PYQ Vault
EbooksTutor

Relations and Functions

JEE Mains Maths. Try each one first, then open its answer.

Top 10 JEE Mains PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 13 times: 2021 Paper 17, 2021 Paper 22, 28 Jun 2022, 27 Jul 2022, 28 Jul 2022, 24 Jan 2023, 29 Jan 2023, 31 Jan 2023, 1 Feb 2023, 8 Apr 2023, 28 Jan 2025, 29 Jan 2025, 23 Jan 2026 S2. This one: 23 Jan 2026 S2 See all 13 of this type

    66
    Let A={0,1,2,….9)\mathbf{A = \{ 0,1,2,\ldots.9)}. Let R be a relation on A defined by (x,y)∈R(x,y) \in R if and only if ∣x−y∣|x - y| is a multiple of 3. Given below are two statements: Statement I: n(R)=36n(R) = 36 Statement II: RR is an equivalence relation. In the light of the above statements, choose the correct answer from the options given below

    Tap an option to check your answer.

  2. Question 2

    This type asked 9 times: 8 Apr 2023, 13 Apr 2023, 31 Jan 2024, 6 Apr 2024, 3 Apr 2025, 4 Apr 2025, 21 Jan 2026 S2, 22 Jan 2026 S1, 23 Jan 2026 S1. This one: 23 Jan 2026 S1 See all 9 of this type

    56
    Let A={−2,−1,0,1,2,3,4}\mathbf{A = \{ - 2, - 1,0,1,2,3,4\}}. Let R be a relation on A defined by xRy if and only if 2x+y≤22x + y \leq 2. Let ll be the number of elements in R. Let m and n be the minimum number of elements required to be added in R to make it reflexive and symmetric relations respectively. Then l+m+nl + m + n is equal to :

    Tap an option to check your answer.

  3. Question 3

    This type asked 7 times: 10 Apr 2023, 11 Apr 2023, 15 Apr 2023, 9 Apr 2024, 24 Jan 2026 S1, 2 Apr 2026 S2, 5 Apr 2026 S2. This one: 5 Apr 2026 S2 See all 7 of this type

    71
    Let A={1,4,7}A = \{ 1,4,7\} and B={2,3,8}B = \{ 2,3,8\}. Then the number of elements, in the relation R={((a1, b1) R = \left\{ \left( \left( a_{1},{\text{ }b}_{1} \right) \right.\ \right.,  (a2, b2))∈((A×B)×(A×B)):a1+b2\left. \ \left( a_{2},{\text{ }b}_{2} \right) \right) \in ((A \times B) \times (A \times B)):a_{1} + b_{2} divides  a2+b1}\left. \ a_{2} + b_{1} \right\} is ____\_\_\_\_

  4. Question 4

    This type asked 6 times: 8 Apr 2023, 15 Apr 2023, 30 Jan 2024, 4 Apr 2024, 3 Apr 2025, 22 Jan 2026 S1. This one: 22 Jan 2026 S1 See all 6 of this type

    64
    If the domain of the function f(x)=sin⁡−1(5−x3+2x)+1log⁡e(10−x)f(x) =\sin^{- 1}\left( \frac{5 - x}{3 + 2x} \right)+\frac{1}{\log_{e}(10 - x)} is (−∞,α]∪[β,γ)−{δ}\mathbf{( - \infty,\alpha\rbrack \cup \lbrack\beta,\gamma) - \{\delta\}}, then 6(α+β+γ+δ)6(\alpha + \beta + \gamma + \delta) is equal to

    Tap an option to check your answer.

  5. Question 5

    This type asked 6 times: 31 Jan 2023, 29 Jan 2024, 1 Feb 2024, 4 Apr 2024, 8 Apr 2024, 23 Jan 2025. This one: 23 Jan 2025 See all 6 of this type

    139
    Let X=R×RX = R \times R. Define a relation R on X as:
    (a1,b1)R(a2,b2)⇔b1=b2.\left( a_{1},b_{1} \right)R\left( a_{2},b_{2} \right)\Leftrightarrow b_{1}=b_{2}.
    Statement-I: R is an equivalence relation. Statement-II: For some (a,b)∈X(a,b) \in X, the set S={(x,y)∈X:(x,y)R(a,b)}\mathbf{S = \{(x,y) \in X:(x,y)R(a,b)\}} represents a line parallel to y=xy = x. In the light of the above statements, choose the correct answer from the options given below:

    Tap an option to check your answer.

  6. Question 6

    This type asked 5 times: 29 Jan 2023, 6 Apr 2024, 24 Jan 2025, 28 Jan 2026 S2, 6 Apr 2026 S2. This one: 6 Apr 2026 S2 See all 5 of this type

    51
    Let f:R→Rf:R \rightarrow R be defined as f(x)=2x2−3x+23x2+x+3f(x) =\frac{2x^{2}- 3x + 2}{3x^{2}+ x + 3}. Then ff is :

    Tap an option to check your answer.

  7. Question 7

    This type asked 5 times: 2021 Paper 9, 2021 Paper 11, 11 Apr 2023, 4 Apr 2026 S1, 6 Apr 2026 S1. This one: 6 Apr 2026 S1 See all 5 of this type

    51
    Let [.] denote the greatest integer function. If the domain of the function f(x)=sin⁡−1(x+[x]3)f(x) =\sin^{- 1}\left( \frac{x+ \lbrack x\rbrack}{3} \right) is [α,β)\lbrack\alpha,\beta), then α2+β2\alpha^{2}+\beta^{2} is equal to:

    Tap an option to check your answer.

  8. Question 8

    This type asked 5 times: 14 Jun 2022, 29 Jul 2022, 9 Apr 2024, 21 Jan 2026 S1, 24 Jan 2026 S2. This one: 24 Jan 2026 S2 See all 5 of this type

    63
    If the domain of the function f(x)=sin⁡−1(1x2−2x−2)f(x) =\sin^{- 1}\left( \frac{1}{x^{2}- 2x - 2} \right), is (−∞,α]∪[β,γ]∪[δ,∞)( - \infty,\alpha\rbrack \cup \lbrack\beta,\gamma\rbrack \cup \lbrack\delta,\infty), then α+β+γ+δ\alpha + \beta + \gamma + \delta is equal to

    Tap an option to check your answer.

  9. Question 9

    This type asked 5 times: 2021 Paper 4, 27 Jun 2022, 24 Jan 2023, 24 Jan 2025, 28 Jan 2025. This one: 28 Jan 2025 See all 5 of this type

    54
    If f(x)=2x2x+2,x∈Rf(x) =\frac{2^{x}}{2^{x}+\sqrt{2}},x \in R, then ∑k=181f(k82)\sum_{k = 1}^{81} f\left( \frac{k}{82} \right) is equal to :

    Tap an option to check your answer.

  10. Question 10

    This type asked 5 times: 24 Jan 2023, 30 Jan 2023, 29 Jan 2024, 31 Jan 2024, 23 Jan 2025. This one: 23 Jan 2025 See all 5 of this type

    61
    Let R={(1,2),(2,3),(3,3)}\mathbf{R = \{(1,2),(2,3),(3,3)\}} be a relation defined on the set {1,2,3,4}\mathbf{\{ 1,2,3,4\}}. Then the minimum number of elements, needed to be added in R so the R becomes an equivalence relation, is :

    Tap an option to check your answer.