JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 31 August 2021, Shift 2, Maths Q78

Question 78 of 90 in this shift, Maths question 18 of 30, Section A.

The number of solutions of the equation

32^{\tan^2 x}+32^{\sec^2 x} = 81

0 \le x \le \frac{\pi}{4}

is :

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

Official answer

Option 2

NTA final key.

Chapter: Trigonometric Functions
Topic: General Solutions
Idea tested: Quadratic Substitution in Trigonometry

Same idea in other shifts

Asked 12× in all

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 2 · Q13The number of solutions of the equation…HardSingle correct
1 Feb 2024, Shift 2 · Q20The number of solutions of the equation $4\sin^2x-4\cos^3x+9-4\cos x=0$ ; $x\in[-2\pi,2\pi]$ is :HardSingle correct
31 Jan 2024, Shift 2 · Q2The number of solutions, of the equation $e^{\sin x}-2e^{-\sin x}=2$ , is :MediumSingle correct
10 Apr 2023, Shift 2 · Q2Let $S = \left\{x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) : 9^{1-\tan^2 x} + 9^{\tan^2 x} = 10\right\}$ and…MediumSingle correct
11 Apr 2023, Shift 1 · Q16The number of elements in the set $S = \{\theta \in [0, 2\pi] : 3\cos^4\theta - 5\cos^2\theta - 2\sin^6\theta + 2 = 0\}$ isMediumSingle correct
26 Jul 2022, Shift 1 · Q18Let $\mathrm{S} = \{\theta \in [0,\ 2\pi] : 8^{2\sin^2\theta} + 8^{2\cos^2\theta} = 16\}$ . Then…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.