Consider the following statements regarding the function f(x) = 1/(x - 5) Statement-I: f(x) is decreasing on the intervals x 5 Statement-II: f''(x) > 0 for all x ≠ 5. Which one of the following is correct in respect of the above statements?

Statement-I is correct but Statement-II is not correct

Both Statement-I and Statement-II are correct and Statement-II explains Statement-I

Both Statement-I and Statement-II are correct but Statement-II does not explain Statement-I

Statement-I is not correct but Statement-II is correct

Application Of Derivatives — NDA Previous Year Questions

36 solved PYQs · 2021–2025 · Mathematics

Solved PYQs: 36
Years covered: 2021–2025
Avg / year: ~7
Subject: Mathematics

How many NDA questions come from Application Of Derivatives?

Application Of Derivatives has contributed 36 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 36 questions carries a written, step-by-step solution, and each is tagged to Application Of Derivatives 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 Application Of Derivatives questions from real NDA papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 36 Application Of Derivatives questions (with full written solutions) are available in practice.

Question 1 · NDA 2025
What is ∠A equal to if the area of the triangle is maximum?
1. (A) $π/6$
2. (B) $π/4$
3. (C) $π/3$
4. (D) $5π/12$
Show answerAnswer
$Answer: (C) π/3$
Question 2 · NDA 2025
What is the slope of the tangent to the curve y = f(x) at x = 0.5
1. (A) $4 π 3 / 27$
2. (B) $8 π 3 / 27$
3. (C) $4 π$
4. (D) $8 π$
Show answerAnswer
$Answer: (A) 4 π 3 / 27$
Question 3 · NDA 2025
Consider the following statements:

I. f(x) is an increasing function.

II. f(x) has local maximum at x = 0

Which of the statements given above is/are correct?
1. (A) $I only$
2. (B) $II only$
3. (C) $Both I and II$
4. (D) $Neither I nor II$
Show answerAnswer
$Answer: (D) Neither I nor II$
Question 4 · NDA 2025
Consider the following statements regarding the function f(x) = 1/(x - 5)

Statement-I: f(x) is decreasing on the intervals x < 5 and x > 5

Statement-II: f''(x) > 0 for all x ≠ 5.

Which one of the following is correct in respect of the above statements?
1. (A) $Both Statement-I and Statement-II are correct and Statement-II explains Statement-I$
2. (B) $Both Statement-I and Statement-II are correct but Statement-II does not explain Statement-I$
3. (C) $Statement-I is correct but Statement-II is not correct$
4. (D) $Statement-I is not correct but Statement-II is correct$
Show answerAnswer
$Answer: (C) Statement-I is correct but Statement-II is not correct$
Question 5 · NDA 2022
If xy = 4225 where x, y are natural numbers, then what is the minimum value of x + y ?
1. (A) $130$
2. (B) $260$
3. (C) $2113$
4. (D) $4226$
Show answerAnswer
$Answer: (A) 130$

Application Of Derivatives questions by year

Year	Questions	Share of chapter questions
2025	9
2024	7
2023	4
2022	5
2021	11

Practise these 36 questions with solutions

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FAQs

How many NDA questions have been asked from Application Of Derivatives?

EByAi's bank holds 36 real NDA questions from Application Of Derivatives, asked between 2021 and 2025 — about 7 per year on average. Every count is measured from actual papers, not estimated.

Is Application Of Derivatives important for NDA?

36 questions over 5 papers make Application Of Derivatives a steady-weightage chapter in NDA Mathematics. The year-wise table above shows exactly how often it appears.

Can I solve Application Of Derivatives 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

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