JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 10 April 2023, Shift 2, Maths Q2

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

Let

S = \left\{x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) : 9^{1-\tan^2 x} + 9^{\tan^2 x} = 10\right\}

and

\beta = \sum_{x \in S} \tan^2\left(\frac{x}{3}\right)

, then

\frac{1}{6}(\beta - 14)^2

is equal to

(1) $8$
(2) $16$
(3) $32$ Official answer
(4) $64$

Official answer

Option 3

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
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
29 Jun 2022, Shift 1 · Q24The number of elements in the set $S = \{\theta \in [-4\pi, 4\pi] : 3\cos^2 2\theta + 6\cos 2\theta - 10\cos^2\theta + 5 = 0\}$ is…MediumNumerical value

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.