Binomial Theorem — JEE Main Previous Year Questions

168 solved PYQs · 2016–2026 · Mathematics

Solved PYQs: 168
Years covered: 2016–2026
Avg / year: ~17
Subject: Mathematics

How many JEE Main questions come from Binomial Theorem?

Binomial Theorem has contributed 168 questions to Joint Entrance Examination (Main) papers between 2016 and 2026 — an average of about 17 questions a year. That count is measured from EByAi’s bank of 55,289 JEE Main questions, not estimated from a syllabus. Every one of the 168 questions carries a written, step-by-step solution, and each is tagged to Binomial Theorem within Mathematics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Binomial Theorem questions from real JEE Main papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 168 Binomial Theorem questions (with full written solutions) are available in practice.

Question 1 · JEE Main 2022
The remainder when (2021) 2023 is divided by 7 is :
1. (A) $1$
2. (B) $2$
3. (C) $5$
4. (D) $6$
Show answerAnswer
$Answer: (C) 5$
Question 2 · JEE Main 2020
The coefficient of x 7 in the expression (1 + x) 10 + x(1 + x) 9 + x 2 (1 + x) 8 + ......+ x 10 is:
1. (A) $120$
2. (B) $330$
3. (C) $420$
4. (D) $210$
Show answerAnswer
$Answer: (B) 330$
Question 3 · JEE Main 2020
If the number of integral terms in the expansion of (3 1/2 + 5 1/8)^n is exactly 33, then the least value of n is :
1. (A) $264$
2. (B) $256$
3. (C) $128$
4. (D) $248$
Show answerAnswer
$Answer: (B) 256$
Question 4 · JEE Main 2020
The greatest positive integer k, for which 49 k + 1 is a factor of the sum 49 125 + 49 124 + ..... + 49 2 + 49 + 1, is:
1. (A) $32$
2. (B) $60$
3. (C) $63$
4. (D) $65$
Show answerAnswer
$Answer: (C) 63$
Question 5 · JEE Main 2019
The coefficient of x¹⁸ in the product (1 + x) (1 - x)¹⁰ (1 + x + x² )⁹ is :
1. (A) $126$
2. (B)
  - 84
3. (C)
  - 126
4. (D) $84$
Show answerAnswer
$Answer: (D) 84$

Binomial Theorem questions by year

Year	Questions	Share of chapter questions
2026	17
2025	24
2024	23
2023	36
2022	19
2021	22
2020	12
2019	11
2017	2
2016	2

Practise these 168 questions with solutions

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FAQs

How many JEE Main questions have been asked from Binomial Theorem?

EByAi's bank holds 168 real JEE Main questions from Binomial Theorem, asked between 2016 and 2026 — about 17 per year on average. Every count is measured from actual papers, not estimated.

Is Binomial Theorem important for JEE Main?

168 questions over 10 papers make Binomial Theorem a moderate-weightage chapter in JEE Main Mathematics. The year-wise table above shows exactly how often it appears.

Can I solve Binomial Theorem PYQs online for free?

Yes. EByAi lets you solve JEE Main past-year questions in the browser with written solutions — free daily practice, no card needed.

More JEE Main Mathematics chapters

All JEE Main Mathematics chapters →JEE Main overview →