CPT Mock Test – 2
Test Booklet No. – 110013
(1)
IInd Session
Duration : 2 Hours
Date: - 08.06.2015
Total Marks : 100
Which one of the following agencies in India is responsible for computation of
national income?
(a)
NCAER
(b)
CSO
(c)
NSSO
(d)
RBI
Ans. b
Explanation:
Central Statistical organization is responsible for computation of national income.
(2)
DFEC
(a)
(b)
(c)
(d)
stands far:
Duty Freedom Export Credit
Duty Free Export Credit
Direct Foreign Exchange Control
Duty Free Exchange Credit
Ans. b
Explanation:
DFEC stands for Duty Free Export Credit.
(3)
Consumer surplus means ________
(a)
The area inside the budget line
(b)
The area between the average revenue and marginal revenue curves
(c)
The difference between the maximum amount a person is willing to pay for a
good and its market price
(d)
None of the above
Ans. c
Explanation:
As it is difference between marginal utility & price i.e. consumer surplus = what a
consumer ready to pay - what he actually pays.
(4)
The bargaining power of labour is generally _____:
(a)
Weak
(b)
Strong
(c)
Constant
(d)
Can't say
Ans. a
Explanation:
Since labour doesn't have previous accumulated capital hence he has weak
bargaining power.
(5)
_________ depicts complete picture of consumer tastes and preferences.
(a)
Budget line
(b)
Average cost curve
(c)
Indifference map
(d)
Marginal revenue curve
MITTAL COMMERCE CLASSES
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Ans. c
Explanation:
Indifference curve is based on consumer preference and indifference map consists of
various combinations of two goods which gives equal satisfaction.
(6)
With a given supply curve, a decrease in demand causes:
(a)
An overall decrease in price but an increase in equilibrium quantity
(b)
An overall increase in price but a decrease in equilibrium quantity
(c)
No change in overall price but a reduction in equilibrium quantity
(d)
An overall decrease in price and a decrease in equilibrium quantity
Ans. d
Explanation:
Quantity demanded & supplied
(7)
Generally supply curve of industrial products is
(a)
Positively sloped
(b)
Negatively sloped
(c)
Both (a) and (b)
(d)
Parallel of to Y axis
Ans. a
Explanation:
Law of supply states that price increase supply also increases & vice versa.
(8)
Which
(a)
(b)
(c)
(d)
of the following statements is incorrect?
Both AP and MP can be calculated from T.P.
When AP rises then MP>AP
When AP is maximum then MP = AP
When AP falls, MP also falls but MP>AP
Ans. d
Explanation:
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As when AP falls, MP also falls but MP < AP
(9)
Production function refers to a
(a)
Relationship between Output and cost
(b)
Physical relationship between input and output
(c)
Relationship between capital and labour expressed in terms of wage rental
ratio
(d)
None of the above
Ans. b
Explanation:
Production function refers to the physical relationship between input & output.
(10)
Labour intensive technique would get chosen in a :
(a)
Labour surplus economy
(b)
Capital surplus economy
(c)
Developed economy
(d)
Developing economy
Ans. a
Explanation:
In labour surplus economy labour will be available in abundance.
(11)
Which
(a)
(b)
(c)
(d)
of the following is considered as production in economics?
Stage performance.
Tilling of soil.
Painting a picture for pleasure.
Preventing a child from an accident.
Ans. b
Explanation:
Tilling of soil leads to production as it turns into output.
(12)
A firm
(a)
(b)
(c)
(d)
encounters its “shutdown point” when:
Average total cost equals price at the profit-maximizing level of output.
Average variable cost equals price at the profit-maximizing level of output.
Average fixed cost equals price at the profit-maximizing level of output.
Marginal cost equals price at the profit-maximizing level of output
Ans. b
Explanation:
As shut down is the point where firm will not be able to recover even its average
variable cost.
MITTAL COMMERCE CLASSES
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(13)
The economist who gave cobb - douglas production function was an _______ :
(a)
Japanese
(b)
German
(c)
British
(d)
American
Ans. d
Explanation:
Since the economist who gave cobb - douglas production function was an American.
(14)
Which
(a)
(b)
(c)
(d)
of the following is not the name of LAC curve?
Planning curve
Enveloping curve
Round curve
None of the above
Ans. c
Explanation:
LAC curve is also known as Planning Curve and Enveloping Curve.
(15)
Which of the following is incorrect?
(a)
The shape of the average cost and marginal cost curve is U’
(b)
The AR and MR curves of a firm under perfect competition are parallel to Xaxis.
(c)
At Equilibrium AR=MR
(d)
At Equilibrium MC=MR
Ans. c
Explanation:
Since AR=MR is not the condition of equilibrium point and equilibrium occurs at MC =
MR
(16)
Which
(a)
(b)
(c)
(d)
is the other name given to Average revenue curve?
Profit curve
Demand curve
Indifference curve
Income curve
Ans. b
Explanation:
As they both have same characteristic i.e. downwards sloping curve.
(17)
In a perfect competitive market :
(a)
Firm is the price-giver and industry is the price taker
(b)
Firm is the price taker and industry is the price giver
(c)
Both are the price takers
(d)
None of the above
Ans. b
Explanation:
Industry determines price by intersection of demand and supply and firm adopts the
price decided by industry.
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(18)
The following table provides a breakdown of a country’s population (millions):
Total population
114 Children (below the working age)
Unemployed people looking for
9
Full-time students (not looking for a job)
a job
Retired people
14 Employed people
People confined to correctional
1
Other adults not in the labour force
institutions
Based on the information in the table, the country’s unemployment rate is
(a)
7.9%
(b)
12.5%
(c)
20.2%
(d)
22.2%
18
2
63
7
Ans. b
Explanation:
9
100  12.5%
72
Unemployed
100
Employed  Unemployed
(19)
MGNREGS Scheme gives guarantee of at least ____ days to rural households.
(a)
55
(b)
100
(c)
125
(d)
200
Ans. b
Explanation:
Since MGNREGS Scheme gives guarantee of at least 100 days to rural households.
(20)
India has a long coast line of:
(a)
7517 Km, 12 major ports
(b)
7518 Km, 12 major ports
(c)
7517 Km, 11 major ports
(d)
7577 Km, 12 major ports
and
and
and
and
200 minor ports
87 minor ports
200 minor ports
187 minor ports
Ans. a
Explanation:
India has a long cost line of 7517 Kms, 12 major ports & 200 minor ports.
(21)
TRIPs
(a)
(b)
(c)
(d)
stand for:
Trade Related Intellectual Property Rights
Transaction Related Intellectual Property Rights
Trade Related Intelligence Property Rights
Trade Related International Property Rights
Ans. a
Explanation:
TRIPS stands for Trade Related Intellectual Property Rights.
(22)
Which of the following has not been a part of the land reforms programme in India?
MITTAL COMMERCE CLASSES
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(a)
(b)
(c)
(d)
Ceiling an holding
Consolidation of holding
Abolition of zamindari system
Agricultural holding tax
Ans. d
Explanation:
Since it is a part of taxation pattern in India.
(23)
The programme of industrialization during second five year plan was based on the
model given by ______.
(a)
The Britishers in India
(b)
V.V. Bhatt
(c)
P.C. Mahalanobis
(d)
Vera Anstey
Ans. c
Explanation:
P.C. Mahalanobis focused on set up of capital goods.
(24)
According to NSSO the reference period used in URP is :
(a)
30 days
(b)
365 days
(c)
7 days
(d)
15 days
Ans. a
Explanation:
Since according to NSSO the reference period used in Uniform recall period is 30
days.
(25)
Liberalisation process in India was initiated by
(a)
Yashwant Singh
(b)
Manmohan Singh
(c)
Jaswant Singh
(d)
Both (a) & (b)
Ans. b
Explanation:
He was the former Finance Minister.
(26)
Restriction (s) on banking sector before economic reforms is/are
(a)
Quantitative restrictions on credit flows
(b)
High reserves requirements under CRR.
(c)
Keeping significant part of loanable fund for the priority sector under
Statutory Liquidity Ratio (SLR).
(d)
All of the above.
Ans. d
Explanation:
As they all are in pre-economic reform period
(27)
The objective of selective credit controls is mainly to :
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(a)
(b)
(c)
(d)
Selectively allocate credit to commercial banks
Selectively allocate credit among borrowers
Regulate the quantity of demand deposits created by commercial banks
Regulate the quantity of credit created by commercial banks
Ans. b
Explanation:
As qualitative credit control measure relates to the distribution of credit among
selective groups.
(28)
The banks are required to maintain a certain ratio between their cash in hand and
total assets, this is called
(a)
CLR (Central Liquidity Reserve)
(b)
SLR (Statutory Liquidity Ratio)
(c)
SBR (Statutory Bank Ratio)
(d)
CBR (Central Bank Reserve).
Ans. b
Explanation:
The part of cash which is kept by bank itself is known as statutory liquidity ratio.
(29)
Deposit mobilization is highest in :
(a)
Maharashtra
(b)
Tamil Nadu
(c)
Kerala
(d)
Rajasthan
Ans. a
Explanation:
Since in Maharashtra deposit mobilization is 22%.
(30)
If a firm’s output is zero, then
(a)
AFC will be positive
(b)
TFC will be zero
(c)
Both of (a) and (b)
(d)
None of (a) and (b)
Ans. (a)
Explanation:
Since TFC is there even if the firm's output is zero.
(31)
Which
(a)
(b)
(c)
(d)
curve is never U-shaped?
TFC curve
AVC curve
AC curve
MC curve
Ans. a
Explanation:
Since the shape of TFC is horizontal.
(32)
From the following details, find out the average variable cost of 10 units:
OUTPUT :
0
10
20
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Total cost :
Rs. 200
(a)
Rs. 40
(b)
Rs. 20
(c)
Rs. 200
(d)
Rs. 400
Rs. 400
Rs. 800
Ans. b
Explanation: AVC = TVC / Q
TVC = TC – TFC
TC = 400
TFC = 200
Hence TVC = 200, AVC = 200/10 = 20
(33)
The total cost incurred for 10 units is rs. 400 and 20 units is Rs. 800.Find the
marginal cost.
(a)
Rs. 400
(b)
Rs. 40
(c)
Rs. 200
(d)
Rs. 20
Ans. b
TC
Q
800  400
MC =
20  10
Explanation: MC =
MC = 40
(34)
In the
(a)
(b)
(c)
(d)
long-run in perfect competition a firm have
Losses
Must earn super normal profits
Normal Profit
None of these
Ans. c
Explanation:
Since in the long-run in perfect competition a firm have normal profit.
(35)
Oligopoly having identical products is:
(a)
Pure oligopoly
(b)
Imperfect oligopoly
(c)
Price leadership
(d)
Collusion.
Ans. a
Explanation:
Since in pure oligopoly there are identical products e.g. Aluminum
(36)
National Bank for Agriculture and rural development is_______________.
(a)
Co-operative bank
(b)
Commercial bank
(c)
Apex bank of agriculture and rural development
MITTAL COMMERCE CLASSES
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(d)
Subsidiary bank of SBI
Ans. c
Explanation:
Since NABARD is the Apex bank of agriculture and rural development established in
1982.
(37)
What
(a)
(b)
(c)
(d)
is the nature of income tax?
Direct and Progressive
Indirect and progressive
Indirect and regressive
Direct and regressive
Ans. a
Explanation:
Since direct tax is according to the income hence it is progressive.
(38)
Which
(a)
(b)
(c)
(d)
of the following state has the highest literacy ratio?
Goa
Tamil nadu
Kerala
Uttar Pradesh
Ans. c
Explanation:
Since Kerala has the highest literacy ratio of 92%.
(39)
The creation of Indian Postal Department happened in.
(a)
1837
(b)
1857
(c)
1951
(d)
1751
Ans. a
Explanation:
Since the creation of Indian Postal Department happened in 1837.
(40)
____________provides crop storage facility in India.
(a)
IDBI
(b)
ICICI
(c)
FCI
(d)
IFCI
Ans. c
Explanation:
Since FCI provides crop storage facility in India.
(41)
Devaluation Means:
(a)
To reduce the value of home currency in comparison of a external currency
(b)
To appreciate the value of home currency
(c)
To constant the value of home currency
(d)
None of the above
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Ans. a
Explanation:
Since devaluation means to reduce the value of home currency in other currency.
(42)
__________is a systematic record of all transactions of a county in a year.
(a)
Balance of payment
(b)
Balance of Trade
(c)
Current account of balance of payment
(d)
None.
Ans. a
Explanation:
Since balance of payment is a systematic record of all transactions of a county in a
year.
(43)
___________is known as privatization.
(a)
Divestment
(b)
Making a private sector as a public
(c)
Liberalization
(d)
All of the above
Ans. a
Explanation:
Since Divestment is a method of doing privatization.
(44)
WB replaced which organization in 1945?
(a)
IBRD
(b)
GATT
(c)
IMF
(d)
None of these
Ans. d
Explanation:
(45)
The nationalization of 6 commercial banks happened in:
(a)
1944
(b)
1949
(c)
1956
(d)
1980
Ans. d
Explanation:
Since in 1980 nationalization of 6 commercial banks was done.
(46)
Which
(a)
(b)
(c)
(d)
of the following is not the objective of RBI?
Lendor of last resort
Banker’s Bank
lending to the public
Banker to the Government
Ans. c
Explanation:
Since RBI never lend to the public directly.
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(47)
The Quantitative measure of credit regulation by RBI is:
(a)
Bank Rate policy
(b)
Open market operations
(c)
Variable Reserve Ratio
(d)
All of the above
Ans. c
Explanation:
Since variable reserve ratio is the quantitative measure of credit regulation by RBI.
(48)
At present in India a post office serves______ average persons.
(a)
7069
(b)
7175
(c)
7215
(d)
7275
Ans. b
Explanation:
Since in India a post office serves 7175 average persons.
(49)
At the time of independence ____percent of population was dependent on
agriculture.
(a)
72 percent
(b)
58 percent
(c)
54 percent
(d)
62 percent
Ans. a
Explanation:
Since at the time of independence 72 percent of population was dependent on
agriculture.
(50)
The full fledged family programme was started in the year _____ :
(a)
1956
(b)
1966
(c)
2005
(d)
2009
Ans. b
Explanation:
Since the full fledged family programme was started in the year 1966 by the
government of India.
(51)
Evaluate
11
k
∑(2 + 3 )
k=1
3
11
2
3
− 1)
11
2
3
− 1)
10
− 1)
(a)
22 + (3
(b)
11 + (3
(c)
22 + (3
2
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(d)
None
Ans. a
Explanation:
11
k
∑(2 + 3 )
k=1
= (2+3) + (2+32) + (2+33) + ... + (2+311)
= 22 + (3 + 32 + 33 + ... + 311)
3
= 22 +
(52)

1
3 1
11
= 22 + 3
3 11
(3 – 1)
2
Lim √n2 +n−6−√3n2−6
is
2n+5
n→∞
(a)
1 + √3
(b)
1 − √3
(c)
1−√3
(d)
1+√3
2
2
Ans. c
Explanation:
lim
n
=
(53)
n 2  n  6  3n 2  6
2n  5
1 3
2
The value of ‘a’ for which the roots ∝, β of the equation x2 − 6x + a = 0 satisfy the
relation 3 ∝ +2β = 20 is :
(a)
-16
(b)
18
(c)
20
(d)
16
Ans. a
Explanation:
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   6
∵
 a
3  2   20
 2  2   20
 2      20
 26   20
 8
3  2   20
38  2   20
  2
 a
8  2  a
∵

(54)
a=–16
2
If x = 1 + a + a2 + _ _ _ _∞ , y = 1 + b + b + _ _ _ _∞ , Where |a𝑎| < 1 and |b𝑎| < 1, then
(1 + 𝑎𝑏 + 𝑎2 𝑏 2 + … … … . . ∞) =
xy
(a)
x+y
x+y
(b)
xy
xy
(c)
x+y+1
xy
(d)
x+y−1
Ans. d
Explanation:
x = 1+a+a2+...+
x=
1
1 a
∵a=
x 1
x
y = 1+b+b2+...+
y=
1
1 b
∵b=
y 1
y
1+ab+a2b2+...+
S =
1
1  ab
=
(55)
1
xy

 x 1  y 1 x  y 1
1 


 x  b 
A mixture contains milk and water in the ratio 5:1. In adding 5 liters of water, the
ratio of milk and water becomes 5:2 the quantity of milk in the original mixture is:
MITTAL COMMERCE CLASSES
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(a)
(b)
(c)
(d)
16 liters
25 liters
22.75 liters
32.5 liters
Ans. b
Explanation:
Milk = 5x, water = x
5x
5

x5 2
10x = 5x+25
x= 5
The quantity of milk in the original mixture = 5 × 5 = 25 litres
(56)
There are 10 questions to be answered to be yes or no. how many ways can these
be answered?
(a)
1024
(b)
1023
(c)
2048
(d)
2047
Ans. a
Explanation:
2n
=
210
=
1024
(57)
If x  71/3  7 1/3 then value of 7x 3  21x is
(a)
(b)
(c)
(d)
48
49
50
51
Ans. c
Explanation:
given is x  71/3  7 1/3
find out 7x 3  21x
put the value of x in 7x 3  21x
7(71/3  71/3 )3  21(71/3  71/3 )
(a  b)3  a 3  3ab(a  b)  b3
and solution is 50
(58)
Value of (8)
3
log 5 8
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(a)
(b)
(c)
(d)
5
25
125
625
Ans. c
Explanation:
3
(8) log5 8

1 
loga b 

log b a 

= 83log8 5
 a log a b  b 


3
= 8log8 5
= 53  125
(59)
If n  2
Cr =
(a)
(b)
(c)
(d)
n2
C10r
then
n C6 equals to
8
28
56
None
Ans. b
Explanation:
n2
n2
C10r
Cr
or n  2  r  10  r
or n = 8
then 8C6  28
(60)
How many ways can the letters of the word ‘MATHEMATICS’ be arranged so that
vowels as well as consonants occur together.
(a)
74
2 2
(b)
74
3 3
(c)
7 4
2 3
(d)
None of these
Ans. a
Explanation:
We have vowels A, E, A, I and
Consonants M,T,H,M,T,C,S
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Total No. of arrangements.
(61)
=
4! 7!

 2!
2! 2! 2!
=
4!  7!
2!  2!
Sum of all natural number till 300 which are not divisible by 3
(a)
45150
(b)
15150
(c)
30000
(d)
29700
Ans. c
Explanation :
Sum of natural numbers till 300
S300 =
300(300 + 1)
= 45150
2
n(n + 1) 

Σn = 2 
Natural numbers which are divisible by 3
3 + 6 + 9 + 12 + ………. 300
n=
300 - 3
+1
3
Tn = a+(n-1)d
= 100
n
Sn = (a + L)
2
a=3
L = 300
n = 100
=
100
300 + 3 = 15150
2
So sum of the numbers which are not divisible by 3 is S300  Sn
= 45150 - 15150 = 30000
(62)
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 selecting at least 3 from each part. In how many maximum
ways can the candidate select the questions ?
(a)
350
(b)
210
(c)
520
(d)
None
Ans. d
Explanation :
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The candidate can select 8 questions by selecting at last three from each part in the
following ways:
(a)
3 questions from part A and 5 questions from part
B= 7C3 x 5C5 = 35 ways
(b)
4 questions from part A and part B each
B= 7C3 x 5C4 = 175 ways
(c)
5 questions from part A and questions from part
B= 7C5 x 5C3 = 210 ways
Hence, the total number of ways in which the candidate can select the question will
be=35+175+210=420 ways.
(63)
The Interest on a certain deposit at 4.5% p.a. is Rs. 202.50 in one year. How much
will the additional interest in one year be on the same deposit at 5% p.a.?
(a)
23.50
(b)
22.50
(c)
25
(d)
None
Ans. b
Explanation :
S.I 100
R T
202.50 100
=
4.5 1
P
= Rs. 4,500
Additional Interest =
4500  5 1
 202.50
100
= Rs. 225 – 202.50
= Rs. 22.50
(64)
A manufacturer produces 80 T.V. sets at a cost Rs. 2,20,000 and 125 T.V. sets at a
copy of Rs.2,87,500. Assuming the cost curve to be linear find the cost of 95 sets.
(a)
Rs. 3,52,500
(b)
Rs. 1,45,550
(c)
Rs. 2,42,500
(d)
None of these
Ans. c
Explanation :
Since the cost curve is linear we consider cost curve as y=Ax+B where y is total
cost. Now for x=80, y=2,20,000. ∴ 2,20,000 = 80A+B…….(i)
and for x = 125; y=2,87,500 ∴ 2,87,500 = 125A+B………(ii)
Subtracting (i) from (ii) 45A=67,500 or A=1500
From (i) 2,20,000 – 1500 (80) = B or B =2,20,000-1,20,000=1,00,000
Thus equation of cost line is y = 1,500x+1,00,000.
For x=95, y=1,42,500+1,00,000=Rs. 2,42,500.
MITTAL COMMERCE CLASSES
17 | P a g e
∴ Cost of 95 T.V. set will be Rs. 2,42,500.
(65)
In what time Rs. 12000 will amount to Rs. 13230 at 5% C.I.
(a)
2
(b)
4
(c)
3
(d)
5
Ans. a
Explanation :
r 

A  P 1 

 100 
n
5 

1323  12000 1 

 100 
13230  21 

12000  20 
2
 21   21 
 20    20 
   
n
n
n
n=2
(66)
The Difference between compound and simple interest on a certain sum of money for
3 years at 10% p.a. is Rs. 155. The Sum is
(a)
Rs. 5000
(b)
Rs. 10000
(c)
Rs. 15000
(d)
None of these
Ans. a
Explanation :
S.I.  P  3 
10
100
(P is the Sum)
3
10 

C.I.  P 1 
 P
 100 
and difference of C.I. − S.I. = 155
3
10 
3P  10

P 1 
 155
 P
100
 100 
P  Rs.5000
(67)
If the equation x 2 + 2(k + 2)x + 9k = 0 has equal roots, the values of k are :
(a)
(b)
(c)
(d)
1, 4
−1, 4
1, −4
−1, −4
MITTAL COMMERCE CLASSES
18 | P a g e
Ans. a
Explanation :
For roots to be equal, discriminant = 0  B2  4AC  0
2(k  2)2  4(1) (9k)  0

 4(k 2  4k  4)  36k  0
 4k 2  20k  16  0
 k 2  5k  4  0
 k 2  4k  k  4  0
 k(k  4)  (k  4)  0
 (k  4) (k  1)  0
 k  4, 1
(68)
The system of equations x  2y  3 and 2x  ky  6 has infinite solutions then find out
the value of k
(a)
2
(b)
4
(c)
6
(d)
8
Ans. b
Explanation :
Equation a1x  b1y  c1 and a 2 x  b 2 y  c 2 have Infinite Solution if
a1 b1 c1


a 2 b2 c2
then
1 2 3
 
2 k 6
k4
(69)
If A =
1,2,3,4
(a)
A B
(b)
A
(c)
A B
(d)
B
and
B  5,6,7 then (A-B)  (B-A) is
Ans. c
Explanation :
A  B  1,2,3,4
B  A  5,6,7
MITTAL COMMERCE CLASSES
19 | P a g e
So (A-B)  (B-A) = {1,2,3,4,5,6,7}
and
(70)
A B  1,2,3,4,5,6,7 also (A-B)  (B-A). Hence option (C) is correct.
The Domain of the relation
(b)
1,3,7
2,8,6
(c)
(d)
{1,3,6}
None of these
(a)
(1,2)(3,8)(7,6)
Ans. a
Explanation :
Left hand side elements of open brackets are called domain so 1,3,7
(71)
If F :R  R is a bijection function given by f(x)  (x  1)  2 then f −1 (x) is
3
(a)
(x  2)1/3  1
(b)
(x  2)1/3  1
(c)
(x  2)1/3  1
(d)
None of these
Ans. a
Explanation :
f(x)  (x  1)3  2 (bijection function)
Let (x  1)  2  y
3
(x  1)3  y  2
x  (y  2)1/3  1
So f
(72)
1
 (x  2)1/3  1
If the salary of P is 25% lower than that of Q and the salary of R is 20% higher than
that of Q, the ratio of the salary of R and P will be :
(a)
5:8
(b)
8:5
(c)
5:3
(d)
3:5
Ans. b
Let Salary of Q
Salary of P
Salary of R
MITTAL COMMERCE CLASSES
=
=
=
=
=
=
100
100
100
75
100
100
– 25% of 100
– 25
+ 20% of 100
+ 20
20 | P a g e
= 120
Ratio of salary of R and P = 120 : 75 = 8 : 5
(73)
Solution space of the inequalities 2x + y < 10 and x – y < 5 :
(i) includes the origin.
(ii) includes the point (4 ,3)
which one is correct ?
(a)
Only (i)
(b)
Only (ii)
(c)
Both (i) and (ii)
(d)
None of the above
Ans. a
Explanation :
Given : 2x + y < 10 _____ (1)
Adding (1) & (2) we get
3x < 15  x < 5
Putting x < 5 in eqn(1) we get
y<0
hence x < 5 and y < 0 is the solution space.
(74)
6x  4
 x  2 x  3 dx is equal to
(a)
(b)
(c)
(d)
22
11
22
22
log
log
log
log
(x–3)
(x–3)
(x–3)
(x–3)
– 16 (2–x) + c
– 8 (x–2) + c
–16 log (x–2) + c
+ 16 log (x–2) + c
Ans. c
Explanation :
6x  4
 x  2 x  3 dx
or,
6x  4

A

B
x  2 x  3 x  2 x  3
(Partial fractions)
6x + 4 = A (x – 3) + B (x – 2)
Put x = 3
We get B = 22 Put x = 2
We get A = –16
16
22
 x 2   x 3
= –16 log (x–2) + 22 log (x–3)
= 22 log (x–3) – 16 log (x–2) + c
(75)
If xy (x–y) = 0, find
(a)
(b)
y 2x  y
x 2y  x
dy
:
dx
x 2x  y
y 2y  x
MITTAL COMMERCE CLASSES
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y 2y  x
x 2x  y
None of these
(c)
(d)
Ans. a
Explanation :
xy (x – y) = 0
x2y – xy2 = 0
Differentiating both sides wrt x
dy
 2 dy
 

 y2x    x 2y
 y 2  1  0
x
dx
dx

 

x2
dy
dy
 2xy  2xy
 y2  0
dx
dx


dy 2
x  2xy  y2  2xy
dx
dy
y 2  2xy
 2
dx
x  2xy
dy 2 xy  y 2

dx 2 xy  x 2
dy y 2 x  y 

dx x 2 y  x 
(76)
In indirect oral investigation:
(a)
Data is not capable of numerical expression
(b)
Not possible or desirable to approach informant directly.
(c)
Data is collected from the books.
(d)
None of these
Ans. b
Explanation : Indirect oral investigation is a method in which a third person is
contacted who is expected to know the necessary details about the person for
whom the enquiry is mean. This method is suitable when it is not possible or
deliverable to approach informant directly.
(77)
Five competitors in a contest are ranked by two judges in the order 1, 2, 3, 4, 5
and 2, 3, 1, 5, 4 respectively. Calculate the Spearman’s rank correlation
coefficient.
(a)
-0.5
(b)
-0.6
(c)
0.5
(d)
0.6
Ans. d
Explanation :
Rank -I
Rank –II
D2
MITTAL COMMERCE CLASSES
1
2
1
2
3
1
3
1
4
4
5
1
5
4
1
22 | P a g e
Spearman’s Rank Correlation coefficient = 1 −
=1
6 ∑ D2
n(n2 −1)
6x8
− 5 (52 −1)
= 0.6
(78)
In a binomial Distribution with 5 independent trials, probability of 2 and 3
successes are 0.4362 and 0.2181 respectively. Parameter ‘p’ of the binomial
distribution is:
(a)
3/4
(b)
1/3
(c)
2/3
(d)
1/4
Ans. b
Explanation : Given
P(x=2)
P(x=3)
10p2 q3
10p3 q2
0.4362
= 0.2181
=
0.4362
0.2181
q = 2p
p + 2p = 1
1
p=3
(79)
A bag contains 5 Red balls, 4 Blue Balls and ‘m’ Green Balls. If the random
probability of picking two green balls is 7/40. What is the no. of green Balls (m).
(a)
5
(b)
7
(c)
6
(d)
None of the above
Ans. b
Explanation : probability of picking two green balls =
MC2
9+MC2
7
= 40
M=7
(80)
If two variables x and y are related by 2x+3y-7=0 and the mean and mean
deviation of x about mean are 3 and 0.3 respectively, then the co-efficient of
mean deviation of y about mean is:
(a)
-5
(b)
4
(c)
12
(d)
60
Ans. d
Explanation : x = 3, MDx = 0.3
2x + 3y − 7 = 0
1
y=3
2
1
3
5
MD of y = | | MD of X =
MITTAL COMMERCE CLASSES
23 | P a g e
co-efficient of mean deviation of y about mean =
=
(81)
M.D of Y
y
x 100 = 60
From the following data
Commodity
A
Group Index
120
Weight
6
The general Index I is given by:
(a)
111.90
(b)
113.45
(c)
117.25
(d)
114.75
Ans. a
Explanation :
Commodity
Group Index (R)
Weight (W)
(RW)
General Index =
(82)
A
120
6
720
∑ RW
∑W
=
2238
20
B
132
3
C
98
4
D
115
2
E
108
1
F
98
4
B
132
3
396
C
98
4
392
D
115
2
230
E
108
1
108
F
98
4
392
= 111.90
In a Normal Distribution
(a)
The first and second quartile are equidistant from median
(b)
The second and third quartiles are equidistant from the median
(c)
The first and third quartiles are equidistant from the median
(d)
None of the above.
Ans. c
Explanation : The first and third quartiles are equidistant from the median in
normal
distribution
(83)
Given
(a)
(b)
(c)
(d)
the observations: 4,9,11,14,37. The mean deviation about the median is
11
8.5
7.6
7.45
Ans. c
Explanation : median = 11
∑|X − M| = 38
38
MD = = 7.6
5
(84)
The average age of a group of 10 students was 20 years. The average age
increased by 4 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
MITTAL COMMERCE CLASSES
24 | P a g e
(d)
32 years
Ans. c
Explanation : Average age of 10 students = 20 yrs
The sum of age of 10 students = 20 x 10 = 200 yrs
If two boys are increased
The total no of students = 10+2=12
And average increased by 4 yrs
Then new average = 20 + 4 = 24
The sum of age of 12 student = 24 x 12 = 288
The sum of age of two boys = 288 – 200 = 88
88
Average age of two boys = 2 = 44
(85)
A simple random sample of size 10 is drawn without replacement from a
universe containing 85 units. If the mean 90 and S.D. 4 is obtained from the
sample, what is the estimate of the standard error of sample mean?
(a)
0.1176
(b)
0.58
(c)
1.19
(d)
1.26
Ans. d
Explanation : Here, n=10, N= 85, x = 9, s=4
S. E. (x) =
=
=
4
√10−1
4
√9
4
s
√n−1
N−n
x√N−1
85−10
x√
75
85−1
4
x√84 = 3 x √0.893
= x 0.945
3
= 1.26
(86)
Regression coefficient are ……………
(a)
dependent of change of origin and of scale.
(b)
independent of both change of origin and of scale.
(c)
dependent of change of origin but not of scale.
(d)
independent of change of origin but not of scale
Ans. d
Explanation : Regression coefficient are independent of change of origin but not
scale (As per Fundamental Principle)
(87)
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
Ans. b
MITTAL COMMERCE CLASSES
25 | P a g e
Explanation : r =
0.28 =
Cov (x,y)
SDx . SDy
7.6
3 x SDy
SDy = 9.048
Below
50
Below
40
Below
30
Marks
Below
20
The data given below refers to the marks gained by a group of students:
Below
10
(88)
No. of
15
58
77
94
100
Students
Then the no. of students getting marks more than 30 would be _________.
(a)
35
(b)
28
(c)
23
(d)
22
Ans. c
Explanation : No. of students getting marks more than 30 = Total students - no.
of students getting marks less than 30 = 100 - 77 =23
(89)
Mean and S.D. of a given set of observations is 1,500 and 400 respectively. If
there is hiked by 20% in the first year and each observation is an increment of
100 in 2nd year, then find new mean and S.D.
(a)
1920, 480
(b)
1900, 480
(c)
1600, 480
(d)
1600, 400
Ans. b
Explanation : x = 1500, SD = 400
After 1st year
Mean = 1500 + 20% of 1500=1800
SD = 400 + 20% of 400 = 480
After 2nd year
Mean = 1800 + 100 = 1900
SD = 480 (no change)
(90)
Rahul Sinha draws 2 balls from a bag containing 3 white and 5 Red balls. He gets
Rs. 500 if he draws a white ball and Rs.200 if he draws a red ball. If he is asked
to pay Rs.400 for participating in the game, would he consider it a fair game and
participate?
(a)
Yes,
(b)
No,
(c)
Can’t Say
(d)
None
MITTAL COMMERCE CLASSES
26 | P a g e
Ans. a
Explanation : We denote the amount by x. Then x assumes the value 2 x Rs. 500
i.e. Rs. 1000. If 2 white balls are drawn, the value Rs. 500 + Rs. 200 i.e. Rs. 700
if 1 white and 1 red balls are drawn and the value 2 x Rs. 200 i.e. Rs. 400 if 2
red balls are drawn. The respective probabilities are given by
P(WW)
=
P(WR)
=
and P(RR)
=
3C
1x
8C
5C
2
8C
2
5C
1
2
=
3C
2
8C
2
3
= 28
15
= 28
10
28
Probability Distribution of x
X:
Rs. 1000
P:
Hence E(x) =
3
28
=
Rs. 700
Rs. 400
3
15
10
28
28
x Rs. 1000 +
15
28
x Rs. 700 +
28
10
28
x Rs. 400
𝑅𝑠.3000+𝑅𝑠.10500+𝑅𝑠.4000
28
= 625 > 400, Therefore the game is fair and he would participate.
(91)
Divided bar chart is goods for:
(a)
Comparing various components of a variable
(b)
Relating the different components to the whole.
(c)
(a) and (b)
(d)
(a) or (b)
Ans. c
(92)
For any two events A1, A2 let P(A1) =
are:
(a)
(b)
(c)
(d)
2
3
1
, P(A2)= and P(A1  A2)= then A1, A2
3
8
4
Mutually exclusive but not independent events
Mutually exclusive and independent events
Independent but not mutually exclusive
None of these
Ans. c
2 3
1
Explanation : P(A1). P(A2 ) = 3 x 8 = 4 = 𝑃(𝐴1⋂𝐴2 )
So, A1 and A2 are Independent but not mutually exclusive
(93)
A manufacturer, who produces medicine bottles, find that 0.1% of the bottles
are defective. The bottles are packed in boxes containing 500 bottles. A drug
manufacturer buys 125 boxes from the producer of bottles. Using poission
distribution, find how many boxes will contain at least two defectives:
[Given: e-0.5 =0.6065]
(a)
7
(b)
13
MITTAL COMMERCE CLASSES
27 | P a g e
(c)
(d)
9
11
Ans. d
Explanation : m=np=500 x 0.001 = 0.5
P(x ≥ 2) = 1 − [P(x = 0) + P(x = 1)]
e−0.5 (0.5)0
= 1−|
0!
+
e−0.5 (0.5)1
1!
|
= 1 − 0.9097
= 0.0902
Hence, the approx, number of boxes containing atleast 2 defective
bottles.
125 x 0.0902=11, approx.
(94)
Which
(a)
(b)
(c)
(d)
sampling adds flexibility to the sampling process?
Systematic sampling
Multistage sampling
Stratified sampling
Simple random sampling
Ans. b
Explanation : Multistage sampling.
(95)
The Choronological classification of data are classified on the basis of:
(a)
Attributes
(b)
Time
(c)
Area
(d)
Class Interval
Ans. b
Explanation : The Choronological classification of data are classified on the basis
of Time
(96)
The criteria for an ideal estimator are:
(a)
unbiasedness, expectation, estimation and sampling
(b)
estimation, efficiency, expectation and sufficiency
(c)
consistency, efficiency, sufficiency and unbiasedness
(d)
estimation, consistency, efficiency and sufficie.
Ans. c
Explanation :
(97)
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.
MITTAL COMMERCE CLASSES
28 | P a g e
Ans. a
(98)
A lady travel at a speed of 120km/h and returned at quicker speed. If her
average speed of the whole journey is 150km/h, find the speed of return journey
(in km/h).
(a)
250
(b)
300
(c)
200
(d)
None
Ans. c
Explanation : Average speed =
2ab
a+b
150 =
2x120xb
120+b
b = 200km/h
(99)
If the 1970 index with base 1965 is 200 and 1965 index with base 1960 is 150,
the index 1970 on base 1960 will be:
(a)
700
(b)
300
(c)
500
(d)
600
Ans. b
Explanation : The index 1970 on base 1960 will be =
150 x 200
100
= 300
 X  60 

 X  50 
(100) If X follows a normal distribution with  =50 and  =10. What is the value of P
: [Area under the normal curve from z=0 to z=1 is 0.3413].
(a)
0.6826
(b)
0.7354
(c)
0.1983
(d)
0.5492
Ans. a
X ≤60
Explanation : P ( X>50) =
=
MITTAL COMMERCE CLASSES
p(0<𝑍<1)
1−Φ(0)
p(x ≤60) ∩p(x >50)
=
p(x >50)
Φ(1)−Φ(0)
1−Φ(0)
=
0.8413−0.5
1−0.5
= 0.6826
29 | P a g e