a- b
(b) a- b
a+b
(c) (a- b)2
a+b
3
(d) (a +b)
a-b
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#3
[46] What must be added to each term of
the ratio 49 : 68, so that it becomes 3 : 4
?
(a) 3
(b) 5
(c) 8
[51) If A:B= 2:5, then (1OA + 3B):(5A+28)
is equal to:
(a) 7:4
(b) 7:3
(c) 6:5
{d) 7:9
(d) 9
the ratio 5 : 7, if 1O students left from
each class, the remaining students
are in the ratio of 4 : 6 then the
number of students in each class ·is:
!
= mi where ('m' is a positive ·
integer > 2) then the value of : ·
1
1
1
l g4n
logmn
- +- +- + ...........+.
!
log3 n
n
40, 60 ·
I 2010 -December
I
(48] The value of
2
3
2 log x + 2 log x +2 log x +-------+
2 log x' will be :
(a) n(n + l ) log x
2
{b) n(n+ 1) log x
(c) n2 log x
{d) None of these .
[49) The recurring decimal
can be expressed as:
(a) 24/9
[57) The value of
.
[53) In a film shooting, A and B received
money in a certain ratio and B and C
(a)
(b)
(c)
(d)
also received the money inthe same
ratio. If A gets t 1,60,000 and C gets
f 2,50,000. Findthe amount received
( log0 -
3)
1/5
(3n• 1 + 3")
3n+ 3 _
3n
•1
+
b
abc
c
(c) log (abc) = 0
(d) log (a + b + c) O
[621Find two numbers such that mean
,is equal to:
proportional between them is 18and
=
third proportional between them is
144
.
1/4
(d) 6,24
[2m 1- December
+
I
1/9
1/6
(c)
7, 28
[54) The ratio Compounded of 4:5 and subduplicate of •a•:g is 8:15. Then Value of
•a• is:
(d) ,1,50,000
=2
..
.
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I
og o)
( 1 1 1) =
(a) 9, 36
(b) 8, 32
by B ?
(a) ,2,00,000
(b) ,2,50,000
(c) ,1,00,000
+ ( 11 -
2.nn........
{b) 22/9
(c) 26/9
{d) 25/9
ab
abc
be ca
(a) log (ab + be + ca) = abc
a
(c) -1
(d) 2
[61] Which of the following is true.
If ...! + _!_ + ...! = -1-
(b) log-
j 2012 :... June
(b) 0
(d) 6
(c) · 1/3
(d) 1/9
-
(a) 1
(d) 50, 70
[50) Solve :
(b) 4
(c) 2
and given that Y = 2 for X = 1, then
the Value of X for Y = 6 will be:
(a) 3
(b) 9
(52) If n
1
(a) 30, 40
(b) 25, 24
I
2011-June
I
[60] Find the value of x, if x (x)'" = (x"')•
(a) 3
[56) If X Varies inversely as square of Y
[47] The students of two classes are in
(c)
! 2012 - December
[55) If log2x + log4x = 6, then the Value of
x is :
(a) 16
(b) 32
(c) 64
(d) 128
Downloaded From www.castudynotes.com
[58) If logx y = 100 and log2 x = 10,then
the value of 'y' is :
(a) 210
(b) 2100
(c) 21.000
(d) 210.000
[59) Which of the numbers are not in
proportion ?
(a) 6, 8, 5, 7
(b) 7, 14, 6
(c) 18, 27, 12, 18
[2013
June
I
[63) For what value of x, the equation
(log_rx2)2 = log/ is true?
(a) 16
(b) 32
(c) 8
(d) 4
(a)
(b)
(c)
(d)
10·1
102
· 10
103
(a)
(b)
(c)
(d)
2
(d) 8, 6, 12, 9
3
4
5
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(64) The mean proportional between 24
and 54 is :
(a) 33
(b) 34
(c) 35
(d) 36
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#4
{31) If x = 'f , y = i' and z = x" then abc
is:
[26) If 2x -2x-, = 4 then x' ls equal to :
(a) ·7
(a) 2
(b) 1
(b) 3 .
(c) 27
(d) 9
[27] If x =
e "- e -•
e "+ e -•
1
(a)
_ 1+
, then the value of nis:
X
1- x
(c) loge 1+ X
1- x
(d) loge 1 +X
(c) 3
is :
(d) 4
(a) 1
(b) -1(7
[32) If log2 [log3 (log2 K)] = 1, then x
equals :
(a) 128
j 2008 - December
[28] log 144 is equal to :
(a) 2 log 4 + 2 log 2
[33) If log ( a b)
=i
-+ -
b
I
per kg be mixed with tea worth f 14
per kg, so that the average price of ·
the mixture may be f 11 per kg?
(a) 2:1
(b) 3:1
(c) 3:2
(d) 4:3
[30) The ages of two persons are inthe
ratio 5:7. Eighteen years ago their
ages were inthe ratio of 8:13,their
present ages (in years) are :
(a) 50, 70 ·
(b) 70, 50
2
2p -q
(log
a + log b)
(c) 1!7
(d) 7
[36) Fourth proportional to x, 2x,(x+1) is:
(a) (x+2)
(b) (x-2)
(c) (2x+2)
(d) (2x-2) •
[37] If x = 3 113 + 3 -113 then find value of
3x 3 -9x
(a) 3
(d) 10
a
(38] Find the value of :
(1 - {1 - (1 - x 2 )°1}" 1]"112
(a) 12
(b) 14
(a) 1fx
{b) x
(c) 16
[29) In what ratio should tea worth f 10
- - --]
3
(b) 9
(c) 12
then:
a b
(b) 4 log 2 + 2 log 3
(c) 3 log 2 + 4 log 3
(d) 3 log 2 - 4 log 3
I 2008 - June
q
(c) 512
(d) None.
1+X
(b) loge 1- x
I
[35] If !!..= - then the value of p+q
(b) 256
21oge 1-x
I 2009 -June
(d) 8
(c) 1
(c) 40, 56
(d) None.
(34] If A, B and C started a business by
investing f 1,26,000, f 84,000 and
f 2,10,000. If at the end of the year
profit is f 2,42,000 then the share of
eachi
s:
(a) 72,600, 48,400 1,21,000
(b) 48,400, 1,21,0CO, 72,600
[40) log4 (x 2 + x) - log4 (x+ 1) = 2.
Find x
(a) 16
(b) 0
(c) - 1
(d) None of these.
[2009-
December
j
[41] 2" + 2n-1
2n•1-2n
(a) 1/2
(b) 3/2
(c) 2/3
(d) 1/3
[42) If 2x x 3v x
s• = 360 Then what is the
vatue of x, y , z.?
(a) 3, 2, 1
(b) 1, 2, 3
(c) 2, 3, 1
(d) 1, 3, 2
[43}Find the value of
[1og10126- log10 (23 )+ log10{4)2f
{d) None of these.
[39)l
og (m + n) = log m + log n, m can be
expressed as :
(a) m =
n·
n-1
(b) m =
!:
n+1
(c) 72,000, 49,000, 1,21,000
(d) 48,000, 1,21,4(,0, 72,600
.
(c) m =
n+ 1
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(d) m = n + l
n
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n -1
(a) x
(b) 10
(c) 1
(d) None.
!2010
June
i
[44) Same as Q 26 Feb.2008
(45] If log.b + log. c = 0 then
(a) b = C
(b) b
= -c
(c) b = c = 1
(d) b and c are reciprocals.
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#5
(83) If log x = m + n and log y = m - n,
then log (10x/y2) =
(a) 3n - m + 1
{b) 3m - n + 1
(c) 3n + n + 1
· {d) 3m 2+ n2+ 1
[84) If 15(2p
- q ) = 7pq, where
1
[92) 1f log4 (x2 + x) -log4 (x+1)= 2, then
(88) The value of 2" + 2"" is:
.
2"+1- 2"
(a)
the value of X is:
(a) 2
.!
(b)
p and q
!
2
I2015 - December
[97] There are total 23 coins of ,1,
(93) Value of
(c)
!
l
. 1 2016 -June
=i
[85] The ratio of third proportion of 12, 30
to the mean proportion of 9, 25 is:
(a) 2:1
, (b) 5:1
1-+
1
and
is :
called
and the decimal
part of a logarithm iS called _
· _.
(a) Mantissa, Characteristic
(b) Characteristic, Mantissa
5_in a bag. If their value is,43
(b) 1
(c) 5
(b) 5
(d) 60
(c)
(d)
(89) The integral .part of a logarithm is
·
2
and the ratio of coins of 1 and ,2
is 3:2. Then the number of coins of
1i
s:
(a) 12
(a) O
(d) 2
.·
1
--+
1og:O log!° 1og:' .
3
.:!
2
16
(d) 8
(c)
are positive, then p :q will be:
(a) 5 : 6
(b) 5 : 7
3 :: 35 ·
(c) . 8
(d)
{b) 2
(c) 3
(d)
(b) 3
2
(a) 1
10
14
I 2017 JUNE
1 2017 DECEMBER
[94) If 3• = SY = 75•, then
3:b :c = 4 :5 and c :d =
(a) x + y - z = O
(98) If a :b = 2 :
(c) Whole, Decimal
(d) None of these.
[90] The value of
(c) 7:15
(d) 3:5
(86] The value of log5 3 x log3 4 x ICQi 5.
(a)
o
(a)
(87] What number must be added ·to
each of the numbers 10, 18, 22, 38
to make the numbers is proportion?
(c) 8
z 2 -{x -y)2]
o
(b) 1
2
(a) 2
y 2 -(x -z)2
is
1
(b) 4
(c)
x,2 •(y-z)2
•[(x +z)2-y 2 + {x +y)2 -z 2 + (y +z)2-x 2
(b) 1
(c) 2
(d)
(b)
(c) -1
(d) ...
[91] X, Y, Z together starts a business.If
X invests 3 . times as much as Y
i
nvests and Y invests two third of
(d)
2
1 1
+- =-
x
.!+
x
y
y
6 :7,then a :d is:
(a) 24 :35
z
(b) 8 :15
= .!.
(c) 16:35
(d) 7 :15
z
2 1 1
- =-+
x
z
(99) The value of log (13 + 23 + 33 +
y
.......n3) is equal to:
[95]I
f log 2 = 0.3010 and log 3 = , then
the value of log 24 is:
(a) 1.0791
(a) 3 log 1+ 3 log 2 + ...... + 3l
og n
(b) 2 1og n + 2 1og (n+1) - 2 1og 2
(c) log n + log (n+1) + log (2n+1) -
(b) 1.7323
(c) 1.3801
(d) 1.8301
(96] Ifabc = 2, then the value of
1 -+
Downloaded
From
www.castudynotes.com
what Z invests,
then the
ratio of
1
+
log 6
(d) 1
(100) If a =
1
.E
./6
+ {5 and b = /6 - ,/5 then
{6 - {5
{6 + ./5
1
1
{d) None of these.
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From www.castudynotes.com
1
capitals of x, y z is:
I
(a)
(b)
(c)
(d)
3:9:2
6:3:2
3:6:2
6:2:3
_1+a +2b·
1
1+.!.b+c -1 1+c+a-
2
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the value of
(a) 480
(b) 482
(c)
484
(d) 488
82
+
b2 i
s equal to:
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#6
(a)
(b)
(c)
(d)
[65] The triplicate ratio of 4 :5 is:
(a} 125 :64
(b) 16 :25
(c) 64 : 125
(d) 120 :46
i 2013 - December
[66] If
of
+
+
( a +:+ Cr
...
I
j
25, 55
35, 45
40, 40
15, 65
(b)
I
(c}
9abc
[67] Find three numbers in the ratio 1 :2
: 3, so that the sum of their squares
is equal to 504
(a). 6, 12, 18
(b) 3, 6, 9
(c) 4, 8, 12
(d) 5, 10, 15
[68] The value of log4 9 . log3 2 is:
(a) 3
(b) 9
(c) 2
(d) 1
[69] The value of (logy x .log, y . log. z}3
.
0
(b) - 1
1
(c)
(d) 3
[70] Divide 80 into two parts so that their
product is maximum, then the
numbers are:
x
..!. (log x + log y}
..! + ..! = ---y
..!. (log x / log y)
1: 2
(c) 52
(d) 5
a 2 +ab b2
r
v a Iu e
2
of
:
(
)
X ( ;: ·bc•c\( ::r·•c·a•
is equal to _ .
(a) Y
(b) - 1
(c) 1
(d) None of these
[74) If the salary of P is 25% lower than
that of Q and the salary of R is 200/o
higher than that of Q, the ratio of the
salary of A .and P will be:
(a) 5 :8
(b) 8 : 5
(c) 5 : 3
(d) 3 : 5
(d) 3
"
worth
[80] For three months, the salary of a
person are in the ratio 2 : 4 :5. If the
f 1,48,200. He wish to divide it
amongst his wife, son and daughter
difference between the product of
[76] A
(d) 7 : 3
[72) If (25)150 = (25x)50; then the value of
x will be :
(a) 53
(b} 54
[73) T he
(b) 1
(c) -1
..!. (log x + log y)
3
(a) 19 : 3
(b) 16 : 3
z
(a) 0
3
(d)
= O, then the valu
(d) _
1
[79) If x = 1 + log qr,.y = 1 + IQgq rp and
z = 1 + log. pq then the value of ..! +
2
[71] If x : y = 2:3, then (5x+2y):(3x-y)=
(a) abc
(b) 9abc
(c) _.1_
abc
<x+y) = -·
(a} (log x+log y}
2014 -June
(c>
(a)
[75) lf x2+y2=7xy, then log
person
has
assets
in the ratio 3 : 2 : 1 respectively.
From this assets, the share of his
son will be:
(a) f 24,700
(b) f 49,400
(c) ? 74,i OO
(d) f 37,050
[77] If x = 10924 12, y = log3624 and z =
log48 36, then xyz + 1 = _
(a) 2xy
{b) 2xz
salaries of the first two months and
last two months is f 4,80,00,000;
then the salary of the person for the
second month will be:
(a) f 4,000
(b) f 6,000
(c) f 8,000
(d) f 12,000
I
j
2015:.. June
(c) 2yz
(d) 2
j 2014 - December
I
[78) If log x = a + b, log y = a - b then the
value of log 1ox
_
y2
(a) 1 - a + 3b
(b) a - 1 + 3b
(c) a + 3b + 1
(d) 1' - b + 3a
(81] A dealer mixes rice costing f 13.84
• per Kg. with rice costing f 15.54 and
sells the mixture at f 17.60 per Kg.
So, he earns a profit of 14.6% on his
sale price. The proportion in which
he mixes the two qualities of rice is:
(a) 3 : 7
(b) 5 : 7
(c) 7 : 9
(d) 9 : 11
(82) If p' = q, qY = r and r2
value of xyz will be:
(a) 0
(b) 1
(c)
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(d)
3
6
= p6, then the
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#8
2006 JUNE
[2] Find the positive value of kfor which
the equations : x2 + kx + 64 = O and
x2 - ax + k = O will have real roots :
(a) 12
(b) 16
(c) 18
(d) . 22 .
[3] The equation of the straight line
through the point of intersection of
x + 2y - 5 = o arid x - 3 y - 7 = o
and passing through the point (1,0)
is :
(a) x + 12y 1
(b) x - 12y = 1
(c) x - 12y = 11
(d) None
CHAPTER • EQUATION
S
2
=
I 2007 - February
- ]
[4] A man sells 6 radios and 4 televisions
for ? 18,480. If 14 radios and ?
televisions are sold for the
same amount, what is the price of a
television?
(a) f 1,848
(b) t 840
(c) t 1,680
(d) t 3,360
_
[5] If one root of a equation is 2 + ,Is ,
then the quadratic equation ·is :
13
Downloaded From www.castudynotes.com
(a) 2x - 5y - 18 = O
(b) 2x + 5y + 18 0
(c) 2x + 5y - 18 = O
(d) None of these.
=
! 2007 -May
J
[7] A man starts his job with a certain
monthly salary and earns a fixed
increment every year. If his salary
was f 1,500 after 4 years of service
and f 1,800 after 1O years of
service,what was his starting salary
and what is the annual increment in
rupees?
(a) f 1,300, t 50
(b) f 1,100, { 50
(c) f 1,500, f 30
(d) None.
[8] The area of a triangle with vertices
(1,3), (5,6) and (- 3,4) in terms of
square units is :
(a) 5
(b) 3
(c) 8
(d) 13
! 2007-August
-]
[9] The line joining (- 1, 1) and (2, -.
Downloaded From Iwww.castudynotes.com
#7
I 2017 - December
.
[103) If log (
x?) =
(log x
+ log y) ,
[101) The ratio of the number of , 5
57. (b)
61. (d)
65. (c)
58. (c)
62. (a)
66. (a)
59. (a)
63. (a)
67. (a)
60. (b)
64. (d)
68. (d)
coins and ,1O coins is 8 : 15. If the
69. (c)
70. (c)
71. (b)
72. (b)
73. (c)
77. (c)
81. (a)
85. (b)
89. (b)
93. (b)
97. (a)
101.(c)
74. (b)
78. (a)
82 . (d)
86. (c)
90. (b)
94. (c)
98. (c)
102.(c)
75. (b}
79. (b)
83. (a)
87. (a)
91. (d)
95. (c)
99. (b)
103.(d)
76. (b)
80 . (c)
84. (a)
88. (b)
92 . (c)
96 . (a)
100.(b)
104.(a)
then the value of
value of f 5 coins is,360, then-the
number of ,1O coins will be:
(a) 72
(b) 120
(c) 135
(d) 185
[102) If log3 [log4 (1092 x}J = 0, then the
value of 'x' will be:
x2 + y2
=
(a) 2xy
(b) 4xy
(c) 2x2y2
(d) 6xy
[104) If .!
.! and .! are in
2 ' 3' 5
x
proportion, then the value of 'x' will
be:
'
(a) .!_5 .
(a) 4
2
(b) 8
(b)
(c) 16
(d) 32
!
5
(c) .!_O
3
(d)
6
Answer
1. (b}
2. (d)
3. (a)
5. (c)
9. (b)
6. (a)
7. (b)
10. (c)
11.. (a)
13. (a)
17. (c)
21. (d)
25. (d)
29. (b)
14. (c)
15. (d)
19. (a)
23. (a)
27. (a)
31. (b)
18. (c)
22. (a)
33. (b)
26. (c)
30. (a)
. 34.,(a)
37. (d)
38. (b)
41. (b}
42. (a)
46. (c)
50.(a)
54. (c)
45. (d}
49. (d}
53. (a)
4. (c)
8. (a)
12. (b)
16. (b)
20. (a)
24. (d)
28. (b)
32. (c)
35. (c)
39. (a)
43. (c)
44. (c)
47. (c)
51. (a)
48. (b)
52. (a)
55. (a)
56. (d)
36. (c)
40. (a)
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
#1O
[26] Find the equation of the line passing
[31] Positive value of 'k' for which the
through the point (1, 1) and parallel
roots of equation 12x2 + kx + 5 = O
(3-A)y + 5
to the line 3x + Sy + 17 = O
(a) 3 x + 5y + 8 = o
(b) 5 x + 3y + 8 = 0
are in ratio 3:2, is:
(a) 5/12
(b) 12/5
fixed point, then the fixed point is
(c) 5 x + 3y - 8 = O
. (d) 3 x + Sy - 8 = 0
[27] The graph of straight line x = 5 will
·
be :
·
(a) Intersecting both the axis
(b) Parallel to y- axis
(c) Parallel to x - axis
(d) None of these
[28] Find the equation of the line joil")ing
the point (3,5) with the point of
intersection 2x + 3y - 5 0 and 3x +
Sy - 7 = 0.
(a) Gx + y + 23 = 0 .
(b) 6x + y - 23 = 0
(c) 6 + 2y + 14 = 0,
(d) 2x + Sy + 5 = 0
=
I
1 2010 -Tune
[29] Roots of the equation 3x2 -14x + k =
O will be reciprocal of each other if :
(a) k = - 3
(b) k = 0
(c) k = 3
(d) k = 14.
I
(c)
5/fO
(d)
s[fo
I
010 - December
(c) 2
(d) 10
[30} The lines 3x + 4y + 10 = 0 and
4x - 3y + 5 = 0 are
_
(a) Parallel
(b) Perpendicular to each other
(c) Bisect each other
(d) Coincide with each other .
I
[33] If the ratio of (Sx - 3y) and (5y - 3x)
is 3 : 4, then the value of x : y is :
(a) 27 :29
(b) 29 :27
(c) 3 : 4
(d) 4 :3
[34] If roots of equation x2 + x + r = O are
'oc' and 'P' and 0::3 + 133 = - 6. Find
the value 'r' ?
(b)
(c) ..=_4
3
(d) 1
(b)
-
2cx + C2 - b2
::::: 0
't!- - 2bx + C2 + b2 = 0
c o
(c} Bc't!- .'.. 2(b + c)x + 2 =
(d) x2 + 2bx - (C2 - b2) = O
j 2012 - June
.,
(c) (1,-1)
(d) (-1,1)
(b) 0
3
7
3
passing through a
(b} (-1,-1)
[32) If one root of the equation
x2-3x+k=O is 2, then value of k will .
be:
(a) - 10
(a) ..=_5
=O
(a) X2
(a) (1,1)
2
1 2011. une
[35] For all AER, the line (2 + A)x +
[40] If arithmetic mean between roots of
a quadratic equation is 8 and the
! 2011 - December
]
[36] A straight line "L"is perpendicular to
the line 2X + Y - 6 = O and Cuts the
axis at (3, O}. Find the distance from
ttie point (2, - 3} to the line "L".
,(a) 1/,/5
(b) 5
(c)
./5
(d) 2./5
2
[37] If one root of the Equation px + qx +
r = 0 is r then other root of the
Equation will be:
(a) 1/q
(b) 1/r
(c) 1/p
1
(d) ·p.+ q
[38] If the ratio2· of the roots of the
Equation 4x
]
-
6x + p = 0 is 1:2 then
the value of p is:
(a) 1
(b) 2
(c) - 2
(d) - 1
[39] If p & q are the roots of the Equation
't!- - bx + C = 0, then what Is the
Equation whose roots are (pq+p + q)
and (pq - p - q)?
Downloaded From www.castudynotes.com
geometric mean between them is 5,
the equation is
.
(a) x2 -·1sx - 25 = o
(b) x2 - 16x + 25 = 0
{c) x2 - 16x + 5 = 0
(d) None of these.
[41] The equation of the straight line
passing through the intersection of
4x - 3y - 1 = 0 and 2x - Sy + 3 = 0
and parallel to 4x + Sy = 6 is:
(a) · 4x + 5y - 12 = 0
(b} 4x + 5y - 16 = 0
(c) 4x + Sy - 9 = O
(d} 4x + Sy - 4 = 0
(42] The minimum value of the function
x2 - 6x + 10 is
_
(a) 1
(b) 2
(c) 3
(d) 10
(43] Find the point which divides the line
joini ng the points (2, - 2) and (- 4, 1)
in the ratio 5 :2 externally:
(a) (- 5, 8)
(b) (- 8, 3)
(c) (- 5, 4)
(d) (- 8, 5)
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
. ·
#9
(1 C] The sides of an equilateral triangle
!2008 - February
are shortened by 12 units, 13 units
.
·· ·=i
[14] A man wentto the Reserve Bank of
angled triangle is formed. The side
of the equilateral triangle is :
(a) 17 units
(b) 16 units
(c) 15 units
(d) 18 units.
lridia with , 1,000. He asked the .
cashier to give him , 5 and , 10
notes only in return. The man got
175 rotes in all. Find how many
notes of
5 and , 10 did he
rEJCEiYe?
(a) (25, 150)
(bl (40, 110)
(c) (150, 25)
(d) None.
115) The centroid of the triangle ABC is
at the point (2, 3). A and 8 are the
poims(5, 6) and (-1,4) respectively.
[11] The value of
(a) -3
./a-+ V6==+=J;=s=+.=..=..""
is :
(b) 2
(c) 3
(d) 4
! 2001:... Noven,b
I
(12} Area of a rectangular garden is 8000
square metres. Ratio in length and
breadth is 5:4. A path of uniform
width, runs all roundthe inside of the
,garden. If the path occupies 3200
rn2, what is its width?
(a) 12m
(bl 6m
(c) 10m
(d} 4m.
[13]The value of k for which the points
(k, 1), (5, 5) and (10, 7) may be
collinear is:
(a) k = - 5
(b) k = 7
(cl
k =9
(d) .k = 1
is :
2+
and 14 units respectively and a right
I 2009 - June
(17] The value of
2•
I
[21) A straight line passes lllro1Jgh the
point (3, 2). Find the equation of the
straight line. ·
(a) x + y = 1
(b) x + y = 3
(c) x + y = 5
(d) x + y 2
[22) One root of the equation:
2 ----
1•
z•
............................................ 00
./2
/5
2 :t ../3
=
(a) 1 ±
(b) 2 ±
x' -2(5+ m)x+ 3(7+ "'}= 0 is
(c)
(d) None:
! 2oo8 -DECEMBER.
reciprocal of .the o1her. .
Find the value of M.
j
[18] If x3 -6x2 + ; 1:>< -6 = O then find the
The coordinates of C are :
(a) c1. -2)
value of (3x - 4).
(a) (1, 2. 3)
(b} c2. -1)
(c)
(b) (-1, 2, 5)
(c) (-1, 3, 5}
(d) (2, 3, 5)
(1, 2)
(d) (2, 3)
!2008 -June
I
[16] A man rowing at the rate of 5 km in
an hour instill water takes thrice as
much time in going 40 km up the
river as in going 40 km down. Find
the rate at which the river flows :
(a) !lkm/hr
(b) 2.5 km/hr
(c) 12 km/hr
. (o) Hone.
I
(19] If (2+J3) i$ a root of a quadraic
equation x2 • p. + q = O then find the
value of p and q.
·
(a) (4,-1)
(b) (4,1)
(c) (-4,1)
(d) (2,3)
l20] If area and p erimeter of a rectangle
<a> - 1
(b) 7
(c) 1!7
(d) - 1!7
(23) A straight line ol x = 15 is :
(a) Parallel to Y axis
(b) Parailel to X axis
(c) A diagonal line.
(dl Passes through origin.
I 2009 - December
•
]
[24) If the length of a recia.rt;ile is 5 cm
more than the breadth and If the
perimeter of the reclahlJe is 40 cm,
then the length & beadth of the
rectangle will be :
(a) 7.5 cm, 2.5 cm
(b) 10 cm, 5 cm
is 6000 cm2 and 340 cm
(c) 12.
5 cm, 7.5 cm
respective. then the length of
(d) 15.5 cm, 10.5 C111.
rectangle is :
- [25] The point of lntersectioo of the lines
(a) 140
2.x - 5y 6 and x + y 3 is:
(bl 120
·
(a) (0, 3)
(c) 170
=
(d} 200
(b) (3, 0)
(c) . (3, 3)
(d) (0, 0)
Downloaded From www.castudynotes.com
=
Downloaded From www.castudynotes.com
#12
! 2015 - June
I
[62] The number of students in each
section of a school is 36. After
admitting 12 new students,l
our new
· sections were started. If total
number of students in each .section .
now is 30, than the number of
sections initially were.
(a) 6
(c) 68 years
(d) 63 years
[66] The roots of the cubic equation
7x + 6 = O are:
(a) 1, 2 and 3
(b) 1, -2 and 3
(c) 1, 2 and - 3
(d) 1, -2 and - 3
x3 -
! -2015 - December
{b) 10
(c) 14
{d) 18
[63] If a and 13 be the roots of t.he
quadratic equation 2x2 - 4x = 1, the
2
value of
Al
+
a
is
[67] If the roots of the equation 4x2 -12x
+ k = O are equal, then the value of k
is:
(a) -3
[71) Let E, and E2 are two linear
equations in two variables x and y.
(0,1) is a: solution of both equations
E, and E2• (2, -1) is a solution of
equation E1 only and (-2, -1) is
solution of E2 only then E, and E2
are
.
(a) X = o , y = 1 ·
) 2x - y = - 1, 4x + y = 1
(c) x + y = 1, x - y = - 1
(d) x + 2y = 2, x + y = 1
[72) If a line passes through the mid
point of the line segment joining the
(b) 3
-
(c) -9
(d) 9
[68] If 3x - y = 2, 5x + ay = 3 and 2x +y = 3
(a) -11
(b) 22
(c) -22 ·
(d) 11
[64] A person on a tour has , 9,600 for
his expenses. If his )our is eldended
by 16 days, he has to cut down his
daily expenses by ,20, his original
duration of tour had been.
(a) 48 days
(b) 64 days
(c) 80 days
(d) 96 days
[65) The present age of a man is 8 years
more than thrice the sum of the ages
of his two grandsons who are twins.
After 8 years, his age will be 10
years more than twice the sum of
the ages of his grandsons. The age
of a man when his grandsons were
born was:
(a) 86 years
(b) 73 years
·
are concurrent lines, then the value
of 'a' is:
(a) -1
(b} -2
(c} 2
(d) 3
[69] The equation of line pas.sing through
the point of intersection of the lines
y=3 and x+y=O and parallel to the 2x
- y = 4 is:
(a) 2x - y + 9 0
(b) 2x - y - 9 = 0
(c) x - 2y + 9 = o
(d) x + 2y • 9 = 0
[70) If a + 13 = -2 and a fl = -3, then a, 13
· are the roots of the equation, which
=
is:
(a) x2 - 2x - ·3= O
(b) x2 + 2x - 3 = 0
(c) x2 + 2x + 3 = O
(d) x2 - 2x + 3 = 0
!
[ 2016 -June
points(- 3, - 4) and (- 5, 6) and its
.
slope is
.± , then the equation of the
5
.
.
line is:
(a) 4X - SY + 21 = 0
(b) 4X - 5Y + 11 = 0
(c) 5X - 4Y + 21 = 0
(d) 5X + 4Y + 11 = 0
[73) If difference between the roots of .the
equation x 2 - kx + 8 = 0 is 4, then
the value of K is:
(a)
O
e,/3
(d) ± 4,/3
[74) If zx•y = z2x-y =..fa ,
then
the
respective values of X and Y are -.
(a) 1,
..!.
2
,1
(b)
..!. ..!.
2' 2
(d) None of these.
. I 201
December
[75}A cottage industry produces
2
Downloaded From www.castudynotes.com
!
if.
certain number of pottery articles in
a day. It was observed on a
particular day that the cost of each
article (in ") was 2 more than thrice
the number of articles produced on
that day. If the total cost of
production on that day was , tmo,
the number of articles produced was
(a) 14
(b) 16
(c) 12
(d) 18
'.
(76) The triangle formed by lines
x+2y = 3, 2x - y =1 and y = 0 is
(a) Right angled ·
(b) Equ!lateral
(c) Isosceles
(d) None ol these.
j 201 i-June
(b) ± 4
(c) ±
(c)
I
[77] If the sides of an equilateral triangle
are shortened by 3units, 4 units and
5 units respectively and a .right
triangle is formed, then the side of
an equilateral triangle Is:
(a) 6 units
(b) 7 units ·
(c) 8 units
(d) 10 units.
Downloaded From www.castudynotes.com
4)
#11
2
[441 If one of the roots of the equation x
+ px + E is ,/3+ 2, then the value of
'p' and· ·is:
(a) - 4, -1
[49] The quadrat ic equation x - 2kx +
i6 = O vril have equal roots when
lhe value c f 'k' is
·
(a) ± 1
(b) ± 2
(c) ± :3
(d) ± 4
·(b) 4, - 1
(c) - 4, 1
· (cl) 4, 1
I I 2013 - June ·
[ 2012 - December
=
[45] If log10 5 + log,0 (Sx +1) log,0 (x +
5) + 1 then, the value of x
(a} 7
(b) :3
(c) 5
(d) 10
[46] If I x -2 I + I x - 3 I = 7 then, 'x' will
be equal to
(a) 6
I
[50) If a arid J3 are the roots of the
equation x= + 7x + 12·= 0, then the
equation ""flose roots (a + 13)2 and
(:x -13)2 \'\ illbe:
(a) x2 - 14.x + 49 = O
(b) x2 - 24x + 144 = o
{c) x2 - 50x + 49 = 0
(d) x2 - 19x + 144 = 0
[51] State th3 type of Quadrilateral
formed by 1he vert ices (1, 1), (4, 4),
(4 , 8). (1, 5,: .
(b) - 1
(c) 6 and - 1
(d) No;ie of the above.
[47) Roots of equation 2x2 + 3x + 7=0 are
a and p. The value of cx t3·1 + pa·1 is
(a) 2 .
(b) 'J/7
(c) 7f2
(d) -19/14
[48) If the point (k, 3) is at a distance
of ,fs units from the points (2, k), the
value of 'k' is
(a) 1
(b) 4
(c] 1 and 4 both
{d}
2
None of these.
I
f.
(a) Parallelogram
(b) Squares
(c) Rhombus
(d) Rectangle.
[52) If three pdn1s (1, 3), (-2, 1) and
(k, - 1} are coR inear then the value of
'k' is:
(a) O
(b) · 5
(c) -5
(d) 3
! 2013
Decermer
[54] A seller makes a11 offtr o1 elling
certainarticles !hat :antE dribed
by the equatior J<=25 ·'2y 11Sre 'x'
is the price per u,i:a n:; y motes
the number of un't .The :::ost ice of
the artid e is f 10 per u - The
maximum quantity ll'at (11 be
offered in a single de3.lb a'Vd loss
is
.
(a) 6
(b) 7
(c) B
(d) 9
[55) If kx - 4 = (k - 1) flen rvtiicof the
following Is true?
(a) x = - S
(b) x =
-4
x= -3
(c)
(d) x = - 4
[56] The value of ' K' far w hich the,1stern
of equatbns lo: + 2y = !ani3x + y
= 1 has rio soil.ti on is :
(a) 5
(b) _g_
3
(c) 6
(d)
2
I ! 2014
[53] If b2 - 4ac is a perfect square but not
equal o zero than the roots are:
(a) real and equal
(o) real, rrational and equal
(c) real, ,-alional and unequal
(d) lmag1 n3.ry.
June
I
[57]The lines 3>i-..y+-5=0, x -H-5=0,
4x+5y-45=0 are
_
(a) Con:::urrert
(b) Parallel ·
(c) Not Concurrem
(d) Nomt of te
[58] The roots of the equation y3+y2-y1= 0 are:
(a) (1, 1,-1)
{b) (-1, -f. 1)
(c) (1, 1, 1)
(d) · None of these
[59] The distance from the origin to the
point of intersection of two straight
lines having equations 3x-2y-6 and
3x+2y=18 is:
(a) 2 units
{b) 3 units
(c) 4 units
{d) 5 units
! 2014 - December
I
[60] The equation x + 5y = 33; x + Y =
x -y 3
has the solution (x, y) as:
(a) (4, 8)
(b) (8, 5)
(c) (4, 16)
(d) (16, 4)
[61] The equation of a line patallel to the
line joining the points (7, 5) and (2,
9) which passes through the
point (3,- 4) is:
(a) 7x - 4y + 8 = 0
(b) ·7x - 4y - 8 = 0
(c) 5y + 4x + 8 = 0
(d) 5y • 4x + 8 = 0
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Downloaded From www.castudynotes.com
#14
CHAPTER 3 :INEQUALITIES
k :x + y = 9
I 2007 - February
I
:5x + 3y = 30
I
'-'J •·Y=
X
L4 : y =
3
2
The common region (shaded part}
shown in the diagram refers to the
inequalities :
y s x/2
below :
+
>
18
17}
{x : 97 s x s 9
-19}
(b) (3,0), (0, 3), (4, 2)., & (7, 6) .
(c) (5, O), (0, 1O), (4, 2) & (7, 6)
(d) .(0, 18), (12, 0),(4,2), (0, O} and
(7, 6)
! 2001- May
I
[5] A
then[:
(a) x < -3 or x > 2
2
(b) x < - 2 or x >
2
3
ne
s x s 29}
18
18
(d) None of these.
[4] On solving the inequalities 6x + y
18, x + 4y 12, 2x + y:.: 10, we get
the following situation :
(a) (O, 18), (12, 0), (4, 2) & (7, 6)
y :1: ·9
y f. x/2
x :i:O, y :.: 0.
Ix i I
12
(c) {x : -29 ,s; x ,s;
x :.: 0, y :.: 0
(b) 5x + 3y :.: 30
x+y 9
·
y :.: x/3
y s x/2
x :.: 0, y :.: 0.
(c) 5x + 3y :.: 30
x+y 9
y s x/3
y :.: x/2 .
x :.:. 0, y 0.
(d) 5x + 3y > 30
x + y <9
2) If
4
, the solutio set
is :
(b)
2
[1] Graphs of lnequations are drawn
x- 4 1 s
18
ys - x
=1
3
(a) {x :
(a) 5x + 3y s 30
x +y 9
1
I 2006-November
[3] If I
(c) - 2 <X < 2
(d) None of these.
Downloaded From www.castudynotes.com
car manufacturing company
manufactures cars of two types A .
and B. Model A requires 150 man­
hours for assembling, 50 man-hours
for painting and 10 man-hours for
checking and testing. Model B
requires
60
man-hours
for
assembling, 40 man-hours for
painting and 20 man-hours for
checking .and testing. There are
available 30 thousand man-hours for
assembling, 13thousand man-hours
for painting and S thousand man­
hours for checking and testing.
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13 are the roots of the equation
pz
·
2
x2 + x + 5 = 0 then + is equal to
[78) If a,
a
#13
[82) The point of intersection between
straight lines 3x + 2y = 6 and 3x - y
I
= 12 lie inthe:
(a) ·1st quadrant
(a)
5
(b) · 2
(c) 3
. (d)
4
3
2
1
1
x +y
x -y
[79) 1f -+ -=-1 and -- x4+y
=·
x -y .
(b) 2nc1 quadrant
(c) 3rc1 quadrant
(d) 4"'.quadrant
(83) If the sum of two numbers is 13 and
the sum of their squares is 85, then
the numbers will be:
(a) 3, 10
(a)
8. (c)
9. (d)
10. (a)
11. (c)
12. (c)
13. (a)
14. (c)
18. (b)
15. (b}
19. (c)
16. (b)
20. (b)
23. {a)
24. (c)
(c) 4, 9
· 27. {b}
31. {d}
35. {b}
39. {a) ,
43. (b)
28. (b)
32. (c)
36.(c)
40. (b)
44. (c)
(d) 6, 7
45. (b)
46. (c)
47. {d}
48. (c)
49.
(d)
53. (c)
50.
54. (c)
(b)
51.
55. {a}
{d}
52.
56. (c)
(c)
57. (a)
61. (c)
65. (b)
58. (b)
62. (d)
66. (c)
59. {d}
63. {c}
67. (d)
60. (b)
64. (c)
68.(b)
69. (a)
70. (b)
74. (a)
71. {c}
72. (a)
75. {b)
79. {b)
83. (d)
76.(a)
80. (c)
84. (d)
the value of xy + xz - 2yz will be:
(a) 5
J
(80) The roots of the cubic equation x3 +
7x2 - 21x -27 = O are
(a} -1, 3, 9
1,-3, 9
1, 3, - 9
(d) - 1, - 3, 9
(c}
(81) The difference between the roots of
the equation x2 - 7x - 9 = O is :
(a) 7
(b)
4. (d)
7. (a}
22. (a)
(b) 2
(b)
3. (a}.
6. . (c) ·
.26. (d)
30. (b)
34. (a)
38. (b)
42. (a)
[84) If u = v5Y = w5• and u2 = vw, then
(c) (- 1, 2)
(d) (- 2, 1)
j .2017 - December
2. (b)
25. (b)
29. (c)
33. (a)
37. (c)
41. (c)
'
5
(b) (1, 2)
1. (a)
5. (b)
j
17. (a)
21. (c)
(b) 5, 8
then (x, y is :
)
3 (2, 1)
Answer
(c)
1
(d) 0
[85) If the line through the points (- 2, 6)
and (4, 8) is perpendicular to the line
through the points (8, 12) and (x, 24)
then the value of x is:
(a) 4
(b) - 4 .
(c) 44
73. (d)
77. (c)
81. (b)
85. (a)
78. (d)
82. (d)
·
0
(d) None of the above
./is
(c) 9
(d) 2./85
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#16
J
I 2011- December
.
I
[2013 ...:. June
[16) On an average, experienced person
[19) The union forbids employer ·to
e(nploy less than two experienced ·
does 5 units of work while a fresh
person (x) to each fresh person (y).
person does 3 units of work daily but
This situation can be expressed as:
the employer has to maintain the
·
(a) x s y/2
output of atleast 30 units of work per
(b) y s x/2
day. The situation can be expressed
as.
(c) y x/2
(a) 5x + 3y s 30
(d) None of!
hese.
(b) 5x + 3y .! 30
(c) 5x + 3y > 30
ro1a:oecember
(d) 5x + 3y = 30
(a)
(b)
(c)
(d)
BCDB and DEFD
Unbounded
HFGH
ABDFHKA
I 2014 - December
I
[22) The graph to express the inequality
x + y s 6 is:
I
`
The common region
inequalities will be:
(a) OABCEO
(a)
of
the
(20] The solution of the inequality 8x + 6
I
[2012 -Jue
[17) Find the range of real values of x
satisfying the inequalities 3x - 2 > 7
and 4x - 13 > 15
(a) x > 3
(b) x > 7
(c) x < 7
(d) x < 3
j 2012 -- December.
(b) ECDE
< 12x + 14 is:
(a) (- 2, 2)
(c)
(d)
(b) (0, • 2)
(c) (2, oo)
·-· =1
I
[24) The common region in the graph of
8, x + y
· linear inequalities 2x + y
(b)
12 and 3x + 2y s 34 is:
(a) unbo:.mded
(b) infeasible
(c) feasible and bounded
(d) feasible and unbounded
(21) The graph of linear inequalities
7x+9ys63, x+y 1, Osxs6 and
,-e
v_G
(18] On the average, experienced person
does 5 units of work while a fresh
one 3 units .work daily but the
employer have to maintain the
output of at least 30 units of work
per day. The situation can be .
expressed as.
· (a) 5x + 3y s 30
(b) 5x + 3y 30
(c) 5x + 3y = 30
(d) None of these.
I
[ 201s - June
(d) (· 2, ex>)
I 2014:..: June
·
Line Segment DC
Line SegmenJ BC
I
s -- December
j 201
(c)
(25] The common shaded region in the
-1
I
V
1·
"•
x
Common region of the inequalities
is: .
'
JI X
(d) None of these.
[23) The graph of linear inequalities x + y
5; x + y s 5; O s x s 4 and O s y
2 is given below:
Downloaded From www.castudynotes.com
graph represents
inequalities as:
the
linear
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#15
Express the above situation using
linear inequalities . Let the company
manufacture x units of type A model
of car and y units of type B model of
car. Then, the inequalities are:
(a} 5x + 2y 1000;5x + 4y 1300,
x + 2y s 500; x 0, y 0,
(b) 5x + 2y s 1000, 5x + 4y s 1300,
x + 2y 500; x
y 0.
(c) 5x + 2y s 1,000, 5x + 4y s
1300,
x + 2y s 500; x 0, y 0.
(d) 5x + 2y = 1000, 5x + 4y :I! 1300,
x + 2y = 500 ; x 0, y 0. '
o.
I 2007 - August
x
(a) 3x + 2y s 24, + 2y :1: 16, x + y
s 10x, x
() 3x + 2y s 24, x + 2y s;16, x + y
10. x :1: 0. y
(c) 3x + 2y s 24, x + 2y s 16, x + y
s 10,x :1:0, y .!:O
(d) None of these.
o
I
[2001 - November
more than 5 experienced hands to 1
fresh one and this fact is represen­
ted by :(Taking experienced person
as x and fresh person as y)
(a) Y
s
(b) 5y s; x
X' ,( _ f£/'.A..;<1.,
X
c
y..
(a) 3x + 5ys 15,Sx + 2y
(b) 3x + 5y s; 15, 5x + 2y s 10, x, no
(c) 3x + 5y :1: 15,Sx +2y 10, x, y, .!:O
(d) None of these.
I
(9) The shaded region represents :
y
.
llo
x
(a) 7x + Sy < 35
(b) 7x + Sy s 35
(c) 7x + Sy > 35
(d) 7x + Sy 35
(c) x + y > 6,2x -y-< 0
(d) None of these
(11] If a >0 and b <0, it follows that :
(a) .!.> .!.
a b
(b)
.!. < .!.
(c)
.!. = .!.
[201.1une-
b
[2.00S:-December
Y'
Y'
_j
X
-
l
[15) Solution space of the inequalities 2x
+ y s 10 and x - y s 5 :
b
(d) None of these.
•
I
X9 H?:-..c::.::: ..i-. x
X' o( _ j
I
-·...
as :
a
;·<<.,
None of these.
but the employer has to maintain an
output of atleast 35 units of work per
day.The situation can be expressed
(a) x + y > 6, 2x -y > O
(b) x + y < 6, 2x - y > 0
a
8
xs 8
x=8
x
(14] On the average an experienced
person does 7 units of work while a
fresh one work 5 units Qf work daily
Y'
10, x, y O
(a)
(b)
(c)
(d)
6
[201o:..: Deceml>er
(0,6)
>a...:: •
y
X'
_
4<D D>Y ....
(c) 5y :I! x
(7) The shaded region represents :
]
y
I 2008 - February
(ci) None.
3
OJ The shaded region represents :
[8] The shaded region represents :
- s is
(S -2x)
! 2oos -June
(1
I
·
(13) The solution of the inequality
,.,,
I
(6) The rules and regulations demand
that the employer should employ not
! 2010 -June
(a) x + y s 5, x 2. y s 1
(b) x + y s 5, x 2. y :1: 1
(c) x + y 5. x 2 . y :1: 1
(d) None of these.
o. y o
es in an inequality :
[12) The Linear relationshipbetween two
variabl
(a) ax + by s c
(b) ax by s c
(c) axy + by s c
(d) ax + bxy s c
(i) includes the origin.
(ii) includes the point (4, 3)
which one is correct ?
(a) Only (i)
(c) Both (i) and (ii)
(b) Only (ii)
(d) None of the bove.
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#18
CHAPTER 3 :INEQUALITIES
CHAPTER 4
Simple and Compound Interest
Including Annuity Applications
(29) The common regions by the
inequalities 4x + 3y !!: 60; y :cc 2x; x
3, x <! 0 and y ::!: O is
20
•3
y •2x
20 1
(c) .
•3
·Y • 2x
(a)
4x + 3y •60
10
4x + 3y • 60
10
15
(d). None of these.
15
(b)
Answer
1. (b)
5. (c)
9. (b)
13. (a)
17. (b)
21. (d)
25. (d)
2. (b)
6. (a)
10. (a)
14. (d)
18. (b)
22. (a)
26. (a)
3. (b)
4. (a)
7. (c)
8. (b)
11. (a)
12. (a)
15. (a)
16. (b)
20. (d)
24. (c)
28. (d)
19. (b)
23. (c)
I
2006 - November
(1) t' 8,000 becomes t' 10,000 in two
years at simple interest. The amount
29. (c)
I)
Downloaded
From www.castudynotes.com
27. (a)
(2) The difference between the simple
and compound interest on a certain
sum for 3 year at 5% p.a. is
t' 228.75. The compound interest on
t
h
a
t
w
i
ll become t' 6,875 in 3 years at the
same rate of interest is :
(a) t' 4,850
(b) t' 5,000
(c) t' 5,500
(d) t' 5,275
•
Downloaded From www.castudynotes.com
t
h
e
s
u
m
788
f
o
r
2
y
e
a
r
s
a
t
5
%
p
.
a
.
i
s
:
(
a
)
t
'
Downloaded From www.castudynotes.com
3
,
1
7
5
(
b
) t' 3,075
(c) t' 3,275
(d) t' 2,975 .
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"
#17
y
y
(28] A dietician wishes to mix together
two kinds of food so tnat the
vitamins content of the mixture is
atleast 9 units of vitamin A, 7units of
vitamin B, 10 units of vitamin C, 12
units of vitamin D. The vitamin
content per kg. of each food is
shown intable. Assuming 'x' units of
food Iis to be mixed with 'y' units of
food II the situation can be
exeressed as:
(b)
, r ,,.,I\
>
x
(b)
x.
-+- x
(c)
X+y=6
(a) x + y 6
2x - y -2 O
X, y
j
ff: I
>,
>c
•X
A
B
c
D
Food I
2
1
1
2
Food II
1
1
2
3
X+Y-3 X+Y-6
O
. (d) None the these.
(b) x + y 6
2x - y -2 s O
x. y O
(c) x + ys_ 6
2x - y - 2 _s 0
x.y O
(d) x + y 6
2x - y -2 0
x, y o
201& - June
.
I
f201s=0ecember
(c)
(a) 2x + y s 9
[27] The
common region by the
inequalities x 1 + 2x2 s 5, x 1 + x2 .!: 1
, x1 .!: 0,
-1: O is given as shaded
portion in:
x,
I
x.
(26] The common region of x+ys6;x+y1:3; x-1:0; y-1:0, Is (as shown by
shaded region):
x,
y
(d)
(a)
x,
x
I
j 2011-June
x.
x+ys 7
x + 2y s 10
2x + 3y s 12
x > O, y > 0
(b) 2x + y -1: 30
xx + y s 7
+ 2y
3y-1:.1:10
12
2x +
x > O, y > O
(c) 2x + y .!: 9
x + y .!: 1
x + 2y s 10
x + 3y s 12
x 0, Y > O
(d) 2x·+ y .!: 9
x + y i. 7
x + 2y .!: 10
2x + 3y .!: 12
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x
o. y .!: o
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#20
a sinking (20) aged 40 wishes his wife R'ni
fund to provide for the payment of
o have, 40 lakhs at his death.If his
2,00,000 debt maturing in 20
_ 11><oectatior1 of life Is another 30
years. Contributions to the fund are
rears and he starts making equal
to be made at the end of every year .
Lmual ln.,estments commencing
Find the amount of each annual
IDN at 3% compound interest p.a.
deposit if Interest is 5% per annum :
-kw much shoulc:J he invest
(a) t 6,142
umually?
(17) A company establishes
(b) t 6,049
(c)
a) ,84,0n
,6,052
b) '81,628
c) ,84,449
(d) t 6,159
d.) !!'. 64,247
[ioo1 - November
·1
(18] A person borrows , 5,000 for 2
years at 4% p.a. Simple interest .He
immediately lends to another person
at 6 ..!.% p.a. for 2 years. Find his
4
I I OIJ8 -June
[2.e - February
(2'1-VI.O equal sums of money were lent
Lt s in1)1a interest at11% p.a. for s..!.
'2
•
gain inthe transaction per year :
(a) ,112.50
(t,) ,125
(c) ,225
(d) ,167.50
I
[N] In row much time would Ile simple
interest on a certain sum be 0.125
times ttie principal at 10% per
a nnum?
rears and 4 ..!. years respectively.
2
f tne difference in interests for two
1eriods was , 412.50 , then each
IUSl iS :
(19] A person deposited , 5,000 in a
bank. The deposit was left to
accumulate at 6% compounded
quarterly for the first five years and
at 8% compounded semi-annually
a machine
either by leasing it for 5 years
{useful life) at an amual rent of
, 2,000 or by purchasing the
mactJine for t 8,100. If the company
can borrow money at 18% per
anr um, which allernative is
prei
erable ?
{a) Leasing
{b) Purchasing
[c) Can't say
{d) None of these
[23] A company may obtain
a) f 3,250
b) r 3,500
c:)
r 3,750
..
(a) 1 ..!. years
{b} · 1 years
"
{c) 2..!. years '
4
{d} 2!years
d) f 4,350
(2Zn;hul's father wishes to have
' 75,000 ina bank account when his
4
[25] The diference between compound
for the next eight years. The
compound amount at the end of 13
1"St college expenses begin. How
in•esi and simple interest on a
c::&rlain sum for 2 years @ 10% p.a.
years is :
(a) ,12621.50
(b) ,12613.10
eposit now at 6.5% compounded
nnually IIAnshul Is 1o start college
years hence from now ?
(c) ,13613.10
(d) None.
1>) , 46,360
rllCh amount his father should
(26] A ma<tine worth , 4,90,740 is
depreciElted at 15% on its opening
value each year. When its value
woul(J r,.Juce to f 2,00,000 :
(a) !5 years 6 months
(bl !5 years 1months
(c) !5 years 5 months
(d) No-e.
(27] A sinkin f und is • created for
reoning debentures worth , 5 _
lacs at Ile end of 25 years. How
much pl"J'lision needs to be made
cut ol p-ofits each year provided
slnkirig l.Jn<I i
nv.estments can earn
intarast a14% p.a.?
(a) , 12,006
(bl :('.' 12,040
(c) :{' 12,039
(d) :{' 12,035
! 2001 - December
(a) A (1' i) =
is ,10. Find the sum :
(b) A (
•) ,"5,360
(c) t 1,000
(cl) t 900
1c) - A (1' i}·=
r
+ 1]
A[ 1-(1/ if ]
(d) A (r1, i} = A [(1+ /)'1- 1]
.
Downloaded From www.castudynotes.com
A[ (1 + "- 1]
iJ = A [ (1+
(a) f 1,010
(b)
t 1,095
i) - ,48,360.
I
(28] If 1he <llference between simple
irrterest anc:I compound interest is
f 11 al trE rate of 10% for two years,
then findltM sum.
(a) f 1,200
(bl f 1,100
(c) f 1,000
(d) NOl'19 of these
(29] Future value of an ordinary annuity:
,e
,::) ,55,360
, _
1(1 +
11
Downloaded From www.castudynotes.com
#19
[3) Mr. X Invests f 10,000 every year
starting from today for next 10 years
suppose interest rate is 8% per
annum compounded annually.
(a)
(b)
(c)
(d)
25 years
15 years
20 years
None.
j
J
2001-May
[10] A certainsum of money amounts to
f 6,300 in two years and f 7,875 in
Calculate future value of the annuity:
[7J Inwhat time will f 3,90,625 amount
three years nine months at simple
(Given that (1 + 0.08)10 = 2.15892500]
(a) f 156454.88
(b) f 144865.625
(c) f 156554.88
(d) None of these
[4) The present value of an annuity of
f 3,000 for 15 years at 4.5°/ p.a. C.I.
is :
.
to f 4,56,976 at 8%1 per annum,
when the interest is compounded
semi-annually?
[Given :(1.04)4 = 1.16986)
(a) 2 years
(b) 4 years
(c) 5 years
· (d) 7years
interest. Find the rate of interest per
annum :
(a) 20%
(b) 18%
(c) 15%
(d) 10%
[11] How long will f 12,000 take to
amount to f 14,000 at 5% p.a.
converted quarterly ?
(a)
(b)
(c)
(d)
f 45,130.43
f 45,230.43
f 45,330.43
None of these
! 2001 - August
- --]
[14] If f 1,000 be invested at interest rate
of 5% and the interest be added to
the principal every 10 years, then
the number of years in which it will
amount to f 2,000 is :·
12 4
[Given that (1.045)15 = 1.935282]
(a) f 23,809.67
(b) f 32,218.67
(c) f 32,908.67
(d) None of these
[2007 - February
I
[5] The rats of simple interest on a sum
of money is 6% p.a. for first 3 years,
8% p.a. for the next five years and
10% p.a. for the period beyond 8
years. If the simple interest accrued
by the sum for a period for 1O years
is f 1,560. The sum is :
(a) f 1,500 (b) f 2,000
(c) f 3,000
(d) f 5,000
[6] A sum of money doubles itself in 1O
years. The number of years it would
treble itself is :
[8] A machine can be purchased for
f 50,000. Machine will contribute
f 12,000 per year for the next five
years. Assume borrowing cos\.. is
10% per annum. Determine whether
machine should be purchased or
not :
(a) Should be purchased
.(b) Sho;.ild not be purchased
(c) Can't say about purchase
. (d) None of the above
[9] How much amount is required to be
invested every year so as to
accumulate r 3,00,000 at the end of
10 years, if interest is compounded
annually at 10%?
[Givs (1.1)10 = 2.5937]
(a) f 18,823.65
(b) r 18,828.65
(c) f 18,832.65
(d) f 18,882.65
[Given : (1.0125) · = 1.1666]
(al 3 years
(b) 3.1 years
(c) 13.5 years
(d) 12.4 years.
[12] A company is considering proposal
of purchasing a machine either by
making full payment of t 4,000 or by
leasing it for four years at an annual
rate of f 1,250. Which course of
action is preferable, if the company
can borrow money at 14% compo­
unded annually?
[Given :(1.14)4 = 1.68896)
(a) Leasing is preferable
(b) Should be purchased
(c) No difference
(d) None of these
[13) Vipul purchases a car for f 5,50,000.
He gets a loan of f 5,00,000 at 15%
p.a. from a Bank and balance
f 50,000 he pays at the time of
purchase. He has to pay the whole
amount of loan in 12 equal monthly
instalments with Interest starting
from the end of the first month.The
money he has to pay at the end of
every month is :
[ Given (1.0125)12 = 1.16075452)
(a) 16 _gyears
3
(b) 6 .!years
4
(c) 16 years
(d) 6 _g years .
3
[15) The annual birth and death rates per
1000are 39.4 and 19.4 respectively .
The number of years in which the
population will be doubled assuming
there is no immigration or
i€Jration
is :
(a) 35 years
(b) 30 years
(c) 25 years
(-ct) None of thee.
[16) The effective rate equivalent to
nominal rate of 6% compounded
monthly is :
(a) 6.05
_ (b) 6.16
(c) 6.26
(d) 6.07
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#22
[ 2011-Ju ne
I
[45] If the difference of S.I and C.I is ,72
at 12% for 2 years. Calculate h
Ia
amount.
(a) f 8,000
(b) f 6,000
(c) · f 5,000
(d) f 7,750.
[46) If a simple interest on a sum of
money at 6% p.a. for 7 years is .
equal to twice of simple interest on
another sum for 9 years at 5% p.a..
The i:alio will be :
(a) 2 : 15
'4t] N>niiria rate of interest is 9.9% p.a.
lf 1 nlerest is Compounded monthly,
Wu;t II be the eftective rate of
ine,est
12
. (gven(
(a 1o.36"/o
(Cl ·9.36°/o
(o 1'1.36%
(d 9 .9%
r 2»12-
t 60,690
(b) ? 60,960
(c) t 90,660
(d) f 90,690
The diffe rence in amounts at
matur ity is f 9 774. Find the period
lor which 1he s Jm was invested:
(a) 7 vears
(b) 5 .8 years
(c) 6 -.,ears
(d) 6 vears
(c) 12 years
(d) 16 years
[58] What principali
'l.i l anount to 370 in
6 years at E% p.a. at simple
interest?
(a) ,210
[SC] rte S . I. on a sum of money Is 4 of
ne ·
of mor1ay for 2 years .at 4% p.a. is
·
f 1. The sum (h f ) is:
amum r
(a) 625
(b) 630
ia 5%
tb) 201::0/o
(d) 635
(c) 640
(55) A sum of rroney compounded
annually becomes
1,140 in two
years and f i,
, 1O in three years.
[511 Sin1=f e interest on , 2,000 for 5
J 011 2
December
(b) ,.250
(c) t 310
(d) ? 350
(2014 - June
·
-
]
and simple interest on a certainsum
tu principal and the no. of years is
oo..JI to the rate ·of interest per
amun. Finc:l 1he rate' of interest per
IC] 22/r'lo
•c:11 6%
I
[54) The difterenc between compound
9
15:7
(d) 1:7
[47] By mistake a clerk, calculated the
simple interest on principal for 5
months at 6.5% p.a. instead of 6
months at 5.5% p.a. If the error in
calculationwas ?25.40.The original
sum of principal was
.
(a)
[57] In what time wil a sum of money
double its y at 5.25% p.a. simple
interest?
(a)
5 years
(b) 8
years
I r201
June
(b) _ 7 :15
(c)
) _= 1.1036 (approx))? _
[53) Mr. X invests 90,500 in post office
at 7.5% p.a. s mple interest. While
calculaiing · the rate was wrongly
taken as 5.7% p .a.
I
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[48) If the Simple Interest on , 1,400
[59] The partners A cl'id B together lent
? 3,903 at 4% 1e1 nnum interest
compounded anrualy. After a span of
7 years, A gets thE same 2mount as B
gets after 9 yaare. The share of A in
the sum of f 3,9(H IHOJld have been:
(a) ,1,875
(b) t 2,280
(c) ,2,028
for
3 years is . less than the simple interest
·on ? 1,800 for the same period by f
80, then the rate of interest is
(a) 5.67%
(b)
Downloaded
From
m<.nhs ct 16%
p.a. is www.castudynotes.com
_
Find the rate ot interest per annum.
C3.) f 133.33
(t>) f 133.26
6.67°/o
(c) 7.20%
(d) 5.00"/o
(a)
(b)
(c)
(d)
(c) i134.00
(ct) i 132.09
I
12 - l>ecember
I
[52] Hew rnudl lnves1ment is required to
ed an Annual income of ,420 at
i°lc pa.SirTl)le interest.
(a)
6,COO
(i>)
(¢)
6,420
(d)
5,f:80
5,C:00
(d) f 2,820
(60] If a sum triples il'l15 years at simple
rate of interest, ti:: rate of interest
per annum will bt:
(a) 13.0%
3J%
40'Yo
50%
60%
[2013 - Decemt>er
I
[56) On whei s1Jm difference between
compound inlarest and simple
interest fo r two years at 7% p.a.
interest is 29.i
(a) f SOCO _
(b) f SSCO
(c) f 6000
(d) ?6500
Downloaded From www.castudynotes.com
(b) 13.3%
(c) 13.5%
(d) 18.0%
(61) How much amou,1.s 'equired to be
invested everr year as to
accumulate 6,0>,000 at the end of
1O years, if interest is compounded
annually at . 100,,; rat: of interest
[Given: (1.1)'0= 259374].
Downloaded From www.castudynotes.com
#21
(30) Find the numbers of years in whicn
a sum doubles itself at the rate of
8% per annum.
(a)
11!
2
(b)
12!
2
(c) 9_!
2
(d)
13!
2
I 2009 - June
I
[31) In how many years, a sum will
become double at 5% p.a.
compound interest.
(a) 14.0 years
(b) 14.1 years
(c) 14.2 years
(d) 14.3 years
[32) The time by which a sum of money
is 8 times of itself if it doubles itself
in 15 years.
(a) 42 years
(b) 43 years
(c) 45 years
(d) 46 years
[33) What is the rate of simple interest if
a sum of money amounts to t 2,784
in 4 years and f 2,688 in 3 years ?
(a) 1% p.a.
(b) 4% p.a.
(c) 5% p.a.
(d) 8% p.a.
[34) A sum amount to t 1,331 at a
principal of t 1,000 at 1O %
compounded annually. Find the
time.
(a) 3.31 years
{b) 4 years
(c) 3 years
(d) 2 years
[35] Paul borrows t 20,000 on condition
to repay it with compound interest
at 5% p.a. in annual instalment of
t 2,000 each. Find the number of
.. years in which the debt would be
paid off.
(a) 10 years
(b) 12 years
'(c) 14 years
(d) 15 years
I2009 - December.
j
[36) In how many years, a sum of t 1000
compounded annually @ 10%, will
amount to t 1331? ·
(a) 6 years
(b) 5 years
(c) 4 years
(d) 3 years
[37) The compound interest for a certain
sum @ 5% p.a. for first year is f 25.
The S-1 for the same money @ 5%
p.a. for 2 years will be.
(a) f 40
(b) f 50
(c) t 60
(d) f 70
j 2010 -June·-- ··
I
(38) At what% rate of compound interest
(C.I) will a sum of money become 16
times in four years, if interest is
being calculated compounding
annually: ·
(a) r = 100%
(b) r = 10%
(c) r = 200%
(d) r = 20%
(39) Find the present value of an annuity
of t 1,000 payable at the end of
each year for 10 years. If rate of
interest is 6% compounding per
annum (given (1.06)"10 = Q.5584) :
(a) t 7,360
(Ii>) f 8,360
(c) t 12,000
(d) None of these.
[40) If the simple interest on a sum of
money at 12% p.a. for two years is
f 3,600. The compound interest on
the same sum for two years at the
s·ame rate is :
(a) t 3,816
(b) f 3,806
(c) t 3,861
(d) f 3,860
I 2010 _: December
.....- ]
[41) The future value of an annuity of
f 5,000 is made annually for 8 years
at interest rate of 9% compounded
annually [Given that
(1.09)8
=1.99256) is
_
(a) f 55,142.22
(b) f 65,142.22
(c) f 65,532.22
(d) f 57,425.22
(42] The effective annual rate of interest
corresponding to nominal rate 6%
p.a. payable half yearly is
(a) 6.06%
(b) 6.07°k
(c) . 6.08% ·
(d) 6.09%
(43) The cost of Machinery is f1,25,000/­
lf its useful life is estimated to be 20
years and the rate of depreciation of
its cost is 10% p.a., then the scrap
value of the Machinery is
[given that (0.9)2°= 0.1215)
(a) f 15,187 .
(b) f 15,400
(c) f 15,300
(d) f 15,250
[44) Mr. X invests 'P' amount at Simple
Interest rate·10% and Mr. Y invests
·'Q' amount at Compound Interest
rate 5% compounded annually. At
the end of two years both get the
same amount of interest, then the
relation betweentwo amounts P and
Q is given by :
(a) P = 410
80
(b)
P = 41Q
40
(c)
P = 41Q
100
(d) P = 410
200
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
#23
(a) l' 40,000
(b) l' 4-,50,000
(c> l' 48 ,000
(o) f 50,000
j 2017-
[79) The elbctwe rate of interest
equa 1lo the rominal rate of 7,%
COIW9 rtef
inonllly:
(a) ?.2s>h
(bl 7'.22h'
I
December
(c) 7'.02
'/o
. (d] 7'.20/'::i
[78) If compound interest on any sum at
the rate of 5% for two years is
,512.50 then the sum would be:
(a) f 3,000
(b) f 4 ,000
(cf f 5 ,000
(di r 6 ,000
Answer ·
. . 1. . .{l>l
5.
{l>I
9.
n.
{al
{al
(bl
21.
(c]
13.
3.
(a ]
(c)
6.
10. (a)
'14. (a)
' 18. {a)
7.
11.
15.
19.
(a)
(b)
(a)
(bl
22. . {a)
23.
(a)
20. (b)
24. (a)
{a)
{b)
{c)
27.
(a)
(d)
(d)
32. (c}
36. (d)
2.
'
25. (c)
29
3' . . (a)
(b)
'"·
(b l
26.
30.
34.
3,.
41.
. .45.
42.
5' "
(b l
38.
. ...
(a)
(c)
(a}
(c)
31.
35.
{a)
42. {d)
46 . (c)
50. (b)
54. (a)
<
39. (a)
43. (a}
47. (b)
51. (a}
55. (c)
57.
58.
61.
65.
(c)
(c)
72.
(c}
(c)
77.
(d)
6!:,
i2. (a)
i6. (b)
28. (b)
40. (a)
44. (a)
48. (b)
52. _ (a)
55. (c)
(d]
(b)
62.
(b)
66. (b) .
70.
74.
78.
4. (b)
8. (b)
59.(C)
63. (c)
. 67.
(c)
(c)
(b)
(a)
71.
(c)
79. . (b) ,
(c)
64. (c)
68. (c)
72 (b)
60. (b)
Downloaded From
75. (b) www.castudynotes.com
76. (c)
Downloaded From www.castudynotes.com
#24
C
CHAPTER5
Basic Concepts of Permutations
and Combinations
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
#30
CPT Scanner :Quantitative Aptitude (Paper 4)
(a} 20 years
(a) ,37,467
(b) ·,37,476
. (c) ,37,647
(d) ,37,674
I 2014 - December
(b) 12 years
I
[62] The future value of an annuity of
,1,000 made annually for 5 years at
the interest .of 14% compounded
annually is:
(Given (1.14}5 = 1.92541}
(a) ,5,610
(b) ,6,610
(c) ,6,160
(d) ,
5,160
[63] A sum of money invested of
compound interest doubles itself ir.
four years. It becomes 32 times of
itself at the same rata of compound
interest in
(a) 12 years
(b) 16 years
(c) 20 years
(d) 24 years
[64] A certain . sum of money was
invested at simple rate of interest for
three years. If the same has been
invested at a rate that was seven
percent higher, the interest amount
would have been t' 882 more. The
amount of sum invested is:
(a) ,12,600
(b) ,6,800
(c) ,4,200
(d) ,2,800
1 201s- J une
j
I
[65] A sum of money doubles itself in 8
years at simple interest. The number
(c} 16 years
(d} None of these.
[66) A sum of f 44,000 is divided into
three parts such that
the
corresponding interest earned after
2 years, 3 years and 6 years may be
equal. If the rates of simple interest
are 6% p.a., 8% p.a. and 6% p.a.
respectively, then the smallest part
of the sum will be:
(a} f 4,000
' (b) f 8,000
(c) ,10,000
(d} · f 12,000
of years it would triple itself
is
[73] A compound interest on a sum for 2
years is f 30 more than the simple
interest at the rate of 5% per annum
then the sum is
(a) ? 11,000
(b) ? 13,000
(c) 1( 12,000
(d) , 15,000
[74] A person lends ,6,000 for 4 years
. and 1( 8,000 for 3 years at simple
j 2016 - June . · ···
interest. If he gets t' 2,400 as total
interest, the rate of interest is:
[70] Mr. X bought an electronic item for .
(a) 5%
, 1,000. What would be the future
(b) 4%
value of the same item after 2 years,
(c) 6%
if the value is compounded semi
.(d) 7%
annually at 22% per annum?
[69) The simple interest for a certain sum
for 2 years at 10% per annum is
,90. The corresponding compound
interest is (In ,}:
(a) 99
(b) 95.60
(c) 94.50
(d) 108
I
[ 2015-December
I
[67) Suppose your parent decides to
open a PPF (Public Provident Fund)
account in a bank towards your
name with f ·10,000 every year
starting from today fer next 15 years.
When you receive and get 8.5% per
annum interest rate compounded
annually. What is the present value
of this annuity? (Give answer in
,without any fraction.)
(Given P (15,0.085) "'8.304236576)
(a} 83,042
(b) 1,66,084
(c} 93,042
(d) 8,30,423
[68] In how many years will a sum of
money become four times at 12%
p.a. simple interest? (a} 18
years
(b} 21 years
(c} 25 years
(d) 28 years
Downloaded From www.castudynotes.com
(a) ,1488.40
(b) ? 1518.07
(c) ,2008.07
(d) ? 2200.00
[71] If an amount is kept at simple
interest, it earns an interest of ,600 in
first two years but when kept at
compound interest it earns an
interest of ? 660 for the Sfime period, then
the rate of interest and principal amount
respectively are:
(a) 20%, ? 1,200
(b)· 10%, '1,200
(c) 20%, ? 1,500
(d) 10%, , 1,500
I
2016:ciecember
j
[72) The sum invested at 4% per annum
compounded
S emi-annually
· amounts to ,7,803 at the end of one
year, is: .
(a) ? 7,000
(b) n.soo
(c) ? 7,225
(d) f 8,000
Downloaded From www.castudynotes.com
#31
2017-June
l
· [75] The future value of an
annuity of f 1,500 made
annually for five years at
interest
rate
10%
compounded annually is
(Given that (1.1)5 = 1.61051)
:
(a) ,9517.56
(b) 1( 9157.65
(c) ,9715.56
(d) 1( 9175.65
[76] The difference between
the Compound interest
and Simple interest
at
10% per annum for 4
·years on ,10,000 is ,
·
(a) 650
(b) 640
(c} 641
(d) 600
[77) How much amount is
required to be invested
every year as to
accumulate t 7,96,870 at the end of
10 years,
if
interest
compounded annually at
10% given that A(10, 0.1)
= 15.9374?
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
#26
Chapter 5 - Basic Concepts of Permutations and Combl1121lons
(b) 210
(c) 220
(d) None
(21] Six persoAs A, B, C, D, E and F are
to be seated at a circular table. In
how many wavs can this be done, if
A must always ha\le either B or C on
his right aoo B must always have
either C or D on his right?
(d) 18
I
(22] If "P, = "P,. , and "C, = "C,_ 1 then find
the
(a)
(b)
.(c)
(d)
value of 'n'
2
3
4
5
[23] How many si)( digit telephone
numbers can be formed by using 10
distinct digits'l
(a) 106
(b)
510
(c)
10c6
(d) ,ope
(24] In how many ways a committee of 6
members can be formed from a
·group of 7 boys and 4 girls having at
least 2 girls in the committee_
(a) 731
(b) 137
(c) 371
(d) 351
804
I I
[25] Number of ways of painting a face
o1 a cube by 6 colours i ::;
_
(a] 36
(b] 6
(c) · 24
(d) 1
[26) If
18
Cr =
11
Cr + 2 find the
value of ;C5•
(a) 55
{b) 50
(c) 56
(a) 3
(bl 6
(c) 12
[2oos - December
803
(d) None of 1hese
(27) 7 books are to be;
mc:nge d in such
a way so that two part: cula ' books
. are always at firs1 and last place.
Finalthe number of a1r.2ngements.
CPT Scanner : Quantitative Aptitude (Paper 4)
09 -December
! 2010 - December
I
[35] A garden having 6 tall trees in a
committee is to be fanned fird th&
number of ways the committea can
row. In how many ways 5 children
stand, one in a gap between the
be formed such that it comprisEs of
at least 2 gents and at least the
number of ladies should .be double
of gents.
trees in order to pose for a
photograph ?
(a) 24
(a) 94
(c) 720
(d) 30 .·
(b) 132
(c) 136
(d) 104
[32) Six points are on a circle. The
(29] In how many way.s can 17 billiard
balls be anangec:I f 7 cf them are
(d) 819
(31] Out of 4 gents and 6 laci. a
(b) 120
(c) 240
( -480
(c) 96
(d) None.
(c) 728
(b) 5
(c) . 4
(d) 10
(a) 60-
which the letters of t he word
'MONDAY' be arranged so tha1 the
words thus formed bagin with '"'1'
and do hot encl with · ·.
(a) 720
(b) 120
(a)
(30) (n + 1) ! = 20 (n - 1) I, find n
(a) 6
f::w:1oune
[28] Find the numbero' arrar.gements in
I585
[36)
"C
'. "Cu is equal to :
(a) 16c,
1·
number of quadrilaterals that can be
formed are:
·
(a) 30
. (b) 360
(c) 15
(d) None of the above
(33) The number of ways of arranging 6
boys and 4 girls in a row so Iha! all 4
girls are together is :
(a) 6!. 4!
(b)
(c) 2 (7!. 4!)
black, 6 red and 4 whi'.e ?
{b) 1
Downloaded
(a) 4084080 From www.castudynotes.com
(c) 8048040
(b) 120
..
(b) 30c
(c) 1Sc,a
(d)
15c,s
[37) How many ways a team of 11
players can be made out of 15
players if one particular player is not
to be selected in the team.
· (a) 364
(b) 728
(c) 1,001
(d) 1,234
, . 2011-.ii.ni e
·
I
(d] None of these
Downloaded From www.castudynotes.com
(38] Findthe number of arrangements
7!.(61.
4! 41)
(d) 2.
[34] How many numbers not exceeding 1000 can be made from the
digts 1, 2, 3, 4, 5, 6, 7, 8, 9 if repetition s not allowed.
of 5 things taken out of 12
things, In which one particular
thing must always 'be included.
#25
'
l1
(3) A boy has 3 library tickets and 8
books of his interest in the library of
these 8, he does not want to borrow
Mathematics part-II unless Mathe­
matics part-I is also borrowed? In
how many ways can he choose the
three books to be borrowsd?
(a) 41
(b) 51
(c) 61
(d) 71
j
(4) An examination paper consists of 12
questions divided into two parts A
and B. Part A contains 7 questions
and part B contains 5 questions. A
candidate is required to attempt 8
questions setecting at least 3 from
each part. in how many maximum
ways can the candidate select the
questions?
(a) 35
(b) 175
(c) 210
(d) 420
[5] A Supreme Court Bench consists of
5 judges. In how many ways, the
bench can give a majority division?
(a) 10
(b) 5
(c) 15
(d) 16
[6) Given : P (7, k) = 60 P(7,
- 3).
[11] The value of
books can be arranged on a shelf so
that two particular books are not
together is :
(a) (n - 2) x (n - 1)!
(b) (n - 2) x (n + 1)!
(c) (n - 1) x (n + 1)!
(d) (n - 2) x (n + 2)!
! 2001- May
I2007 ,;,. Februar/
5
[7] The number of ways in which n
· the word FAILURE be arranged so
that the consonants may occupy
only odd positions?
·
(a) 576
(b) 476
(c) 376
(d) 276
[9] Five bulbs of which three
are
defective are to be tried in two lights­
points in a dark-room. In how many
trials the room shall be lighted?
<a> 10
(b) 7
(c) 3
(d) Non of these
[10) In how many ways can a party of 4
men and 4 woman be seated at a
circular table, so that no two woman
l
e adjacent?
(a) 164
(b) 174
[16) How many numbers greater than a
million can be formed with the digits
.
4, 5, 5,
4, 5, 3 ?
5
C, is :
o.
r= 1
(a) 260
(a) 29
(b) 360
(b) 31
(c) 280
(c) 35
(d) 380
(d) 26
[ 2007 - August
I
[8] Inhow many ways can the letters of
L
[17) A building contractor needs three
I
[12) If 6P, = 24 6C,, then find r .:
(a) 4
- (b) 6
(c) 2
(d)
· helpers out of ten men supply. In
how many ways can these
selections take place?
(a) 36
(b) 15
(c) 150
(d)
120
[13) Find the number of combinations 9f
I 2008 ... February
the letters of the word COLLEGE
taken four together :
(a) 18
(b) 16
(c) 20
(d) 26
[14) How many words can be formed
with the letters of the word
'ORIENTAL' so that A and E always
occupy odd places:
(a) 540
(b) 8640
[18) There ar three blue balls, four red
balls and five green balls. In how
many ways can they be arranged in
a row?
(a) 26,720 .
(b) 27,720
(c) 27,820
(d) 26,620
[19) If C(n, r) : C(n, r +1) = 1 : 2 and C
(n, r + 1): C (n, r + 2) = 2:3,
determine the value of nand r :
(a) (14, 4)
(c) 8460
(d) 8450
j
(b) (12, 4)
(c) (14, 6)
(o) None.
I ! 2ooa :.::.J..,ne
j2001
- November
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www.castudynotes.com
,.
I
Downloaded From
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[15) If
C + "C
find x :
Then :
(c) 144
(d) 154
(a) k = 9
1000
C98 =
999
90, •
97
[20) Six seats of articled clerks are
(a) 999
(b) 998
(c) 997 .
(b) k = 8
(c) k = 5
(d) k = 0
vacant in a 'Chartered Accountant
Firm'. How many different batches
of candidates can be chosen out of
ten candidates ?
(d) 1000
I
(a) 1024
(b) 945
(a)
8
P3
IL
[57) The four digit numbers that can be
(c) 1005
(b)
3
P3
IL
! 2o June
formed out of the seven digits 1, 2,
3, 5, 7, 8, 9 such that no digit is
repeated in any number and are
greater than 3000 are:
(a) 120
(b) 480
(c) 600
(d ) 840
[58) A person has ten friends of whoin
six are relatives. If he invites five
guests $UCh that three of them jire
(d) 1022
[61) If "p, = 720 and "c, = 120, then value
of 'r' is:
his relatives, then the total number
be fonrned of them,if the committee
?f ways inwhich he can invite them
are:
is to include at least 2 women are:
(c)
5
(c) 6
I 2016 - December
•
[60) An examination paper
with 1o .
questions
consists of 6
questions in
mathematics
and
4
questions in statistic part. At
least one question from each
part is to be attempted in how
many ways can this be done?
I
1
c,.1 : "C, : "' C,.1 = 8 : 3 : 1, then
'ALLAHABAD' is:
(b) 16
I2016 -June
I
[63) In how many ways can a selection
of 6 out of 4 teachers and 8
students be done so as to include at
. least two teachers?
(a) 720
(b) 180
(c) 360
(d) 540
(a) 220
Downloaded
From www.castudynotes.com
(b) 672
I
(c) 596
(d) 968
(d) 45
[71) The number of words which can be
formed by letters of the word
n is equal to:
(a) 20
(d) 105
[59) A student has three books on
. comput e r, tllree books on
Economics and live books on
Comme rce. If tes& books are to be
arranged subject \Vise, then these
can be placed on a shelf in the
number of ways: ·
(c) 12
(d) 13
[70] The number of parallelograms,
formed from a set of six parallel
lines intersecting another set of four
parallel lines is:
(a) 360
(b) 90
(c) 180
(b) 186
(c) 120
...
= "C5 then
(b) 11
(d) 180
[66) If 0 1
(d ) 75
(a) 25290
[2015
(b)- December
25920
(c) 4230
(d) 4320
u_o
(a) 2
(b) 20
(c) 90
(a) 180
(b) 60
(c) 120
5
value of n is:
(a) 10
[65) The maximum number of points of
inter section of 10 circles will be:
(d) 3
[62) There are 6 men and 4 women in a
. group, then the number of ways in
which a committee of 5persons can
(a) 30
3
I
[69) If 10C + 2. · 10C4 + 1°C
(d) None of these.
(a) 4
(b)
8 p3
#29
I 2017 - June
[64) There are 1O students in a class
inciuding 3 girls. The numbr of ways to
arrange them in a row when any two girls
out of three never comes together:
(c) 10
Downloaded From www.castudynotes.com
(d) 15
[67) he number of numbers between 1,000
and 10,000, which can be
formed by the digits 1, 2, 3, 4, 5, 6
without repeUtion is:
[68) The number of ways in which 4 persons
can occupy 9 vacant seats is:
(a) 6048
(b) 3024
(c) _ 1512
(d) 4536
j 2011 - December
-
(a)
(b)
(c)
(d)
7560
3780
30240
15120
:J
[72) If "P : n+1P = 3:4, then the
value of 'n' will be:
(a) 13
(b) 15
(c) 18
(d) 31
[73) If 3 books on computer, 3
books on commerce, . and
5 books on economics
are arranged
in such
away that the · books of
same subject are kept
together, then the number
of ways in which this can
be done are: ·
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13
(a) 4320
(b) 35820
(c) 35920
(d) 25920
12
Downloaded From www.castudynotes.com
#27
(a)
(b)
(c)
(d)
39,000
37,600
39,600
36,000
2012 - December
I2011 -December'
I
[39]In how many ways 3 prize out of5
can be distributed amongst 3
(b)
45
(c) 60
(b)
5
P3
(c) 63
not be separated ?
(d} 120
[40] There are 12 questions to be
Answered to be Yes or No. How
many ways canthese be Answered?
(a) 1024
· (b) 2048
(c) 4096
(d) ·None
I 2012 - June
I
[41) The letters of the word "VIOLENT'
are arranged so that the vowels
occupy even place only. The
number .of permutations is
(a) 144
(a) 720
(b) 1,440
(c) 140
(d) 1,000
(45] If 13C6 + 2 i3Cs +
then, x =
(a) 6
(b) 7
(c) 8
(d) 9
13C4
= ,sc,
.
i
(46) A polygon has 44 diagonals then
the number of its sides are:
(a) 8
(b) 9
10
(d) 11
(d) 72
[42) If "P, = 20 ("P2) then the value of 'n'
.
-2
7
- 2 and 7 both
None of these.
(48) Number of ways of shaking hands in
a group of 10 persons shaking
hands to each other are:
(a) 45
(b) 54
(c) 90
(d) 10
!201
· ··1
::0ecember
(49) If _15C3r = 15Cr+3, then 'r' is equal is
(a) 2
(b) 3
[47] The number of words that can be
formed out of the letters of the word
"ARTICLE" so that vowels occupy
everi place is:
(a) 36
(b) 144
(c) 574
[53) If six times the number of
permutations of 'n' items taken 3 at
a time is equal to seven times the
number of permutation of (n-1)
items taken 3 at a time , then the
value of 'n' will be:
(a) 7
(b) 9
(c) 13
(d) 21
1 2014 ---December
(c) 4
[54] If
(50] How many different words can be
formed with the letters of the word
"LIBERTY"
(a) 4050
(b) 5040
(c) 5400
(d) 4500
(51) In how many ways can a family
consist of three children here
different
birthdays in a leap year
(a) 365C3
{b)
3 -3
(c) 366 x 365 x 364
(d) 386C3
-·c
I
!2014 -Ju. ne
[52] If
1000
C98
=
999
C97 + '
value of x will be :
(a) 999
(b) 998
(c) 997
(d) None of these.
1•
J
8
(d) 5
201 3 - June
(c}
(b) 120
(c) 24
(a)
(b)
(c)
(d)
(43) A man has 3 sons and 6 schools
within his reach. Inhow many ways,
he can send them to school, if two
of his sons are to read in the same
school?
(a) 6P2
(d) 36
(44) How many permutations can be
formed from the letters of the word
"DRAUGHT", if both vowels may
brothers Equally?
(a) 10
is
· ·1
then the
P, = 360, then the value of 'r' Is:
(a) 5
(b) 3
(c) 4
(d) None of these.
[55] There are 5 books on English, 4
Books on Tamil and 3 books on
Hindi. In how many ways canthese
books be ·placed on e shelf if the
books on the same subj& cts are to
be together?
(a) 1,36,800
(b) 1,83,600
(c) 1,03,680
(d) 1,63,800
(56] 5 Men and 4 Women to sit in a row
in such a manner that the woman
always occupy the even places.
The number of such arrangement
(a) 126
(b) be:
1056
will
(c) 2080
(d) 2880
(d) 754
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
Chapter 6 - Sequence and Series Arithmetic and Geometric Pro..
[3] The sum of an A P, whose first term
= b11V = c1
[7] If a1
32
(a)
10, 8,
5, ............·,
(b)
10, 8,
10
9
81
10
_
(d) .!_ (10"•1 81
I
j 2007 - February
[5]
(c) .!_ (1 on.1 - 1O} -
9,..........
.
j 2001 - May
6
(b)
n( n + 1)
2
(c)
[n
(11/
l)] 2
(d) None of these
[6] . Divide 30 into five parts in A .P., such
that the first and last parts are in the
ratio 2 :3 :
[12] If the sum of n terms of an A.P. is
7
24 27
(a)
6
33 36
5' 5' '5• 5
s 27
6• 5'5•5•
s 5
:l6 33 24
(b)
(b)
9
I
is 6, then its first term is :
(a) 3
7
1O} + "
9
(a) mn
I
rapped to the
.
ground rebounds to
5 of the height
from which it falls; it is dropped from
a height of 100 metres find the total
distance it travels before finally
coming to rest :
y(n-p)
[x<n·q)r-q)
I 2007 - November
5·
J
[16] The sum of the series :
0.5
+ 0.55
terms
is : + 0.555 + .......... to n
(a)
Sn
+
S
[1 - (0.1)"]
9 9
(b)
Sn
-
S
9 81
(1 - (0.1)"]
5
9 + 81 (1 - (0.1)"]
Sn
5
9
+ 81 [1 + (0.1)"]
[17] A contractor who fails to complete a
building in a certainspecified time is
compelled to forfeit f 200 for the
first day of extra time required and
thereafter forfeited amount is
increased by ,25 for every day. If
he loses ,. 9,450, for how many
days did he over-run the contract
time?
(a) 19 days
(b) 21 days
(c) 23 days
(d) 25 days
'5·6
5·4·
36 33
24 27 33 36
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From www.castudynotes.com
(c)
6
•
n2
[18] The first, second and seventh term
(a) 600m
(d)
{d)
(d)
(b) 8870
4 th
./mn
(c) m2
(c)
(c) 4
(d) 1
[13] Find the sum of the series :
2 + 7 + 12 +. ...................... 297.
(a) 8970
(c) 7630
(d) 9875
(14] A certain ball when
(b)
- 5n
(b) 2
x(n·q)]
[
27 24
-
(3n2 - n) and its common difference
"
between 250 and 1,000 which are
exactly divisible by 3 :
(a) 1,56,375
(b) 1,56,357
(c) 1,65,375
(d) 1,65,357
(10) If the pth term of a G.P. is x and the
qth term is y, then find the nth term :
(a)
instalments, each instalment is less
than former by 5. The amount of
first instalment is 100. In what time
will the entire amount be paid?
. (a) 26 months
(b) 15 months
(c) Both (a) & (b)
(d) 18 months
9
(9] Find the sum of all natural numbers
n( n+ 1)(2n + l)
975 in monthly
I 2007 - August
Ln 2 defines :
(a)
[11] A person pays
7
(b) !_ (10"'1 - 10) + "
2 , ..............
(c) 10,
3,
(d) None
and a, b, c are in
G.P; the x, y, z are in :
(a) A.P .
(b) G.P.
(c) Both (a) & (b)
(d) None
(8] Find the sum to n terms of the series
: 7 + 71+ n7 + .........to n terms :
(a) !_
9 (10n+1 - 10) - 7n
9
5
CPT Scanner :Quantitative Aptitude (Pape 4) .
812
1z
1X
is - 4 and last term is 146 is 7171.
Find the value of n.
(a) 99
(b) 100
(c) 101
(d) 102
[4] If the first term of a G.P exceeds the
second term by 2 ar:id the sum to
infinity is 50, the series is :
I 811
'5· 5
yin-Pl
(c) t
(d)
[xln-q)
y<n-p)
Downloaded
From www.castudynotes.com
of A.P.are in G.P. and the common
(b) 700
r-
m
(c) 900
m
(d)
200m .
[15] In a G.P
if the (p
+ q)th
term Is
m and
(p - q)th
term is
n, then
the pth
term is :
difference is 2, the 2nd term of A.P.
is :
(a) 5/2.
(b) 2
(c) 312.
(df 112
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
#32
Chapter 5 -·Basic Concepts of Permutations and
Combinations
Answer
1. (a) ·
2 . (b)
3. (a)
4. (d)
5. (d) ·
{b)
6. (c)
7. (a)
11. (b)
8. (a)
13. (a)
17. {d)
21 (d)
25 (b)
29 (a)
33. (c) 34. (b)
-W
41 . (a)
45. (a)
49. (b)
53. (d)
57. (c)
61. (d) ·
65. (c)
69. (c)
10. (c)
14. (b)
18. (b)
22. (b)
26. (c)
15. (a)
19. (a)
30. (c)
35. (b) 36. (a}
23. (d)
27. (c)
31 . (b)
-
3
43. (b)
47. (b)
42. (b)
46. {d)
50. (b)
54. (c)
58. (c)
62. (b) ·
66. (d)
70. (b}
CHAPTER 6
12. (a)
16. {b)
20 (b)
24. (c)
28. (c)
Sequence and Series Arithmetic · and
Progression
32. (c)
51 . (c)
4Q
44. (b)
48. (a)
52. (a)
55. (c)
59. (b)
56. (d)
60.(b)
63. (b)
67. (c)
64. (a)
71. (a)
Geometric
68. (b)
72.(b)
73. (d)
0
I 2006 - November
I
(2) Find n such that
(1] The sum of all natural numbers
between 100 and 1000 which are
multiple of 5 is:
(a) . 98,450
may
an • 1 + bn + 1
n
n
a
be the geometric
between a and b :
(a) 1/2
(b) 1
(c) -1/2
(b} 96,450
(c) 97,450
(d) 95,450
(d) 0
810
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+
b
mean
Downloaded From www.castudynotes.com
#34
r
I
2011 -June
[43] If sum of 3 arithmetic means
between "a" and 22 is 4. then "a" =
(38] If Sum (Sn) of 'n'- terms of an
Arithmetic Progression is (2n2 + n).
What is the difference of its 10111 and
1•1 term ?
(a) 207
(b) 36
(c) 90
(d) 63.
E39] Find the product of :
(243), (243) 116, (243) 1136,........oo
(a) 1,024
(b) 27
(c) 729
(d) 246
means
(40) Insert two Arithmetic
between 68 and 260
(a) 132, 196
(b) 130, 194
(c) 70, 258
(d) None of the above.
[41) Geometric Mean of P,P2,P3
........,
P" will be :
(a)
(a) 14
(b) 11
(c) 1O
(d) 6
[44] If each month 100 increases inany
sum then find out the total sum after
10 months, if the sum of first month
is t 2,000.
(a) ,24,500
(b) f 24,000
(c) ,50,000
(d) f 60,000
[45] The · sum of all two. Digit odd
numbers
(a)
2475is
(b) 2575
(c) 4950
(d) 5049
(46] If 5t11 term of a G.P. is 3,/3 , then the
(a) 8
(b) 27
(c) 243
pn +1
1+n
(b)
p-2-
(d) 9
.!!..l!!..:.!l
[47] The sum of the third and ninth term
of an A.P. is 8. Find the sum of the
(c) P 2
(d) None of the above.
!2011 - December
first 11 terms of the progression.
(a) 44
I
. [42] Find the numbers whose arithmetic
mean is 12.5 and geometric mean is
10.
(a)
(b)
(c)
(d)
20 and 5
10 and 5
5 and 4
None of these
. -
]
[48] If 9t11 term of an A.P is 15, then sum
product of first nine terms is
....
I 2012 -June
· (b) 22
(c) 19
(d) 11
(b) 0
(c) 225
(d) 225/2
(d) 1
[49] Find the sum of the infinite terms 2,
8
16
term is 8 will be:
(a) 6
(b) 3
(c) 4
of its 15 terms is
(a) 15
4
(52]The first term of a G.P. where
second term is 2 and slim of infinite
· ..
[53] If the sum of n terms of an A.P be
2n2 + Sn, then its 'n"'term is:
(a) 4n - 2
-, -. -............., ,f y > 2
y y2 y3
(b) 3n - 4
(a)
(d) 3n + 4
(c) 4n + 3
y-2
!2013-June
(b)
y-2
(c)
(54] I3n
f the
sum of
2
y-2
- nand
(d) None of these.
[50] The 4t11 term of an A.P. is three limes
the first and the rt' term exceeds
twice
the 'a'
third
Find the
by 1.difference
first term
andterm
common
n terms of an A .P be
its common difference is
6, then its first term is :
(a) 2
(b) 3
(c)
(d) 4
5
[55) If the sum of the 4" term and the 12"
'd'.
(a)
(b)
(c)
(d)
I
a = 3, d = 2
a = 4, d = 3
a = 5, d = 4
a = 6, d = 5
j 2012 - December
.
J
[51] In an A.P., if common differenceis 2,
Sum of n terms is 49, 1" term is 13
then n
(a) O
=
,
term of an A.P. is 8, what is the sum
of the first 15 terms of the
progression?
(a) 60
(b) 120
(c) 110
(d) 150
[56) If 'n' arithmetic means are inserted
between 7 & 71 and 5.. arithmetic
mean is 27, then 'n' is equal to:
(a) 15
(b) 5
(b) 16
(c) 7
(d) 13
(d) 18
Downloaded From www.castudynotes.com
(c) 17
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
#33
]
(23) On 1st January every year a person
buys National Saving Certificates of
[19) A man employed in a company is
value exceeding that of his last
promised a salary of t' 3,000 every
month for the first year and an
increment of 1,000 in his monthly
salary every succeeding year. How
much does the man earn from the
company In20 years?
(a)
30,00,000
(b)
2?,50,000
(c)
19,10,000
(d)
7,90,000
(20) If a, b, c are in A .P. and x, y, z are in
G .P, then the value of
x !b-c). y(c-a) . z(a-b) is :
(a) 1
(b) 0
(c) b(c - a)
(d) None
[21) Insert 4 A.M.'s between 3 and 18 :
(a) 12, 15, 9, 6
(b) 6, 9, 12, 15
year's purchase by 190. After 10
years, he finds that the .total value of
the certificates purchased by him is
t' 54,500. Find the value of
certificates purchased by him in the
first year :
(a) t' 6,000
(b) t' 4,000
(c) t' 5,000
(d) t' 5,500
(24) Find three numbers in G.P. such
that their sum is 21, and the sum of
their squaressi_189 :
(a) 5, 7, 9
(b) 3, 7, 11
(c) 3,6, 12
(d) 4,8, 9
[ 2008 - February
(c) · 9, 6, 12, 15
I2008 -
/2, s..fi , 9..fi ,..........
(a)
·1
1
1
[22) If x = 1 + 3 + 32 + .............. co
1 1
y = 1+ 4 + 4Z + ..............• co
Find xy.
==::]
(25) Find the ninth term of
the .series :
(d) 15, 12,9, 6
I 2008 - June
cember
2s..fi
(b) 31..fi
(c) · 33..fi
(d) S2..fi
(26) The sum of how many
terms of the sequ&nce
256, 128, 64,........is 511.
I2010 - June
(27) (x + 1), 3x, (4x + 2) are in A.P. Find
the value of x
2
(a)
[34) If a,, a , a represents first , second
2
(b) 3
(c) 4
(d) 5
[28) Find two numbers whose A .M. is 10
and G.M. is 8.
(a) [10,1O]
(b) [16, 4]
(c) [18, 2)
(d) [14,6)
I
j 2009 - June
(29) Same as Q 5 [Feb. 07]
[30]The sum of terms of an infinite GP is
15. And the sum of the squares of the
term is 45. Find the common ratio.
(a) 3/2
(b) 1
(c) - 2/3 .
(d) 2/3
(31) If in an A.P., Tn represents nth term.
= 5:7 then /
If 1 :t
7
(a)
(b)
(c)
(d)
I
10
=
:t
8
3
and third terms
of an AP
respectively,the first term is 2 and
(a; + a2)a3 is minimum, ·then the
common difference is equalto
(a) 5/2
(b) - 5/2
(c) 2/5
(d) - 2/5
[ 5] Divide 144into three parts which are ·
in AP and such that the largest is
twice the smallest, the smallest of
three numbers will be :
(a) 48
(b) 36
(c) 13
(d) 32
[36) Sum of series 1+ i+ !_+ .!Q+.... "" is
.
s
52
(b) 1
(c) 8/9
(d) !-2
(b) · 9
(c) 7
(d) None of these.
15/36
(b) 35/36
(c) 35/16
(d) 15/16
11
j 2010 - December
13 : 16
17 : 23
14 : 17
15 : 19
I 2009 - December
[32) Same as Q 3 [Nov. 06)
I
(33) Find · the sum to infinity of the
02-a2
02-b2
.
(a) · G2
(a) 1
(b)
Downloaded From www.castudynotes.com
(c)
1
/2
I
-- - - -
(37) If G be Geometrrc Mean between
two numbers a and b, theri .the value
of __
l +-1
-is equal to
following series:
1 - 1 + 1 - 1 + 1-1+ .................co
00
•
(al
(a) 8
(a) 2
53
(d)
Does not exist
.
(b) 3 G2
(c) 1/G2
(d) 2/G2
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
#36
[74) A G. P. (Geometric Progression)
consists of 2n terms. If the sum of
the terms occupying thelodd places
is S, and that of terms in the even
places is S2, the common ratio of the
progression is:
[78) The number 2.353535
q
(a)
(a) n
s
(c)
-3
S1
S2
- 1
[75) If
1
I
1
,-,
I
I2016 - December
[76) The income of a person is
,5,00,000 in the finn in the first year
and he receives an increase of ·
. f 15,000 per year for next 1O years.
The total amount he receives in 1O
years is:
(a) ? 56,75,000
(b) ? 72,50,000
(c) ? 15, 67,500
None of these
[77) If the Sum 50 + 45 + 40 + 35
+
is zero, then the number of
(a) 44550
{b) 66770
(c) 55440
(d) 33440
230
99
233
99
2011-June
I I
[79) The sum of nterms of the series 1 +
(1 + 3l + (1 + 3 + 5) + ............ is
(a) n(n + 1)(2n + 1)
6
(b)
n(n + 1) (n + 2)
(c)
6
n(n + 1)(2n + 1)
3
{d) None of these .
(80] The sum of first 20 terms of a GP is
1025 times the sum of first 10 terms
of same GP then common ratio is:
(al ./2
(b) 2
(c) 2./2
(d) 1/2
(81] The value C such that a, - 3, b, 5, c
are inA .P.is:
(a) -7
terms is:
(b) 1
(a) 22
(c) 13
{dl · 9
(b) 20
(c) 21
(d) 25
100 and 1000 which are divisible by
11 will be:
(al
2. (c)
Answer
3. (c)
5. (al
(al
13. (a)
17. (b)
21 (b)
6. (al
7. (a)
10. {d)
11. (b)
15. (b)
19. (a)
23. (c)
1.
... J
4: (a)
-are inarithrnf3tic
b+c c +a a +b
·
progression then a2 , b2 , c! , are in
(al Arithmetic Progression
(bl Geometric Progression
(c) Both
in
arithmetic
and
geometric Progression
(d) None of these.
(d)
J
[82] The sum of all numbers between
235
99
(dl
s1
(d)
I 2017 - December
(b) 234
99
(b) 2S1
(c)
in
£ form is:
9.
14. (c)
18. (a)
22. (a)
-
-
29. (a)
30. (d)
-l
37. (c)
41. (b)
45. (a)
49. (a)
53. (c)
57. (b)
61. (b)
(d)
69. (d)
73. (d)
77. (c)
81. (d)
as:
34.
l
)
38. (b)
42. (a)
46. (b)
50. (a)
54. (a)
58.(d} ·
62. (c)
32. (c)
-
-
39. (c)
43. (d)
47. (a)
51. (c)
40. (a)
44. (a)
48. (c)
52. (c)
56. (a)
55. (a)
70. (a)
74. (c)
78. (d)
82. (a)
Downloaded From www.castudynotes.com
31. (b)
59. (al
63. (bl
67. (b)
71.(cl
75. (a)
79. (a)
66. (c)
0
8. (cl
12. {b)
16. (b)
20 (al
24. (cl
60. (a)
64. (b)
68. (c)
72. (b)
76. (al
80. (b)
Downloaded From www.castudynotes.com
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Downloaded From www.castudynotes.com
#35
[57] In a G.P. the sixth term is 729 and
the common difference is 3, then the
first term of G.P. is:
is equal to:
(a) [ m <;+1)r
(a) 2
I
[62] The value of 13+23+33+43+........+m3
(b) 3
{c) 4
. (b)
(d) 7
I2013
December:
I
[58] An Arithmetic progression has 13
terms whose sum is 143. The third
farm is 5 so the first term is:
(c)
m(m+1) (2m+ 1)
6
{b) 7
(c) 9
(d) 2
[59] If Geometric mean (G.M.) Of a, b, c,
dis 3, then G.M. of .!.).).,.!.will be:
a b cd
(a) 1/3
(b) 3
(c) 81
(d) None of these.
I
[60] The sum to m terms of the series
1+11+111+....upto mterms, isequal
to:
1-9m-10)
...!..(10"'·
81
(b) ...!..(10"' 1-9m-10)
27
(c) 10",.1-9m-10
(d) None of these
[61] The sum of the infinite G.P.
1
1+..........1s equal to:
1+ -1+
- +3 9 27
(a) 1.95
(b) 1.5
(a)
I
in G.P then P2R" =
(a)
(a)
P2
(b)
p3 '
(b) S"
(c)
(d)
s-2n
s-n
[68] The sum of the series 1 + 11 +
111 + ......................... to n terms is
2
27
28
(c)
t4
(d) 26
[71] If a, b,
c
are
in
Arithmet ic
!_ (10°•1 ·Sn ·10)
(a) a
(b) -b
(c)
(d)
b
c
[72] Find the two numbers whose
geometric mean is 5 and arithmetic
mean in 7.5.
(a) 10 and 5
(b) 13.9 and 1.91
(c) 12 and 3
(d) None of the above
I
j 2016 - June
27
=
(b) 10••1 • 9n • 10
(c)
(c) 1.75
(d) None of these
.
52n
(a)
the sum of an A .P., then SP
(d) 1/81
I
[67] If S be the sum, P·the product and A
is the sum of reciprocals of n-terms
[
] If x, y, z are the terms in G.P. then the
terms x2 + y2, xy + yz, y2 + z 2 are in:
(a) A P.
(b) G.P.
(c) H.P.
of these.
= n p·and
Sm = m p (m ,. n) is
[64] If(d)
S., None
2
r 2014 -June
! 2015 -June
[ m(;+1)r
(a)
(b)
Progression (A.P.), then the value of
a-b+c is:
(c) 48
(d) 24
j 2014 - December
(a) 4
[66Jlf the sum of first 'n' terms of an A.P.
is 6n2 + 6n, then the fourth term of
the series:
(a) 120
(b) 72
!_ (1on+ 1 • 9n •
10) 81
(c) 2p3
{d) p'
[65] The arithmetic mean of the square
of first 2n natural numbers is:
1
(a) ...'.. (2n + 1)(4n • 1)
6
.
(b) .!. (2n • 1) (4n • 1)
6
(c)
.6!. c2n - 1.) (4n + 1)
[73] The sum of n terms
x2 of the series
x3 log
x
+ log
-
+ log
y
-· +
y2
(d) None of these
[69] If third term and seventh term of an A .P
are
eighteen
and
thirty
respectively,then sum of first twenty
terms will be:
(a) 540
(b) 610
(c) 740
(d) 810
I 2015 - December
1
(d) . .!. (2n + 1)(4n + 1)
[70] If the sum of 'n' terms of
Downloaded From www.castudynotes.com
6
an Arithmetic
Progression (A.P) is 3x2 + Sx and its m111
term is 164, then the value of m is:
Downloaded From www.castudynotes.com
......................... is
(a)
[2n log() +1og xy]
(b)
[n logxy+log( )]
(c)
[n log ( ) -1og xy]
(d)
[n log ( ) • k)gxy]
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
#37
12ooa -June
2+ X
(10) If f(x) = - , then
2- x
(a) 2(x - 1)
X+1
(b)
I
· [14] X = { X, y, W, z}, y = {1,2,3 ,4}
r - (x) :
1
H= { (x, 1), {y, 2) , (y, 3), (z, 4), (x, 4)}
(a) H is a function from X to Y
. (b) · H is not a function from X to Y
(c) H is a relation from Y to X
(d) None of the above
2(x + 1)
x-1
(c)
then the value of f(2x) -2f(x) + 3 will
be :
x+ 1
X-
(a) 3
1
·
I
(d) 0
[16] If f (.x) = 2x + h then find f{ x+ h) - 2f
(.x)
[11] If A = [1, 2, 3, 4,}
8 = {2,4, 6, 8,}
f (1) = 2, f (2) = 4, f (3) = 6 and
f (4) = 8, And t : A- 8 then r-- 1 is :
(a) l(2,1), (4, 2), (6, 3), (8, 4)}
(b) {(1, 2), (2, 4), (3, 6), (4, 8)}
(c) l(1, 4), {2, 2), (3, 6), (4, 8)}
(d) None of these
[12] If f (x) = x2 + x-1 and 4f (x) = f (2x)
then find 'x'.
(a) 413
(b) Y2
(c) - 3/4
(d) None of these
A = {p, q, r, s}
[13] If
B = {Ci, s, 1}
C = {m, q, n}
Find C - (A fl 8)
. (a) {m, n}
{p, q}
(c) Jr, s}
(d) lP, r}
(b)
j 2010 - December
=
(c) 1
(a) h-2x
(b) 2x - h
(c) 2x + h
(d) None of these
I
[ 2010 - June
(b) {1}
(c) {1,2}
(d) {2, -6}
[18] If F :A -+ R is a real valued function
, then
defined by f(x) =
x
A=
(a) R
(b) R-{1}
(c) R-{O}
-
j·
.
,
(a) AnB
(b) AuB
(c) A'uB
(d) None of these
[21] If f : R--+R , f(x) = x +1,
g : R-+R g(x) = x2+ 1
then fog(-2) equals to
(a) 6
(b) 5
(c)
[17] If A = {x :x2 - 3x + 2 = O},
8 = {x : x2 + 4?( - 12 = O}, then
B - A is Equal to
(a) {- 6}
I
j 2011- June
(24] There are 40 students, 30 of them
passed in English, 25 of them
passed in Maths and 15 of them
passed in both.Assuming that every
Student has passed at least in one
subject. How many student's passed
in English only but not in Maths.
[20] For any two sets A and B, An (A'
uB)
where A' represent
the compliment of the set A ·
(b) 2
x+1
[2008 - December
[19] In the set N of all natural numbers
the relation R defined by a R b •if
and only if, a divide b", then the
relation R is :
(a) Partial order relation
(b) Equivalence relation
(c) Symmetric relation
(d) None of these.
[15] Given the function f(x) = (2x + 3),
x-1
(d)
I
1 200s- December
B.
(b) One to one function from A onto
B.
(c) Many to one function from A
onto B.
(d) Many to one function from A
into B.
-2
(d) None
[22] If AcB, then which one of the
following is true
(a) AnB =B
(b) AuB =B
(c) . AnB =A1
(d) AnB = 4>
[23] If f(x-1) = x2-4x + 8 ,then f (x + 1)
(a) 15
(b) 20
(c) 10
(d) 25
[25] If A = {± 2, ± 3}, B = {1,4,9} and
F = {(2, 4), (-·2, 4), (3, 9), (-3, 4)}
then 'F' Isdefined as :
(a) One to one function frbm A into
[26] If f (x) =
Find fog ?
(a) x
(b)
=
(d) A - N
Downloaded From www.castudynotes.com
..!.
x
x
(c)
(a) x2+8
(b) x2+7
(c) x2+4
(d) x2- 4x
x
(d)
x
J l+ x 2 and g (x) = J 1 - x 2
/I - x2
x Ji -x
2
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#36
CHAPTER7
Sets, Functions & Relations
(3) Let R is the set of real numbers,
such that the function f :R-R and g
:R - R are defined by f(x) = x2 + 3x
X+1 and g(x)
= 2x - 3. Find (fog) :
-I
[4] In a survey of 300 companies, the
number of companies usingdifferent
.media - Newspapers (N), Radio (R)
and Television (T) are as follows :
n(N) = 200, n(R) = 100, n(T) = 40,
n(NnR) = 50, n(RnT) = 20, n(NnT) =
25 and n(NnRnT) = 5.
Find the numbers of companies
using none of these media :
(a) 20 companies
(b) 250 companies
(c) 30 companies
(d) 50 companies.
(5) If R is the set of real numbers such
that the function f :R - R is defined
by f(x) = (x2+ 1)2, then find (fof) :
r2000 - November
I
j 2ooi February
I
[1) Out of 20 members in a family, 11
(2) In a group of 70 people, 45 speak
like to take tea and 14 like coffee.
Hindi, 33 speak English and 1o
Assume that each one likes at least
one of the two drinks. Find how
many like both coffee and tea :
(a) 2
(d) 5
(b) 3
J
found that 40% families buy
newspaper A, 20% families buy
newspaper B and 10% families buy
newspaper C, 5% families buy A
and B, 3% buy B and C and 4% buy
A and C. If 2% families buy all the
three newspapers, then the number
of families which buy A only is:
(a) 6600
(b) _ 6300
(c) 5600
(d) 600.
[8) Let f : R - R be such that I (x) = 2•.
then f (x + y} equals :
(a) f (x) +·t(y)
(b) f (x) .f(y)
(c) f (x) + I (y)
(d) None of these
I2008 -February
-1
(9) Out of total 150 students, 45 passed
in Accounts, 30 in Economics and
(a) (x + 1) + 1
(b) x2 + 1
50 in Maths, - 30 in both Accounts
(c) {(x + 1)2 + 1}2
(d) None
and Maths, :,2 in both Maths and
Economics, 35inboth Accounts and
Economics, 25 students passed in
Downloaded From www.castudynotes.com
(c) 4
-
[7] In a town of 20,000 families it was
(a) 4x2 + 6x + 1
(b) x2 + 6x + (c)
4x2 - 6x + 1 (d)
x2 - 6x + 1.
I2007 - May
! 2007 - November
821
s
p
e
a
k
n
e
i
t
h
e
r
H
i
n
d
i
n
o
r
E
n
g
l
i
s
h
.
F
i
r
i
d
h
o
w
m
a
n
y
c
a
n
s
p
e
a
k
b
o
t
h
E
Downloaded From www.castudynotes.comall the three subjects. Find
nglish as well as Hindi :
(a) 13
(b) 19
(c) 18
(d) 28.
!2007 -August
J
(6) x) = 2x + 7, then If f : R - R, f(the
inverse of f is :
(a) f- 1 (x) = (x - 7)/2
(b) f-1 (x) = (x + 7)/2
(c) r 1 (x) = (x - 3)/2
(d} None.
the
numbers who passed at least inany
one of the subjects :
(a) 63
(b) 53
(c) 73
(d) None.
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#39
I
[ 2014- December
[45) Let N be the se1 of all Natural
numbers; E be the set of all even
natural numbers then the function
f :N _- Edefined as f (x) = 2x v x EN
- is:
{a) One-one into
{b) One-one onto
I
[2015 - December
[50] If A = {x, y, z}, 8 = {a, b, c, d}, then
which of the following rel
ation from
the set A to set B is a function?
(c)
(a) {(x, a), (x, b), (y, c), (z, d)}
(b} {(x, a), (y, b), (z, d}}
y
) .zj,(
= {5, 6},
(c) {{2, 4), (3, 5}}
(d) {(3, 5), (2, 6)}
(47] If S = {1, 2, 3} tten the relation
{(1, 1}, (2, 2), (1, 2) , (2, 1)} is
symmetric and
(a] Reflexive but not transitive
. .zj. .x)}
students can play only table tennis
and the remaining students can
play both the games. In all how
many students can play cricket?
(a) 55
(b} 44
(c) 36
(d) 28
[52] If f(x) = 2x + 2 and g(x)
x2, then
=
I
[59] The range of function f defined by
-f-is:
x
1
f(x) =
+·
(a) {x: -- < X <
2
[55] The domain (D) and range (R) of the
[51] In a class of 80 students, 35%
students can play only cricket, 45%
. ! 2017 -June
-1
EA
{d) xy E A
(c) {(x, c), (z, b}, (z,c)}
(c) Many-one into
(d) Many-one onto
(46] If A = {2, 3}, B = {L, 5}, C
then A x (B n C) = --(a) {(5, 2), (5, 3)}
. (b) {{2, 5), (3, 5)}
[54) Let A be the set of squares of natural
numbers and let XEA, y EA then
(a) X + Y E A
(b) X - Y E A
(b) {x:
-1
2
=
function f(x) 2 - Ix+ 1\ is
(a) D = Real numbers, R = (2, oo)
(b} D Integers, R = (O, 2)
(c) D = Integers, R = (- ""• oo)
(d) D = Real numbers, R = (- "°• 2)
=
1 2015 ... Decernber
I
[56) If R is the set of all real numbers,
then the function f: R-R defined by
f(x) = 2•
-1
(c) {x:
2
SX<
1
2}
1
2}
1
s x s . 2}
1
-1
}
2 or x < 2
·[60] Ina group of students 80 can speak
Hindi, 60 can speak English and 40
can speak English and Hindi both,
then number of students is:
(d) {x:x >
(a) 100
(b) 140
(c) 180
(d) 60
1
{b) Reflexive as well as transi!ive
(c) Transitive but rot reflexive
the
(a) value
18 of fog (4) is:
(d) Neither transiti,e nor reflexive
(48) If
j(x)
=
. then
x -1
f (x/y) =
f(y/x)
(a) x/y
I
[49] If N be the set of all natural numbers
and E be the set of all even natural
numbers then the fullCtion /: N - E,
such that f (x) = 2x for all X EN is
(a) one-one onto
(b) one-one into
I
-June
[53] If set A
= {x:
1
e z,
0
i:
x
:!::
10},
(c) many-one into
(d) many-one onto
[57] The inverse function t1 of f(x)
is:
(a)
(d) None of these
e N, x :!:: 12}
then A n (BnC) Isequal to -
x
= 100x
100x
and C = {x:
-x
(c) 1 - x
(d) - x
I
j 2011- December
[62) If /(x)
.:!.
x
[58] The number of subsets of the set
formed by the word Allahabad Is:
(a) 128
Downloaded
From www.castudynotes.com
y(c) man
=1 - then
(fog) (x) is equal to:
(a) x -1
(b) x
(b) _
1
(c)
¢
[61] If f(x) = -and g(x)
10
B = {x:x is one digit prime number}
(a)
x -1
(b) one-one into
(b) 22
(c) 34
(d) 128
j 2016
(b) y/x
(c} -x/y
{d) -y/x
! 2015 - June
(a) one-one onto
= :: ,
(a)
2x +3
3x +5
(b)
2x +5
3x +2
3x +2
o
then
1{1(-;)} =
ne onto
(d) constant
Downloaded
From www.castudynotes.com
(b) Set A
(b) 16
(c) Set B
(c) 32
(d) Set C
(d) 64
Downloaded From www.castudynotes.com
(c)
(d)
5x +3
5x +2
2x +3
Downloaded From www.castudynotes.com
#38
I 2011
l)ecember
--==i
[27] f(x) = 3+x, for - 3< x <0 and 3 - 2x
for 0< x <3, then Value of f(2) will be
(a) - 1
(b) 1
(c) 3
(d) 5
[28) If A = (1, 2, 3, 4, 5), B = (2, 4) and
C = (1, 3, 5) then (A - C) x B is
[32) The range of the function f : N
f(x) = (- 1)"1, is
N;
(a) {O, - 1}
(b) {1, - 1}
(c) {1, O}
(d) {1, 0, - 1}
I2012 - December
!
=
(5, 2), (5, 4)}
(c) {(2, 2), (4, 2), (4, 4), (4, 5)}
both music and swimming, 20 in
(d) {(2, 2), (2, 4), (4, 2), (4, 4)}
photography and swimming and 1O
in all the three. How many are
interes!ed in photog'raphy but not in
music and swimming?
(a) 30
(b) 15
[29] For any two sets A and B the set
(AUB')' is Equal to (where' denotes
compliment of the set)
(a) B - A
(b) A - B
(c) A' - B'
(d) B' - A'
!
[30] The number of proper sub set of the
set {3, 4, 5, 6, 7} is
(a) 32
(b) 31
f : R - R is a function,
(c) Transitive
(d) None of these.
(c) 30
{d) 25
being
x-5
(b) 7• + 2
(c) 49 (7")
(a)
[38) If /(x)
t(
)
1+
(a)
=
log
1
( +
x) ,
then
(d) not defined
1- - x
! 2014 -June
is equal to:
x2
f (x)
(b) 2/(x)
(c) 3/(x)
j
j
2013 - December
= 10x - 7, if g(x)
g(x) is equal to
f ( x)
(a)
= r1(x), then
(d) Not a function
(c) Infinite
(d) lndetermined
o:-
1
7
1
1Ox + 7
(c)
x+ 7
10
(d)
x-7
I
[42) Let A=0 ,2,3} and 8={6,4,7}. Then,
the relation R={(2,4) , (3 ,6)} willbe:
(a) Function from A to B
(b) Function from 8 to A
(c) Both A and B
(d) -f (x)
defined by
o
{b) 1
(c) 10
(d) None of these
(b)
lines,
(d) 18
(a) 7• . x + 2 . 7x
(c) 25
(d) 20
[34] If
phone, 60 had both a two-wheeler
and a mobile phone, and 10 had all
three. How many candidates had
none of the three?
(a) O
(b) 20
(c) 10
[41] If f (x) = x z - 25 , then f (5) is
interested in music, 70 in
photography and 40 in swimming,
Further more 40 are interested in
both music and photography, 30 in
(b) {(1, 2), (1, 4), (3, 2), (3, 4),
(31) On the set of
perpendicular is a
relation.
(a) Reflexive
(b) Symmetric
[36) Let A = {1, 2, 3}, then the relation R =
{1, 1), (2, 3). (2, 2), (3, 3), (1, 2)} is:
(a) Symmetric
(b) Transitive
(c) Reflexive
(d) Equivalence
[37) If f (x) x + 2, g (x) = 7", than g of (x)
[33) For a group of 200 persons, 100 are
(a) {(2, 2), (2, 4), (4, 2), (4, 4),
(5, 2), (5, 4)}
I 2012 - June
I
2013 -June
10
[35) The number of elements in range of
constant function is
(a) One
(b) Zero
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
[43) In a class of 50 students, 35
[39) If f (x)
= (a - x")1'". a > 0 and 'n' is a
positive
integer, then
/ (f (x)) =
(a) x
(b) a
(c) x11n
(d)
a1/n
[40) Of the 200 candidates who were
.interviewed for a position at call centre,
.100 had a two-wheeler, 70
had a credit card and 140 had a
mobile phone, 40 of them had both a twowheeler and a credit card, 30 had both a
credit card and a mobile
opted for Mathematics and
37 opted for Commerce.
The number of
such
students who opted for both
Mathematics
and
Commerce are:
(a)
13
{b) 15
(c) 22
(d) 28
[44] The range of {(1,0), (2,0), (3,0),
. (4,0), (O,O)} is:
(a){1,2,3,4,0}
(b) {O}
(c)
{1,2,3,4}
(d) None of these
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
l
l
j
832 CPT Scanner : Quantitative Aptitude (Paper 4)
I 2001-=ebruary
#41
(a) 6
·-
x 2 -1
]
(c)
9
(15] The points of discontinuity of the
_ function : 2
*1
[11] If f{x) = "x-T for x
f (x) = 2 for x = 1
{b) 0
(2x +6x- 5)
[3] If f(} =s.x2 +- DX + c then
h·O
h
IS :
I 2007 - August
(a) ll+ 21:i
(b) 2 .u: + b
(c) 2 u - b
(d) 'lxie
[4] A fuci::>r't f(x) is defined as follows :
·x when x < 1
f (x)= 1.+ x when lC > 1
l
3/2 wien x
The 1[:x:} is :
=
[8)
.
(a) )sconliruous at x = 1
(b) J1define ,j at x = 1/2
(c) ),tinuoJs at x = 1
(d) 'l ,ne of t1& se
j 2001-h.,
I
2
(b)
.!
x-0
3
(a)
{b)
(c)
(d)
3x ,
C(x)= {100 + 2x ,
500 + X
At x
(a)
(b)
(c)
(d)
1s equal to :
I
1
(c) -
e.
(d) l
1s equal to :
10) Lim X
[
.
2
+X
3
n
(b)
2 _9
45
- and·
-
3
5
and - 4
---=i
2
x +x- 6
(x - 2)
-then lim f (x)
·X -2
(a) 4
{d) 1
(17] lim _1_ is :
x-b (x-b)
(a)
(b) - 00
(c) does not exist
3
3
2
(d) 0
[18] Let a function be defined as follows:
None
- -- -]
f (x) =
when O < x < 1
{4x,
5 - x, when x
o
X ·1
(a) continuous at x = 1
Um 3x+ !xl .
n(n+1}
(b) continuous at x = O
(c) continuous no where.
[14) x-o 7x- Slxl 1s equal to :
2
Downloaded From www.castudynotes.com
[7] The u11ctionf(:c)=>_
< _ is undefined
5
4
and
(b) 5
(c) 3
x -1
the value of f (x) at x = 1 such that it
is continuous at x = 1 is :
3
(a) 2
(c)
(d)
(c)
4
[16) lff (x) =
2
1 2008 -June
(a) n
(C) I
-3
3
5
December
(b)
I
+ X .......+X - n
X• 1
(b) I
(d)
= 500, the function C (x) is:
Continuous
Discontinuous
Both (a) & (b)
Neither (a) nor (b)
{b)
5
4
I 2008.::
·
Does not exist
Exists and is equal to 2
Exists and is equal to 4 log.,2
None of these
.
100<x :. 500
X>500
I 2007 - November
Lim ,iii- bx} .
x-(a) I
,
2x
[13) f (x) = x 3 • 1 is undefined at x = 1,·
O ,; x s 100
-- and -
(d)
[12) Lim 4x•1 .4 .
certain commodity is given by
(b) .;
[6)
1
(a)
Lim ;- ...- e-; .
[5) x- 1
(a)
1 2oosruary ·--. --- -]
(c) 2
(d) 1
[SJ The total cost C of purchasing of a
-
None of these
are:
5
(a)
(c) Not defined
(d)
Lim ( -1+ -1+-1+.........+ 1 ) .1s equal
n-.. 3 32 33
3"
(12x2 +x-20)
4
(b) Discontinuous
J
to :
1
f (x) =
Then the function f(x) at x = 1 is :
(a) Continuous
{d) 3
Lim 1(c+h} -f(:x:) •
x
-
3
at > = 3. W hat value must be
(c) (n + 1)
(d) n ( n + 1)
Downloaded From
www.castudynotes.com
1
(a)
(d) c
...,
o
n
t
i
n
u
o
u
s
f
o
r
a
l
l
,
e
x
c
e
p
t
x
6
=
1
assitnd to 1(3), if f(x) is to be
conliltJous at = 3?
(bj 1
(c) does not exist
(d) 2
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
#40
one
students
football?
CHAPTER8 Limits and ContinuityApproach
(a)
(a)
]
x
(a)
(d)
(a)
(d)
(b)
(a)
(a)
(b)
when x > O
[2] Let f(x) = { o when x • o
-x
when x < 0
Now f(x) is :
2008NOVEMBER x
2 x" - 2 "
Um
[1]
" ""'x-2 = 80 and nEN, then :
(a) Undefined at x = o
(a) n = 5
(b) .n = O
(c) n = 4
=o
Discontinuous at x = o
(b) Continuous at x
(c)
(d) Noneof these.
(d) None
830
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
#44
[36] Find
J
+ l) • dx
2
I 2011--June
[44) If x2 + y2 = 4 then
(40] x = at2 y = 2 at,dx
dy = ?
Xl
(x
.
ctx 2
(a) 1/t
(a) 1/4 (x' + I) -' + l / 2(x 2 + 1) - 1 + C
(b) - 1/t
(b) 1/4 (x + 1) - -l / 2 (x + 1)+ C
(c) 1/4 ( x ' + l) _,-1/ 2 ( x 2 + 1) _ , + C
2
(d)
1
2
f (/x
-]
) dx
+
<Jx2
(a) 1/2 (x+ 1r112
(b) -1/4 (x+1r
(c) 1/4 (x+1r1r.1
. (d)
dy)2
-1
+
(b) 1
(c) 12
dx
(c)
d2
(d )
y1
<Jx2- _J_dx
(d)
y
d2 x 2 (-dy)2
+
dx2
2x
2x
(
x -1) ·
·
(c)
(d)
None of these.
(b)
r
1
Jo
(a)
(b)
(c)
(d)
(
1
112
-
(
(a)
+
[49] Solve : J (log x i
+ 1= 0
dx
2
2[
3
[39] x = 2 t + 5 and y = t2 -5, then dy = ?
dx
(c) 1/t
.
[46)
(43] (2 x dx =
J1 x 2+2 --(a) log
3
,/2
(b) log /3
(c) log _
1
(47]
(log x)3 + C
(c)
6
(d)
7
(logx)3 + C
xc
(a)
.!
(b)
_:_1
3 ; then
/'(1)
=?
6
J(:x-6;! _
(a)
(b)
(c)
{d)
(log x)3 + C
(log xi3 + C
(b)
(b) 2
(c) 1
(d) 4
(d) None of these.
None of these
(a) t
{b) -1/t
(a) 3
.
2
[5()] If f (x) =
equal to
-[(3x + 4)312 + (3x +1)312 ]+ c
27
·
(c)- (3x + 4)312 - (3x+1)_312 ]+c
2 log 2 -1
4 1og 2 -1
2 log 2
I
C(x) = 2x3 - 15x2+ 36x+15
The cost will be minimum when 'x' is
dx
J3x+ 4-J3x+1
[(3x + 4)312 - (3x +1)312 ]+ c
x) dx
(a)
of x units of a commodity is given by
f .
.dx
xa
.
(45] The cost function for the production
27
1+x
2
None of these.
[42). Equal to
x 1)
2 ( {x+ x ,12)
(b)
(38]
112
(d) None of the above.
- 1= 0
!2010 -June ----------------- I !2Q10 - December
(a)
(a) O
1= 0
2
[41] Find the.second derivative of y =
Jx+1
None of these
[2009 - December
(37]
(c) t
(d) None of th$3 above
[48] Solve : I (e x - e-'") dx
dx
d21 + (
y-
(b)
l
1
2
(a) y d y - (2dy) \ 1= 0
6
3>
dx is equal to
22 log (x-3) -16 (x-2)
11 log (x-3) - 8 (x-2)
22 log (x-3) -16 log (x-2)
22 log (x-3) + 16 log (x-2)
J .,.... .\
2
to (a) • 2( I
l+log.r
dx is equal
)2 + C
Downloaded
I
,/2 From www.castudynotes.com
(b)
(c)
6
{d) _:_5
6
(51)
Gtlar\ y= J(fi'logX + 9'logictx;fm dy
dx
(a) x• ax
{b) x• + ax
(c)
ax- - 1 + ax log a
(d)
0
Downloaded
From www.castudynotes.com
(d) log_
1
(l+logx) + C
/3
(c) - (l+.!sx) + c
(d) None of these
Downloaded From www.castudynotes.com
(d) None of the above.
Downloaded From www.castudynotes.com
#43
.[19] If xy (x - y)
= 0, find
(23) If y = 1 + x +
:.
x2
xs
-+ 21 31
(a)
y)
y (2x x (2y - x)
(b)
x (2x
(c)
x)
y
y {2y
(2y - -x)
dx
(b)
I2008 -February
_Y_
logx
[21]
:
J
J4 -
y=
x.2at the point, where the
ordinate and the abscissa are equal,
x(2 - yy2 logx)
e•" (1 + log x)x"
(a)
!
y
(b)
y
+ log x)
·
yr·".
dy.;
. then find dx
(a) log (x - a) - log (x + a) + C
(b) log x - _
a_ + C
x +a
_!_ log ( x
-a )
+
J
(d) None
[25] The value of
C
(a)
is:
(a) 1
0
(a) 4l
o
g
3
J f (5 - x)dx - f f(x)dx
2
{c)
x 5-1
) +C
XS )
5
+C
x +1
X S-) + C
1log ( (c)-
3
(d)
f
log ( x - )
2
x 5+1
.!1og ( xs+ 1) + C
.3
1
x - 1
3
log(
5
xs·.
dx :
·
(b) log [(x - 2) (x - 1)] + C
2 .
2a
x +a
(d) None of these
1
(a) -1
(b) 1
{c) O
dx
5
1log ( ·
(b)-
(c) xy
(d) None
(29] Evaluate
1
x (x +1)
· (x - 1) (x - 2)
2
(a) log ( x - ) + C
is :
J x2 - a2 dx is:
[22] The value of
·
[24) The slope of the tangent to the curve
(d) None
1
(c)
(c)
J·
x
r_
2 - ylogx
(c)
x• (1 +log x)
(28] If '¥!" yn =.(x +
(d) None
[32)
(b)
(d) e•" (1
(a) 1
(b) -1
(c) o
dx
2
(c) f (x) [-loga]
(d) f (x) [a + x log a)
(a) (1 + log x)
· then dy -y is equal to :
rx.rx ····
I
(27] Differentiate e <x "> :
n
- y)
I 2ooa -June
.
x n .........°"
-+
x (2x - y)
(d) None of these
then dy is equal to :
[20] If.y =
(a)
+ ........ +
I 2009 -June
(33) Find the i/alue of :) x 8-•' dx
(a) 1
(b) - 1
(c) 0
+ C
(d) None
(d) None of these
4
(2x + 5)dx and the value is :
(30) {
I
[34] If x 3y 2 =(x -y)' . Find
1
(1 +www.castudynotes.com
Downloaded From
dx
dy al (1,2).
dx
x) (2 + x)
(b) 0
(c)
is :
1
(d) N
o
n
e
loge•
[26)
dx is :
!
Downloaded From www.castudynotes.com
(a) .-7/9
(
a
)
(b) 7/9
(c) 9/7
(d) - 9/7
1
[0
.
(3
b
)5
3
](c) 3
0
E
f
(d) N
v
o
n
al
e
u
2 ate
o J
o x.
a c•
.D. dx
e
c
e
m
b
e
r
I
(b} log
3
(c) log 12
(d) None
(a) x·1 + C
(b) x + C
(c)
x2 + C
(d) None
(31] If f (x) = a•
(a) ez (x +1) + c
(b) ez ( x -l ) + c
then find f '(x).
(a) f (x) [a + log a)
(c) . ez + c
(b) f (x) [;-toga]
(d)
Downloaded From www.castudynotes.com
x -e' + c
Downloaded From www.castudynotes.com
#42
[4]
r
2
dx is equal to :
Sx
(x:i + 2)3
(a) -
(b) log (x +
.
(c) log (x
3
2
3 (x + 2) + C
(d)
(x3 + 2r 2 + c
(b) -
Jx 2 + a2) + C
.
fo ./x + ./x
j
. [16) The value of
(a) x2.e3x - 2xe3x + 2e3x + C
(b)
3
. dx is :
9
:;,c
(c) !.....:!
-
2
3
3x
9
+ logx) dx is :
x
[Given Loge =1)
(a)
1/2
.!_ - !.:..!.._ + 2e3x + C
2
<1
1
3x
3X
2 109 (x Jx 2 + a2} + C
[8] The value of
3
f
[12) x 2 eSxcJx is :
./x2 + a2) + C .
2
+ -e 3x+ C
27
(b) 3/2
(c)
1
(d) 5/2
f
.! (x3 + 2)2 + C
(c)
(d) None of these
3
{d) None of these
! 2001..:February
I
·
(a) O
2
(b) 3
(c) 2
[131 f
I
= y log (xy), then dy is equal to:
(a)
(b)
dx
x
x (1 + logxy)
(a) 10
x - y
x (1 + logxy)
{b) -10
(c) 1/10
{d) None .
+
is calculated as :
(a) t
x - y
x (logx + logy)
· (a) log,
(c)
dx
2
, then x2 d 2y + x dy _
. (b) -
log.
d
2- [ 2x
+ 1]
4 (x2 + 1)2
2
5
(c) ..!_ [ 2x + 1]
2 (x2
j
+
1)2
2
(d) _ .:!_ [ 2x + 1 ]
2 (x2 + 1)2
[14) If xY = y', then cly gives :
.
(a)
dx
x (x logy - y)
==i
! 2001- November
y (y logx - x)
Downloaded From
www.castudynotes.com
x
x
[6] If Y = 2x +
l
4 (x2 + 1)2J
2
I 2ooi= August .
x (logx + logy)
(d)
(a) ..!_ [ 2x2 + 1
(d) None of these
[1OJ Given x = 2t 5 ; y = t2 - ·2, then dy
x .+ y
(c)
(x2 + 1)3
(b) log05 - log.2 + 1
[9) If f(x) = xk and f ' (1) = 10, then the
value of k is :
+ y
x2
dx :
X
dx :
1
(d) 1
[2001 -May
[5] lf x
.
1 +
3
(17] Find
2
dx
(b) 1
/t
Downloaded
From www.castudynotes.com
[18) If y = (x + ./x 2
(b) x (y
(c)
-1/t
(d) None
+
m2
)"
then
dy = :
logx
:... x)
Y (x
log y
- y)
y yields
(a) 3
[11) The Integral of (e3x + e·
(b) 1
(c) O
{d) 4
J
dx ·. :
[7] Evaluate :
.
Jx2 + a2
log (x + /x2+ a2) + C
(a)
2
e2x
e 4x
(a) -+ -+C
2
4
e2x
e 4x
(b) - - -+C
2
4
(c)
e2x - e·4x + C
. (d) None of these
d
x
I a• s :
(c)
y (x logy - y)
x (y logx - x)
(d) None of these .
[15) If x3 - 2x2y2 + 5x + y= 5, then dy at
dx
X = 1 Md y = 1 is:
w
-
Downloaded From www.castudynotes.com
(a)
ny_
./x2 + m 2
(b) n y
(c) -
ny
Jx 2 + m 2
(d) None
Downloaded From www.castudynotes.com
,.
Chapter 8 - Limits and Continuity Intuitive Approach
(52] lim (n - 1f is equal to:
n-oo
(54] Um 2x2 +3x is equal to:
x - 3x2+ 4
00
n"
(a)
(a) e
(b)
e
#45
.
!
4
.!
(b)
(c) -e
(d) _::_1
i
(c) O
(d)
e
3
I
r 2017 - December
(53) Lim e• - e-• is equal to :
x - ..
x·
(a) 0
(b) 2
(c) 1
(d) -1
,
I
Answer
CHAPTER9
Basic Concepts of Differential and Integral Calculus
1. (a) ·
5. (b)
9. (b)
13. (b) ·
17. (c)
21. (a)
2. (b)
6. (b)
10. (b)
14. (c)
18. (a)
22. (d)
3. (b)
7. (a)
11.(a)
15. (b)
19. (a)
23.(a)
4. (a)
8. (a)
12. (c)
16.(b)
20. (d)
24. (a)
25. (c)
29. (b}
33. (b)
37. (b)
26. (a)
30. (b)
34. (c)
38. (a)
27. (d)
31.(b}
35. (a)
39. (b)
28. (d)
32. (b)
36. (d)
40. (b)
41. (c)
42. (d)
43.(a)
44. (b)
O is given by :
45. (c)
49. (c)
53. (b)
46. (d)
50. (b)
54. (d)
47. (c)
51.(a)
48. (d)
52. (b)
(a) O
(b) 1
(c) -1
i)
I 2006 - November
I
[1] The slope of the tangent at the point
(2, -2) to the curve x2 + xy+ y2 - 4 =
(2) The derivative of x2 log x is :
(a} 1 + 2 Jog x
(b) 2 log x
(c) x ( 1 + 2 log x)
(d) None of these
1
[3]
j (e x ,+
e-X)dx is :
0
(a) e - e:1
(d) None
Downloaded From www.castudynotes.com
(b)
e·1 - e
(c) e + e- 1
Downloaded From www.castudynotes.com (d)
Downloaded From www.castudynotes.com
None
Downloaded From www.castudynotes.com
#47
l
x - 1 When x>O
2
(37] If Lim x - ax + x - a I,then which
X-t 2
X- 2
of the following is correct?
(a) a = 1, 1 = 2
(b) a = ·2, 1 = 3
(c) a = -2, l = -1
[41] 1f f(x) = - } . When x = O
x+1
then f (x) is:
(a) Continuous at x = 0 .
(d) a = -2, I = 3
I
j 2015 -June
xl
(a)
·
When
xs1
1
The value of 'p' for which f(x) is
continuous at x = 1 will be:
(a) 1
5- px, When
X>
(b)
-j
(c) -1
(d) -2
(40] The value of
lim (x + 2)513 - (k + 2)513 _
x-k
x -k
(c)
to n terms) is equal to
-6
7
-
31
40
2) is equal to
(46] xlim
1x -- 21
- 2 (x
c5
- 0 log/1
e2x _+1x) is
o] xlim
. equal to:
(a) 0
then f(x) is
(a) undeftned
(b) continuous at x = 0
(c) continuous
at x = 2
2
(d) not continuous.
13 X>O
[43] The value of Limo 9" - 3x is
4x _ 2x
X-
(b) 1
(c) - 1
{d) Does not exist
[47] If f (x) =
x-3
x n_ 3n
'
= 405 ,
x -3
(c) -3
(b) 5
(d) 4
,
xsO ] • is a
continuous function, then
(a) "' = 0, 13 is any real number (b) . "' ;= -0,
13 = 1
(c) 13 = 0, "' is any real number
(d) "' = 0, 13 = 2
I
[2016 - Dec.ember
I 2015 - December
[44) If lim lim
[x
<X X +
(a) log 3 I log 2
(b) log (3/2)
(c) log 6
(k + 2)213
(1< + 2)513
3
{d)
value of 'n' is:
(a) 3
3
(c)
+
9
I
k213
3
n
-
+ 0.07 + ·0.007
9
(d) 1
(b) 2
(b)
0.and f(O) = 2,
(d) None of th.ese
[39] A function f (x) is defined as under:
(a)
'f'.
x
2014 - December
{x + 2
,x
(0.7
98
]
(42] If f (x) =
3
(c)
(d) None of these
j(x)=
n-"'
=
(b) + 00
j
f(x) = { x + 1 when x 1
3 - px when x 1
The value of 'p' for which f(x) is
continuous at x=1 is:
(a) 0
[ 2016 -June
12 +2 +32+42+ .............+x 2
.x-oo
.(a)
[49] lim
(b) -1
(c) 1
(d) 2
Undefined at x = 0
(c) Discont(nuous at x = 0
(d) None of these.
(b)
[iiti - June
(38] lim
when x<O,
[45] A function f(x) defined as follows:
Downloaded From www.castudynotes.com
)
then the
x3 + a3
.
(48] If f(x) =-, when x 'f'. - a x + a
= k if x = - a
then f(x) is continuous at x = - a, if k is equal
to
(a) - 2a2
(b) -3a2
(c) 2a2
(d) 3a2
(a) 1
{b)
.!
Downloaded From www.castudynotes.com
[51] The function f(x) = (/1-x
j 2011- June
2
(c)
1
2
(d) - 1
I
2t/17)is not defined
at x =
1,the value of f(x) .
which will make f(x)
continuous at x = 1 will be
:
(a)
Downloaded From www.castudynotes.com
(b)
3
l.e) ,
{d)
2
./3
!
3
Downloaded From www.castudynotes.com
#46
I
j 2009.:.. June
[19] Lim x" - 3"
x .-+ 3
= 108. Find n
f:
(d) None of these
Jim (x +2) 312 - (c+ :i)"2
x .-+c
x -c
[20)
(c) 0
(d) None of the above.
x2
I
5- -,
0<X < 5
0
X=5
5
53
5- -
.
x2
Then f(x) is :
X >5
=
(a) Continuous at x 5
(b) Discontinuous at x = 5
·(c) Undefined at x = 5
(d) None of the above
[221
(
231
lim
9x 2 -1
x- -1/3
(a) °"
3x+ 1
(b)
(c)
(d)
1t
j
Find limk (3x + 4)
(b) 2 ,P.
(c) [2
(a) 5
(b) -1/3
(c) 1
(b) 6
(d)
x-
(c) 8
[26] If f(x) = { x +k( 1
I 2011 - December
function, F(x) =
!2010-Decernber . .
[27] Value of Um
X-0
I
·-·
.µ;:;3i. X
.
IS
(a) 3/4
!2012 -June
(32] Evaluate
IYI -
y-O 7y - 5IYI (a) 2
(b) 14
(b) · 1/6
(c) 4
(d) None
(c) 3/7
(d) Does not exit
·-
n3
n-
00
(n + 2)1 - (n + 1)1.
(a) 1
(b) 2
(c) ""
(d) 0
j201 3 -December
[36j Lim
I
Um 2 + 8 + 18 + ........................+ 2n 2
n-oo
-
are
(C) X = 0, X = 2
(d) None of these
(c) 0
(d) 312
c2a1 um 3y -+
x-0 log(1+2x)
x2 - 3x + 2
(a) X = 0, X = 1
(b) X = 1, X = 2
(b) 5/2
(a) 7
I
(31] The points of discontintJity
x 2 + 2x + 5 of the ·
2
1
· (a) -3
(b) 0
(c) 2
(d) 4
(35] Evaluate . lim (n + 2)1 + (n + 1)! .
(d) -2
(a) O
(b) -1
(c) 1
lim 2eic - 3x _
x-o·
ex+x
(b) 1
and f (x) = 2 if x = 2
is continuous at x = 2 then k =
(d)
(341
(c) -1
x-2
I
1
(a) 2
-x>-2x} if x,.2
2
None of these .
! 2013 -June
(d) None of the above.
(30] Function f (x) = K.x - 1 for x < 2
for x 2
=x - k
is continuous at x = 2
The value of 'k' is
.
1
6x + axe x
(2x
(a) 1/2 [2
X =O
!
[33) Lim
(x - 1)
is equal to
2 - 7x + 5)
x -1
(a) 1/3
(x 2 - 4) = k,
x - 2 (x 2 + 2x _ B)
2
-2
I ! 2012 -December
2011-June
(29] If Jim
equal to
=
(b) 1/c
I 2009 - December
1
(d) 0
[25] The function y Ix I is
(a) Discontinuous at x = 0
(b) Discontinuous every where.
(c) Continuous every where.
(d) Continuous everywhere except
(a) C
[21] f(X) = \
x+
4
(b) - 4
(c) 1
J
-·· ·
(24) Lim x -too
x -3
(a) 4
I
j 2010 -June
I
apter 8 - Umits and Continuity Intuitive Ap#46
Ch
.!.is
x .... O x
(a) + ""
(b) • 00
(c) o
(d) does not exist
(a) 1/3
(b) 2/3
(c) 4/3
1
Downloaded From (d)
www.castudynotes.com
I
Downloaded From www.castudynotes.com
#47
I [2014 - December
I 2013 - December
[69) fhe points on the curve y = x 3 - x2 x + 1, where the tangent is parallel
to x - axis are
32
(a) ( .:..!., ) and (1, O)
3 27
(b) (O, O) and ( 1, 0)
(c) (1, 0) and (1, 1)
(d) (0, 1) and ( 1, 1)
[70)
(a)zx dx
_
--
loga
2•.loga
a:
(c)
2
None of these
(d)
I
j 2014 - ,June 5
[71]
f 11 - xl dx =
x z dx
2
is equal to
(b)
_§_
2
(b) 2 log
-1
.
. 2
1
3
(c) - log -- 1
y
[78)
(d)
.eq
(d)
If e•Y - 4xy = 4 then
dy
the value of. dy - y =
.
dx
_ --(a) 1
(b) 0
(c) 2
ld) -1
(a)
(c)
2
(a) 1
(b) 1 • ./312
1
(c)
./3 - ./2
(d)
,/2 - ./3
None of these
2
dx 2
[76] The value of
O
dx
(a)
3
1
3
(b)
16
·X
-
(c)
y
-x
.!
4
1
(d)
y
4
j 201 s - December
. .....
---- 1 I 201s--=-.1u
value of du at t = -1 is:
(a)0
2
0
2
is
J3 -2x
2
-
16
[79j If U= 3t' + 5t3 + 2t2 + t + 4, then the
f
-
x+2
-y
x
(d)
r 1/2
2
1 log 22- 1
(81]The slope of the tangent to the curve
x-1
·· .
y=
at X = 2 IS.
¥.
x
(b)
I
J
=
dx
.
[72) If y= ae"" + be=, then d Y is equal
to
3
(a) log - - 1
x
xn
.
b + [_g +.............+ [n
[75] The value of
5
(c)
(d)
x2
X
x e • dx is
dx is equal
1+X
to:
x
(c)
1 -x
2
1
(b) y
+(5.-x)2
(a)
(80] The value of
to _-(a) .9.
p
_
(201S -June
j
0x
dx
+..............,then
2.a2x
(b)
[77) If '1f' yq = (x + y)P+\ then dy is.equal
2
(74] If y = 1 +
a'lx
21oga
(a)
- ---- ]
[73) The value of definite integral
0
(a) O
(b) 1/2
(c) 3/2
(d) 1
f
-
(b) 1·
(c) 2
dt
Downloaded From www.castudynotes.com
[82]
I
f-
3_
..rxx dx is equal to
0
(a)
{X
2,/2
loge3
(b) 0
1
_
(a)
rty
(b) -n2y
(c) ny
(ct) None of these
Downloaded
From www.castudynotes.com
(d) 5
(a) 1
(c) - 2
-(3v'i - 1)
(b) e - 1
(c) (e/2) - 1 ·
4
.(d) .2! (e - 1)
Downloaded From www.castudynotes.com
log/
(d)
3,/2
./2
Downloaded From www.castudynotes.com
#46
[52] lf f(x) = 3x 2
-
.
x3
- - x- 2 - 2
(d)
x 3+ x 2 +2
d
(1 + log x)
Ydx
dx
3
(b)
dY
-(1 + log x) -
(c)
x3
(a)
! 2012 - December
dY
. d
(b) . -(1 + log x} + -(1 + log x)
dx
dx
./(1) = 0andf(x)
dY (1 + log x) - - (1 + log x)
dx
dx
l 2011- December
j
1
• [53]
f
dx =
[zo12 - June
--
[57] If
g(x)
x1
. (c)" 1
(d) 2
dx
[2
J2s - x 2 ,
then
. ·
-
x-1
(a) 0
(a)" - 1
(b) 0
[54]
-
. Lim g(x) - 9( ) is equal to -
-1
109
"']
1
=­
_
dx
·.
•
1
x + log y
(a)
1
(b) · x + x log Y
1
1 + x logY
1
(c)
(c) 23x. 32x_ 5x +
C log {180)
23x 32x 5x
(d)
]
[65) If = logy x, then dy i;equal to:
log(360)
---· --- --- ::]
=
=
l 2013 y- June
23• 32x 5•
. . +
(a)
c
log(720) ·
23x 32x 5x
. .. + c
(b)
(c) x 3 + x -2 - 2
(d) None of these.
f
[61] 23'. 32x_ 5•. dx
j
+c
log (90)
[62] For the functions y = x3 - 3x, the
(d)
y + log x
f2 ·
.8
(log (ex)t
[66]
1
2
dx (n + -·1) is equal
x
(b) 11../24
(c) ../24
valu of d Y at which dy is zero, is
dx
dx 2
to :
(d) None of these.
(a) ± 1
(b) ± 3
(c) ± 6
(a) [(loge {2e)f ' 1 - 1]
n +1
(b) [(loge (2e))(n+ 1> + 1]
(d)
(c) (loge {2e))"., _ (log 2)" • 1
[58) If x = c t, y = cit, then dy ·is equal to:
dx
·
0
(a) 1
(a) 1/t
(b) 0
(c) 1/2 .
(c)
{b) t.e'
(d) 2X.log2x
e•
[55)
· {d) None of these.
ex
f (1+-Ox)3dx - f 2(1 + x)2 dx =---
(a)
(b)
e•
2(1 + x)2 + C
e•
-1/t2
[59]
r1
dx
= · ---Jo [ax + b (1 - x)J2
(a) alb
None of these.
[63] The equation of the tangent to the
·curve, f = x2 - 3x + 2, at the point
(2, 7) is -
(d)
[67] If x = log t, y
y = 2x - 13
(b) y = 10x
{d) 1/ab .
dx
(a) 1/t
(b) t.e'
(c) -1/t2
(c) y = 10x - 13
(d) y = 10
5 4 2
[64) If y = log ( - x
3 + 5x 2
n +1
= e', then dy =
(a)
(d) None of these
23x. 32x, 5• dx
f
Downloaded From www.castudynotes.com
(b) b/a
(c) ab
n+1
None of these
then dy = -.
) ,
dx
[68]
=
_
Downloaded
From www.castudynotes.com
(a) _
(a)
=
s_ _ _!Q_
[60] If y = e• log• + e• 1oga' then
(c) - 2(1 + x)2 + C
4x - 5 3 + 5x
e•
{d)
(1 + x)2 + C
[56] If Y = xx then d 2Y
=
_
{a)
d)1
(b) (4x2 -5) - (3 + 5x2)
(b) a x•· + a• log a
(c)
(c) a x•1 + x a•·1
· (d) x• + a•
dx 2
d
dY
dx (1 + log x) + Y
(a) x• + 1a•
+ log x)
4x 2 - 5
(d) Sx -10
(b)
- 32x. 5• + C
log (270)
- s2X. 5•+ C
log (360)
3 + 5x 2
(c)
(d)
23•·32x ·s• + C
log (180)
23x. 32x_ s• + c
log (90)
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
#48
Chapter 9 - Basic Concepts
I
f Differential and .•.
Answe r
1. (b)
5. (b)
j
2.
6.
10.
14.
3. (a)
7. (b)
11 . (b)
15. (a)
17. (b)
(c)
(c)
(a)
(c)
18 (a)
21. (c)
22. (b)
23. (c)
·g _ (a)
13. (a)
-
29. (a)
-
37. (b)
41. (b)
-W
49. (b)
53. (b)
57. (b)
61. (b)
65. (b)
69. (a)
77. (c)
81. (a)
19. (a)
- )
v.
30. (c)
-
31. (c)
-
)
38. (a)
42. (b)
39. (a)
43. (a)
-
-
50. (b)
54. (a)
58. (c)
62. (c)
66. (a)
70. (a)
51. (b)
55 (c)
59. (d)
63. (c)
67. (b)
71. (b)
M.
78. (b)
82. (c)
4.
8.
12.
16.
(b)
(d)
(c)
(b)
20 . (c)
24. (a)
- )
32 . (b)
-
40. (a)
44. (b)
-W
52. (c)
56. (a)
60. (b)
64. (c)
68. (b)
72. (a)
-
-
79. (a)
83. (b)
80. (b)
84. (a}
)
85. (a)
86. (c)
87.(b)
88. (a}
89. (b)
90. (a)
91. (a)
92. (c}
-
-
w. }
ga
'A'
"-
CHAPTER10 : Statistical Descriptin of Data
j
2006 - November
--
I
[2] Which of the fo11owmg statement is
true?
(a) Statistics is derived from the
French word 'Statistlk'
(b) Statistics is derived from the
Italian word 'Statista'.
(c) Statistics is deriVed from the
Latin word 'Statistique' .
(d) None of these
[1] The quickest method to ·collect
primary data is :
(a) Personal Interview
(b) Indirect Interview
(c) Mailed Questionnaire Method
(d) Telephonic Interview
852
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
#
#54
[83)
f
dx
x
is
(x 2 + 1) (x 2 + 2)
to
(a)
(c)
_
log(x
2
+
1
) +c
)+c
..!. 1og( x _+_
2..!.1og(
. xx-2-+
2
_+_
+
)+c
1 - x , then dy is equal to -
[84] If y=
1+X
(b} _
y_
._
Y_
1+X 2
I 2016 - December
(a)
I
Co-efficient
of
loge
) with respect to x is:
_1
is equal
(a)
x to:
1
(b) y
2b
(c)
-
.
-=i
1
·
1
J
[94] x.e•2 dx is equalto:
(c)
.········
·1
(a) 2y = 3x2 - Bx + 9
(b) y = 6x2 - Bx + 9
(c) y x2 - Bx + 9
(d) 2y
3x2 -Bx + c
=
=
(a) 2ex2 + C
(b)
(a) e• f (x) + c
(b) e' f1(x) + c
X
f (x)
(d) e• [ f (x> ] + c
/1(x)
[92] If xY = e•·v then dy is equal to:
dx
(a) , 21ogx
(d) xex2 + c
[95] If x = at2, y = 2at then the value of
dy at t = 2 is:
dx
(a) 2
(b) 4 .
(c) _!.
2
(1 + logx)2
logx
(1 + logx)
(c)
logx
(1 + logx) 2
(a) log. (
2
I
i)
X2+
ex2 + c
2
[t,(x)J + c
(b)
.
(c) · ..!._e,..+ c
(d) None of the above
(d) _!.
4
(96) If y = log xx then dy is equal to:
dx
(a) log ex
(b) log
is equal to:
J, _x _dx
1
Downloaded From www.castudynotes.com(c)
(89] The vlue of
.
J e'[f (x) + f (x)J dx
dx is.equal to:
has the slope 3x - 4 at any point
(x, y) is:
y2-1
2
e
(88] The equation of th'e curve which
passes through the point (1, 2) and
_y_
(rx-:T +
e x (xlog x + 1)
!2011:.. June
1-x 2
[85] Differential
9
dx
J_
2b
[91J The value of
(a) e + 1
(b) ee
(c) e - 1
(d) e• + 1
x 2 -1
(d)
f
"", then the value of dy
! 2017 :..December
1
dx
y_
(a) _
(c)
[87]
+
(d) 0
. (d) ± ,/2 .
2
X'
•
+ --
.fi
(c) ±
-log(x__
2+
(d)
· (a) O
1
(c)
- +-· X2
--
(a) 2b
{b) -2b
+ ./01
x+1
x 2 + 21
x
1
X
(93] If y = 1 +
dx
of x at which f'(x) = 1, is
(b) 1
2
(d)
then the value of dy at t = O is :
1
[86J If f(x) = log.( x - ) , then the value
1
(c)
2
2 (x2 - 1)
) +c
(b}
I.
[90] If x = at3 + bf - t and y = at2 - 2bt,
(d)
x 2 +2 2
2
1
equal
x
log
e
Downloaded From www.castudynotes.com
(d) 1
1
(b}
2
(b)
log.( )
(c) log (5) - log.2 + c
(d) None of these.
Downloaded From www.castudynotes.com
Downloaded From www.castudynotes.com
#51
[19]0ut of 1000 persons, 25 per cent
were industrial workers and the rest
were agricultural workers. 300
· persons enjoyed world cup matches
on T.V. 31J per cent of the people
who had not watched world cup
matches were indus1rial workers .
What is the number of agricultural
workers who had enjoyed world cup
matches on TV?
(a) 230
(b) 250
(c) 240
(d) 260
[20] Median of a distribution can be
obtained from ;
(a) Histogram
(b) Frequency Polygon
(c) Less than type Ogives
,,. {d) None of these
I
! 2008-June
(21) In indirect oral investigatio!1 :
(a) Data is not capable of
numerical expression
(b) Not possible or clesirable to
approach informant directly.
(c) Data is collected from the
books.
(cl) None of these
(22) Circular diagrams are always :
(a) One - dimensional
{b) Two - dimensional
(c) Three - dimensional
(d) Cartograms
(23) The column headings of a table are
known as :
(a) Body
(b) Stub
(c) Box - head
(d) Caption
(24] Some important sources of
secondary data are
:
(a) International and Government
sources
(b) Internationa l and primary
sources
· (c) · Private and primary sources
(d) Government sources
j 2oos - December
!
(25) From the following data find the
number class intervals if class length
is given as 5.
" 73, 72, 65, 41, 54, 80, 50, 46, 49, 53.
(a)
6
(b) 5
(c) 7
(d) 8
[26] The most appropriate diagram to
represent the data relating to the
monthly expenditure on different
items by a family is
(a) Histogram
(b) Pie-diagram.
(c) Frequency polygon
(d) Line graph.
[27] Which of the following is a statistical
data ?
(a) Ram is 50 years old.
(b) Height of Ram is 5'6" and ot
Shyam and Hari is 5•3• and 5'4"
respectively.
(c) Height of Ram is 5'6" and
weight is 90kg
(d) Sale of A was more than B
and C.
[28] Sales of XYZ Ltd. for 4 months is :
Months Sales
Jan.
10,000
Feb.
15,000
May
18,000
Apr.
9,000
The above data represents :
(a) Discrete
(b) Continuous
(c) Individual
(d) None of these.
I2009 -June
I
(29] Mid values are also called
(a) Lower limit
(b) Upper limit
(c) Class mark
(d) None.
(30] Which of the following is not a two­
dimensional figure ·-,
(a) line Diagram
(b) Pie Diagram
(c) Square Diagram
(d) Rectangle Diagram.
Downloaded From www.castudynotes.com
(31] Less than type and more than type
gives meet at a point known as :
(a) Mean
(b) Median
(c) Mode
(d) None
(2oo9 - December
·· ···
.
]
(32] Arrange the dimensions of Bar
diagram, Cube diagram, Pie
diagram in sequence.
(a) 1, 2, 3
(b) 2, 1, 3
(c) 2, 3, 1
(d) 3, 2, 1
[33] With the help of histogram one can
find.
(a) Mean
(b) Median
(c) Mode
(d) First Quartile.
(34] Nationality of a person is :
(a) Discrete variable
(b) An attribute
(c) Continuous variable
(d) None
[35] If we plot less than and more than
type frequency distribution, then the
graph plotted is
_
(a) Histogram
(b) Frequency Curve
(c) Ogive
(d) None of these
Downloaded From www.castudynotes.com
#49
(7) Find the number of observations
[3) The following data relates to tt,e
between 350 and 400 from
followingdata :
incomes of 90 persons :
Income in f :
No. of Persons :
15001999
13
2000- ' 2500- 30002499 2999 3499
32
20
Value·:
(d)
Footnote
350
48
25
12
0
(a) 13
(b) 15
(c) 17
(d) 19
[8], When the width of all classes is
same, frequency polygon has not
the same area as the Histogram :
{a) False
(b) True
(c) Both
(d) None
[9] The graphical representation of a
j
[5] Divided bar chart is good for :
(a) Comparing various components
of a variable
(b) Relating the different compo­
nents to the whole.
{c) (a) and (b)
(d) (a) or (b)
! 2001-May
200
More More
than than
400 450
observations :
is shown in the :
{a) Stub
(b) Body
Caption
than
No. of
[4] In tabulation, source of data, if any,
{c)
More
than
25
What is the percentage of persons
earning more than t 2,500 ?
{a) 45
{b) 50
(c)" 52
{d) 55
I 2007 - February
More
the
[6] Relative frequency for a particular
class lies between :
{a) O and 1
(b) O and ·1, both inclusive
{c) -1 and o
(d) -1 and 1
j 2007 - November
called :
(a) Histogram
(b) Ogive
(c) Both
(d) None .
related series, we consider :
(a) Multipla Bar Chart
(b) Grouped Bar Chart
(c) (a) or (b)
(d) (a) and (b)
[14) An area diagram is :
(a) Histogram
(b) Ogive
(c) Frequency Polygon
(d) None of these
[15) Most extreme values which would
ever be included in a class interval
are called:
(a) Class Interval
(b) Class Limits
(c) Class Boundaries
(d) None of these
(1O] A table has
parts.
(a) Four
(b) Two
(c) Five
(d) None
(11] Cost of sugar in a month under the
heads raw materials, labour, direct
· production and others were 12, 20,
35 and 23 units respectively.What is
the difference between the central
women empl.>yed was 200 of which
175 did not belong to a trade
2004 ,
union. '1n
the re
were
1,800 employees who belong to a
trade union and 50 who did not
belong to trade union.Of all the
employees in 2004,
300 were
women of whom only 8 did not
belong to the trade union. On the
basis
of
this information, the
ratio of female members of the trade
union in 2000 and 2004 is :
(a) 292 :25
(c) 175 : 8
(d) 25 :292
[13) In order to compare two or
I
[16) In 2000, out of total of 1,750workers
of a factory , 1,200 were members of a
trade union. The
number of
(b) .8 : 175
j
cumulative frequency distribution is
I2007 -August
I
angles for the largest and smallest
components of the cost of sugar ?
(a) 72°
(b) 48°
(c) 56°
(d) 92°
[12] Frequency density corresponding to
a class interval is the ratio of :
(a) Class Frequency to the Total
Frequency
(b) Class Frequency to the Class
Length
(c) Class Length to the Class
Frequency
(d) Class
Frequency
to the
Cumulative Frequency.
more
[ 2008 - Fet>ruary
I
[17] The lower class boundary is :
(a) An upper limit to Lower Class
Limit
(b) A lower limit to Lower Class
Limit.
(c) Both (a) & (b)
(d) None of these
(18) The distribution of profits of a
company follows :
(a) J - shaped frequency curve
(b) U ·shaped frequency curve
{c) Bell - shaped frequency curve
(d) Any of these
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#53
I · ! 2014 - June
I 2013 -June
the following data:
Customs Excise Income Wealth
tax
tax
240
180
Revenue in
million rupees:
120
180
The central angles in the pie
diagram correspondi ng to income
tax and wealth tax respectively:
(a) (120°, 90°)
(b) (90°, 120°)
(c) (60°, 120°)
(d) (90°, 60°)
[2013 - December
office in which 150 were married.
Total male employees were 160 out
of which 120 were married. What
was the number of female unmarried
employees?
(a) 30
(b) 10
I
and minimum value of a given data
is called
(a) Width
(b) Size
(c) Range
(d) Class
[56] If class interval is 1O - 14, 15 - 19,
20 - 24, then the first class is
(a) 10 - 15
(b) 9.5 - 14.5
(c) 10.5 - 15.5
(d) 9 - 15
[57] The difference between the upper
and lower limit of a class is called
distribution should be:
{a) Inclusive type
(b) Exclusive type
(c) Inclusive and Exclusive type
(d) None of these .
j 2014 - December
···--=1
[62] The most appropriate diagram to
represent the five - year plan outlay
(d) 50
of India indifferent economic sectors
(a)
·
[61]To draw Histogram, the frequency
(c) 40
[59] "The less than Ogive" is a:
[55] Difference between the maximum
(a) Class Interval
(b) Mid Value
(c) Class boundary
(d) Frequency
I
[58) There were 200 employees in an
[54] A pie diagram is used to represent
Source:
- · ··
U-Shaped Curve
(b) J-Shaped Curve
(c). S-Shaped
(d) Bell Shaped Curve
[60) The following data relates to the
marks of a group of students.
Marks
No. of
Students
More than 70%
07
More than 60%
18
More than 50%
40
More than 40%
60
More than 30%
75
More than 20%
100
How many students have got marks
less than 50%?
(a) 60
(b) 82
(c) 40
(d) 53
is:
(a) Pie diagram .
(b) Histogram
(c) Line-Graph
(d) Frequency Polygon
[63] If the fluctuations in the observed
value are very·small as compared to
the size of the item, it is presented
by:
(a) Z chart
(b) Ogive curve
(c) False base line
(d) Control chart
[64) For constructing a histogram, the
class-intervals of a· frequency
distribution must be
(a) equal
(b) unequal
(c) equal or unequal
(d) none of these
[65) 100 persons are classified into
male/female and graduate/non­
graduate classes. This data
classification is:
'
Downloaded From www.castudynotes.com
(a) Cardinal data
(b) Ordinal data
(c) Spatial Series data
(d) Temporal data
1 201 s:... June
.
J
[66) If we draw a perpendicular on x-axis
from the point of inter-section of both
'less thar)' and 'morethan' frequency
curves we will get the value of
(a) mode
(b) median
(c) arithmetic mean
(d) third quartile
[67] Histogram is used for the
presentation of the following type of
series
(a) Time series
(b) Continuous frequency distribution
(c) Discrete frequency distribution
(d) Individual observation
[68] Curve obtained by joiningthe points
whose x coordinates are the upper
!imits of the class intervals and y
coordinates are the corresponding
cumulative frequencies is called.
(a) Frequency Polygon
(b) Frequency curve
(c) Histogram
(d) Ogive.
[69] The number .of observations
between 150 and 200 based on the
following data is
Downloaded From www.castudynotes.com
#52 2010 - June
·
-
]
[42) The statistical measure computed
from the sample observations alone
have been termed as
I 2011 - December
I
(47] The frequency of class 20-30 in the
[51] The data given below refers to the
marks gained by a group
·students:
of
[36) The primary rules that should be
observed in classification
(i) As far as possible, the class·
should be of equal width
(ii) The
classes
should .be
exhaustive
(iii) The classes
should
be
unambiguously defined.
Then which of the following is
correct
(a) only (i) and (ii)
(b) only (ii) and (iii)
.(c) only (i) and (iii)
(d) all (i) , (ii) and 1,;;;
[37] Using Ogive Curve, we can
determine
(a) Median
(b) Quartile
(c) Both (a) and (b)
(d) None.
[38) Same as
1 201o
a 33 [Dec. 09]
- oecember
[39) Mode can be obtained from
(a) Frequency polygon.
{b) Histogram.
(c) Ogive
(d) All of the above.
[40) Same as
•
a 26 [Dec. 08)
[41] The data obtained by the internet
are
(a) Primary data
(b) Secondary data
(c) Both (a) and (b)
(d) None of these.
I
(a) estimate
following data is
(b) parameter.
(c) statistic
(d) attribute.
1 201 1 -June
;:
;:
o o oo
Marks
ai .,... ai "'
m
Class
0-1O 10-20 20-30 30-40 40-50
38
Cumulative 5
13 · 28
34
I
[43] When the two curves of ogive
intersect, the point of intersection
.provides :
·
(a) First Quartile
(b) Second Quartile
(c) Third Quartile
(d) Mode. ·
[44] Frequency Density can be termed as:
(a) Class frequency
to th·e
cumulative frequency
(b) Class frequency to the total
frequency
(c) Class frequency to the class
length
(d) Class length to the class
· frequency .
[45] The Choronological classification of
data are classified on the basis of :
(a) Attributes
{b) Area
(c) Time
(d) Class ln.terval
(46] Arrange the - follow ing dimension
wise :pie-diagram, bar-diagram and
cubic diagram.
(a) 1,2,3
(b) 3,1,2
(c) 3,2, 1
(d) 2,1,3
No. of
Frequency
(a) 5
Students
CD
15
;:
.Q o
(]) (,:)
co
38
;:
CD
65
;:
c o co
cii ¢ ai U)
CD
84
100
Then the no. of students gettirig
marks more than 30 would be
(b) 28
(c) _ 15
(d) 13
[48] The Graphical representat ion by
(a) 50
which median is calculated is called
(a) Ogive Curve
(b) Frequency Curve
(c) Line diagram
(d) Histogram
(49] Which of the following is not a two
dimensional diagram?
(a) Square diagram
(b) Une diagram
(c) Rectangular diagram
(d) Pie-chart
(b) 53
(c) 35
I 2012 -June
(d) 62
[52] Cost of Sugar in a menlh under the
heads raw materials, labour, direct
production andothers were 12,20 ,35
& 23 units respectively. The
difference between their central
angles for the largest & smallest
components of the cost of Sugar is
(a) 92° •
(b) 72°
I
(50] From which graphical represen­
tation, we can calculate partition
values ?
(a) Lorenz curve
(b) Ogive curve
(c) Histogram
(d) None of the above.
(c) 48°
(d) 56°
I 2012 - December
J
[53] What is a exclusive series'?
(a) Inwhicli both upper and lower
limit are not included in class
frequency.
(b) In which lower limit is not
included in class frequency.
(c) In which upper limit is not
includedi
n class frequency .
(d) None of the above.
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#
45
Chapter 10 - Statistical. Description of Data
CHAPTER 11 :
Measures of Central Tendency
and Dispersion
Answer
1. (d)
5. (c)
2. {b)
3. (b)
6. (a)
7. (a)
9. (b)
10. (c)
11. (d)
13. (c)
17 . (b)
14. (a)
18 (c)
15. (c)
21 .(b)
22. {b)
26. (b)
23. (d)
30. (b)
31. (b)
34. (b)
38. (c)
42. (c)
35. (c)
25_. (d)
29 . (c)
33. (c)
37..(c)
41. (b)
45. (c)
49. (b)
53. (c)
57. (a)
61. (b)
65. (b)
69. (b)
73. {a)
77. {c)
81. (b)
19. (d)
27. (b)
39. (b)
43. (b)
47. (c)
51. (c)
55. (c)
59. (c)
46. (d)
50. (b)
54. (a)
58. (b)
62 . (a)
66 . (b)
70. (c)
63. (c)
67. (b)
71 . (a)
74. (b1 .
75. (b)
78. (c)
79. (d)
83. (d)
82. (c)
4. (d)
8. (a)
12. (b)
16. (d)
20. (c)
24. (a)
28. (c)
32. (c)
36. (b)
40. (b)
44. (b)
48 . (a)
52. (a)
56. (b)
60. (3)
64. (a)
68. (d)
72. (d)
76. (d)
80. (a)
84. (b)
"
I 2006 - November
j
(1) lfx and y are related by x - y - 10 =0
and mode of x is known to be 23,
then the mode of y is :
(a) 20
(b} 13
(c) 3
(d) 23
Downloaded From www.castudynotes.com
(2) A man travels at a speed o 20 km/hr
and then returns at a speed of 30
km/ hr. His average_ speed· of the
whole journey is :
(a) 25 km/ hr ·
(b) 24.5 km/hr
(c) 24 km/hr
(d) None
Downloaded From www.castudynotes.com
#46
:
Value:
No. of
observations:
{a) 46
[73] The chart that uses logarithm of
variable is known as:
(a) Ratio chart
(b) Line chart
(c) Multiple line chart
(d) Component line chart
[74) Find the number of observation
between 250 and 300 from the
followi ng data:
More More More More
than than than than
100
150
200
250
76
63
28
05
(b) 35
(c) 28
(d) 23
(70) The number of car accidents in
seven days in a locality are given
below:
No. of accidents : 0 1 2
Frequency:
12 9 11
3 4 5 6 7
13 8 9 6 '3
What will be the number of cases when 4
or more accidents occurred?
(a) 32
V alue more than:
1200 I 250
No. of observation:
I 56 ·I 38
I 300 I 500
15 I
o
(a) 38
(b) 23
(c) 15
(d) None of the above
I 2016 -June
·
··· ·
J
(b) 41
(c) 26
[75] Data collected on religion from the
census reports are:
(d) 18
! 2015 - December
]
(71] The most common form of
diagrammatic representation of a
grouped frequency distribution is:
{a) Histogram
{b) Ogive
{c) Both
{d) None
(72) Classification is of
kinds.
(a) Two
(b) Three
{c) One
{d) Four
(a) Primary data
[2011- June
(b) Secondary data
(c) Sample data
(d) (a) or (b)
I 2016 - December
[77) For constructing a histogram the
class intervals of · a frequency
distribution must be of the following
type:
(a) Equal
(b) Unequal
(c) Equal or Unequal
(d) None of these
[78) Profits made by XYZ Bank in
different years refer to:
(a) An attribute
(b) A discrete variable
(c) A continuous variable
(d) None of these.
[79] Mode of presentation data
(a) Textual presentation
(b) Tabulation
(c) Oral presentation
(d) (a) and (b)
j
[76] In collection of data which .of the
following interview methods:
(a) Personal interview method
(b) TeleptlOne interview method
(c) Published data
(d) (a) and (b)
{c) Class length to the class
frequency
{d) Class frequency
to the
cumulative frequency
[82] The point of intersection of less than
ogive and greater than ogive curve
gives us:
(a) Mean
{b) Mode
(c) Median
(d) None of the above.
[ 2017 - December
[83] 'Stub' of a table is the
{a) Left part of the table describing
the columns
(b) ·Right part of the table
the columns
(c) describing
Right pa:1
of the table
i
[80] If the data represent costs spent on
conducting an examination under
various needs, then the most
suitable diagram will be:
(a) Pie diagram
{b) Frequency diagram
(c) Bar diagram
(d) Multiple bar diagram
[81) Frequency density corresponding to
class interval is the ratio of :
(a) Class frequency to the total
frequency
(b) Class frequency to the class
length
J
describing the rows
{d) Left part of the tabl c:lescribing
the rows.
[84] Frequency density corresponding to
a class interval is the ratio of
(a) Class frequency
to total
frequency
(b) Class frequency to the class
length
(c) Class length to class frequency
t the
(d) Class frequency
cumulaUve frequency.
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#47
CHAPTER11 : Measures of Central Tendency and Dispersion
(36) The average salaiy of 50 men was
80 but it was found that salary of 2
of them were 46 and 28 which
· was wrongly taken as 64 and 82.
The revised average salary is :·
(a)
80
(c)
78.56
85.26
(d)
t 82.92
(b)
(37) Inter Quartile Range is
of
Quartile Deviation.
(a) Half
(b) . Double
(c) Triple
(d) Equal
(38] The sum of squares of deviation
from mean of 1O observations is
250. Mean of the data is 1O. Find the
co-efficient of variation.
(a) 10 %
(b) 25 %
=·
[41) If L, = highest observation and
smallest
observation,
then
Coefficient of Range =
(a) L, x li x 100
L1/li
(b)
- x 100
L, + li
(c)
1 -x 100
-Li
L+
(a) 3.09
(b) 5.01
(c) 4.01
\
(d) None of these
(c) 50 %
(d) 0 %
[39] If A be the A .M. of two positive
unequal quantities X and Y and G
be their G.M., then ;
(a) A < G
(b) A > G
(c) A !; G
(d) A
G
! 2009 - December
[40) When mean is 3.57 and mode is
2.13 then the value
of median
is
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From
www.castudynotes.com
--·
,(d)
/ x 100
L1x
(b)
15
(c) 5
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(d) -13
(42) The equation of a line is 5x + 2y =
17. Mean deviation of y about mean
is 5. Calculate mean deviation of x
about mean.
(a) - 2
(b) . 2
(c) -4
(d) None
[43] If variance of x is 5, then find the
variance of (2 - 3x)
(a) 10
[45] The mean weight of 15 students is
110 kg. The mean weight of 5 of
them is 100 kg. and of another five
students is 125 kg. then the mean
weight of the remaining students is :
(a) 120
(b) 105
· (c) 115
(d) None of these
[46] Ina class of 11 students, 3 students
were failed in a test. 8 students who
passed secured 10,11, 20, 15, 12,
14, 26 and 24 marks respectively.
What will be the median marks of
the students : ·
(a) 12
(b) 15
! 2010 -June
[44) The harmonic mean of 1, 1/2, 1/3
........ 1/n is
(a) 1/(n + 1)
(b) 2/(n + 1)
(c) (n + 1)/2
(d) 1/(n - 1)
journey (in km/h)
{a) 25
(b) 30
(c) 35
(d) · 38 .
13
(d) 13.5
(c)
I 2010 - December
[47] The variance of data : 3,4,5,8 is
(a) 4.5
(b) 3.5
{c) 5.5
(d) 6.5
[48] A lady travel at a speed of 20km/h
and returned at quicker speed. If her
average speed of the whole journey
is 24km/h, find the speed of return
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[49] Let the mean of the
variable 'x'.be 50, then the
[51] If the difference between mean and
Mode is 63, then the difference
Downloaded
From www.castudynotes.com
between Mean and Median will be
mean of u=10+5x will be :
(a) 250
(b) 260
(c) 265
(d) 273
[50] Given
the
observations
4,9,11,14,37. The Mean
deviation about the Median
is
(a) 11
(b) 8.5
(c) 7.6
(d) 7.45
<a> 63
(b) 31.5
(c) 21
(d) None of the above.
[52] If the Arithmetic mean between two
numbers is 64 and the Geometric
mean between them is 16. The
Harmonic Mean between them is
(a)
64
(b) 4
(c) 16
(d) 40
j 2011 - June
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#48
[53] If all observations in a distribution
are increased by 6, then the
variance of the series will be
(a) Increased
(b) Decreased
(c) Unchanged
(d) None of these.
[54] The average of 5 quantities is 6 and
the average of 3 is 8. what is the
average of the remaining two.
(a) 4
(b)
(c)
5
3
(d) 3.5
j 2011 - December
[55] The standard deviation of the
weights (in kg) of the students of a
class of 50 students was calculated
to be 4.5 kg. Later on it was found
that due to some fault in we!ghing
machine, the weight of each student
was under measured by 0.5 kg. The
Correct standard deviation of the
weight will be:
(a) Less than 4.5
(b) Greater than 4.5
(c) · Equal to 4.5
(d) Can not be determined
(56] For Normal distribution the relation
between quartile deviation (0.D) and
standard deviation (S.D) is
(a) 0.0 > S.D
(b) 0.0 < S.D
(c) 0.1::'.> = S.D
[57] The median of following numbers,
which are given is ascending order
is 25. Find the Value of X.
·
11 13 15 19 (x + 2) (x + 4)
30 35 39 46
(a) 22
(b) 20
(c) 15
(d) 30
[58] The average age of a group of 1O
students was 20 years. The average
age increased by two years when
two new students joined the group.
· What is the average age of two new
students who Joined the group?
(a) 22 years
(b) 30 years
(c) 44 years
(d) 32 years
j 2012 - June
[59] If standard deviation of first 'n'
natural numbers is 2 then value of
'n' ls
(a) 10
(b) 7
(c) 6
(d) 5
[60) Geometric Mean of · three
observations 40, 50 and X is 10. The
value of X is
(a) 2
(b) 4
(c) 1/2
{d) None of the above.
(d) None of the above
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(61) The mean of first three term is 14
and mean of next two terms is 18.
The mean of all five term is :
(a) 14.5
(b) 15
(c) 14
. (d) 15.6
[62)The standard deviation is indep­
endent of change of
(a) Scale
(b) Origin
(c) Both origin and scale
(d) None of these.
(63) In a normal distribution, the
relationship between the three most
commonly used measures of
dispersion are:
(a) Standard Deviation > Mean
Deviation > Quartile Deviation
(b) Mean Deviation > Standard
Deviation > Quartile Deviation
(c) Standard Deviation > Quartile
Deviation > Mean Deviation
(d) Quartile Deviation > Mean
Deviation > Standard Deviation
!2012 - December
[64] If Standard deviation of x is a, then
Standard deviation of ax +b, where a, b
and c (c ± 0) are arbitrary constants,
will be
(a) o
ao + b
c
(c)
.a
c
(b)
(d)
/ lo
(65] The mean salary of a group of 50
persons is 5,850. Later on it is
'°
discovered that the salary of one
· employee has been wrongly taken
as '° 6,000 instead of. ,7,600. The
corrected mean salary is
(a) · 5,854
(b) "5,846
(c) ,5,650
(d) None of the above.
[66) Which of the following measures of
dispersion is usedfor calculating the
consistency between two series?
(a) Quartile deviation
(b) Standard deviation
(c) ·Coefficient of variation
(d) None of the above.
(67] If the mode of a data is 18 and mean
is 24, then median is ·
(a) 18
(b) 24 ·
(c) 22
(d) 21
(68) For data on frequency distribution of
weights:
70, 73, 49, 57, 56, 44, 56, 71, 65,
62, 60, 50, 55, 49, 63 and 45
If we assume class length as 5, the
number of class Intervals would be
(a) 5
(b) 6
(c) 7
(d) 8
(69) The point of intersection of the 1ess
than• and "more
correspond to
(a) Mean
(b) Mode
(c) Median
(d) 1011 Percentile
than· ogives
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#49
(70) A man travels from Agra to Gwalior
at an average speed of 30 km per
hour and back at an average speed
of 60 km per hour. What is his
average speed?
(a) ·3a km per hour
(b) 40 km per hour
(c) 45 km per hour
(d) 35 km per hour
j 2013 -June
=
(71) If sum of squares of the values
3390, N= 30 and standard deviation
7, find out the mean.
(a) 113
(b) 210
(c) . 8
(d) None of these
[72]1f the mean of a frequency
dist;ibution is 100 and coefficient of
variation is 45% then standard
deviation is:
(a) 45
=
(b) 0.45
(c) 4.5
(d) 450
(73) Which of the following measures of
central tendency cannot
be
calculated by graphical method?
(a) Mean
(b) Mode
(c) Median
(d) Quartile
[74) Geometric mean of 8, 4, 2 is
(a) 4
(b) 2
(c)
8
(d) None of these
(75] The average age of 15 students of a
class is 15 years. Out of them, the
average age of 5 students is 14
years and that of the other 9
students is 16 years. The age of the
15111 student is:
(a) 11 years
(b) 14 years
(c) 15 years
(d) None of these
I 2013 - December
(76) Find at the variance given that the
Arithmetic Mean = (8 + 4)/2
(a) 2
(b) 6
(c)
1
(d) 4
[77) In normal distribution mean, median
and mods are
(a) Equal
(b) Not Equal
(c) Zero
(d) None of above
(78) Coefficient of mean deviation about
mean for the first 9 natural m.1mbers
is
(a) 200/9
(b) 80
(c) 400/9
(d) 50
(79) The price of averages whose value
can be determined graphically?
(a) Mode, Median
(b) Mean, Mode
(c) Mean, Median
(d) None of the above
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[80) If mean
=
5, Standard
deviation
= 2.6, median = 5 and quartile
deviation = 1.5, then the coefficient
of quartile deviation equals
(a)
35
(85) The third decile for the numbers 15,
10, 20, 25, 18, 11, 9, 12, is:
(a) 13
(b) 10.70
(b) 39
(c) 11
(c) 30
(d) 11.50
[86) A random variable X has uniform
distribution on the interval (-3, 7).
The mean of the distribution is:
(d) 32
! 2014 -June
(81) What will be the probable value of
mean deviation? When 03 = 40 and
0, = 15
(a) 17.50
(b) 18.75
1
(a) 2
(b) 4
(c) 5
(d) 6
[87) If the first quartile is 142 and semi­
(c) 15.00
(d) None of the above.
[82) Which of the following statements is
true?
(a) Median is based on all the
observations
(b) The mode is the mid value
(c) The median is the second
quartile
{d) The mode isthe fifth decile.
(83) The mean of the following data is 6.
Find the value of ·p·.
x : 2 4 6 10 P+5
f: 3 2 3
! 2014 - December
2
(a) 4
(b) 6
(c) 8
.(d) 7
[84) The formula for range of middle 50%
items of a series is :
(a) 03-01
(b) 03-02
inter quartile range is 18, then the
value of median is:
(a)
151
(b) 160
(c) 178
(d) None of these
(88) The quartil deviation is:
(a) 2/3 of S.D.
(b) 4/5 of s.o.
(c) 5/6 of S.D.
(d) None of these
(89) If the arithmetic mean of two
numbers is 10 and the geometric
mean of these numbers is 8, then
the harmonic mean is:
(a) 9
(b) 8.9
(c) 6.4
(d) None of these
(e) QZ.Ql
Cd)
2-
aa - a,
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#50
j 2015 - June
[90] The standard deviation of a variable
x is known to be 10. The standard
deviation of 50 + 5x is
(a) 50
(b} 100
(c) 10
(d) 500
[91) The harmonic mean H of two
numbers is 4 and their arithmetic
mean A and the geometric mean G
satisfy the equation 2A + G2
27,
then the numbers are
=
(a) (1, 3)
(b) (9, 5)
(c) (6, 3)
(d) (12, 7)
[92] Coefficient of quartile deviation is
· equal to
(a) Quartile deviation x 100/median
. (b) Quartile deviation x 100I mean
(c) Quartile deviation x 100 I mode
(d) None
(93] If all the observations are increased
by 5, then
(a) S.D. would be increased by 5
(b) Mean deviation would be
increased by 5
(c) Quartile deviation would be
increased by 5
(d) All the three would not be
increased by 5
I 2015 - December
(94] What is value of mean deviation
about mean from the number 5, 8 ,
6, 3 and 4 ?
M
(95) For the observation of 6, 4, 1, 6, 5,
10, 4, 8 the range is:
(a) 10
(b) 9
(c) 8
(d) None
[96) If a variance of a random variable 'x'
is 23, then what is variance of 2x +
10?
(a) 56
(b) 33
{c) 46
·(d) 92
x
(97] If variance = 148.6 and
= 40,
then the coefficient of variation is:
(a) 37.15
(b) 30.48
(c) 33.75
(d) None of the above
can be determined
graphically using:
(a) Histogram
(b) Frequency polygon
(c) Ogive curve
(d) Pie chart
[99) In a class of 50 students, 10 have
failed and their average marks in
2.5. The total marks secured by the
entire class were 281. The average
marks who have passed is:
(a) 5.32
(98) Qartiles
(b) 7.25
(c) 6.40
(d) None of the above.
s.20
(b) 7.20
(c) 1.44
(d) 2.23
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j 2016 - June
[100)
j 2016 - December
The SD of first n
number is
(a) W
natural
_
(b)
[104) For moderately skewed distribution
of marks in commerce for a group
of 200 students the mean marks
and mode marks were found to be
55.60 and 46; What is the media·n
marks?
(a) 55.5
(b) 60.5
(c) . n(n - 1)
6
(d) None of these.
(101] If mean and coefficient of variation
of the marks of 1o students is 20
and 80 respectively. What will be
variance of them?
(a) 256
(b) 16
(c) 25
(d) None of these.
(102) If same amount is added to or
subtracted from all the values of
an individual series then the
standard deviation and variance
. both shall be
_
(a) changed
(b) unchanged ·
(c) same
(d) none of these
(103) If the mean of two numbers is 30
and geometric mean is 24 then
what will be these two numbers?
(a) 36 and 24
(b) 30 and 30
(c) 48 and 12
(d) None of these
(c) 52.4
(d) None of these
[105) Mean for the data 6, 4, 1, 6, 5, 10,
3 is 5 when each observation
added by 2, what is mean of the
data
(a) 5
(b) 6
(c) 7
(d) 10
[106) The average of 10 observations is
14.4. If the average of first 4
observations is 16.5. The average
of remaining 6 observations is:
(a) 13.6
(b) 13.0
(c) 13.2
(d) 12.5
[107] The ordering of a particular design
of a cloth show room, a
_
size be more appropriate.
(a) median
(b) mean
(c) mode
(d) all of these
(108) The second and third moments of
a sample of seven observation (-6,
-4, -2, 0, 2, 4, 6) are
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#51
(a) (12, O)
(a) f 40 crores
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(b) (0, 12)
(b) f 40 x 10 crcires
(c) (0, 16)
11
(d) {16, O)
[109) The geometric mean of three
numbers 40, 50 and x is 10, the
value of x is
(a) 5
(b) 4
(c) 2
2
(d)
1
! 2011-June
.
,
(c) More than ,40 crores
(d) None of the above.
[113) A person purchases 5 rupees·
worth of eggs from 10 different
markets. You are to find the
average number of eggs per rupee
purchased from all the markets
taken together . The suitable
average in this case is:
. (a) A.M.
(b) G.M.
(c) H.M.
[110) The rates of returns from three
different shares are 100%, 200%
and 400% respectively. The
average rate of return will be:
(a) 350%
(b) 233.33%
(c) 200%
(d) 300%
(111] If geometric
mear:i is 6 and
arithmetic mean is 6.5, then
harmonic mean will be:
(a) 6
6.5
(b)
6
6.52
(c)
s
6.5
(d) None of the above.
[112) A company's past 10 years
average earning Ist' 40 crores. To
have the same average earning for
11 years including these 10 years,
how much earning must be made
by the company in the eleventh
year?
(d) None of the above.
(114) For a moderately skewed
distribution, the relationship
between mean, median and mode
is :
(a) Mean - Mode = 2 (Mean Median)
(b) Mean - Median = 3 (Mean Mode)
(c) Mean - Median = 2 (Mean Mode)
(d) Mean - Mode = 3 (Mean Median).
[115) If arithmetic mean and coefficient
of variation of x are 1O and 40,
respectively then the variance of
-15 + 3x will be:
2
(a) 64
(b) 81
(C) 49
(d) 36
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! 201i - December
(116] is the reciprocal of the AM of the
reciprocal of observations .
(a) HM
(b) GM
(c) Both (a) and (b)
(d) None of the above.
(117] Mean deviation is the least when
deviations are taken from
(a) Mean
(b) Median.
(c) Mode
(d) Harmonic mean
(118] If the mean value of seven
mimbers 7, 9, 12, X, 4, 11 and 5 is
9, then the missing number X
be:
will
(a) 13
(b) 14
(c) 15
(d) 8
(119] When all observations occur with
equal frequency
does not
exist.
(a) median
(b) mode
(c) mean
(d) none of the above.
Answer
1. (b)
5. (d)
9. (d)
13. (d)
17. (c)
21. (c)
25. (b)
29. (c)
33. (a)
37. (b)
41. (b)
45. (b)
49. (b)
53. (c)
57. (a)
61. (d)
65. (b)
69. (c)
73. (a)
2. (c)
6. (a)
10.(b)
14. (a)
18 (a)
3. (a)
7. (c)
11. (a)
15. (d)
19. (a)
22. (a)
23'. (d)
24. (c)
26. (a)
30. (a)
34. {b)
38. (c)
42. (b)
46. (a)
50. (c)
54. (c)
27. (d)
31. (a)
35. (a)
39. (b)
43. (b)
47. (b)
51. (c)
55. (c)
59. (b)
63. (a)
67. (c)
71. (c)
75. (a)
28. (b)
32. (b)
36. (b)
40. (a)
44. (b)
58. (d)
62. (b)
66. (c)
70. (b)
74. (a)
4. (d)
8. (c)
12. (c)
16. (b)
20. (d)
48. (b)
52. {b)
56. (b)
60. (c)
64. (d)
68. (c)
72. (a)
76. (d)
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#52
Chapter 11 - Measures of Central Tendency and Dispersion
77. (a)
78. (c)
79. (a)
81. (c)
82. (c)
83. (d)
85. (b)
86. (a)
90. (a)
87. (b)
91. (c)
88. (a)
92. (a)
94. (c)
98. (c)
95. (b)
96. (d)
99. (c)
101. (a)
105. (c)
102. (b)
100.(a)
104. (c)
109. (d)
113. (c)
110. (c)
103.(c)
107. (c)
111. (a)
108. (d)
112. (a)
114. (d)
115. (d)
116. (a)
117. (b)
118. (c)
119. (c)
89. (c)
93. (d)
97. (b)
106. (b)
80. (c)
84. (d)
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#53
CHAPTER 12 : Correlation
I 2006 - November
(1) The coefficient of correlation r
between x and y when :
Cov (x, y) = -16.5, Var (x) = 2.89,
Var (y) = 100 is :
(a) -0.97
(b) 0.97
(c) 0.89
(d) -0.89
and Regression
[2) Take 200 and 150 respectively as
the assumed mean for X and v
series of 11 values, then dx = X 200, dy = Y - 150, Edx = 13, Edx2 =
2667, :Edy = 42, :Edy2 = 6964, Edx
dy = 3943.The value of r is:
(a)
{b) 0.98
(c) 0.92 ·
(d) 0.82
o.n
880
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[3] For some bivariate data, the
following results were obtained for
the two variables x and y :
i
= 53.2, y = 27.9, byx = - 1.5, bxy =
-0.2
The most probable value of y when
x = 60 is :
(a) 15.6
(b) 13.4
(c) 19.7
{d) 17.7
I 2007 - February
[4) If the sum of squares of the rank
difference in mathematics and
physics marks of 10 students is 22,
then the coefficient of
rank
correlation is:
(a) 0.267
2
3
• then the coefficient of
correlation between u and v is :
(a) 0.6
(b) 0.4
(c) 0.8
(d) 1
[7] Forthe following data, the coefficient
of rank correlation is :
Rank In Botany: 1 2 3 4 5
Rank In Chemistry 2 3
54
(a) 0.93
(b) 0.4
(c) 0.6
(d) None
[8) The following data is given, based on
450. students · for marks in
Statistics and Economics at a
certain examination :
Mean marks in Statistics
= 40
Mean marks in Economics
· 48
S.D.of marks (Statistics)
12
=
(b) 0.867
=
(c) 0.92
(d) None
[5] Two random variables have the
regression lines 3x + 2y = 26 and
6x + y = 31. The coefficient of
correlat_ion between x and y is :
(a) -0.25
(b) 0.5
(c) -0.5
Variance of marks (Economics)
= 256
Sum of the products oi deviations of
marks from their respective mean =
42075
The average marks in Economics of
candidates who obtained 50 marks
in Statistics is :
(a) 45
(b) 54.5
(d) 0.25
(c) 54
(d) 47.5
! 2001 -May
[6)
V= Y -
The coefficient of correlation
between X and Y is 0.6. Uand V are
two variables defined as U= x .:. 3
2.
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#54
j 2001·- August
[9] For 1O pairs . of observations ,
number of concurrent deviations
was found to be 4. What is the value
of the coefficient of concurrent
deviation ?
(a)
./02
(b) 1/:i
(c) -%
(d) -
./02
[10] If the covariance between two
variables is 20 and the variance of
one of the variables is 16, what
would be the variance of the other
variable?
(a) More than 1o
(b) More than 100
(c) More than 1.25
(d) Less than 10
I 2007 - November
[11J Assume 69 and 112 as the mean
values for X and Y respectively.
Ectx = 47, Edx2 = 1475, Ecty = 108,
Edy2 = 3468, Edx dy = 2116 and N
= 8.
.
Where dx = X - 69, dy = Y - 112.
Then the value of r is :
(a) 0.95
, (b) 0.65
(c) 0.75
(d) 0.85
(12) In rank correlation, the association
need not be linear :
(a) True
(13) The lines of regression are as
follows :
5x - 145 = - 10y ; 14y - 208 = -Bx.
The mean values (i, y) is :
(a) (12, 5)
(b) (5, 7) .
(c)
(7, 12)
(d) (5, 12)
I 2008 ..;. February
(14] The coefficient of rank correlation of
marks obtained by 1o students in
English and Economics was fond
to be 0.5. It was later discovered that
the difference in ranks in the two
subjects obtained by one student
was wrongly taken as 3 instead of 7.
The correct coefficient of rank
correlation is :
(a) 0.32
(b) 0.26
(c) 0.49
(d) 0.93
[15] Given the following data :
b•v 0.4 & by x 1.6. The coefficient
of determination is :
(a) 0.74
(b) 0.42 ·
(c) 0.58
(d) 0.64
(16) The mthod applied for deriving
regression equations is known as :
(a) Concurrent deviation
(b) Product moment
(c) Least squares
(d) Nornial equation
=
=
(b) False
(c) Partly True
(d) Panly False
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j
I 2008 - December
2008 -June
[17] The coefficient of correlation
between x and y series from the
following data :
X series V series
15
15
(b) 0.40
25
18
(c) 0.36
3.01 3.03
from mean
136 138
Sum of the product of the deviations
of x and y series from their
respective means = 122, is :
(a) 0.89
(b) 0.99
(c) 0.69
(d) 0.91
(18) If the lines of regression in a
bivariat9 distribution are given by x +
2y = 5 and 2x + 3y = 8, then the
coefficient of correlation is :
(a) 0.866
(b) -0.666
(c) 0.667
(d) -0.866
[19) If the correlation coefficient between
two variables is 1, then the two lines
of regressions are :
(a) Parallel
(b) At right angles
(c) Coincfdent
(d) None of these
then what is the value of rank
correlation coefficient.
(a) 0.59
Number of pairs
of observations
Arithmetic Mean
Standard Deviation
Sum of the squares
of deviation
[20] If the sum of square of differences of
rank is 50 and number of items is 8
(d) 0.63
[21] If coefficient of correlation between
x and y is 0.46. Find coefficient of
correlation between x and
Y..
2
(a) 0.46
(b) 0.92
o.46
(d) -0.92
(cj
[22) Given the regression equations as
3x + y = 13 and 2x +Sy = 20. Find
regression equation of y on x.
(a) 3x + y = 13
=
(b) 2x + y 20
(c) 3x + Sy = 13
(d) 2x + 5 y = 20
(23) The coefficient of correlation is
significant if :
(a) .r > 5 P. E
(b)
(c)
(d)
r < 6 P. E
r 6 P. E
r :a 6 P.E
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#55
I 2009 -June
[24] The two regression equations are :
2x + 3y + 18 = 0
x + 2y - 25 = 0
find the value of y if x = 9
(a) - 8
(b) 8
(c) - 12
(d) 0
(28] If the rank correlation co-efficient
between marks in Management and
Mathematics for a group of students
is 0.6 and the sum of the squares of
the difference in ranks is 66. Then
what is the number of students in
the group?
(a) 9
{b) 10
(c) 11
(d) 12
[25] The correlation coefficient between
x and y i
s - 1/2 . The value of bxy =
- 1/8. Find by x.
(a) - 2
(b) - 4
(c) o
• (ct) 2
[26] Ranks of !wo
.characteristics
by two judges are in reverse order
then find the value of Spearman
rank correlation co-efficient.
(a) - 1
(b)
(c)
0
1
(29) Correlation coefficient between X
and Y will be negative when:(a) X ahd Y are decreasing
(b) X is increasing, Y is decreasing
(c) X and Y are increasing
(ct) None of these
· [30] The two regression lines are 7x 3y-18 = 0 and 4x-y-11 = O.Find
the values of brx and b-'>'
(a) 7/3, 1/4
(b) - 7/3, - 1/4
(c) -3/7, - 1/4
(d) None of these.
(d) 0.75
j
I 2009 - December
[27] Which of the following regression
equations represent regression line
of Y on X :
7x + 2y + 15 = 0, 2 x + 5y + 1O = 6
(a) 7x + 2y + 15 o
=
(b) 2x + Sy + 10 = 0
(c) Both (a) and (b)
2010 -June
(31] If 'P' is the simple correlation
coefficient, the quantity P2 is known
as:
(b) Coefficient of determination
(c) Coefficient of Non-determi­
nation
(d) Coefficient of alienation
(e) None. of the above.
(d) None of these
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[32)
of the
regression
Coefficients is greater than the
correlation coefficient
(a) Combined mean
(b) Harmonic mean
(c) Geometric mean
(d) Arithmetic mean.
(33] If the correlation coefficient between
x-5
x and y is r, then between U = -
10
and V = y - 7 is
2
(a) r
(b)
-r
(c)
(r-5)/2
[34) If the two lines of regression are
x + 2y -5 =0 and 2x + 3y - 8 = 0
The regression line of y on x is
(a) x+2y-5;;;0
(b) 2x+3y-8=0
(c) Any of the two line
(d) None of the two lines.
_
(a) dependent of change of origin
and of scale.
(b) independent of both change of
origin and of scale.
(c) dependent of ctiange of origin
but not of scale.
(d) independent of change of origin
but not of scale
= 16 ,
y = 20 ;oy
OX
c..:
= 4.8
9.6
(a) 0.03
(b) 0.3
(c) . 0.2
(d) 0.05
(39] Same as Q 34 [June 10]
[35) If the sum of the produQt of
deviations of x and y series from
their means is zero,. then the
coefficient of correlation will be
(a) 1
(b) -1
o
(d) None of these
(36] The ranks of five participants given
by two judges are
·
Participants
1
2
(37] Regression coefficient are
The coefficient
of correlation
between x and y is 0.6. What will be ·
the regression coefficient of 'x' on
'y'?
! 2010 - December
Judge
Judge
(b) 0
(C} -1
(d) 1/2
[38] Given :
(d} (r -7)/10
(c)
Rank correlation coefficient between
ranks will be
(a) 1
A B C D
E
1
2
3
4
5
5
4
3
2
1
2011- June
[40) The covariance between
two
variables X and Y is 8.4 and their
variances are 25
and 36
respectively.
Calculate
Karl
Pearson's coefficient of correlation
between them.
(a) 0.82
(b) 0.28
(c) 0.01
(d) 0.09
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#56
[41) For a bivariate data, two times of
[45] If one of regression coefficient is
unity, the other must be
unity.
(a) more than, more then
values of x and y
(b) Less than, Less then
(c) more than, less than
(a) 17 and 13
(d) Positive, Negative
(b) 13 and 17
[46) If Y is dependent varia_bie and X is
(c) 13 and -17
Independent variable and the S.D of X
(d) -13 and 17
(42) Three competitors in a contest are and Y are 5 and 8 respectively and
ranked by two judges in the order Co-efficient of co-relation between X
and Y is 0.8. Find the Regression
1,2,3 and 2,3,1
respectively.
coefficient of Y on X. (a) 0.78
Calculate the Spearman's rank
(b) 1.28
correlation coefficient.
(c) 6.8
(a) -0.5
(d) 0.32
(b) -0.8
2012 -June
(c) 0.5
(d) 0.8
(47) If the regression lines are Bx - 1Oy +
regression are 40x - 18y = 214 and
ax - 1Oy + 66 = 0, then find the
=
66
0 and 40x • 18y = 214, the
correlation coefficient between 'x'
and 'y' is :
(a) 1
I 2011- December
(43) Out of the following which one
(b) 0.6
affects the regression co-efficient.
(c)
• 0.6
(a) Change of Origin Only
(d) • 1
(b) Change of scale Only
(48] The coefficient of · correlation
(c) Change of scale & origin both
between two variables x and y is the
(d) Neither Change of origin nor
simple
of the two
change of scale
regression coefficients.
(44) For a bivariate data, the lines of
(a) Arithmetic Mean
regression of Y on X, and of X on Y
(b) Geometric Mean
are respectively 2.5Y - X 35 and
(c) Harmonic Mean
10X - Y
70, then the Correlation
(d) None of the above.
[49) If 2 variables are uncorrelated, their regression
coefficient r Is equal to:
lines are:
(a) 0.2
(a) Parallel
(b) - 0.2
(b) Perpendicular ·
(c) 0.5
(c) Coincident
(d) - 0.5
(d) Inclined at 45 degrees.
=
=
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[54) The
(50) If the covariance between variables
X and Y is 25 and v.ariance of X and
Y are respectively 36 and 25, then
the coefficient of correlation is
(a) 0.409
(b) 0.416
(c) 0.833
(d) 0.0277
(51) If ,
y denote the arithmetic means,
oY denotes the · standard
deviations. bxy, byx denote the
regression coefficients of the
variables 'x' and Y respectively, then
the point of intersection of regression
lines x on y & y on x is
_
01,
(a)
(x, y)
(b) (0,, Oy)
(c) (b,, b1 )
(d)
(o., o/)
2012 - December
[52) InSpearrnan's Correlation Coefficient,
the sum of the differences of ranks
betweentwo variables shall be
(a) 0
(b) 1
-1
· (c)
(d) None of the above.
(53) For certain x and y series which are
correlated, the two Illies of
regression are
5x - 6y + 9 = 0
1sx - ey '.- 130 = o
The correlation coefficient is
(a) 4/5
(b) 3/4
(c) 2/3
(d) 1/'2
Coefficient of correlation
between x and y series is -0.38.
The linear relation between lC & u
and y & v are 3x + Sv = 3 and -ax iv = 44, what is _the coefficient of
correlation between u & v?
(a) 0.38
(b) -0.38
(c) 0.40
(d) None of the above.
(55) If y = 18x + 5 is the regression line of ·
y on x value of bxy is
(a) 5/18
(b) 18
5
(d) 1/18 .
(c)
! 2013-June
(56) If 'r' be the Karls Pearson's
coefficient of correlation in · a
bivariate distribution then the two
regression lines are at right angle if;
(a) r ± 1
=
(b) r = 0
(c)
=
r
± any finite value whose
numerical value is less than 1
(d) None of these
[57) If the regression eqatlons are
8x-3y+50 = O and 14x-7y - 60 = 0
and standard deviation of yIs1.The
coefficient of correlation is
(a) 2
(b) 1
(c) 0.87
(d) -0.87
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#57
[58)
The coefficient of correlation
between two variables x and y is
0.28. Their covariance is 7.6. If the
variance of x is 9, then the standard
deviation of y is:
(a) 8.048
(b) 9.048
(c) 10.048
(d) 11.048
[59) Two variables x and y are related
according to 4x + 3y = 7. Then x and
y are: ·
(a) Positively correlated.
(b) Negatively correlated.
(c) Correlation is zero.
(d) None of these.
[62) If mean of x · and y variables is 20
and 40 respectively and the
regression·coefficient of y on x is
1.608, then the regression line of y
on x is
(a) y = 1.608x + 7.84
(b) y = 1.5x + 4.84
(c) y = 1.608x + 4.84
(d) y = 1.56x + 7.84
[63) When the value of correlation
coefficient is +1 or -1 , then the two
regression lines will
_
(a) have 30° angle between them.
(b) have 45° angle between them.
(c) coincide.
(d) be perpendicular to each other
j
j 2013 - December
[60) Determine
the coefficient of
correlation between x and y series:
x S<Jries y Series
No. of items ·
Arithmetic mean
Sum of sq. of .
15
15
25
18
deviation of mean
136
138
Sum of product of deviation of x and y
series from mean = 122
·
(a) - 0.89
(b)
0.89
(c)
0.69
(d) - 0.69
[61) Price and Demand is the example
for
(a)
No cwrelation
(b) Positive correlation
(c) Negative
(d) None of the above
2014 -June
[64) Two regression lines for a bivariate
data are: 2x-5y+6=0 and 5x-4y+3=0.
Then the coefficient of correlation
should be:
(a)
-2../2
5
. (b)
:
(c)
(d)
5
E.
5
(65] When each individual gets the exactly
opposite rank by the two Judges, then
the rank correlation will be
.
(a) O
(b) -1
(c) +1
(d)
1
2
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(66) If the mean of the two variables 'x'
and 'y' are 3 and 1 respectively.
Then the equation of two regression
lines are
.
(a) 5x+7y-22=0, 6x+2y-20=0
(b) 5x+7y-22=0, 6x+2y+20=0
(c) 5x+7y+22=0, 6x+2y-20=0
(d) 5x+7y+22=0, 6x+2y+20=0
(67) The equation of two lines of
regression for 'x' and 'y' are
5x=22+y and 64x::;:24+45y then the
value of regression coefficient of 'y'
on 'x' will be
(a)
(b)
5
1
5
(c)
(d)
64
45
45
64
j 2014 -December
(68] If the correlation coefficient between
two variables is zero, then the lines
of regression are:
(a) Parallel
(b) Perpendicular
(c) Coincide
(d) · None of these
[69) If the value of correlation coefficient
(a) 1
(b) -1
(c) -1/2
(d) 1/2
[70) The equations of two regression
10,
lines are x + y = 6 and x + 2y
=
then the value of correlation
coefficient between x and y is:
(a) -1/2
(b) +1/2
(c) -1/,/2
(d) +1/,/2
! 2015 -June
(71) Two regression lines are
16x - 20y + 132= O
80x - 36y - 428 = O
The value of the correlation
coefficient is ·
(a) 0.6
(b) - 0.6
(c) 054
(d) 0.45
[72) When the correlation coefficient r is
equal to + 1, all the points In a
· scatter diagram would be
(a) On a straight line directed from
upper ieft to lower right
(b) On a straight line directed from
lower left to upper right
(c) On a straight line
(a)
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#58I
201
s - December
(73) Out of following which is correct?
a.
b ::-: r
yx
a
y
a
byx = r -1.
ax
byx = n.Exy
ox
bvx = n.Exy
ay
(74) In case of •insurance Companies"
profits and the number of claims
they have to pay there is _
correlation:
Positive
Negative
No correlation
None of the above
! 2016 -June
(75) Two regression equations are as
follows: .
Regression equation of x on y :
5x-y = 22
.
Regression equation of y on _x :
64x-45y "' 24
What will be the mean of x and y?
= a ..y 6
(a) i
=
•(b) x = 6 , y = 6
(c) i
•6 , y = e
(d) i
=8 ,y = 8
(76) If the coefficient of
correlation
between X and Y variables Is +0.90
then what will be the coefficient of
determination?
(a) 0.30
(b) 0.81
(c) 0.94
(d) None of these
[77) The two lines of regression become
Identical when
(a) r = 1
(b) r =- 1
(c) r 0
(d) (a) or (b)
=
=
(78) If r
0.6, then the coefficient of
determination is.
(a) 0.4
(b) -0.6
(c) 0.36
(d) 0.64
I 2015 - December
(79) The two regression lines passing
through
(a) 'Represent means
· (b) Represent S.Ds
(c) (a) and (b)
(d) None of these.
(80) Out of the following the one which
effects the regression coefficient Is
(a) Change of origin only
(b) Change of scale only
(c) Change of scaleandoriginboth
(d) Neither change in origin nor
change of scale
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(81) The regression equation x and y is
3x + 2y = 1oo, the value of bxv
(a)
2
3
(b)
100
3
(c)3
(d) 1- 0.6
2
3
[82) In a beauty contest there were 10
competitors. Rank of these
candidates are assigned by
judges A and B.The sum of squares
· of differences of ranks is 44. The
value of rank correlation is:
two
(a) 0.70
(b) 0.73
(c) 0.80
(d) 0.60
!
..
0.6
2
(d)
[85) The coefficient of correlation
between x and y is 0.6. If x and y
values are multiplied by -1, then the
coefficient of correlation will be:
(a) 0.6
(b) - 0.6
1
(c)
2011-June
[83) The coefficient of correlation
between the temperature of
environment andpower consumption
is always:
(a) Positive
(b) Negative .
(c) Zero
(d) Equal to 1
! 2011 - December
[86] If two regression lines are Sy = 9x 22 and 20x = 9y + 350, then the
valueof correlation coefficient (r) will
be:
(a) 0.10
(b) - 0.10
(c) -0.90
(d) 0.90
[87) The regression coefficient is
independent of the change of:
(a) Origin
(b) Scale ·
(c) Both (a) and (b)
(d) Neither (a) nor (b).
[88) If r = 0.6 then the coefficient of non­
determination will be: •
(a) 0.40
(b)
(c)
(d)
[89) The
-0.60
0.36
0.64
correlation coefficient (r) is the
[84) If two regression lines are x + y = 1
and x - y = 1 then mean values of x
and y will be:
(a) 0 and 1 ·
(b) 1and 1
(c) 1 and o
(d) -1 and -1
of the two
regression
coefficients (byx and bxy)
(a) AM
(b) GM
HM
(d) Median
(c)
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#59#
#59
(90) If there is a constant increase in a
series, then the correspondinggraph
will be
(a) Convex curv
(b) Concave curve
(c) Parabola
(d) Straight line from the left to the
right
Answer
1. (a)
5. (c)
9. (c)
13. (d)
(a)
21. (a)
25. (a)
29. (b)
33. (a)
37. (d)
41 . (b)
45. (c)
49. (b)
53. (c)
57. (c)
61. (c)
65. (b)
69. (b)
73. (b)
77. (d)
81. (a)
85. (a)
89. (b)
p.
2. (c)
6. (a)
10. (b)
14. (b)
18 (d)
22. (d)
26. (a)
30. (a)
34. (c)
38. (b)
42. (a)
46. (b)
50. (c)
54. (b)
58. (b)
62. (a)
66. (a)
70. (c)
74. (b)
78. (c)
82. (b)
86. (d)
90. (d)
3. {d)
7. (c)
11. (a)
15. (d)
19. (c)
23. (c)
27. (b)
31. (a)
35. (c)
39. (c)
43. (b)
47. (b)
51. (a)
55. (d)
59. (b)
63. (c)
67. (c)
71. (a)
75. (c)
79. (a)
83. (a)
87. (a)
4. (b)
8. (b)
12. (a)
16. (c)
20. (b)
24. (b)
28. (b)
32. (d)
36. (G)
40. (b)
.,
44. (a)
.48. (b)
52. (d)
56. (b)
60. (b)
64. (c)
68. (b)
72. (b)
76. (b)
80. (b)
84. (C)
88. (d)
0
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CHAPTER 13 : Probability and Expected Value by Mathematical
another
etters
(3] An um contains 9 balls two of
which are red, three blue and four
black. Three balls are drawn at
random. The probability that they
are of same colour is :
(b) 20
31
5
(c)
.84
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(d) None
(a) 237
[4] A card is drawn from a well shuffled
pack of 52 cards. Let E, "a king or a
queen is drawn" & E2 : "a queen or a
jack is drawn", then :
(a) E, and E2 are not indepe11dent
(b) E, and E2 are mutually
exclusive ·
(c) E, and E2 are independent
(d) None of these
1
(a)
4
(b)
4
(c)
5
8
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3
! 2007 - February
(b) 2
7
(c)
7
3
(d)
7
= .!, P(A n 8) = .!, then
a·
4
2
the value of P(A' u 8') is :
one error in an account statement
prepared by A is 0.3 and for B and
C, they are 0.4 and 0.45
respectively. A, 8 and C prepared
20, 1O and 40 statements
respectively. The expected number
of correct statements in all is : ·
(a) 32
(b) 45
7
[6) If A and Bare two events and P(A) =
!
P
(B)
5
[7] The probability that there is at least
(5) In a non - leap year, the probability of
getting 53 sundays or 53 Tuesdays
or 53 Thursdays is :
(a) 4·
(d)
4
(c) 42
(d) 25
! 2007 -May
(8) From a pack of cards, two are
drawn, the firit · being replaced
before the second is drawn. The
chance that the first is a diamond
and the second is king is :
(a)
1
52
(b)
3
2704
(c)
(d)
4
13
3
52
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#60
(9) The theory of compound probability
states that for any two events A and
B:
(a) P (A n B) = P(A) x P(B)
(b) P (A n B) = P(A) x P(B/A)
(c) P (A u B) = P(A) x P(B/A)
+
(d) P (A u B) = P(A)
P(B) - P
(A n B)
[1OJ The probability of getting qualified in
IIT- JEE and AIEEE by a student are
respectively
j_
5
and
.
5
25
22
(c)
25
8
(b)
1
50
1
25
(c)
(d)
13
50
49
. 50
(13) A bag contains 8 red and 5 white
balls. Two successive draws of 3·
balls are made without replacement.
The probability that the first draw will
· produce 3 white balls and second 3
red balls is :
(a)
25
(d)
(a)
The
probability that the student gets
qualified for one of the these tests'is;
(a) 17
·
(b)
and the probability of occurrence of
F given E is 1/10, then the
· probability of non- occurrence of at
least one of the events E and F is :
6
255
3
(b}
25
(11) Amitabh plays a game of tossing a
5
548
7
42
9
dice. If the number less than 3
appears, he is getting ,a, otherwise
(c)
he has to pay
(d) . 3
10. If the game is
fair, find a :
(a)
25
(b) 20
(c) 22
(d) 18
! 2001 - August
[12] Suppose E and F are two events of
a random experiment If the
probability of occurrence of E is 1/5
233
[14) A box contains 12 electric lamps of
which 5 are defectives. A man
selects three lamps at random. What
is the expect9d number of defective
lamps in his selection ?
·
(a) .1.25
(b) 2.50
(c) 1.05
(d) 2.03
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#61
Determine the variance of the
demand.
(a) 2.54
I 2007 - November
(b) 2.93
(c) 2.22
(16) Three identical dice are rolled. The
probability that the same number will
appear on each of them is :
(a) 1/6
(b) 1/12
(c) 1/36
(d) 1
[16) Among the examinees in an
examination 30%, 35% and 45%
failed in Statistics, in Mathematics
and in at least one of the subjects
·respectively. An examinee is
selected at random. Find the
probability that he failed in
Mathematics only :
(a) 0.245
(b) 0.25
(c) 0.254
(d) 0.55
[17] An article consists of two parts A and
B. The manufacturing process of
each part Is such that probability of
defect in A is 0.08 and that B is.
0.05. What is the probability that the
assembled product will not have any
defect?
(d) 2.19
l 2008 - February
[19) If 10 men, among whom are A and
B, stand In a row,· what is the
probability that there will be exactly
3 men between A and B ?
(a) 11/15 (b)
4/15
(c) 1/15
(d) 2/15
[20) The probability of an event can
assum9 any value between :
(a) o and 1
(b) -1 and O
(c) - 1 and 1
(d) None of these
[21] The odds. are 9 : 5 against a person
who is 50 years living till he is 70
and 8 : 6 against a person who is·60
living till he is 80. Find the
probability that at least one of them
will be alive after 20 years:
(a) 11
14
(a) 0.934
(b) 22
(b) 0.864
(c) 0.85
(d) 0.874
49
(c)
[18) Daily demand for calculators is
having the fQllowing probability
distribution :
Demand :
1
2
3
4
5
6
0.10 0.15 0.20 0.25 0.18
0.12
31
49
(d)
35
49
Probeblllty :
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(22] An um contains 6 white and 4 black
balls. 3 balls are drawn without
replacement. What is the expected
number of black balls that will be
obtained ?
(a) 6/5
(b) 1/5
(c) 7/5
(d) 4/5
6 and 7 respectively
5 and 7 respectively
7 and 5 respectively
7 and 6 respectively
I2008 - December
(26] The limiting relative frequency of
probability is :
(a) Axiomatic
(b) Classical
(c) Statistical
(d) Mathematical
[27] If a probability density function is f
j 2008 - June
(23] If P(A) = p and P (B) = q, then :
(a) P (A I 8) q I p
(b) P (A I B) p I q
(c) P (A I B) s p I q
(d) P (A I B)
(x) = {
qIp
[24) The probability that a trainee will
remain with a company is 0.8. The
probability that an employee earns
more than f 20,000 per month is 0.4.
The probability that an employee,
who was a trainee and remained
with the company or who earns
more than t 20,000 per month is 0.9.
What is the probability that an
employee earns more than f 20,000
per month given that he ia trainee,
who stayed with the company?
(a) 518
· (b) 3/8
(c)
(a)
(b)
(c)
(d)
then find E.(x)
,:
(a) ""
(b) 0
(c) 1
(d)
[28] If :
x
-2
3
P (x) :
1/3
1/2
1
1/6
then find E (2x + 5)
(a) 7
(b) 6
(c) · 9
(d) 4
j 2009 - June
1/8
(d) 7/8
(29] If A and B are two independent
(25] A random variable X has the
following probability distribution :
X
-2
3
P (X; x) :
1/3
1/2
Find E (><2) and E (2X -t 5).
1
1/6
events and P(AUB) :,; 2/5; P(B)
1/3. Find P(A).
(a) 2/9
(b) . - 1/3
(c) 2/10
(d) 1/10
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=
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#62
[30] A bag contains 12 balls of which 3
are red 5 balls are drawn at random.
Find the probability that in 5 balls 3
are red.
(a) 3/132
(b) 5;395
(c) 1/36
(d) 1/22
[31] A random ·variable X has the
following probability distribution.
X O
1
2
3
P(x)
02K 3K . K
Then, P (X<3} would be :
·
(a) 1/6
[35] In a bag, ·tfiere were 5 white, 3 red,
and 2 black balls. Three balls are
drawn at a time what is the
probability that the three balls drawn
are white?
·
(a) 1/12
(b) 1/24
(c) 1/120
(d) None of these
(36] In how many ways can the letters of
'REGULATION' be arranged so that
the vowels come at odd places?
(a) 1/252
(b) 1/144
(b) 1/3
(c) 144/252
(d) None of these
(c) 2/3
(d) 5/6
! 2010 -June
I 2009 -December
[32] P(A) = 2/3; P (B) = 3/5; P(AuB)
=
5/6. Find P (B/A)
(a)
(b)
(c)
(d)
11/20
13/20
13/18
None
=
(33] If P (AnB)
P (A) x P (B), then the
events are:
(a) Independent events
(b) Mutually exclusive events
(c) Exhaustive events
(d) Mutually inclusive events
(34) E (XV) is also known as:
(a) E (X) + E (Y)
(b) E (X) E (Y)
(c) E (X) - E (Y)
(d) E (X) + E (Y)
[37] In a pack of playing cards with two
jokers probability of getting king of
spade is
(a) 4/13
(b) 4/52
(c) 1/52
(d) 1/54
[38) Consider two events A and B not
mutually exclusive, such
that
P(A) = 1/4, P(B) = 2/5, P(AuB) =1/2,
then P (A B) is
(a) 3!7
(b) 2/10
(c) 1/10
(d) None of the above
[39] If x be the sum of iwo numbers
obtained when two die are thrown
simultaneously then P(x 7) is
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(a)
(b)
(c)
(d)
(a)
5/12
7/12
1'1115
3/8
(40) E (13x -t 9) =
(a) 13x
(b) 13E(x) .
(c) 13E(x) + 9
_
(d) 9
I 2010 - December
(41) A dice is thrown once. What is the
mathematical expectation of 1he number
on the dice ?
(a) 16/6
(b) 13/2
(c) 3.5
(d) 4.5
[42) If P(A/8) = P(A), then A and B are
(a) Mutually exclusive events
(b) Dependent events
(c}
Independent events
(d) Composite events
(43] A bag contains 3 white and 5 black
balls . and second bag contains 4
white and 2 black balls:-lf one ball is
taken from each bag,th9 probability
that both the balls are white is
(a) 1/3
(b) 1/4
(c) 1/2
(d) None of these
(44] The odds in favour of A solving a
· problem is 5:7and odds against B
solving the same problem is 9:6.
Wllat is tile probability that if both of
them try,the problem will be solved?
117/180
(b) 181/200
(c) 147/180
(d) 119/iSO
[45] Consider Urn I : 2 white balls, 3
black balls
Urn II :4 white balls, 6 black balls ·
One ball is randomly transferred
from first to second Urn, then one
ball is drawn fro"m II Urn. The
probability that drawn ball is white is
(a) 22/65
. (b) 22/46
(c) 22/55
.(d) 21/45
! 2011-June
[46) If P(Av B) = P(A), Find P(AnB).
(a) P(A).P(B)
(b) P(A) + P(B)
(c) 0
(d) P(B)
(47) In how many ways a team of 5 ca!l
be made out of 7 Boys and 8 Girls, if
2 Girls are compulsory to form a
Team.
(a) 2,646
(b) 1,722
(c) 2,702
(d) 980
[48] A bag contains 5 Red balls, 4 Blue
Balls and 'm' Green Balls. If the
random probability of picking two
gre nballs is 1fl. What is the no. of
green Balls (m).
(a) 5
{b) 7
(C) 6
(d) None of the above.
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[49] The probability of Girl getting
scholarship is 0.6 and the same
probability for Boy is 0.8. Find the
probability that at least one of the
categories getting scholarship.
(a) 0.32
(b) 0.44
(c) 0.92
(d) None of the above.
(50] If 15 persons are to be seated
around 2 round tables, one
occupying 8 persons and another 7
persons. Find the number of ways in
which they can be seated.
(a)
28
1
56
(c)
15
28
(d) None.
2011 - December
(54) Two unbiased dice are thrown. The
Expected value of the sum
numbers on the upper side is;
181
(c)
81
(c) 7!.8!
(d) _ 2. 15Cr 6! 7!
(51] A coin is tossed 5 times, what is the
probability that exactly 3 heads will
occur.
5
16
(b)
32
5
36
3
(d) 32
(52] Exactly 3 girls are to be selected
from 5 Girls and 3 Boys. The
probability of selecting 3 Girls will
be
.
of
(a) 3.5
15!
.
(c)
(b)
5
(b) 7
(b) 1sc7 7!
(a)
(a)
12
(d) 6
(54] One Card is drawn from pack of 52,
what is the probaility that it is a
king or a queen?
(a) 11/13
(b) 2/13
(c) 1/13
(d) None of these
[55] In a packet of 500 pens, 50 are
found to be defective. A pen is
selected at random. Find the ·
probability that it is non defective.
(a) 8/9
(b) 7/8
(c) 9/10
(d) 2/3
(56] Four married couples have gathered
ina room. Two persons are selected
at random amongst them, find the
probability that selected persons are
a gentleman and a lady but not a
couple.
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(a) 1'7
(a) 2.5
(b) 3.5
(c) 4.5
(d) 5.5
(b) 3(1
(c) 1/8
(d) 3/8
(57) A team of 5 is to be selected from 8
boys and three girls. .Find the
probability that it incl.udes two
particular girls.
(a) 2/30
(b) 1/5
(c) 2/11 ·
(d) 8/9
2012 - June
[58] Let A and 8 two events in a sample
space S such that P(A) = .!.; P(B) =
2 .
. P(AuB) =
8
(a)
; Find P (An8)
4
3i4
(b) 1/4
(c) 3/16
(d) None of these.
[59] A card is drawn out of a standard
pack of 52 cards. What is the
probability of drawing a king or red
colour ?
(a) 1/4
(b) 4/13
(c) 7/13
(d) 1/2
(60] A player tosses two fair coins, he
wins f 5 if 2 heads appear, t 2 if one
head appears and
1 if no head
occurs. Find his expected amount of
winning.
(61) Arun & Tarun appear for an
interview for two vacancies. The
probability of Arun's selection is 1/3
ar\d that of Tarun's selection is 1/5
Find the probability that only one of
them will be selected.
(a) 2/5
(b) 4/5
(c) 6/5
. (d) 8/5
[62] A company employed 7 CA's, 6
MBA's and 3 Engineer's. In how
many ways the company can form a
committee , if the committee has two
members of each type.
(a) 900
(b) 1,000
(c)
787
(d) 945
j 2012 - December
(63] Two dice are thrown together . Find
the probability of getting a multiple of
2 on one dice and multiple of 3 on
the other. ·
(a) 2/3
(b) 1/6
(c) 1/3
(d) None of the above.
(64) The odds against A solving a certain
problem are 4 to 3 and the odds in
favour of B solving the same
problem are 7 to 5.
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#64
What is the probability that the
problem will be solved if they both
try ?
(a) 15/21
(b) 16/21
(c) 17/21
(d) 13/21
[65] Find the expected value of the
following probability distribution
-20 -:- 10
30 7580
x
p(x) :
3/20 1/5
1/2 1/10
1/20
(a) 20.5
(b) 21.5
(c) 22.5
· (d) 24.5
[66] A bag contains 6 red balls and some
blue balls. If the probability of
drawing a blue ball form the bag is
twice that of a red ball, find the
numGr of blue balls in the bag
(a)
(b)
(c)
(d)
10
(a)
14
16
[67] The probability of selecting asample
of size.'n' out of a population of size
N by simple random sampling with
replacement is:
(a) 1/N
(b) 1/N"
(c) 11"'c0
209
343
(h)
209
434
(c)
12
j 2013 -:- June
(d)1
(68] A box contains 2 red, 3 green and 2
blue balls. Two balls are drawn at
random. What is the probability that
none of the balls drawn is blue?
(a) 10/21
(b) 11/21
(c) 2/7
(d) 5/7
[69) The odds that a book will be
3
favourably
received
by
independent reviewers are 5 to 2, 4
to 3and 3 to 4 respectively. What is
the probability that out of 3 reviewers
a majority will be favourable?
209
443
(d)
.209
350
[70) A player tosses 3 fair coins. He wins
5 if three heads appear, 3 if two
heads appear,
1 if one head
occurs . On the other hand, he
losses
15 if 3 tails occur. Find
·expected gain of the player:
(a) 0.15
(b) 0.25
(c) 0.35
(d) 0.45
t
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[71J Find the probability of_ drawing a
spade on .each of two consecutive
draws from a well shuffled pack of
cards, without replacement ·
2
[75] T wo c oins ar e tos s ed
simultaneously . Find the probability
of getting exactly are head.
(a) 3/4
(a)
(b) 2/3
1/4
(d) 112.
(c)
51
1
(b)
221 .
(c)
4
51
(d)
5
51
j
2014 -June'
(76] If a pair of dice is thrown then the
probability that the sum of the digit is
· neither 7 nor 11 is .
j 2013 - December
1
6
(a)
[72) If P(A) = 0.45, P(B) :: 0.35 and
P(A&B) = 0.25, then P(A/8) =?
(a) 1.4
1
(b). 18
2
(c)
(b) 1.8
0.714
9
(c)
(d) 0.556
[73] The probability of a cricket team
winning match at Kanpur is 2/5 and
hosing match at Delhi is 1/7 what is
the Probability of the team winning
atleast one match?
(a) 3/35
(b) 32/35
(c) 18/35
(d) 17/35
[74) Find the expected value of the
following probability distribution
X:
·
20
P(x):
3/20
(a) 20.5
(b) 21.5
(c) 22.5
(d) 24.5
-10
30
75
80
1/5
112
1/10
*O
(d)
[77) An um contains 2 red and 1 green
balls. Another um contains 2 red
and 2 green balls. An urn was
selected at random and then a ball
. was drawn from it. If it was found to
be red then the probability that ithas
been drawn from um one is_.
(a) 4
7
(b) 3
7
2
(c) 3
{d)12
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#65
[78) For any two events A,,
(a)
(b)
(c)
(d)
let P(A,) =
P(A2)=
and P(A, n A2)
=then A 1, A2 are:
Mutually" exclusive but not
independent events
Mutually
exclusive
and
independent events
Independent but not mutually
exclusive
None of these
2014 - December
[79) An unbiased die is.thrown twice.The
probability of the sum of numbers
obtained on the two faces being
divisible by 4 is:
(a) 7/36
(b) 1/3
(c) 11/36
[80) Let the distribution function of a
random variable X be F(X) = P(X
s X). Then F(5) - F(2) is:
(a) P(2 < X < 5)
(b) P(2 s X < 5)
(c) P(2 s X s 5)
. (d) P(2 < X 5)
[81) A discrete random variable X takes
three values -1, 2 and 3 with
probabilities
1
, p(2) = 1 , p(3) = 1 .then
3
E(IXI) is:
(a) 3/2
(82) The sum of numbers obtained_ _ in
throw of a dice twice is S. Probab1hty
of S will be maximum if S is
(a) 5
(b) 7
(c) 6
(d) 8
(83) An unbiased coin is tossed three
times. The expected value of the
number of heads is
(a) 2.5
(b) 1.0
(c) 1.5
(d) 2.0
[84) For two events A, and A 2, let P(A,)
and P(A, n A2)
= and P(A2) =
3
(d) 1/4
p(-1) =
2015 - June
3
3
8
1
= -, then
4
(a) mutually exclusive but not ·
independent
(b) mutually
exclus ive and
independent
(c) independent but not mutually
exclusive
(d) none of these
(86) From 6 positive and 8 negative
numbers, 4 numbers are chosen at
random without replacement and are
then multiplied. The probability that
the product of the chosen numbers
will be positive number Is
(b) 5/2
(c) 2
· (d) 9/2
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(a)
409
1001
[89] If two letters are taken at random
from the word "HOME", what is the
probability that none of the letters
would be vowels? .
(b)
70
(c)
1001
505
1001
(a)
420
(b)
(d)
(86) If an unbaised die is rolled once, the
odds in favour of getting a point
which is multiple of 3 is:
. (a) 1:2
(b) 2:1
. (c) 1:3
(d) 3:1
[87) A bag contains 15 one rupee coins,
25 two rupees coins and 10 fivo
rupees coins,·if a coin is selected at
random then probability for not
selecting a one rupee coin is:
(a) . 0.30
(b) 0.20
(c) 0.25
(d) 0.70
(88) Three coins are tossed together, the
probability of getting exactly two
head is:
(a)
(b)
6
1
2
1001
I 2015 - December
. 1
(c)
1
3
' (d)
! 2016 -June
(90) In a game, cards are thoroughly
shuffled and distributed equally
among four players. What is the
probability that a specific player gets
all the four kings?
(a)
(b)
•3c, x 48C,.
..c,,
4
48
C x C
•
9
52 c,a
13c x 52c
sa c,,
4
(c)
5
8
3
8
(d)
4
4
39
""c,,c•
C•x
(d)
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#66
[91] A bag contains. 4 Red and 5 Black
balls. Another bag contains 5 Aed
and 3 Black balls. If one ball is
drawn at random from each bag.
Then the probability that one Red
and one Black drawn is -
12
72
(a)
[94] Two dice are tossed. What is the
' probability that the total is divisible
by 3 or 4.
(a)
20
36
(b) 21
36
(c) 14
25
(b) 72
36
(d) None of these.
(c)
I 2016 - December
;
(d)· 13
72
[92] If P(A) =
[95] If two events A, B, P(A)
,P(B) =
3 5
then
P(:,)
and P(AuB) =
6
is
2
= .! and
3
7
12
(b)
(b) 1
152
(c)
(c)
1
4
[93] If two unbiased dice are rolled, what
is the probability of getting points
neither 3 nor 6?
(a) 0.25
(b) 0.50
(c) 0.75
(d) 0.80
u
B)
2 then
3
.!
4
6
2
(d)
3
1
2
(d) 1
2
P (A
P (A n B) is:
(a)
(a)
= .!, P (B)
[96) A bag contains 6 white and 5 red
balls. One ball is · drawn. The
probability that it is red is:
. (a)
5
. (b)
6
11
(c)
11
1
11
(d) None of these
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[97J.For two events A , B let P(A) =
P(B) =
8
2
3.
and P (An B) = .!. then A
4
and B are:
(a) Mutually exclusive but not
independent
(b) Independent but not mutually
exclusive
(c) Mutually
P(A)
exclusive
and
[98] Let A and B are two events with P(A)
= 1 and P(AnB) = 1
1/8
(d) 8/7
[99] What is the probability of having at
least one 'SIX' from 3 throws of an
unbaised die?
(a) 5
6
5) 3
(b) ( 6)
(c) 1 - (
(d) 1 _ (
[100] For any two events A and B:
(a) P(A - B) = P(A) - P(B)
(b) P(A - B) = P(A) - P(AnB)
(c)
then what is the value
4
9
5
9
,
12
then P(B/A) will be :
(a) 7/8
(b) 1/3
(c)
5
of P (B)?
(b)
4
= -2
. (a) _i_
15
I 2017-June
, P(B)
(d) P(B - A) = P(B) + P(AnB)
[101) If fqr two mutually exclusive
events A and B P (AuB) = and
independent
3
P(A - B) = P(B) P(AnB)
j 201 - December
(d) None of these
=
(c)
7
(d)
15
[102) The probability distribution of the
demand for a commodity is give:,
below:
Demand(x) 5
6
7
8
9
10
Probabilit 0.05 0.10 0.30 0.40 0.10 0.05
y
P( ll The expected value of demand
will be
(a) 7.55
(b) 7.85
(c) 1.25
(d) 8.35
[103) Given P(A)
P(AnB)
= , P(B) = ;and
= , the value otP(A/B) is
(a) 1/2
(b) 1/6
(c) 213
(d) 3/4
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\
#67
brother and his sister appear in an interview for two vacancies for
the same post. The probability of
brother's selection is
i
and the
probability of sister's selection is
i.
The probability that (i) both are selected (ii) only one of
them is selected and (iii) none of them is selected will be:
(a)
1 10 24
35' 35 • 35
24
1
10
(
b). 35' 35' 35
(c) _!Q J_ 24
35' 35'35
(d)
24 _!Q J_
35 ' 35 ' 35
Answer
1. (c)
2. (b)
5. (c)
6. (b)
3. (c)
7. (c)
9. (b)
13. (c)
17. (d)
21. (c)
25. (a)
29. (d)
_ 33. (a)
37. (d)
41. (c)
45. (c)
49. (c)
53. (b)
10. (a)
14. (a)
18 (c)
22. (a)
26. (C)
30. (d)
11. (b)
15. (c)
19.(d)
23.(c)
27. (C)
31. (d)
34. (b)
38. (d)
35. (a)
57. (c)
61. (a)
42. (c)
46. (d)
50. (d)
54. (b)
58. (b)
62. (d)
39. (b)
43. (b)
47. (c)
51. (a)
55. {c)
59.(c)
63. (b)
4. (a)
8. (a)
12. (d)
16. (a)
20. (d)
24. (b)
28. (a)
32. (b)
36. (a)
40. (c)
·44. (a)
48. (c)
52. (a)
56. (b)
60. (a)
64. (b)
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FROM KINSHUK
INSTITUTE
BY : JATIN
DEMBLA
COMPILED BY :
SURBHI JAIN
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!!THANK YOU!!
YOUR QA COURSE IS
READY !!!
NOW YOU ARE
READY FOR
EXAMS
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