Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Application of Derivatives

NDA 2019 · Mathematics · Application of Derivatives

Paragraph: A curve y = m e^ m x where m > 0 intersects y-axis at a...

Paragraph: A curve y = memxm e^{m x} where m > 0 intersects y-axis at a point P.
Question: How much angle does the tangent at PP make with yy-axis?

Options

  1. Atan⁡−1m2\tan ^{-1} m^2
  2. Bcot⁡−1(1+m2)\cot ^{-1} \left(1+m²\right)
  3. Csin⁡−1(11+m4)\sin ^{-1} \left(\frac{1}{\sqrt{1+m⁴}}\right)
  4. Dsec⁡−11+m4\sec ^{-1} \sqrt{1+m^4}

Correct answer

A. tan⁡−1m2\tan ^{-1} m^2

Step-by-step solution

tan⁡α=dydx=m2∴α=tan⁡−1(m2)\begin{aligned} & \tan \alpha=\frac{d y}{d x}=m^2 \\ & \therefore \quad \alpha=\tan ^{-1}\left(m^2\right)\end{aligned}$$
Practice Application of Derivatives on Quantrex Academy →

More from Application of Derivatives

Passage: Let S and T be the sets where f(x)=(x^3)/(3)-(5x^2)/(2)+6x+7 decreases and… NDA 2026What is the length of the longest interval in which the function f(x)=2 ^2 x-1 is… NDA 2026Passage: Let S and T be the sets where f(x)=(x^3)/(3)-(5x^2)/(2)+6x+7 decreases and… NDA 2026For the following three (03) items: Let y = f(x) = x ^ -1 x 1 - x^2 + 1 - x^2 . What is… NDA 2025Consider the following statements regarding the function f(x) = (1)/(x - 5)… NDA 2025Consider the following for the two (02) items that follow: Let ABC be a triangle… NDA 2025Consider the following for the two (02) items that follow: Let ABC be a triangle… NDA 2025A wire of length 20 cm is to be bent into a rectangle. Which of the following statements… NDA 2025Consider the following for the two (02) items that follow: Let the function f(x) = x^2 +… NDA 2025For the following two (02) items: Consider the function f(x) = 1 - [3] (x-1)^2 . The… NDA 2025Consider the following for the two (02) items that follow: The slope of the tangent to… NDA 2025For the following three (03) items: Consider the function f(x) = x|x| . Consider the… NDA 2025Consider the following statements: Statement-I: The function f(x) = (x^3 + 128)/(x) has a… NDA 2025Paragraph: Let f(x)= 2 x+x on [(-π)/(2), (π)/(2)] Question: What is the greatest value of… NDA 2024Let f(x)=(x)/( x) ;(x > 1) Consider the following statements: 1. f(x) is increasing in… NDA 2024Paragraph: Let f(x)= 2 x+x on [(-π)/(2), (π)/(2)] Question: What is the least value of… NDA 2024 Full Application of Derivatives list Application of Derivatives JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs