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10M
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Examinations
TirunelvallL D
Comiuon wo
Standard 10
MATHEMATICS
Time Allowed: 3.00 Hours
Maximum Marks: 100
PART I
Choose the correct answer:
1)
there are 1024 relations
If
humber of elements in B is
from a set A
{1,2, 3, 4,
5) to a
d) 8
c) 4
a) 3
2) The range
((x, x*)/x
R
of the relation
is a
14x1=14
B, then the
set
is
b) {2, 3, 5, 7, 11
a) 2, 3, 5, 7)
d) 1, 4,9, 25, 49, 121
{4,9, 25, 49, 121)
3) If the ordered pairs (a+2, 4) and (5, 2a+b) are equal then (a, b)
b) (5, 1)
c) (2, 3)
b)2P-1
pq
is
d) (3, -2)
l.i
n
a) (2, -2))
13)
prime number less than
4) Let n(A) = p and n(B) = q then the total number relations
3) 200
5) The
d) pq-1
of
of the exponents of the prime factors in the prime factorization
sum
1729
da
b) 2
) 3
1
6) Given F = 1, F, = 3 and F, = Fa-1tFn-2 then F,
a)
b)
3
c)8
5
d) 4
d) 11
7) The first term of an arithmetic progression is unity and the common differencee
next term of the sequence
term of this A.P?
c 7881
d) 13531
IS
vi
al
least number that is divisible
1
)
by all the numbers from 1
81
to 10
d) 2520
c) 5025
b) 5220
If x-6 is the HCF of x*-2x-24 and x-kx-6 then the value of k is
d) 8
C) 6
a) 3
b)5
.k
a) 2025
10)
a
16'18
a) 24
9) The
will be
b) 10091
a) 4551
8) The
following
ka
is 4. Which of the
w
11) Which of the following should be added to make x*+64 a perfect square?
4x
12) The number of points of
w
c) 8x
bY16x2
intersection of the
d)-8x2
quadratic polynomial
x*+4X+4
with the X-axis is
b1
a) 0
c) 0 or 1
d) 2
c) 48xy2
d) 8xy
w
13) L.C.M. of 8x*y, 48x*ys
a 48xy
b) 8xy2
x+3x-28
14) Sum and product of the roots of the quadratic equations
a) 3, -28
-3,-28
b) -3, 0
0
d) 0, -3
PART-II
10x2=20
Answer any 10 questions. Question No. 28 is compulsory.
15)
16)
If BxA
=
{(-2, 3), (-2,
4), (0, 3), (0, 4), (3, 3), (3, 4)} find
A and B.
A Relation R is given by the set {(x, Y)/y = x+3, xe {0, 1, 2, 3, 4, 5}}
Determine its domain and range.
17) IfA= {1,3, 5} and B = {2, 3)} then show that n(AxB) = n(BxA) = n(A)xn(8).
18)
Find the greatest number that will divide 445 and 572 leaving remainders
4 and 5 respectively.
19) Use Euclid's Division Algorithm
20) If 13824
2x3° then
find
a
to find the HCF of 867 and 255.
and b.
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10M
21) If the nh term
5n
find
an
and
a,
a
22) Find x, y and z, given that the numbers x, 10, y, 24, z are in A.P
3 ) Find the number of terms in the A.P 3, 6, 9, 12, . .
111.
t
24)
Find the excluded value o2 -5t+6
25)
st
Simplity 4t-8
6t-12
10t
26) Add:
Y
Y-x
28) If the difference between a number and its reciprocal is ,
find the number.
da
PART-III
Answer any 10 questions. Question No. 42 is compulsory.
l.i
n
27) Solve by completing the square method: 9x2-12x+4 = 0
29) Let A = {xeN/1<X<4}, B = {xe W/0sx<2} and C = {xe N/x<3).
10x5-50
Then verify that Ax(BuC) =
(AxB)U(AxC).
30) Represent the relation {(x, y)/y = X+3, X, y are natural numbers < 10, by
ka
(a) an arrow diagram (b) a graph and (C) a set in roster form.
31) Find the HCF of 396, 504, 636.
32) The sum of three consecutive terms of an A.P is 27 and their product is 288.
vi
Find the three terms.
33) The gener
term of a sequence is defined as an
nn+3): neN is odd
n+1; ne N is even
al
Find the eleventh and eighteenth terms.
.k
34) Solve: 3x-2y+z =2, 2x+3y-z= 5, x+y+Z= 6.
35) Find the GCD of the polynomials x'+3x-x-3, x+x?-5x+3.
1
1
Simplity2-5x+6-3x+2 x-8x +15
37)
If
w
A
w
36)
T
2x+1
2B
1
A-B A2 -B2
38) If 9x+12x3+28x+ax+b is a perfect square, find the values of a and b.
w
39) If the roots of the equation (c-ab)x<-2(a4-bc)x+b-ac = 0 are real and
equal prove that either a = 0 or a?+b3+c3= 3abc.
4) If one root of the equation 3x+kx+81 = 0 is the square of the other then
find k
41) Find thee square root of: (6x2+x-1) (3x2+2x-1) (2x2+3x+1)
42) A girl is twice as old as her sister. Five years hence, the product of their
ages will be 375. Find their present ages.
PART IV
Answer the following:
2x8=16
43) Discuss the nature of solutions of the quadratic equation x+x-12 = 0.
(OR)
Draw the graph of y = x*+3x-4 and hence use it to solve x<+3x-4 = 0.
44) Discuss the nature of solutions of the quadratic equation x2-6x+9 = 0.
(OR)
Draw the graph of y = 2x and hence solve 2x-x-6 = 0.
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