Limits, Continuity & Derivatives · NDA previous year questions

2020 11 questions

1. Q152020 · 6 Sept 2020

   What is the maximum number of points of intersection of 5 non-overlapping circles?

   1. A.10
   2. B.15
   3. C.20
   4. D.25
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   Answer: C

2. Q722020 · 6 Sept 2020

   The radius of a circle is increasing at the rate of $0.7cm/sec$. What is the rate of increase of its circumference?

   1. A.$4.4cm/sec$
   2. B.$8.4cm/sec$
   3. C.$8.8cm/sec$
   4. D.$15.4cm/sec$
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   Answer: A

3. Q732020 · 6 Sept 2020

   If ${\lim }_{x\to 1}\frac{x^4-1}{x-1}={\lim }_{x\to k}\frac{x^3-k^3}{x^2-k^2}$, where $k\ne 0$, then what is the value of $k$?

   1. A.$\frac{2}{3}$
   2. B.$\frac{4}{3}$
   3. C.$\frac{8}{3}$
   4. D.4
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   Answer: C

4. Q812020 · 6 Sept 2020

   If $f(x)=\frac{\sin x}{x}$, where $x\in \mathbf{R}$, is to be continuous at $x=0$, then the value of the function at $x=0$

   1. A.should be 0
   2. B.should be 1
   3. C.should be 2
   4. D.cannot be determined
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   Answer: B

5. Q892020 · 6 Sept 2020

   What is the minimum value of $|x-1|$, where $x\in \mathbf{R}$ ?

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

6. Q912020 · 6 Sept 2020

   Consider the following statements for $f(x)=e^{-|x|}$ : 1. The function is continuous at $x=0$. 2. The function is differentiable at $x=0$. Which of the above statements is/are correct?

   1. A.1 only
   2. B.2 only
   3. C.Both 1 and 2
   4. D.Neither 1 nor 2
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   Answer: A

7. Q922020 · 6 Sept 2020

   What is the maximum value of $\sin x\cdot \cos x$ ?

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

8. Q932020 · 6 Sept 2020

   What is ${\lim }_{x\to 0}\frac{3^x+3^{-x}-2}{x}$ equal to?

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

9. Q942020 · 6 Sept 2020

   What is the derivative of ${\tan }^{-1}x$ with respect to ${\cot }^{-1}x$ ?

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

10. Q962020 · 6 Sept 2020

    What is the minimum value of $3\cos \left(A+\frac{\pi }{3}\right)$, where $A\in \mathbf{R}$ ?

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

11. Q1002020 · 6 Sept 2020

    Let $l$ be the length and $b$ the breadth of a rectangle such that $l+b=k$. What is the maximum area of the rectangle?

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