Differentiation — NDA Previous Year Questions

How many NDA questions come from Differentiation?

Differentiation has contributed 34 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 34 questions carries a written, step-by-step solution, and each is tagged to Differentiation 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 Differentiation questions from real NDA papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 34 Differentiation questions (with full written solutions) are available in practice.

1. Question 1 · NDA 2023

   What is the derivative of f(f(x)), where 1 < x < 2 ?
   1. (A)$\frac{1}{\ln x}$
   2. (B)$\frac{1}{x\ln x}$
   3. (C)$-\frac{1}{\ln x}$
   4. (D)$-\frac{1}{x\ln x}$
   Show answerAnswer

   Answer: (B) $\frac{1}{x\ln x}$

2. Question 2 · NDA 2023

   If f is differentiable, then what is f'(0.5) equal to?
   1. (A)$\frac{1}{4}$
   2. (B)$\frac{2}{3}$
   3. (C)2
   4. (D)4
   Show answerAnswer

   Answer: (C) 2

3. Question 3 · NDA 2023

   If f(x) = |ln|x|| where 0 < x < 1, then what is f'(0.5) equal to ?
   1. (A)-2
   2. (B)-1
   3. (C)0
   4. (D)2
   Show answerAnswer

   Answer: (A) -2

4. Question 4 · NDA 2022

   If y = (xx)x, then which one of the following is correct ?
   1. (A)$\frac{\text{dy}}{\text{dx}}$ + xy(1 + 2 ln x) = 0
   2. (B)$\frac{\text{dy}}{\text{dx}}$ − xy(1 + 2 ln x) = 0
   3. (C)$\frac{\text{dy}}{\text{dx}}$ − 2xy(1 + ln x) = 0
   4. (D)$\frac{\text{dy}}{\text{dx}}$ + 2xy(1 + ln x) = 0
   Show answerAnswer

   Answer: (B) $\frac{\text{dy}}{\text{dx}}$ − xy(1 + 2 ln x) = 0

5. Question 5 · NDA 2022

   Let f(x) be a function such that f'(x) = g(x) and f''(x) = −f(x). Let h(x) = {f(x)}^2 + {g(x)}^2. Then consider the following statements :
   

   1. h'(3) = 0

   2. h(1) = h(2)

   
   Which of the statements given above is/are correct ?
   1. (A)1 only
   2. (B)2 only
   3. (C)Both 1 and 2
   4. (D)Neither 1 nor 2
   Show answerAnswer

   Answer: (C) Both 1 and 2

Differentiation questions by year

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