Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Application of Derivatives

NDA 2021 · Mathematics · Application of Derivatives

The tangent to the curve x^2=y at (1,1) makes an angle θ with the...

The tangent to the curve x2=yx^2=y at (1,1)(1,1) makes an angle θ\theta with the positive direction of xx-axis. Which one of the following is correct?

Options

  1. Aθ<π6\theta < \frac{\pi}{6}
  2. Bπ6<θ<π4\frac{\pi}{6} < \theta < \frac{\pi}{4}
  3. Cπ4<θ<π3\frac{\pi}{4} < \theta < \frac{\pi}{3}
  4. Dπ3<θ<π2\frac{\pi}{3} < \theta < \frac{\pi}{2}

Correct answer

D. π3<θ<π2\frac{\pi}{3} < \theta < \frac{\pi}{2}

Step-by-step solution

Given curve is x2=yx^2=y or  y=x2dydx=2x at (1,1)dydx=2⇒tan⁡θ=2⇒θ∈(π3,π2)\begin{aligned} & \text{\text{ or } } y=x^2 \\ & \frac{d y}{d x}=2 x \\ & \text{ at }(1,1) \frac{d y}{d x}=2 \Rightarrow \tan \theta=2 \\ & \Rightarrow \theta \in\left(\frac{\pi}{3}, \frac{\pi}{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