Relations & Functions (Basic) JEE Main PYQs PDF, 2020–2026

Relations & Functions (Basic) questions per year

in the free PDF asked, not in the PDFThe PDF only has questions we can print in full with a checked answer, so it holds 137 of the 139 asked.

Topic-wise weightage by year

How many Relations & Functions (Basic) questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Swipe the table sideways for older years.

Newest questions (2026)

The 12 newest of the 21 JEE Main 2026 Relations & Functions (Basic) questions in the free PDF, latest shift first.

1. JEE Main 2026 · 8 Apr · Shift 2 · Types of Relations

   Consider the relation $R$ on the set $\{-2,-1,0,1,2\}$ defined by $(a,b)\in R$ if and only if $1+ab>0$. Then, among the statements :

   I. The number of elements in R is 17

   II. R is an equivalence relation

   Solve it online →

2. JEE Main 2026 · 6 Apr · Shift 1 · Greatest Integer and Fractional Part

   Let [ • ] denote the greatest integer function. If the domain of the function $f(x)=\sin^{{-1}}\left(\frac{x+[x]}{3}\right)$ is $[\alpha,\beta)$, then $\alpha^{2}+\beta^{2}$ is equal to:

   Solve it online →

3. JEE Main 2026 · 6 Apr · Shift 2 · Types of Relations

   Let ${\mathrm{R}}=\{(x,y)\in {\mathbf{N}}\times {\mathbf{N}}:\log_{{{\mathrm{e}}}}(x+y)\leq 2\}$. Then the minimum number of elements, required to be added in $R$ to make it a transitive relation, is $\_\_\_\_$ .

   Solve it online →

4. JEE Main 2026 · 6 Apr · Shift 2 · Types of Functions

   Let $f:{\mathbf{R}}\rightarrow {\mathbf{R}}$ be defined as $f(x)=\frac{2x^{2}-3x+2}{3x^{2}+x+3}$. Then $f$ is :

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5. JEE Main 2026 · 5 Apr · Shift 1 · Types of Functions

   Let ${\mathrm{A}}=\{1,2,3,4,5,6\}$. The number of one-one functions $f:{\mathrm{A}}\rightarrow {\mathrm{A}}$ such that $f(1)\geq 3,f(3)\leq 4$ and $f(2)+f(3)=5$, is $\_\_\_\_$ .

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6. JEE Main 2026 · 5 Apr · Shift 2 · Cartesian Product

   Let ${\mathrm{A}}=\{1,4,7\}$ and ${\mathrm{B}}=\{2,3,8\}$. Then the number of elements, in the relation $R=\{((a_{1},b_{1}),(a_{2},b_{2}))\in ((A\times B)\times (A\times B)):a_{1}+b_{2}$ divides $a_{2}+b_{1}\}$ is $\_\_\_\_$ .

   Solve it online →

7. JEE Main 2026 · 4 Apr · Shift 1 · Greatest Integer and Fractional Part

   Let [•] denote the greatest integer function. If the domain of the function
   
   $f(x)=\cos^{{-1}}\left(\frac{4x+2[x]}{3}\right)$ is $[\alpha,\beta]$, then $12(\alpha+\beta)$ is equal to :

   Solve it online →

8. JEE Main 2026 · 4 Apr · Shift 1 · Types of Functions

   The number of functions $f:\{1,2,3,4\}\rightarrow \{a,b,c\}$, which are not onto, is :

   Solve it online →

9. JEE Main 2026 · 2 Apr · Shift 2 · Cartesian Product

   Let $A=\{2,3,4,5,6\}$. Let $R$ be a relation on the set $A\times A$ given by $(x,y)R(z,w)$ if and only if $x$ divides $z$ and $y\leq w$. Then the number of elements in $R$ is _________.

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10. JEE Main 2026 · 28 Jan · Shift 1 · Composition of Functions

    If $g(x)=3x^{2}+2x-3,f(0)=-3$ and $4g(f(x))=3x^{2}-32x+72$, then $f(g(2))$ is equal to:
    Solve it online →

11. JEE Main 2026 · 28 Jan · Shift 2 · Even, Odd and Periodic Functions

    The sum of all the elements in the range of $f(x)=\text{Sgn}(\sin x)+\text{Sgn}(\cos x)+\text{Sgn}(\tan x)+\text{Sgn}(\cot x)$, $x\neq \frac{n\pi}{2},n\in {\mathbb{Z}}$, where

    $\text{Sgn}(t)=\left\{\begin{array}{cc}1, & \text{if}t>0 \\ -1, & \text{if}t<0\end{array}\right.$

    is :

    Solve it online →

12. JEE Main 2026 · 28 Jan · Shift 2 · Types of Functions

    Given below are two statements :

    Statement I : The function $f:{\mathbb{R}}\rightarrow {\mathbb{R}}$ defined by $f(x)=\frac{x}{1+|x|}$ is one-one.

    Statement II : The function $f:{\mathbb{R}}\rightarrow {\mathbb{R}}$ defined by $f(x)=\frac{x^{2}+4x-30}{x^{2}-8x+18}$ is many-one.

    In the light of the above statements, choose the correct answer from the options given below :

    Solve it online →

Practise the 2026 Relations & Functions (Basic) questions online

Sample questions from recent papers

The free PDF above has all 137 questions grouped by topic, with an answer key.

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