# JEE Main

Explore popular questions from Sets, Relations and Functions for JEE Main. This collection covers Sets, Relations and Functions previous year JEE Main questions hand picked by experienced teachers.

## Mathematics

Sets, Relations and Functions

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Q 1. If {tex} \mathrm { A } {/tex} and {tex} \mathrm { B } {/tex} are two sets, then {tex} \mathrm { A } \cap ( \mathrm { A } \cup \mathrm { B } )' {/tex} is equal to-

A

{tex} \mathrm A {/tex}

B

{tex} \mathrm B {/tex}

{tex} \phi {/tex}

D

none of these

##### Explanation

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Q 2. If {tex} \mathrm { A } {/tex} is any set, then-

A

{tex} \mathrm A \cup \mathrm A ^ { \prime } = \phi {/tex}

{tex} \mathrm A \cup \mathrm A ^ { \prime } = \mathrm U {/tex}

C

{tex} \mathrm A \cap \mathrm A ^ { \prime } = \mathrm U {/tex}

D

none of these

##### Explanation

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Q 3. If {tex} A , B {/tex} be any two sets, then {tex} ( A \cup B ) ^\prime {/tex} is equal to-

A

{tex} A ^ { \prime } \cup B ^ { \prime } {/tex}

{tex} A ^ { \prime } \cap B ^ { \prime } {/tex}

C

{tex} A \cap B {/tex}

D

{tex} A \cup B {/tex}

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Q 4. If {tex} \mathrm { A } {/tex} and {tex} \mathrm { B } {/tex} be any two sets, then {tex} ( \mathrm { A } \cap \mathrm { B } )' {/tex} is equal to-

A

{tex} \mathrm A ^ { \prime } \cap \mathrm B ^ { \prime } {/tex}

{tex} \mathrm A ^ { \prime } \cup B ^ { \prime } {/tex}

C

{tex} \mathrm A \cap \mathrm B {/tex}

D

{tex} \mathrm A \cup \mathrm B {/tex}

##### Explanation

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Q 5. Let {tex} \mathrm U = \{ 1,2,3,4,5,6,7,8,9,10 \} , \mathrm A = \{ 1,2,5 \} {/tex}
{tex} \mathrm B = \{ 6,7 \} {/tex} then {tex} \mathrm A \cap \mathrm B ^ { \prime } {/tex} is-

A

{tex} \mathrm { B }' {/tex}

{tex} \mathrm A {/tex}

C

{tex} \mathrm { A } ^ { \prime } {/tex}

D

{tex} \mathrm B {/tex}

##### Explanation

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Q 6. If {tex} \mathrm { A } {/tex} and {tex} \mathrm { B } {/tex} are two sets, then {tex} \mathrm { A } \cup \mathrm { B } = \mathrm { A } \cap \mathrm { B } {/tex} if-

A

{tex} \mathrm A \subseteq \mathrm B {/tex}

B

{tex} \mathrm B \subseteq \mathrm A {/tex}

{tex} \mathrm A = \mathrm B {/tex}

D

none of these

##### Explanation

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Q 7. Let {tex} A {/tex} and {tex} B {/tex} be two sets in the universal set. Then {tex} A - B {/tex} equals-

{tex} A \cap B ^ { \prime } {/tex}

B

{tex} A ^ { \prime } \cap B {/tex}

C

{tex} A \cap B {/tex}

D

none of these

##### Explanation

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Q 8. Two sets {tex} \mathrm { A } , \mathrm { B } {/tex} are disjoint iff-

A

{tex} \mathrm A \cup \mathrm B = \phi {/tex}

B

{tex} \mathrm A \cap \mathrm B \neq \phi {/tex}

{tex} \mathrm A \cap \mathrm B = \phi {/tex}

D

{tex} \mathrm A - \mathrm B = \mathrm A {/tex}

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Q 9. Which of the following is a null set?

A

{tex} \{ 0 \} {/tex}

B

{tex} \{ x: x > 0 \text { or } x < 0 \} {/tex}

C

{tex} \left\{ x: x ^ { 2 } = 4 \text { or } x = 3 \right\} {/tex}

{tex} \left\{ x: x ^ { 2 } + 1 = 0 , x \in R \right\} {/tex}

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Q 10. If {tex} \mathrm { A } \subseteq \mathrm { B } , {/tex} then {tex} \mathrm { A } \cap \mathrm { B } {/tex} is equal to-

{tex} \mathrm A {/tex}

B

{tex} \mathrm B {/tex}

C

{tex} \mathrm { A } ^ { \prime } {/tex}

D

{tex} \mathrm B ^ { \prime } {/tex}

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Q 11. If {tex} \mathrm { A } {/tex} and {tex} \mathrm { B } {/tex} are any two sets, then {tex} \mathrm { A } \cup ( \mathrm { A } \cap \mathrm { B } ) {/tex} is equal to-

{tex} \mathrm A {/tex}

B

{tex} \mathrm B {/tex}

C

{tex} \mathrm A ^ { \prime } {/tex}

D

{tex} \mathrm B ^ { \prime } {/tex}

##### Explanation

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Q 12. If {tex} \mathrm { A } {/tex} and {tex} \mathrm { B } {/tex} are not disjoint, then {tex} \mathrm { n } ( \mathrm { A } \cup \mathrm { B } ) {/tex} is equal to-

A

{tex} \mathrm { n } ( \mathrm { A } ) + \mathrm { n } ( \mathrm { B } ) {/tex}

{tex} \mathrm { n } ( \mathrm { A } ) + \mathrm { n } ( \mathrm { B } ) - \mathrm { n } ( \mathrm { A } \cap \mathrm { B } ) {/tex}

C

{tex} \mathrm { n } ( \mathrm { A } ) + \mathrm { n } ( \mathrm { B } ) + \mathrm { n } ( \mathrm { A } \cap \mathrm { B } ) {/tex}

D

{tex} \mathrm { n } ( \mathrm { A } ) \cdot \mathrm { n } ( \mathrm { B } ) {/tex}

##### Explanation

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Q 13. Which set is the subset of all given sets?

A

{tex} \{ 1,2,3,4 , \ldots . \} {/tex}

B

{tex} \{ 1 \} {/tex}

C

{tex} \{ 0 \} {/tex}

{ }

##### Explanation

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Q 14. If {tex} Q = \left\{ x: x = \frac { 1 } { y } , \text { where } y \in N \right\} , {/tex} then-

A

{tex} 0 \in Q {/tex}

{tex} 1 \in Q {/tex}

C

{tex} 2 \in \mathrm { Q } {/tex}

D

{tex} \frac { 2 } { 3 } \in \mathrm { Q } {/tex}

##### Explanation

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Q 15. {tex} A = \{ x: x \neq x \} {/tex} represents -

A

{tex} \{ 0 \} {/tex}

{ }

C

{tex} \{ 1 \} {/tex}

D

{tex} \{ x \} {/tex}

##### Explanation

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Q 16. {tex} P ( A ) = P ( B ) \Rightarrow {/tex}

A

{tex} { A } \subseteq { B } {/tex}

B

{tex} B \subseteq A {/tex}

{tex} A = B {/tex}

D

none of these

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Q 17. If {tex} A \times B = \{ ( 5,5 ) , ( 5,6 ) , ( 5,7 ) , ( 8,6 ) , ( 8,7 ) , ( 8,5 ) \} , {/tex} then the value {tex} A {/tex} is

A

{tex} \{ 5 \} {/tex}

B

{tex} \{ 8 \} {/tex}

{tex} \{ 5,8 \} {/tex}

D

{tex} \{ 5,6,7,8 \} {/tex}

##### Explanation

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Q 18. A relation is represented by

A

Roster method

B

Set-builder method

Both (a) and (b)

D

None of these

##### Explanation

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Q 19. Which of the following is/are not true?

If {tex} P = \{ m , n \} {/tex} and {tex} Q = \{ n , m \} , {/tex} then {tex} P \times Q = \{ ( m , n ) , ( n , m ) \} {/tex}

B

If {tex} A {/tex} and {tex} B {/tex} are non-empty sets, then {tex} A \times B {/tex} is a non-empty set of ordered pairs {tex} ( x , y ) , {/tex} such that {tex} x \in A {/tex} and {tex} y \in B {/tex}.

C

If {tex} A = \{ 1,2 \} {/tex} and {tex} B = \{ 3,4 \} , {/tex} then {tex} A \times ( B \cap \phi ) = \phi {/tex}

D

All of the above

##### Explanation

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Q 20. If {tex} ( 4 x + 3 , y ) = ( 3 x + 5 , - 2 ) , {/tex} then the sum of the values of {tex} x {/tex} and {tex} y {/tex} is

0

B

2

C

- 2

D

1

##### Explanation

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Q 21. If {tex} A {/tex} is the set of even natural numbers less than {tex}8{/tex} and {tex} B {/tex} is the set of prime numbers less than {tex}7{/tex} , then the number of relations from {tex} A {/tex} to {tex} B {/tex} is

{tex} 2 ^ { 9 } {/tex}

B

{tex} 9 ^ { 2 } {/tex}

C

{tex} 3 ^ { 2 } {/tex}

D

{tex} 2 ^ { 9 } - 1 {/tex}

##### Explanation

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Q 22. Let {tex} A = \{ x , y , z \} {/tex} and {tex} B = \{ a , b , c , d \} . {/tex} Then, which one of the following is not a relation from {tex} A {/tex} to {tex} B \ ? {/tex}

A

{tex} \{ ( x , a ) , ( x , c ) \} {/tex}

B

{tex} \{ ( y , c ) , ( y , d ) \} {/tex}

C

{tex} \{ ( z , a ) , ( z , d ) \} {/tex}

{tex} \{ ( z , b ) , ( y , b ) , ( a , d ) \} {/tex}

##### Explanation

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Q 23. If {tex} A = \{ 2,3,4,5 \} {/tex} and {tex} B = \{ 3,6,7,10 \}. \ R {/tex} is a relation defined by {tex} R = \{ ( a , b ): a \text { is relatively prime to } b , a \in A {/tex} and {tex} b \in B \} , {/tex} then domain of {tex} R {/tex} is

A

{tex} \{ 2,3,5 \} {/tex}

B

{tex} \{ 3,5 \} {/tex}

C

{tex} \{ 2,3,4 \} {/tex}

{tex} \{ 2,3,4,5 \} {/tex}

##### Explanation

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Q 24. The number of elements in the domain of relation
{tex} \mathrm { R } = \left\{ ( \mathrm { x } , \mathrm { y } ): \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } = 16 , \mathrm { x } , \mathrm { y } \in \mathrm { Z } \right\} {/tex} is

A

1

B

2

3

D

4

##### Explanation

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Q 25. If {tex} A = \{ 1,2 \} , B = \{ 1,3 \} , {/tex} then {tex} ( A \times B ) \cup ( B \times A ) {/tex} is equal to

{tex} \{ ( 1,3 ) , ( 2,3 ) , ( 3,1 ) , ( 3,2 ) , ( 1,1 ) , ( 2,1 ) , ( 1,2 ) \}{/tex}

B

{tex} \{ ( 1,3 ) , ( 3,1 ) , ( 3,2 ) , ( 2,3 ) \} {/tex}

C

{tex} \{ ( 1,3 ) , ( 2,3 ) , ( 3,1 ) , ( 3,2 ) , ( 1,1 ) \} {/tex}

D

None of these