Sasi Math (Revised for 1024)

Scroll:Theory of sets >> multiple Choice Questions: >> mcq (4165)

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 A = { 5,{5,6} 7,} Which of the following is correct

1) {5,6} € A
2) {7} € A
3) {6} € A
4) {5} € A

( )

If n(X) = m, n(Y) =n and n(X∩Y) = p then n(XUY) =

1) m+n+p
2) m-n+p
3) m+n-p
4) m-p

( )

If A = { 3,4,5,6} and B = { 1,2,5,6}, then AUB =

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

( )

If A is a proper subset of B, then A∩B =

1) AUB
2) A
3) ɸ
4) B

( )

The number of subset of the set {10,11,12} is

1) 8
2) 3
3) 7
4) 6

( )

Which one of the following is a finite set

1) { x : x € W, x ≥ 5}
2) {x : x € Z, x < 5 }
3) {x : x is an even prime number}
4) 10} ' title="{x : x € N, x > 10} "/> {x : x € N, x > 10}

( )

If A = {a, b, c}, B = {e,f,g} then A∩B =

1) AUB
2) ɸ
3) A
4) B

( )

The number of elements of the set { x ; x € Z, x² = 1 } is

1) 3
2) 0
3) 1
4) 2

( )

Which one of the following is incorrect

1) Every non-empty set has at least two subsets, Æ and the set itself
2) Every subset of a finite set is finite
3) P = { x: x-8 = - 8 } is a singleton set
4) Every set has a proper subset

( )

10)

If U = {1,2,3,4,5,6,7,8, 9,10} and A= {2,5,6,9,10} A' is

1) {1,3,4,7,8}
2) {1,3,5,10}
3) {2,5,6,9,10}
4) ɸ

( )

If A = { 5,{5,6} 7,} Which of the following is correct

1) {7} € A
2) {6} € A
3) {5,6} € A
4) {5} € A

Answer: 3

SOLUTION 1 :

{5,6} € A

If n(X) = m, n(Y) =n and n(X∩Y) = p then n(XUY) =

1) m+n+p
2) m-p
3) m-n+p
4) m+n-p

Answer: 4

SOLUTION 1 :

Hint: [n(XUY) = n(X)+n(Y) – n[(X∩Y) = m+n-p)]

ans = m+n-p

If A = { 3,4,5,6} and B = { 1,2,5,6}, then AUB =

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

Answer: 3

SOLUTION 1 :

Ans = {1,2,3,4,5,6}

If A is a proper subset of B, then A∩B =

1) AUB
2) ɸ
3) A
4) B

Answer: 3

SOLUTION 1 :

Hint: [ A∩B = set of all elements common to both A and B] A

Ans = A

The number of subset of the set {10,11,12} is

1) 8
2) 7
3) 3
4) 6

Answer: 1

SOLUTION 1 :

Hint: [ Number of subsets = 2^m = 2³ = 8 (Here there are three elements m = 3)]

Ans = 8

Which one of the following is a finite set

1) 10} ' title="{x : x € N, x > 10} "/> {x : x € N, x > 10}
2) {x : x is an even prime number}
3) {x : x € Z, x < 5 }
4) { x : x € W, x ≥ 5}

Answer: 2

SOLUTION 1 :

Hint: [{ x : x is an even prime number} = {2}, which is finite]

If A = {a, b, c}, B = {e,f,g} then A∩B =

1) AUB
2) B
3) A
4) ɸ

Answer: 4

SOLUTION 1 :

Hint: [ A∩B ={ a,b,c,} ∩ {e,f,g} = { } = É¸]

Ans = É¸

The number of elements of the set { x ; x € Z, x² = 1 } is

1) 2
2) 3
3) 1
4) 0

Answer: 1

SOLUTION 1 :

ans = 2

Hint: [ { x : x € Z, x² = 1} = { -1, 1}]

Which one of the following is incorrect

1) P = { x: x-8 = - 8 } is a singleton set
2) Every non-empty set has at least two subsets, Æ and the set itself
3) Every subset of a finite set is finite
4) Every set has a proper subset

Answer: 4

SOLUTION 1 :

Hint: [ The subset of empty set Ø= { { } } . The empty set does not has a proper subset

10)

If U = {1,2,3,4,5,6,7,8, 9,10} and A= {2,5,6,9,10} A' is

1) {1,3,4,7,8}
2) ɸ
3) {1,3,5,10}
4) {2,5,6,9,10}

Answer: 1

SOLUTION 1 :

Hint: [ A" = U – A { 1,2,3,4,5,6,7,8,9,10} – {2,5,6,9,10} ={ 1,3,4,7,8}]

ans = {1,3,4,7,8}