Integral Calculus & Area · NDA previous year questions

2017 5 questions

1. Q612017 · 10 Sept 2017

   Let $f(n)=\left[\frac{1}{4}+\frac{n}{1000}\right]$, where $[x]$ denotes the integral part of $x$. Then the value of ${\sum }_{n=1}^{1000}f(n)$ is

   1. A.251
   2. B.250
   3. C.1
   4. D.0
   Show answer

   Answer: A

2. Q622017 · 10 Sept 2017

   If $f(x)=\frac{4x+x^4}{1+4x^3}$ and $g(x)=\ln \left(\frac{1+x}{1-x}\right)$, then what is the value of $f\circ g\left(\frac{e-1}{e+1}\right)$ equal to?

   1. A.2
   2. B.1
   3. C.0
   4. D.$\frac{1}{2}$
   Show answer

   Answer: B

3. Q812017 · 10 Sept 2017

   The area bounded by the curve $|x|+|y|=1$ is

   1. A.1 square unit
   2. B.$2\sqrt{2}$ square units
   3. C.2 square units
   4. D.$2\sqrt{3}$ square units
   Show answer

   Answer: C

4. Q832017 · 23 Apr 2017

   Let $f(x)$ be an indefinite integral of ${\sin }^{2}x$. Consider the following statements: Statement 1: The function $f(x)$ satisfies $f(x+\pi )=f(x)$ for all real $x$. Statement 2: ${\sin }^2(x+\pi )={\sin }^{2}x$ for all real $x$. Which one of the following is correct in respect of the above statements?

   1. A.Both the statements are true and Statement 2 is the correct explanation of Statement 1
   2. B.Both the statements are true but Statement 2 is not the correct explanation of Statement 1
   3. C.Statement 1 is true but Statement 2 is false
   4. D.Statement 1 is false but Statement 2 is true
   Show answer

   Answer: D

5. Q842017 · 23 Apr 2017
   
   1. A.$\frac{1}{2}$
   2. B.1
   3. C.$\sqrt{3}$
   4. D.None of the above
   Show answer

   Answer: B