Sasi Math (Revised for 1024)

Scroll:set and function >> Choose the correct answer >> mcq (4266)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.

For the sets A and B, A∪B =A if and only if __________

(A) B⊆A (B) A⊆B (C) A≠B (D) A∩B

1) A
2) D
3) B
4) C

( )

For any three sets A,B and C, A∪(B∩C) is ______

(A) (A∪B)∪(B∩C) (B) (A∩B)∪(A∩C)

1) C
2) D
3) B
4) A

( )

If {(x,4)}, (7,y)} represent an identity function,

then (x,y) is _______

(A) (4,7) (B) (7,4) (C) (4,4) (D) (7,7)

1) B
2) C
3) A
4) D

( )

If {(7,12), (2,w)} represent a constant function,

then the value of 'w' is _______

(A) 7 (B) 12 (C) 2 (D) 10

1) 7
2) 10
3) 12
4) 2

( )

If ƒ: A" B is a bijective function and if n(A) = 16,

then n(B) is equal to ____

1) 32
2) -16
3) 256
4) 16

( )

Let A = {1,3,4,7,11}, B = {-1,1,2,5,7,9} and ƒ: A"B be given by ƒ = {(1,-1),(3,2),(4,1),(7,5),(11,9)}. Then ƒis ________

1) bijective
2) one-one
3) onto
4) not a function

( )

If A = {p,q,r,s}, B = {r,s,t,u} then A\B is ______

(A) {p,q} (B) {t,u} (C) {r,s} (D) {p,q,r,s}

1) A
2) B
3) C
4) D

( )

If n[p(A)] = 32, then n(A) is _____

(A) 2 (B) 4 (C) 6 (D) 3

1) 3
2) 4
3) 6
4) 5

( )

If A = {6,7,8}, B = {2,3,4,5,6}

and ƒ:A"B is defined by ƒ(x) = x- 2, then the range of ƒ is ___

1) {6,7,8}
2) {4,5,6}
3) {2,3,4,5}
4) {2,3,4}

( )

10)

If n(A) = 20, n(B) = 60 and n(A∪B) = 20, then n(A∩B) is equal to _______

1) 60
2) 65
3) 70
4) 55

( )

For the sets A and B, A∪B =A if and only if __________

(A) B⊆A (B) A⊆B (C) A≠B (D) A∩B

1) A
2) C
3) D
4) B

Answer: 1

SOLUTION 1 :

By the definition, A∪B =A ⇔ B⊆A

For any three sets A,B and C, A∪(B∩C) is ______

(A) (A∪B)∪(B∩C) (B) (A∩B)∪(A∩C)

1) C
2) A
3) D
4) B

Answer: 4

SOLUTION 1 :

Intersection distribution over union

A∪(B∩C) = (A∩B)∪(A∩C)

Ans (B) (A∩B)∪(A∩C)

If {(x,4)}, (7,y)} represent an identity function,

then (x,y) is _______

(A) (4,7) (B) (7,4) (C) (4,4) (D) (7,7)

1) A
2) D
3) B
4) C

Answer: 1

SOLUTION 1 :

If {(x,4)}, (7,y)} represent an identity function the x = 4, y = 7

(x,y) = (4,7)

Ans (A) ⇒(4,7)

If {(7,12), (2,m)} represent a constant function,

then the value of 'm' is _______

(A) 7 (B) 12 (C) 2 (D) 10

1) 2
2) 12
3) 7
4) 10

Answer: 2

SOLUTION 1 :

If {(7,12), (2,m)} represent a constant function,

then the value of m = 12

Ans (B) ⇒ 12

If ƒ: A" B is a bijective function and if n(A) = 16,

then n(B) is equal to ____

1) 256
2) 32
3) -16
4) 16

Answer: 4

SOLUTION 1 :

ƒ: A" B is bijective ⇒ ƒ is one-one and onto.

ƒ(A) = n(B) ⇒ n(B) = 16

Ans 16

Let A = {1,3,4,7,11}, B = {-1,1,2,5,7,9} and ƒ: A"B be given by ƒ = {(1,-1),(3,2),(4,1),(7,5),(11,9)}. Then ƒis ________

1) onto
2) bijective
3) not a function
4) one-one

Answer: 4

SOLUTION 1 :

Each element in A is associated to a unique element in B.

ƒ is one-one function.

Ans (A) one-one

If A = {p,q,r,s}, B = {r,s,t,u} then A\B is ______

(A) {p,q} (B) {t,u} (C) {r,s} (D) {p,q,r,s}

1) B
2) A
3) D
4) C

Answer: 2

SOLUTION 1 :

A|B = {p,q,r,s} {r,s,t,u}

= {p,q}

If n[p(A)] = 32, then n(A) is _____

(A) 2 (B) 4 (C) 6 (D) 3

1) 5
2) 3
3) 6
4) 4

Answer: 1

SOLUTION 1 :

n[p(A)] = 32

2^n(A) = 32

2^n(A)= 2⁵

n(A) = 5

Ans(A)5

If A = {6,7,8}, B = {2,3,4,5,6}

and ƒ:A"B is defined by ƒ(x) = x- 2, then the range of ƒ is ___

1) {2,3,4}
2) {6,7,8}
3) {2,3,4,5}
4) {4,5,6}

Answer: 4

SOLUTION 1 :

ƒ(x) = x - 2

ƒ (6) = 6 - 2 = 4

ƒ (7) = 7 - 2 = 5

ƒ (8) = 8 - 2 = 6

Range of ƒ = {4,5,6}

Ans (D) {4,5,6}.

10)

If n(A) = 20, n(B) = 60 and n(A∪B) = 20, then n(A∩B) is equal to _______

1) 65
2) 60
3) 70
4) 55

Answer: 2

SOLUTION 1 :

n(A∪B) = n(A) + n(B) - n(A∩B)

20 = 20 + 60 - n(A∩B)

n(A∩B) = 80 - 20

n(A∩B) = 60

Ans (B) ⇒ 60