Definite Integration — 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 Definite Integration?

Definite Integration 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 Definite Integration 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 Definite Integration questions from real NDA papers

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

Question 1 · NDA 2025
What $\int_{2}^{3} f (x) d x$ equal to?
1. (A) $3 - 2$
2. (B) $2 (3 - 2)$
3. (C) $3 - 2$
4. (D) $1$
Show answerAnswer
$Answer: (B) 2 (3 - 2)$
Question 2 · NDA 2025
What is $\int_{n}^{n + 1} (x - [x]) d x$ , where [.] is the greatest integer function and n is natural number?
1. (A) $\frac{4 n + 1}{2}$
2. (B) $\frac{2 n + 1}{2}$
3. (C) $1/2$
4. (D) $1$
Show answerAnswer
$Answer: (C) 1/2$
Question 3 · NDA 2025
If $I_{1} = \int_{e}^{e^{2}} \frac{d x}{l n x}$ and $I_{2} = \int_{1}^{2} \frac{e ^{x}}{x} d x$ then which one of the following is correct?
1. (A) $I_{1} - I_{2} = 0$
2. (B) $I_{1} + I_{2} = 0$
3. (C) $I_{1} - 2 I_{2} = 0$
4. (D) $2 I_{1} - I_{2} = 0$
Show answerAnswer
$Answer: (A) I_{1} - I_{2} = 0$
Question 4 · NDA 2024
What is $\int_{0}^{π /2} \frac{dx}{g ( x )}$ equal to
1. (A) $\frac{l n 2}{2}$
2. (B) $\frac{l n 2}{4}$
3. (C) $ln 2$
4. (D) $2 ln 2$
Show answerAnswer
$Answer: (C) ln 2$
Question 5 · NDA 2024
What is $\int_{- 1}^{1} (3 sin x - sin 3 x) cos^{2} x d x$ equal to?
1. (A) $\frac{1}{4}$
2. (B) $0$
3. (C) $\frac{1}{2}$
4. (D) $\frac{1}{4}$
Show answerAnswer
$Answer: (B) 0$

Definite Integration questions by year

Year	Questions	Share of chapter questions
2025	4
2024	11
2023	10
2022	5
2021	7

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FAQs

How many NDA questions have been asked from Definite Integration?

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

Is Definite Integration important for NDA?

37 questions over 5 papers make Definite Integration a steady-weightage chapter in NDA Mathematics. The year-wise table above shows exactly how often it appears.

Can I solve Definite Integration 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.

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