Questions and Solutions

Class: 12 Subject: Math Type: Mcq Year: 2022

Question 1:

If \(\frac{d}{dx}(f(x))=\log x\), then \(f(x)\) equals:

  • A. \(-\frac{1}{x}+C\)
  • B. \(x(\log x-1)+C\)
  • C. \(x(\log x+x)+C\)
  • D. \(\frac{1}{x}+C\)
Class: 12 Subject: Math Type: Mcq Year: 2022

Question 2:

If \(y = x^x\), then \(\frac{dy}{dx}\) is:

  • A. \(x^x(\log x + 1)\)
  • B. \(x^x(\log x - 1)\)
  • C. \(x^x(1 - \log x)\)
  • D. \(x^x(1 + x)\)
Class: 12 Subject: Math Type: Mcq Year: 2022

Question 3:

The derivative of \(\sin^2 x\) is:

  • A. \(2\sin x\cos x\)
  • B. \(\cos x\)
  • C. \(2\cos^2 x\)
  • D. \(\cos^2 x\)
Class: 12 Subject: Math Type: Mcq Year: 2023

Question 4:

Let \(y=f(\frac{1}{x})\) and \(f'(x)=x^3\). What is the value of \(\frac{dy}{dx}\) at \(x=\frac{1}{2}\)?

  • A. \(-\frac{1}{64}\)
  • B. \(-\frac{1}{32}\)
  • C. -32
  • D. -64
Class: 12 Subject: Math Type: Mcq Year: 2023

Question 5:

If \(y=\log\sqrt{\sec\sqrt{x}}\), then the value of \(\frac{dy}{dx}\) at \(x=\frac{\pi^{2}}{16}\) is:

  • A. \(\frac{1}{\pi}\)
  • B. \(\frac{1}{4}\)
  • C. \(\frac{1}{2}\)
  • D. \(\pi\)
Class: 12 Subject: Math Type: Mcq Year: 2023

Question 6:

If \(x=3 \cos \theta\) and \(y=5 \sin \theta\), then \(\frac{dy}{dx}\) is equal to:

  • A. \(-\frac{3}{5}\tan\theta\)
  • B. \(-\frac{5}{3}\cot\theta\)
  • C. \(-\frac{5}{3}\tan\theta\)
  • D. \(-\frac{3}{5}\cot\theta\)