JEE Main 22 July 2021, Shift 2, Maths Q62

Question 62 of 90 in this shift, Maths question 2 of 30, Section A.

The number of solutions of

\sin^7 x+\cos^7 x=1

x\in[0, 4\pi]

is equal to :

(1) $5$ Official answer
(2) $7$
(3) $9$
(4) $11$

Official answer

Option 1

NTA final key.

Chapter: Trigonometric Functions
Topic: General Solutions
Idea tested: Boundedness and Range Analysis

Same idea in other shifts

Asked 2× in all

2 Apr 2026, Shift 1 · Q12Let $S=\{x \in [-\pi, \pi] : \sin x(\sin x+\cos x)=a, a \in \mathbb{Z}\}$ . Then $n(S)$ is equal to :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.