Sets, Relations & Functions · NDA previous year questions

2015 27 questions

1. Q772015 · 19 Apr 2015

   Consider the function $f(x)=0.75x^4-x^3-9x^2+7$. Consider the following statements : 1. The function attains local minima at $x=-2$ and $x=3$. 2. The function increases in the interval $(-2,0)$. Which of the above statements is/are correct?

   1. A.1 only
   2. B.2 only
   3. C.Both 1 and 2
   4. D.Neither 1 nor 2
   Show answer

   Answer: C

2. Q792015 · 19 Apr 2015

   The integral $\int \frac{dx}{a\cos x+b\sin x}$ is of the form $\frac{1}{r}\ln \left[\tan \left(\frac{x+\alpha }{2}\right)\right]$. What is $\alpha$ equal to?

   1. A.${\tan }^{-1}\left(\frac{a}{b}\right)$
   2. B.${\tan }^{-1}\left(\frac{b}{a}\right)$
   3. C.${\tan }^{-1}\left(\frac{a+b}{a-b}\right)$
   4. D.${\tan }^{-1}\left(\frac{a-b}{a+b}\right)$
   Show answer

   Answer: A