JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 30 June 2022, Shift 1, Maths Q30

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

Let

S_1 = \{x \in [0, 12\pi] : \sin^5 x + \cos^5 x = 1\}

and

S_2 = \{x \in [0, 8\pi] : \sin^7 x + \cos^7 x = 1\}

Then

n(S_1) - n(S_2)

is equal to __________.

Official answer

NTA final key.

Chapter: Trigonometric Functions
Topic: General Solutions
Idea tested: Periodic Root Scaling in Large Intervals

Same topic in other shifts

All General Solutions questions

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
5 Apr 2026, Shift 2 · Q23If $S=\left\{\theta \in [-\pi, \pi] : \cos\theta\cos\frac{5\theta}{2}=\cos 7\theta\cos\frac{7\theta}{2}\right\}$ , then n(S) is equal to…HardNumerical value
6 Apr 2026, Shift 1 · Q14Let $\mathrm{S}=\left\{\theta\in(-2\pi,2\pi):\cos\theta+1=\sqrt{3}\sin\theta\right\}$ . Then $\sum_{\theta\in \mathrm{S}}\theta$ is equal to:MediumSingle correct
2 Apr 2025, Shift 1 · Q3If $\theta\in[-2\pi, 2\pi]$ , then the number of solutions of $2\sqrt{2}\cos^2\theta+(2-\sqrt{6})\cos\theta-\sqrt{3}=0$ , is equal to :MediumSingle correct
2 Apr 2025, Shift 2 · Q13If $\theta \in \left[-\frac{7\pi}{6}, \frac{4\pi}{3}\right]$ , then the number of solutions of…MediumSingle correct
3 Apr 2025, Shift 1 · Q10The number of solutions of the equation $2x + 3\tan x = \pi$ , $x \in [-2\pi, 2\pi] - \left\{\pm\frac{\pi}{2}, \pm\frac{3\pi}{2}\right\}$ 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.