Binomial Theorem JEE Main PYQs PDF, 2020–2026

Binomial Theorem 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 196 of the 197 asked.

Topic-wise weightage by year

How many Binomial Theorem 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 17 JEE Main 2026 Binomial Theorem questions in the free PDF, latest shift first.

1. JEE Main 2026 · 8 Apr · Shift 2 · Binomial Coefficient Identities

   If $26\left(\frac{2^{3}}{3}\left({}^{{12}}{\mathrm{C}}_{2}\right)+\frac{2^{5}}{5}\left({}^{{12}}{\mathrm{C}}_{4}\right)+\frac{2^{7}}{7}\left({}^{{12}}{\mathrm{C}}_{6}\right)+\cdots +\frac{2^{{13}}}{13}\left({}^{{12}}{\mathrm{C}}_{{12}}\right)\right)=3^{{13}}-\alpha$, then $\alpha$ is equal to :

   Solve it online →

2. JEE Main 2026 · 6 Apr · Shift 2 · Binomial Expansion

   If $\left(1-x^{3}\right)^{{10}}=\sum_{{{\mathrm{r}}=0}}^{{10}}{\mathrm{a}}_{{{\mathrm{r}}}}x^{{{\mathrm{r}}}}(1-x)^{{30-2{\mathrm{r}}}}$, then $\frac{9{\mathrm{a}}_{9}}{{\mathrm{a}}_{{10}}}$ is equal to $\_\_\_\_$ .

   Solve it online →

3. JEE Main 2026 · 6 Apr · Shift 1 · Middle Term

   If the coefficients of the middle terms in the binomial expansions of $(1+\alpha x)^{{26}}$ and $(1-\alpha x)^{{28}},\alpha\neq 0$, are equal, then the value of $\alpha$ is:

   Solve it online →

4. JEE Main 2026 · 5 Apr · Shift 2 · General Term

   The coefficient of $x^{2}$ in the expansion of $\left(2x^{2}+\frac{1}{x}\right)^{{10}},x\neq 0$, is :

   Solve it online →

5. JEE Main 2026 · 5 Apr · Shift 1 · Coefficient Problems

   If the sum of the coefficients of $x^{7}$ and $x^{{14}}$ in the expansion of $\left(\frac{1}{x^{3}}-x^{4}\right)^{n},x\neq 0$, is zero, then the value of $n$ is $\_\_\_\_$ .

   Solve it online →

6. JEE Main 2026 · 4 Apr · Shift 2 · General Term

   In the expansion of $\left(9x-\frac{1}{3\sqrt{x}}\right)^{{18}},x>0$, if the term independent of $x$ is (221)k, then k is equal to:

   Solve it online →

7. JEE Main 2026 · 4 Apr · Shift 1 · Coefficient Problems

   Let the smallest value of $k\in {\mathbb{N}}$, for which the coefficient of $x^{3}$ in $(1+x)^{3}+(1+x)^{4}+(1+x)^{5}+\ldots +(1+x)^{{99}}+(1+kx)^{{100}},x\neq 0$, is $\left(43n+\frac{101}{4}\right)\left({}^{{100}}{\mathrm{C}}_{3}\right)$ for some $n\in {\ \mathrm{N}}$, be $p$. Then the value of $p+n$ is :

   Solve it online →

8. JEE Main 2026 · 2 Apr · Shift 2 · Binomial Coefficient Identities

   If for $3\leq r\leq 30$, $\left({{}^{{30}}C_{{30-r}}}\right)+3\left({{}^{{30}}C_{{31-r}}}\right)+3\left({{}^{{30}}C_{{32-r}}}\right)+\left({{}^{{30}}C_{{33-r}}}\right)={{}^{m}C_{r}}$, then m equals :

   Solve it online →

9. JEE Main 2026 · 28 Jan · Shift 2 · Applications of Binomial Theorem

   Given below are two statements :

   Statement I :

   ${25}^{{13}}+{20}^{{13}}+8^{{13}}+3^{{13}}$ is divisible by 7.

   Statement II :

   The integral part of $(7+4\sqrt{3})^{{25}}$ is an odd number.

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

   Solve it online →

10. JEE Main 2026 · 28 Jan · Shift 2 · Binomial Coefficient Identities

    The sum of the coefficients of $x^{{499}}$ and $x^{{500}}$ in $(1+x)^{{1000}}+x(1+x)^{{999}}+x^{2}(1+x)^{{998}}+\ldots +x^{{1000}}$ is :

    Solve it online →

11. JEE Main 2026 · 24 Jan · Shift 1 · Binomial Coefficient Identities

    Let ${\mathrm{S}}=\frac{1}{25!}+\frac{1}{3!23!}+\frac{1}{5!21!}+\ldots$ up to 13 terms. If $13{\ \mathrm{S}}=\frac{2^{k}}{n!},k\in {\ \mathrm{N}}$, then $n+k$ is equal to

    Solve it online →

12. JEE Main 2026 · 23 Jan · Shift 1 · Binomial Coefficient Identities

    The value of $\frac{{}^{{100}}{\mathrm{C}}_{{50}}}{51}+\frac{{}^{{100}}{\mathrm{C}}_{{51}}}{52}+\ldots.+\frac{{}^{{100}}{\mathrm{C}}_{{100}}}{101}$ is:

    Solve it online →

Practise the 2026 Binomial Theorem questions online

Sample questions from recent papers

The free PDF above has all 196 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)
• 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)
• Functions (Advanced) (71 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