Integral Calculus & Area · NDA previous year questions

2020 5 questions

1. Q852020 · 6 Sept 2020

   What is the area of the region enclosed between the curve $y^2=2x$ and the straight line $y=x$ ?

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

2. Q862020 · 6 Sept 2020

   If $f(x)=2x-x^2$, then what is the value of $f(x+2)+f(x-2)$ when $x=0$ ?

   1. A.$-8$
   2. B.$-4$
   3. C.8
   4. D.4
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   Answer: A

3. Q872020 · 6 Sept 2020

   If $x^m{y}^n=a^{m+n}$, then what is $\frac{dy}{dx}$ equal to?

   1. A.$\frac{my}{nx}$
   2. B.$-\frac{my}{nx}$
   3. C.$\frac{mx}{ny}$
   4. D.$-\frac{ny}{mx}$
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   Answer: B

4. Q882020 · 6 Sept 2020

   What is $\int \frac{dx}{x(x^n+1)}$ equal to?

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

5. Q902020 · 6 Sept 2020

   What is the value of $k$ such that integration of $\frac{3x^2+8-4k}{x}$ with respect to $x$, may be a rational function?

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