Jamb Mathematics Questions - CALCULUS
Question 36:
Find the derivative of \(\frac {\sin\theta}{\cos\theta}\)
- A Sec<sup style='font-size: smaller;'>2</sup> \(\theta\)
- B Tan \(\theta\) cosec \(\theta\)
- C Cosec \(\theta\)sec \(\theta\)
- D Cosec<sup style='font-size: smaller;'>2</sup>\(\theta\)
Question 37:
Integrate \(\frac{1 + x}{x^{3}} \mathrm d x\)
- A \(2x^{2} - \frac{1}{x} + k\)
- B \(-\frac{1}{2x^{2}} - \frac{1}{x} + k\)
- C \(-\frac{x^{2}}{2} - \frac{1}{x} + k\)
- D \(x^{2} - \frac{1}{x} + k\)
Question 38:
Integral ∫\( (5x^3 + 7x^2 − 2x + 5)\)dx
- A \( \frac{5x^4}{4} + \frac{7x^3}{3} + 2x + C \)
- B \( \frac{5x}{4} + \frac{7x^3}{3} - x^2 + 5x + C \)
- C \( \frac{5x^3}{3} + \frac{7x^2}{x} - x + C \)
- D \( \frac{2x^2}{3} + \frac{x}{5} - C \)
Question 39:
Integrate \(\frac{2x^3 + 2x}{x}\) with respect to x
- A \(\frac{2x^3}{3}\) - 2x + k
- B X<sup style='font-size: smaller;'>3</sup> + 2x + k
- C \(\frac{2x^3}{3}\) + 2x + k
- D X<sup style='font-size: smaller;'>3</sup> - 2x + k
Question 40:
Integrate \(\frac{2x^3 + 2x}{x}\) with respect to x
- A \(\frac{2x^3}{3}\) - 2x + k
- B X<sup style='font-size: smaller;'>3</sup> + 2x + k
- C \(\frac{2x^3}{3}\) + 2x + k
- D X<sup style='font-size: smaller;'>3</sup> - 2x + k