Integral Calculus & Area · NDA previous year questions

2018 5 questions

1. Q762018 · 9 Sept 2018

   What is $\int {\sin }^{3}x\cos xdx$ equal to? where c is the constant of integration.

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

2. Q772018 · 9 Sept 2018

   What is $\int \frac{dx}{a^2{\sin }^{2}x+b^2{\cos }^{2}x}$ equal to? where c is the constant of integration.

   1. A.$c+\frac{1}{ab}{\tan }^{-1}\left(\frac{a\tan x}{b}\right)$
   2. B.$c-\frac{1}{ab}{\tan }^{-1}\left(\frac{b\tan x}{a}\right)$
   3. C.$c+\frac{1}{ab}{\tan }^{-1}\left(\frac{b\tan x}{a}\right)$
   4. D.None of the above
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   Answer: A

3. Q1182018 · 9 Sept 2018

   What is $\int e^{\ln (\tan x)}dx$ equal to? where c is the constant of integration.

   1. A.$\ln |\tan x|+c$
   2. B.$\ln |\sec x|+c$
   3. C.$\tan x+c$
   4. D.$e^{\tan x}+c$
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   Answer: B

4. Q62018 · 22 Apr 2018

   The number of non-zero integral solutions of the equation $|1-2i{|}^x=5^x$ is

   1. A.Zero (No solution)
   2. B.One
   3. C.Two
   4. D.Three
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   Answer: A

5. Q822018 · 22 Apr 2018

   What is the area of the region bounded by the parabolas $y^2=6(x-1)$ and $y^2=3x$?

   1. A.$\frac{\sqrt{6}}{3}$
   2. B.$\frac{2\sqrt{6}}{3}$
   3. C.$\frac{4\sqrt{6}}{3}$
   4. D.$\frac{5\sqrt{6}}{3}$
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   Answer: C