JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 4 April 2024, Shift 2, Maths Q20

Question 20 of 90 in this shift, Maths question 20 of 30, Section A.

Given that the inverse trigonometric function assumes principal values only. Let

x

y

be any two real numbers in

[-1,1]

such that

\cos^{-1}x-\sin^{-1}y=\alpha,\ \frac{-\pi}{2}\le\alpha\le\pi

. Then, the minimum value of

x^2+y^2+2xy\sin\alpha

(1) $-1$
(2) $\frac{-1}{2}$
(3)0Official answer
(4) $\frac{1}{2}$

Official answer

Option 3

NTA final key.

Chapter: Inverse Trigonometric Functions
Topic: Inverse Trig Identities
Idea tested: Complementary Identities

Same idea in other shifts

Asked 7× in all

9 Apr 2024, Shift 2 · Q30Let the inverse trigonometric functions take principal values. The number of real solutions of the equation…MediumNumerical value
26 Jul 2022, Shift 2 · Q16If $0<x<\frac{1}{\sqrt{2}}$ and $\frac{\sin^{-1}x}{\alpha}=\frac{\cos^{-1}x}{\beta}$ , then a value of…MediumSingle correct
24 Jun 2022, Shift 1 · Q8The set of all values of k for which $(\tan^{-1}x)^3 + (\cot^{-1}x)^3 = k\pi^3,\ x \in \mathbf{R}$ , is the interval :HardSingle correct
30 Jun 2022, Shift 1 · Q10Let m and M respectively be the minimum and the maximum values of $f(x) = \sin^{-1}2x + \sin 2x + \cos^{-1}2x + \cos 2x$ ,…MediumSingle correct
27 Aug 2021, Shift 1 · Q76If $(\sin^{-1}x)^2-(\cos^{-1}x)^2=a$ ; $0<x<1$ , $a\neq 0$ , then the value of $2x^2-1$ is :MediumSingle correct
26 Feb 2021, Shift 1 · Q76If $\frac{\sin^{-1}x}{a}=\frac{\cos^{-1}x}{b}=\frac{\tan^{-1}y}{c}$ ; $0<x<1$ , then the value of $\cos\left(\frac{\pi c}{a+b}\right)$ is :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 108 of the 174 JEE Main shifts held from 2017 to 2026.