JEE Main 2026 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 6 April 2026, Shift 1, Maths Q1

Question 1 of 75 in this shift, Maths question 1 of 25, Section A.

Let

[\cdot]

denote the greatest integer function. If the domain of the function

f(x)=\sin^{-1}\left(\frac{x+[x]}{3}\right)

[\alpha, \beta)

, then

\alpha^2+\beta^2

is equal to:

(1)2
(2)5Official answer
(3)10
(4)13

Official answer

Option 2

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
17 Mar 2021, Shift 2 · Q61The 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…HardSingle 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.