Limits, Continuity & Derivatives · NDA previous year questions

2019 35 questions

1. Q772019 · 21 Apr 2019

   The value of k which makes $f(x)=\{\begin{array}{ll}\sin x& x\ne 0\\ k& x=0\end{array}$ continuous at $x=0$, is

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

2. Q782019 · 21 Apr 2019

   What is the derivative of ${\sec }^2({\tan }^{-1}x)$ with respect to x ?

   1. A.$2x$
   2. B.$x^2+1$
   3. C.$x+1$
   4. D.$x^2$
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   Answer: A

3. Q792019 · 21 Apr 2019

   If $f(x)=\sin (\cos x)$, then $f^{\prime }(x)$ is equal to

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

4. Q802019 · 21 Apr 2019

   A given quantity of metal is to be cast into a half cylinder (i.e. with a rectangular base and semicircular ends). If the total surface area is to be minimum, then the ratio of the height of the half cylinder to the diameter of the semicircular ends is

   1. A.$\pi :(\pi +2)$
   2. B.$(\pi +2):\pi$
   3. C.1 : 1
   4. D.None of the above
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   Answer: A

5. Q812019 · 21 Apr 2019

   The minimum distance from the point $(4,2)$ to $y^2=8x$ is equal to

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

6. Q822019 · 21 Apr 2019

   What is the minimum value of $a^{2}x+b^{2}y$ where $xy=c^2$ ?

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

7. Q832019 · 21 Apr 2019

   What is $\int \ln (x^2)dx$ equal to ?

   1. A.$2x\ln (x)-2x+c$
   2. B.$\frac{2}{x}+c$
   3. C.$2x\ln (x)+c$
   4. D.$\frac{2\ln (x)}{x}-2x+c$
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   Answer: A

8. Q842019 · 21 Apr 2019

   What is $\int e^{x\ln (a)}dx$ equal to ?

   1. A.$\frac{a^x}{\ln (a)}+c$
   2. B.$\frac{e^x}{\ln (a)}+c$
   3. C.$\frac{e^x}{\ln (ae)}+c$
   4. D.$\frac{a{e}^x}{\ln (a)}+c$
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   Answer: A

9. Q852019 · 21 Apr 2019

   ${\int }_0^{\pi /2}|\sin x-\cos x|dx$ is equal to

   1. A.0
   2. B.$2(\sqrt{2}-1)$
   3. C.$2\sqrt{2}$
   4. D.$2(\sqrt{2}+1)$
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   Answer: B

10. Q862019 · 21 Apr 2019

    ${\int }_0^{\pi /2}{e}^{\sin x}\cos xdx$ is equal to

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