Functions (Advanced) JEE Main PYQs PDF, 2020–2026

Functions (Advanced) questions per year

Topic-wise weightage by year

How many Functions (Advanced) 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)

All 8 JEE Main 2026 Functions (Advanced) questions in the free PDF, latest shift first.

1. JEE Main 2026 · 8 Apr · Shift 2 · Functional Equations

   Let $f$ be a polynomial function such that $\log_{2}(f(x))=\left(\log_{2}\left(2+\frac{2}{3}+\frac{2}{9}+\ldots \ldots \infty \right)\right)\cdot \log_{3}\left(1+\frac{f(x)}{f(1/x)}\right),x>0$ and $f(6)=37$. Then $\sum_{{{\mathrm{n}}=1}}^{{10}}f({\mathrm{n}})$ is equal to $\_\_\_\_$ .

   Solve it online →

2. JEE Main 2026 · 4 Apr · Shift 2 · Inverse Functions

   For the function $f:[1,\infty)\rightarrow [1,\infty)$ defined by $f(x)=(x-1)^{4}+1$, among the two statements:

   (I) The set ${\mathrm{S}}=\left\{x\in [1,\infty):f(x)=f^{{-1}}(x)\right\}$ contains exactly two elements, and

   (II) The set ${\mathrm{S}}=\left\{x\in [1,\infty):f(x)=f^{{-1}}(x+1)\right\}$ is an empty set,

   Solve it online →

3. JEE Main 2026 · 4 Apr · Shift 2 · Functional Equations

   Let for some $\alpha\in {\mathbb{R}},f:{\mathbb{R}}\rightarrow {\mathbb{R}}$ be a function satisfying $f(x+y)=f(x)+2y^{2}+y+\alpha xy$ for all $x,y\in {\mathbb{R}}$. If $f(0)=-1$ and $f(1)=2$, then the value of $\sum_{{n=1}}^{5}(\alpha+f(n))$ is :

   Solve it online →

4. JEE Main 2026 · 2 Apr · Shift 1 · Domain and Range

   If the domain of the function
   
   $f(x)=\sqrt{\log_{{(0.6)}}(\left|\frac{2x-5}{x^{2}-4}\right|)}$ is $(-\infty,a]\cup \{b\}\cup [c,d)\cup (e,\infty)$, then the value of $a+b+c+d+e$ is ________.

   Solve it online →

5. JEE Main 2026 · 24 Jan · Shift 2 · Functional Equations

   Let $f$ be a function such that $3f(x)+2f\left(\frac{m}{19x}\right)=5x,x\neq 0$, where $m=\sum_{{i=1}}^{9}(i)^{2}$. Then $f(5)-f(2)$ is equal to

   Solve it online →

6. JEE Main 2026 · 22 Jan · Shift 2 · Domain and Range

   Let the domain of the function $f(x)=\log_{3}\log_{5}\left(7-\log_{2}\left(x^{2}-10x+85\right)\right)+\sin^{{-1}}\left(\left|\frac{3x-7}{17-x}\right|\right)$ be $(\alpha,\beta]$. Then $\alpha+\beta$ is equal to :

   Solve it online →

7. JEE Main 2026 · 22 Jan · Shift 2 · Functional Equations

   Let $f$ and $g$ be functions satisfying $f(x+y)=f(x)f(y),f(1)=7$ and $g(x+y)=g(xy),g(1)=1$, for all $x,y\in {\mathbf{N}}$. If $\sum_{{x=1}}^{{{\mathrm{n}}}}\left(\frac{f(x)}{{\mathrm{g}}(x)}\right)=19607$, then n is equal to :

   Solve it online →

8. JEE Main 2026 · 22 Jan · Shift 1 · Domain and Range

   If the domain of the function $f(x)=\sin^{{-1}}\left(\frac{5-x}{3+2x}\right)+\frac{1}{\log_{e}(10-x)}$ is $(-\infty,\alpha]\cup [\beta,\gamma)-\{\delta\}$, then $6(\alpha+\beta+\gamma+\delta)$ is equal to

   Solve it online →

Practise the 2026 Functions (Advanced) questions online

Sample questions from recent papers

The free PDF above has all 71 questions grouped by topic, with an answer key.

Frequently asked

More Mathematics chapters

• Applications of Derivatives (156 asked · 153 in PDF)
• Area Under Curves (138 asked · 136 in PDF)
• Binomial Theorem (197 asked · 196 in PDF)
• Circles (117 asked · all in PDF)
• Complex Numbers (162 asked · 161 in PDF)
• Continuity & Differentiability (94 asked · all in PDF)
• Definite Integration (225 asked · 223 in PDF)
• Determinants (188 asked · all in PDF)
• Differential Equations (204 asked · 202 in PDF)
• Differentiation (38 asked · all in PDF)
• Ellipse (100 asked · all in PDF)
• Hyperbola (63 asked · 62 in PDF)
• Indefinite Integration (60 asked · all in PDF)
• Inverse Trigonometric Functions (94 asked · all in PDF)
• Limits (110 asked · all in PDF)
• Matrices (111 asked · all in PDF)
• Parabola (107 asked · 104 in PDF)
• Permutations & Combinations (163 asked · 162 in PDF)
• Probability: Advanced (97 asked · all in PDF)
• Probability: Basic (79 asked · 78 in PDF)
• Quadratic Equations & Polynomial Inequalities (129 asked · 128 in PDF)
• Relations & Functions (Basic) (139 asked · 137 in PDF)
• Sequences & Series (247 asked · 246 in PDF)
• Sets (39 asked · all in PDF)
• Statistics (104 asked · all in PDF)
• Straight Lines (130 asked · 123 in PDF)
• Three Dimensional Geometry (297 asked · all in PDF)
• Trigonometric Equations (48 asked · all in PDF)
• Trigonometric Ratios & Identities (85 asked · 63 in PDF)
• Vectors (216 asked · 212 in PDF)

JEE Main PYQs by year: 2026 · 2025 · 2024 · 2023 · 2022 · 2021 · 2020