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.

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

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

( )

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

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

( )

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

1) B
2) A∩B
3) A
4) ɸ

( )

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

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

( )

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

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

( )

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

1) A
2) B
3) AUB
4) ɸ

( )

If X = {a{ b, c }d}, Which of the following is subset of X

1) {b,c}
2) {a,b}
3) {a,d}
4) {c,d}

( )

Which one of the following is incorrect

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

( )

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

( )

10)

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 € W, x ≥ 5}
4) {x : x € Z, x < 5 }

( )

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

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

Answer: 4

SOLUTION 1 :

ans = 2

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

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

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

Answer: 1

SOLUTION 1 :

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

Ans = 8

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

1) A
2) A∩B
3) B
4) ɸ

Answer: 3

SOLUTION 1 :

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

Ans = B

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

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

Answer: 3

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}

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

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

Answer: 4

SOLUTION 1 :

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

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

1) ɸ
2) AUB
3) B
4) A

Answer: 4

SOLUTION 1 :

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

Ans = A

If X = {a{ b, c }d}, Which of the following is subset of X

1) {c,d}
2) {a,b}
3) {a,d}
4) {b,c}

Answer: 3

SOLUTION 1 :

{ c,d}

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

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

1) m-p
2) m-n+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

10)

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 € Z, x < 5 }
3) { x : x € W, x ≥ 5}
4) {x : x is an even prime number}

Answer: 4

SOLUTION 1 :

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