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JEE Main 26 February 2021, Shift 1, Maths Q89

Question 89 of 90 in this shift, Maths question 29 of 30, Section B.

\sqrt{3}(\cos^2 x)=(\sqrt{3}-1)\cos x+1

, the number of solutions of the given equation when

x\in\left[0,\frac{\pi}{2}\right]

is _________.

Official answer

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.