Test Details

Sets, Relations and Functions

For jee mains and Advanced

Dec 08, 10:45 AM

75 minutes

Dec 08, 12:00 PM

25.0 marks

MCQ

25 questions

RC Mathematics classes

Teaching mathematics since 2006

Class Details

Mathematics

TARGET-2022

Mathematics

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Question Text

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

Question 2 :
If A has 5 elements and B has 8 elements such that $\displaystyle A\subset B,$ then the number of elements in $\displaystyle A\cap B,$ and $\displaystyle A\cup B,$ are respectively :

Question 3 :
If {tex} f : R \rightarrow R , {/tex} where {tex} f ( x ) = a x + \cos x . {/tex} If {tex} f ( x ) {/tex} is bijective, then

Question 4 :
Let L denote the set of all straight lines in a plane. Let a relation R be defined by <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e71c2e8b7dd71141d36f4f9' height='18' width='117' >. Then R is

Question 5 :
The period of {tex} \sin ^ { 2 } \theta {/tex} is

Question 6 :
The domain of the function {tex} f ( x ) = \frac { 1 } { \sqrt { | x | - x } } {/tex} is

Question 7 :
If {tex} f ( x ) = \sin \sqrt { [ a ] } x , {/tex} (where [.] denotes the greatest integer func- tion), has {tex} \pi {/tex} as its fundamental period, then

Question 8 :
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 9 :
Let $A$ and $B$ are two finite sets such that $n(A)=3$ and $n(B)=4$ then the number of elements in $A\Delta B$.

Question 10 :
If domain of {tex} f ( x ) {/tex} is {tex} [ - 1,2 ] , {/tex} then the domain of {tex} f \left( [ x ] - x ^ { 2 } + 4 \right) {/tex} where {tex} [ \cdot ] {/tex} denotes the greatest integer function, is

Question 11 :
Let {tex} f: N \rightarrow Y {/tex} be a function defined as {tex} f ( x ) = 4 x + 3 {/tex} where {tex} Y = \{ y \in N: y = 4 x + 3 \text { for some } x \in N \} {/tex} Show that {tex} f {/tex} is invertible and its inverse is

Question 12 :
<img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e71c35482d3c8134c868160' height='89' width='132' > The shaded region in the given figure is

Question 13 :
A relation {tex} R {/tex} is defined from {tex} \{ 2,3,4,5 \} {/tex} to {tex} \{ 3,6,7,10 \} {/tex} by {tex} x R y \Leftrightarrow x {/tex} is relatively prime to {tex} y . {/tex} Then domain of {tex} R {/tex} is

Question 14 :
If {tex} y = f ( x ) = ( x + 2 ) / ( x - 1 ) , {/tex} then {tex} x {/tex} is

Question 15 :
The range of the function {tex} f ( x ) = ^{7 - x} P _ { x - 3 } {/tex} is

Question 16 :
Let {tex} f . R \rightarrow R {/tex} and {tex} g : R \rightarrow R {/tex} be two one-to-one and onto func- tions such that they are the mirror images of each other about the line {tex} y = a . {/tex} If {tex} h ( x ) = f ( x ) + g ( x ) , {/tex} then {tex} h ( x ) {/tex} is

Question 17 :
The set {tex} S = \{ 1,2,3 , \ldots \ldots , 12 \} {/tex} is to be partitioned into three sets {tex} A , B , C {/tex} of equal size. Thus {tex} A \cup B \cup C = S , A \cap B = B \cap C = A \cap C = \phi . {/tex} The number of ways to partition {tex} S {/tex} is

Question 18 :
The range of the function {tex} f ( x ) = \frac { x ^ { 2 } + x + 2 } { x ^ { 2 } + x + 1 } ; x \in R {/tex} is

Question 19 :
The domain of {tex} \sin ^ { - 1 } \left[ \log _ { 3 } \left( \frac { x } { 3 } \right) \right] {/tex} is

Question 20 :
If A, B, C be three sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C, then

Question 21 :
The domain of the function {tex} f ( x ) = \sqrt { x ^ { 12 } - x ^ { 3 } + x ^ { 4 } - x + 1 } {/tex} is

Question 22 :
If $A$ and $B$ are subsets of $U$ such that $n(U) = 700, n(A) = 200, n(B) = 300, n$ $\displaystyle \left ( A\cap B \right )$ $= 100$, then find $n\displaystyle \left ( A'\cap B' \right )$

Question 23 :
A relation on the set {tex} A = \{ x : | x | < 3 , \in x Z \} , {/tex} where {tex} Z {/tex} is the set of integers is defined by {tex} R = \{ ( x , y ) : y = | x | , x \neq - 1 \} . {/tex} Then the number of elements in the power set of {tex} R {/tex} is

Question 24 :
The graph of the function {tex} y = f ( x ) {/tex} is symmetrical about the line {tex} x = 2 , {/tex} then

Question 25 :
The domain of {tex} f ( x ) = \left( x ^ { 2 } - 1 \right) ^ { - 1 / 2 } {/tex} is

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