Question 1 :
If A, B and C are any three sets, then A × (B∩C) is equal to

Question 2 :
If {tex} ( x , y ) \in R {/tex} and {tex} x , y \neq 0 ; f ( x , y ) \rightarrow ( x / y ) , {/tex} then this function is a/an

Question 3 :
The relation R= {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is

Question 4 :
The domain of the function {tex} f ( x ) = ( x - 3 ) / ( x - 1 ) \sqrt { x ^ { 2 } - 4 } {/tex} is

Question 5 :
A relation from {tex} P {/tex} to {tex} Q {/tex} is

Question 6 :
If A, B, C be three sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C, then

Question 7 :
Let <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e71c34ab7dd71141d36f553' height='19' width='75' >. A relation R on A is defined by <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e71c34a82d3c8134c868156' height='19' width='148' >. Then R is

Question 8 :
Let {tex} x {/tex} be a non-zero rational number and {tex} y {/tex} be an irrational number. Then {tex} x y {/tex} is

Question 9 :
The period of the function {tex} f ( x ) = [ x ] + [ 2 x ] + [ 3 x ] + \cdots + [ n x ] - {/tex} {tex} \frac { n ( n + 1 ) } { 2 } x , {/tex} when {tex} x \in N {/tex} is

Question 10 :
Numerical value of the expression {tex} \left| \frac { 3 x ^ { 3 } + 1 } { 2 x ^ { 2 } + 2 } \right| {/tex} for {tex} x = - 3 {/tex} is

Question 11 :
The domain of {tex} \sin ^ { - 1 } \left[ \log _ { 3 } \left( \frac { x } { 3 } \right) \right] {/tex} is

Question 12 :
{tex} f ( x , y ) = 1 / ( x + y ) {/tex} is a homogeneous function of degree

Question 13 :
The domain of {tex} f ( x ) = \left( x ^ { 2 } - 1 \right) ^ { - 1 / 2 } {/tex} is

Question 14 :
Let {tex} y = f ( x ) {/tex} be a real-valued function with domain as all real numbers. If the graph of the function is symmetrical about the line {tex} x = 1 , {/tex} then {tex} \forall \alpha \in R , {/tex} which one is correct?

Question 15 :
Given two finite sets A and B such that n (a) = 2, n (b) = 3. Then total number of relations from A to B is

Question 17 :
Let {tex} A = \{ a , b , c \} {/tex} and {tex} B = \{ 1,2 \} . {/tex} Consider a relation {tex} R {/tex} defined from set {tex} A {/tex} to set {tex} B {/tex} . Then {tex} R {/tex} is equal to set

Question 18 :
If {tex} f ( x ) = \cos | x | + \left[ \left| \frac { \sin x } { 2 } \right| \right] {/tex} , (where [.] denotes the greatest integer function), then<br>

Question 19 :
Let $n(u)=700,n(A)=200,n(B)=300$<br>$n\left( A\cap B \right) =100,n\left( A^{\prime} \cap B^{\prime} \right) =$

Question 20 :
If {tex} f ( x ) = \left\{ \begin{array} { l l } { x , } & { \text { when } x \text { is rational } } \\ { 1 - x , } & { \text { when } x \text { is irrational } } \end{array}, \right. {/tex} then {tex} f\circ f{/tex} (x) is given as

Question 21 :
The range of the function {tex} f ( x ) = ^{7 - x} P _ { x - 3 } {/tex} is

Question 22 :
The domain of the function {tex} f ( x ) = \sqrt { 2 - 2 x - x ^ { 2 } } {/tex} is

Question 23 :
The smallest set A such that A &cup; {1, 2} = {1, 2, 3, 5, 9} is

Question 24 :
If A, B and C are any three sets, then A - (B&cup;C) is equal to

Question 25 :
The range of {tex} f ( x ) = \cos 2 x - \sin 2 x {/tex} contains the set