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.

If the range of a function is a singleton set, then it is _____

1) a constant function
2) a bijective function
3) an identity function
4) an one-one function

( )

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

(A) (A\B) ∩ (A\C) (B) (B∖A) ∩ (B∖C)

(C) (B\A) ∩ (A\C) (C) (A\B) ∩ (B\C)

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

( )

If n(A) = 30, n(B) = 60 and n(A∪B) = 20, then n(A∩B) is equal to _______

1) 75
2) 70
3) 80
4) 65

( )

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

( )

If ƒ(x) = x² + 7, then ƒ(-4) = ____

1) -23
2) 25
3) 23
4) 22

( )

Which one of the following is not true

(A) A∖B = A∩B‘ (B) A\B = A∩B

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

( )

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

(A) (A∪B)∪(B∩C) (B) (A∩B)∪(A∩C)

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

( )

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) D
2) A
3) C
4) B

( )

If A = {7,8,9}, B = {3,4,5,6,7}

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

1) {3,4,5,6}
2) {7,8,9}
3) {5,6,7}
4) {2,3,4}

( )

10)

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

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

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

( )

If the range of a function is a singleton set, then it is _____

1) a bijective function
2) an one-one function
3) an identity function
4) a constant function

Answer: 4

SOLUTION 1 :

Range of a function is a singleton set ⇒ all elements of a domain is associated to unique element in the codomain.

It is a constant function.

Ans ⇒ a constant function.

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

(A) (A\B) ∩ (A\C) (B) (B∖A) ∩ (B∖C)

(C) (B\A) ∩ (A\C) (C) (A\B) ∩ (B\C)

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

Answer: 1

SOLUTION 1 :

Bâˆ–(A∪C) = (Bâˆ–A) ∩ (Bâˆ–C)

Ans (B) ⇒ (Bâˆ–A) ∩ (Bâˆ–C)

If n(A) = 30, n(B) = 60 and n(A∪B) = 20, then n(A∩B) is equal to _______

1) 65
2) 75
3) 80
4) 70

Answer: 4

SOLUTION 1 :

n(A∪B) = n(A) + n(B) - n(A∩B)

20 = 30 + 60 - n(A∩B)

n(A∩B) = 90 - 20

n(A∩B) = 70

Ans (B) ⇒ 70

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

Answer: 1

SOLUTION 1 :

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

ƒ is one-one function.

Ans (A) one-one

If ƒ(x) = x² + 7, then ƒ(-4) = ____

1) 22
2) 25
3) -23
4) 23

Answer: 4

SOLUTION 1 :

ƒ (x) = x² + 7

ƒ (-4) = (-4)² + 7

= 16 + 7 = 23

Ans ⇒ 23

Which one of the following is not true

(A) A∖B = A∩B‘ (B) A\B = A∩B

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

Answer: 3

SOLUTION 1 :

Aâˆ–B ≠ A∩B

Ans (B) ⇒ AB = A∩B

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) B
3) A
4) D

Answer: 2

SOLUTION 1 :

Intersection distribution over union

A∪(B∩C) = (A∩B)∪(A∩C)

Ans (B) (A∩B)∪(A∩C)

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) D
2) C
3) B
4) A

Answer: 4

SOLUTION 1 :

By the definition, A∪B =A ⇔ B⊆A

If A = {7,8,9}, B = {3,4,5,6,7}

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

1) {5,6,7}
2) {7,8,9}
3) {3,4,5,6}
4) {2,3,4}

Answer: 1

SOLUTION 1 :

ƒ(x) = x - 2

ƒ (7) = 7 - 2 = 5

ƒ (8) = 8 - 2 = 6

ƒ (9) = 9 - 2 = 7

Range of ƒ = {5,6,7}

Ans (D) {5,6,7}.

10)

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

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

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

Answer: 3

SOLUTION 1 :

n[p(A)] = 32

2^n(A) = 32

2^n(A)= 2⁵

n(A) = 5

Ans(A)5