Integral Calculus & Area · NDA previous year questions

2014 7 questions

1. Q742014 · 28 Sept 2014

   Consider $\int x{\tan }^{-1}xdx=A(x^2+1){\tan }^{-1}x+Bx+C$, where C is the constant of integration. What is the value of A?

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

2. Q802014 · 28 Sept 2014

   For the next two (02) items that follow: Consider the integral $I={\int }_0^{\pi }\ln (\sin x)dx$ What is ${\int }_0^{\pi /2}\ln (\sin x)dx$ equal to?

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

3. Q812014 · 28 Sept 2014

   For the next two (02) items that follow: Consider the integral $I={\int }_0^{\pi }\ln (\sin x)dx$ What is ${\int }_0^{\pi /2}\ln (\cos x)dx$ equal to?

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

4. Q822014 · 28 Sept 2014

   For the next three (03) items that follow : The line $2y=3x+12$ cuts the parabola $4y=3x^2$. What is the area enclosed by the parabola and the line?

   1. A.27 square unit
   2. B.36 square unit
   3. C.48 square unit
   4. D.54 square unit
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   Answer: A

5. Q832014 · 28 Sept 2014

   For the next three (03) items that follow : The line $2y=3x+12$ cuts the parabola $4y=3x^2$. What is the area enclosed by the parabola, the line and the y-axis in the first quadrant?

   1. A.7 square unit
   2. B.14 square unit
   3. C.20 square unit
   4. D.21 square unit
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   Answer: C

6. Q732014 · 20 Apr 2014

   For the next two (02) items that follow: Consider the integrals $I_1={\int }_{\frac{\pi }{6}}^{\frac{\pi }{3}}\frac{dx}{1+\sqrt{\tan x}}$ and $I_2={\int }_{\frac{\pi }{6}}^{\frac{\pi }{3}}\frac{\sqrt{\sin x}dx}{\sqrt{\sin x}+\sqrt{\cos x}}$. What is $I_1-I_2$ equal to?

   1. A.0
   2. B.$2I_1$
   3. C.$\pi$
   4. D.None of the above
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   Answer: A

7. Q742014 · 20 Apr 2014

   For the next two (02) items that follow: Consider the integrals $I_1={\int }_{\frac{\pi }{6}}^{\frac{\pi }{3}}\frac{dx}{1+\sqrt{\tan x}}$ and $I_2={\int }_{\frac{\pi }{6}}^{\frac{\pi }{3}}\frac{\sqrt{\sin x}dx}{\sqrt{\sin x}+\sqrt{\cos x}}$. What is $I_1$ equal to?

   1. A.$\pi /24$
   2. B.$\pi /18$
   3. C.$\pi /12$
   4. D.$\pi /6$
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   Answer: C