Limits, Continuity & Derivatives · NDA previous year questions

2026 34 questions

1. Q792026 · 12 Apr 2026

   What is the derivative of $\frac{x}{|x|}$ with respect to $x$, where $x<0$ ?

   1. A.$-1$
   2. B.0
   3. C.1
   4. D.$x$
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   Answer: B

2. Q802026 · 12 Apr 2026

   If $f(x)$ is differentiable at $x=a$, then consider the following statements : I. $f(x)$ is continuous at $x=a$ II. ${\lim }_{x\to a}f(x)=f(a)$ 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
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   Answer: C

3. Q862026 · 12 Apr 2026

   What is the length of the longest interval in which the function $f(x)=2{\cos }^{2}x-1$ is decreasing ?

   1. A.$2\pi$
   2. B.$\pi$
   3. C.$\frac{\pi }{2}$
   4. D.$\frac{\pi }{4}$
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   Answer: C

4. Q872026 · 12 Apr 2026

   Passage: Let $\int \frac{\sin \theta d\theta }{(2+\cos \theta )(3+4\cos \theta )}=A\ln |2+\cos \theta |+B\ln |3+4\cos \theta |$. Question: What is the value of $B$ ?

   1. A.$-\frac{2}{5}$
   2. B.$-\frac{1}{5}$
   3. C.$\frac{1}{5}$
   4. D.$\frac{2}{5}$
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   Answer: B

5. Q882026 · 12 Apr 2026

   Passage: Let $\int \frac{\sin \theta d\theta }{(2+\cos \theta )(3+4\cos \theta )}=A\ln |2+\cos \theta |+B\ln |3+4\cos \theta |$. Question: What is the value of $A$ ?

   1. A.$-\frac{2}{5}$
   2. B.$-\frac{1}{5}$
   3. C.$\frac{1}{5}$
   4. D.$\frac{2}{5}$
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   Answer: C

6. Q892026 · 12 Apr 2026

   Passage: Let $f(x)=\sin x$ and $g(x)-f(x)=f(4-x)$. Question: What is ${\int }_0^4\frac{f(4-x)}{g(4-x)}dx$ equal to ?

   1. A.0
   2. B.1
   3. C.2
   4. D.4
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   Answer: C

7. Q902026 · 12 Apr 2026

   Passage: Let $f(x)=\sin x$ and $g(x)-f(x)=f(4-x)$. Question: What is ${\int }_0^4\frac{f(x)}{g(x)}dx$ equal to ?

   1. A.0
   2. B.1
   3. C.2
   4. D.4
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   Answer: C

8. Q912026 · 12 Apr 2026
   
   1. A.$k$
   2. B.$2k$
   3. C.$k(a+b)$
   4. D.$\frac{k}{a+b}$
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   Answer: C

9. Q922026 · 12 Apr 2026
   
   1. A.$\frac{\pi }{4}$
   2. B.$\frac{\pi }{2}$
   3. C.$\pi$
   4. D.$2\pi$
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   Answer: A