Binomial Theorem — NDA Previous Year Questions

37 solved PYQs · 2021–2025 · Mathematics

Solved PYQs: 37
Years covered: 2021–2025
Avg / year: ~7
Subject: Mathematics

How many NDA questions come from Binomial Theorem?

Binomial Theorem has contributed 37 questions to National Defence Academy Examination papers between 2021 and 2025 — an average of about 7 questions a year. That count is measured from EByAi’s bank of 15,695 NDA questions, not estimated from a syllabus. Every one of the 37 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 NDA papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 37 Binomial Theorem questions (with full written solutions) are available in practice.

Question 1 · NDA 2025
If x=(1111)2, y=(1001)2 and z=(110)2, then what is x3−y3−z3−3xyz equal to?
1. (A) $(111001)2$
2. (B) $(100111)2$
3. (C) $(1)2$
4. (D) $(0)2$
Show answerAnswer
$Answer: (D) (0)2$
Question 2 · NDA 2025
If the sum of binomial coefficients in the expansion of (x+y)n is 256, then the greatest binomial coefficient occurs in which one of the following terms?
1. (A) $Third$
2. (B) $Fourth$
3. (C) $Fifth$
4. (D) $Ninth$
Show answerAnswer
$Answer: (C) Fifth$
Question 3 · NDA 2024
What is the remainder when 7n - 6n is divided by 36 for n = 100?
1. (A) $0$
2. (B) $1$
3. (C) $2$
4. (D) $6$
Show answerAnswer
$Answer: (B) 1$
Question 4 · NDA 2024
In the expansion of (1 + x)^p (1 + x)^q, if the coefficient of x3 is 35, then what is the value of (p + q)?
1. (A) $5$
2. (B) $6$
3. (C) $7$
4. (D) $8$
Show answerAnswer
$Answer: (C) 7$
Question 5 · NDA 2023
What is 1 - T_1 + 2T_2 - 3T_3 + ... + (-1)^n n T_n equal to ?
1. (A) $0$
2. (B) $-2n - 1$
3. (C) $n2 n - 1$
4. (D) $1$
Show answerAnswer
$Answer: (D) 1$

Binomial Theorem questions by year

Year	Questions	Share of chapter questions
2025	6
2024	7
2023	10
2022	9
2021	5

Practise these 37 questions with solutions

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FAQs

How many NDA questions have been asked from Binomial Theorem?

EByAi's bank holds 37 real NDA questions from Binomial Theorem, asked between 2021 and 2025 — about 7 per year on average. Every count is measured from actual papers, not estimated.

Is Binomial Theorem important for NDA?

37 questions over 5 papers make Binomial Theorem a steady-weightage chapter in NDA 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 NDA past-year questions in the browser with written solutions — free daily practice, no card needed.

More NDA Mathematics chapters

All NDA Mathematics chapters →NDA overview →