Integral Calculus & Area · NDA previous year questions

2011 8 questions

1. Q252011 · 21 Aug 2011

   What is the area enclosed by the equation $x^2+y^2=2$?

   1. A.$4\pi$ square units
   2. B.$2\pi$ square units
   3. C.$4{\pi }^2$ square units
   4. D.4 square units
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   Answer: B

2. Q262011 · 21 Aug 2011

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

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

3. Q382011 · 21 Aug 2011

   The smallest positive integral value of $n$ for which ${\left(\frac{1-i}{1+i}\right)}^n$ is purely imaginary with positive imaginary part is

   1. A.1
   2. B.3
   3. C.4
   4. D.5
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   Answer: B

4. Q892011 · 21 Aug 2011

   What is the area bounded by the curve $\sqrt{x}+\sqrt{y}=\sqrt{a}(x,y\ge 0)$ and the coordinate axes?

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

5. Q612011 · 17 Apr 2011

   What is $\int {\sin }^{-1}(\cos x)dx$ equal to? where $k$ is a constant of integration.

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

6. Q862011 · 17 Apr 2011

   What is $\int \frac{\sin \sqrt{x}}{\sqrt{x}}dx$ equal to? where $c$ is a constant of integration.

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

7. Q1072011 · 17 Apr 2011

   What is the area bounded by the curves $y=e^x$, $y=e^{-x}$ and the straight line $x=1$?

   1. A.$\left(e+\frac{1}{e}\right)$ square units
   2. B.$\left(e-\frac{1}{e}\right)$ square units
   3. C.$\left(e+\frac{1}{e}-2\right)$ square units
   4. D.$\left(e-\frac{1}{e}-2\right)$ square units
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   Answer: C

8. Q1102011 · 17 Apr 2011

   What is $\int e^x\left(\sqrt{x}+\frac{1}{2\sqrt{x}}\right)dx$ equal to ? where $c$ is a constant of integration.

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