Practice sheet:

MCQs

1.

2. Let A = { 2 } , B = = { 3 , 4 ,5 } and C = = { 5 , 6 } then the number of elements in AX(B – C) are

(a) 1 ( b) 2 ( c) 6 (d) 3∞
3. If x is a negative integer then solution set of -12 x > 30 is
a) {-2, -1} b) {…..-5, -4, -3}
c) {…..-5, -4, -3, -2} d) {-2, -1, 0, 1, 2}

4.

5. If R is a Relation on a finite set having n elements, then the number of Relation on A

is,
(a) 2n ( b) 2n2 ( c) n2 (d) nn
6.

7.

−θ
8. If θ lies in second quadrant, then the quadarant in which lies in
2
a) I quadrant b) II quadrant c) III quadrant d) IV
quadrant
9.

10. The value of 1 + i + i2 +….. in is

a) positive b) negative c) 0 d) cannot
determine
11. The correct value of x is -
of - 3x >9 is
a) x >-3 b) x < -3 c) x ≥ -3 d) x ≤ -3
12.

13. For any two sets A and B, A∩ (A∪B) is equal to-

a) A b) B c) ∅ d) A∩B
14. Let A = {a, b}, B= {x, y, z} then number of relations from B to A is -
a) 8 b) 16 c) 32 d) 64
15.

16.

17. In the arithmetic progression whose common difference is non zero, the sum of first
3n terms is equal to the sum of next n terms. Then the ratio of the sum of the first 2n
terms to the next 2n terms is,
(a) 1/5 ( b) 2/3 ( c) 3/4 (d) none of these
18. If the sum of n terms of an AP is 3n2+5n, then which of its term is 164?
(a) 26th ( b) 27th ( c) 28th (d) none of these

Choose the most appropriate answer from the option given below. (Q19 & Q20)

19. Assertion : The ratio of the radii of two circles at the centres of which two equal arcs
subtend angles of 30o and 70o is 21 : 10.
Reason : Number of radians in an angle subtended at the centre of a circle by an arc to
the radius of the circle.

20. Assertion : The number of non-empty subsets of the set {a, b, c, d} are 15.
Reason : Number of non empty subsents of a set having n elements are 2n - 1.
1.

2. Let A = { 2 } , B = = { 3 , 4 ,5 } and C = = { 5 , 6 } then the number of elements in AX(B – C) are

(a) 1 ( b) 2 ( c) 6 (d) 3∞
3. If x is a negative integer then solution set of -12 x > 30 is
a) {-2, -1} b) {…..-5, -4, -3}
c) {…..-5, -4, -3, -2} d) {-2, -1, 0, 1, 2}

4.

5. If R is a Relation on a finite set having n elements, then the number of Relation on A

is,
(a) 2n ( b) 2n2 ( c) n2 (d) nn
6.

7.

−θ
8. If θ lies in second quadrant, then the quadarant in which lies in
2
a) I quadrant b) II quadrant c) III quadrant d) IV
quadrant
9.

10. The value of 1 + i + i2 +….. in is

a) positive b) negative c) 0 d) cannot
determine
11. The correct value of x is -
of - 3x >9 is
a) x >-3 b) x < -3 c) x ≥ -3 d) x ≤ -3
12.
13. For any two sets A and B, A∩ (A∪B) is equal to-
a) A b) B c) ∅ d) A∩B
14. Let A = {a, b}, B= {x, y, z} then number of relations from B to A is -
a) 8 b) 16 c) 32 d) 64
15.

16.

17. In the arithmetic progression whose common difference is non zero, the sum of first
3n terms is equal to the sum of next n terms. Then the ratio of the sum of the first 2n
terms to the next 2n terms is,
(a) 1/5 ( b) 2/3 ( c) 3/4 (d) none of these
18. If the sum of n terms of an AP is 3n2+5n, then which of its term is 164?
(a) 26th ( b) 27th ( c) 28th (d) none of these

Choose the most appropriate answer from the option given below. (Q19 & Q20)

19. Assertion : The ratio of the radii of two circles at the centres of which two equal arcs
subtend angles of 30o and 70o is 21 : 10.
Reason : Number of radians in an angle subtended at the centre of a circle by an arc to
the radius of the circle.

20. Assertion : The number of non-empty subsets of the set {a, b, c, d} are 15.
Reason : Number of non empty subsents of a set having n elements are 2n - 1.
21.
Let S = {x : x is a positive multiple of 3 less than 100} and P = {x : x is a prime number
less than 20}. Then n(S) + n(P) is

a) 41 b) 30 c) 34 d) 33

22.Two finite sets have m and n elements. The number of elements in the power set of the
first is 48 more than the total number of elements in the power set of the second. Then the
values of m and n are

a) 6, 4 b) 6, 3 c) 3, 7 d) 7, 6
23.Find the value of cot ( 294π ) .
1
a) b) - 1 c) √ 3 d) 1
√3

24.If z¿ ( 1−i
1+i
) , then z ❑ equals.
4

a) 0 b) - 1 c) 1 d) none of these

1
25.The solution set for |3x - 2|≤ is
2

2 1 5 5 1
a) ∮ b) [ ,1] c) [ , ] d) [ , ]
3 2 6 6 2

26.The number of terms in the expansion of {(5x + 2y)❑7 - (5x - 2y) ❑7 } is

a) 6 b) 4 c) 8 d) 3

27.
5 5 5 5 5
❑ C 1 +¿ C 2 +¿ C 3 + ¿ C 4 +¿ C5 ¿ ¿ ¿ ¿ is equal to

a) 33 b) 30 c) 31 d) 32

e
28.If a, b, c, d, e are in G. P., then equals
c

b c d d
a) b) c) d)
a b b c

29.cos 15° - sin 15° = ?

1 ( √ 2−1 ) 1 ( √ 2+ 1 )
a) b) c) d)
2 √2 √2 √2
30.

If A and B are two disjoint sets then A ∩ ( A ∩ B' ) = . . . .

a) ϕ b) A c) A – B d) B

31.Which term of the GP 5, 10, 20 ,40,... is 5120?

a) 9th b) 12th c) 11th d) 10th

32.
 n

∑ 4 r .n C r is equal to
r=0

a) 6❑n b) 5❑−n c) 4❑n d) 5❑n

2 5π 2 π
33.The value ofsin −sin is
12 12

1
a) √ 3/2 b) c) 0 d) 1
2

34.If A = {x : x≠ x} represents

a) {1} b) { } c) {x}
d) {0}

35.

If❑20 C r+ 1=❑20 C r−1 , then r is equal to

a) 19 b) 10 c) 12 d) 11

36.

If x <5 , then

a) −x >−5 b) −x <5 c) x >−5 d) none of these

37.

1
If z¿ , then |z|=
( 1−i )( 2+3 i )

a) 1 b) 1/ √ 26 c) 1/5 d) 5/ √ 26

38.

If A = {1, 2, 3}, B = {1, 4, 5, 9} and R is a relation from A to B defined by x is greater than

y. Then, Range of R is

a) {1, 2, 6, 9}

b) {1}

c) {4, 6, 9}

d) none of these

39.

−1
Assertion (A): If sin x = , then cos x = - 2
3
Reason (R): If the value of cos x is - ve and sin x is - ve then x ∈ [ 3π
2
,2π
]
a) Both A and R are true and R is the correct explanation of A.
b) Both A and R are true but R is not the correct explanation of A.
c) A is true but R is false.
d) A is false but R is true.
40.
Assertion (A): Let A = {1, 2, 3} and B = {1, 2, 3, 4}. Then, A ⊂ B.

Reason (R): If every element of X is also an element of Y, then X is a subset of Y.

a) Both A and R are true and R is the correct explanation of A.

b) Both A and R are true but R is not the correct explanation of A.

c) A is true but R is false.

d) A is false but R is true.