Limits, Continuity & Derivatives · NDA previous year questions

2022 33 questions

1. Q702022 · 10 Apr 2022

   If $y=(x^x{)}^x$, then what is the value of $\frac{\mathrm{d}y}{\mathrm{d}x}$ at $x=1$?

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

2. Q712022 · 10 Apr 2022

   Let y = [x + 1], -4 < x < -3 where [.] is the greatest integer function. What is the derivative of y with respect to x at x = -3.5?

   1. A.-4
   2. B.-3.5
   3. C.-3
   4. D.0
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   Answer: D

3. Q722022 · 10 Apr 2022

   If $\frac{\mathrm{d}y}{\mathrm{d}x}=(\ln 5)y$ with $y(0)=\ln 5$, then what is y(1) equal to?

   1. A.0
   2. B.5
   3. C.$2\ln 5$
   4. D.$5\ln 5$
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   Answer: D

4. Q732022 · 10 Apr 2022

   Consider the following in respect of the function $f(x)=10^x$ : 1. Its domain is $(-\infty ,\infty )$ 2. It is a continuous function 3. It is differentiable at $x=0$ Which of the above statements are correct?

   1. A.1 and 2 only
   2. B.2 and 3 only
   3. C.1 and 3 only
   4. D.1, 2 and 3
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   Answer: D

5. Q742022 · 10 Apr 2022

   What is ${\lim }_{x\to 0}{x}^3(\mathrm{cosec}x{)}^2$ equal to ?

   1. A.0
   2. B.$\frac{1}{2}$
   3. C.1
   4. D.Limits does not exist
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   Answer: A

6. Q752022 · 10 Apr 2022

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

   1. A.0
   2. B.3
   3. C.6
   4. D.Limit does not exist
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   Answer: C

7. Q762022 · 10 Apr 2022

   In which one of the following intervals is the function $f(x)=\frac{x^3}{3}-\frac{7x^2}{2}+6x+5$ decreasing?

   1. A.$(-\infty ,1)$ only
   2. B.$(1,6)$
   3. C.$(6,\infty )$ only
   4. D.$(-\infty ,1)\cup (6,\infty )$
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   Answer: B

8. Q792022 · 10 Apr 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
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   Answer: A