Limits, Continuity & Derivatives · NDA previous year questions

2023 29 questions

1. Q922023 · 16 Apr 2023

   What is the derivative of ${\sin }^{2}x$ with respect to ${\cos }^{2}x$ ?

   1. A.-1
   2. B.1
   3. C.$\sin 2x$
   4. D.$\cos 2x$
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   Answer: A

2. Q942023 · 16 Apr 2023

   What is the derivative of cosec(x°) ?

   1. A.$-\mathrm{cosec}(x^{\circ })\cot (x^{\circ })$
   2. B.$-\frac{\pi }{180}\mathrm{cosec}(x^{\circ })\cot (x^{\circ })$
   3. C.$\frac{\pi }{180}\mathrm{cosec}(x^{\circ })\cot (x^{\circ })$
   4. D.$-\frac{\pi }{180}\mathrm{cosec}(x)\cot (x)$
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   Answer: B

3. Q992023 · 16 Apr 2023

   What is ${\lim }_{x\to 5}\frac{5-x}{|x-5|}$ equal to ?

   1. A.-1
   2. B.0
   3. C.1
   4. D.Limit does not exist
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   Answer: D

4. Q1002023 · 16 Apr 2023

   What is ${\lim }_{x\to 1}\frac{x^9-1}{x^3-1}$ equal to ?

   1. A.-1
   2. B.-3
   3. C.3
   4. D.Limit does not exist
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   Answer: C