JEE Main 2020 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 9 January 2020, Shift 2, Maths Q59

Question 59 of 75 in this shift, Maths question 9 of 25, Section A. NTA dropped this question from the final key; it is left out of every count on this site.

x=2\sin\theta-\sin2\theta

and

y=2\cos\theta-\cos2\theta

\theta\in[0,2\pi]

, then

\frac{d^2y}{dx^2}

\theta=\pi

is :

(1) $-\frac{3}{8}$
(2) $-\frac{3}{4}$
(3) $\frac{3}{4}$
(4) $\frac{3}{2}$

Official answer

Dropped by NTA (marks given to all)

NTA final key (Jan 2020).

Chapter: Continuity and Differentiability
Topic: Chain Rule
Idea tested: No close match in our taxonomy

Same topic in other shifts

All Chain Rule questions

3 Apr 2025, Shift 1 · Q16If $y(x) = \begin{vmatrix} \sin x & \cos x & \sin x + \cos x + 1 \\ 27 & 28 & 27 \\ 1 & 1 & 1 \end{vmatrix}$ , $x \in \mathbb{R}$ , then…MediumSingle correct
9 Apr 2024, Shift 2 · Q8If $\log_e y=3\sin^{-1}x$ , then $(1-x^2)y''-xy'$ at $x=\frac{1}{2}$ is equal toMediumSingle correct
29 Jan 2024, Shift 1 · Q9Suppose $f(x)=\frac{(2^x+2^{-x})\tan x\sqrt{\tan^{-1}(x^2-x+1)}}{(7x^2+3x+1)^3}$ . Then the value of $f'(0)$ is equal toHardSingle correct
31 Jan 2024, Shift 1 · Q3If $f(x)=\begin{vmatrix}x^3 & 2x^2+1 & 1+3x\\ 3x^2+2 & 2x & x^3+6\\ x^3-x & 4 & x^2-2\end{vmatrix}$ for all $x\in\mathbb{R}$ , then…MediumSingle correct
6 Apr 2023, Shift 1 · Q9If $2x^y+3y^x=20$ , then $\frac{dy}{dx}$ at $(2,2)$ is equal to:MediumSingle correct
24 Jun 2022, Shift 1 · Q3The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3…MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.