JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 17 March 2021, Shift 2, Maths Q61

Question 61 of 90 in this shift, Maths question 1 of 30, Section A.

The number of solutions of the equation

\sin^{-1}\left[x^2+\frac{1}{3}\right]+\cos^{-1}\left[x^2-\frac{2}{3}\right]=x^2

, for

x\in[-1, 1]

, and

[x]

denotes the greatest integer less than or equal to

x

, is :

(1) $0$ Official answer
(2) $2$
(3) $4$
(4)Infinite

Official answer

Option 1

NTA final key.

Chapter: Inverse Trigonometric Functions
Topic: Inverse Trig Domains
Idea tested: Inverse Trig with GIF and Fractional Part

Same idea in other shifts

Asked 3× in all

4 Apr 2026, Shift 1 · Q1Let $[\cdot]$ denote the greatest integer function. If the domain of the function $f(x)=\cos^{-1}\left(\frac{4x+2[x]}{3}\right)$ is…MediumSingle correct
6 Apr 2026, Shift 1 · Q1Let $[\cdot]$ denote the greatest integer function. If the domain of the function $f(x)=\sin^{-1}\left(\frac{x+[x]}{3}\right)$ 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.