Q227 / 270 · NDA 2019 (Phase 2) · Mathematics
Paragraph:
A curve y = $m e^{m x}$ where m > 0 intersects y-axis at a point P.
Question:
How much angle does the tangent at $P$ make with $y$-axis?
Question: How much angle does the tangent at $P$ make with $y$-axis?
- Correct answerA$\tan ^{-1} m^2$
- B$\cot ^{-1}\left(1+m^2\right)$
- C$\sin ^{-1}\left(\frac{1}{\sqrt{1+m^4}}\right)$
- D$\sec ^{-1} \sqrt{1+m^4}$
Solution
$\begin{aligned} & \text { } \tan \alpha=\frac{d y}{d x}=m^2 \\ & \therefore \quad \alpha=\tan ^{-1}\left(m^2\right)\end{aligned}$
Hence, the correct answer is option: 'A'.