JEE Main 2025 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 3 April 2025, Shift 2, Maths Q13

Question 13 of 75 in this shift, Maths question 13 of 25, Section A.

The number of solutions of the equation

\left(4 - \sqrt{3}\right)\sin x - 2\sqrt{3}\cos^2 x = -\frac{4}{1+\sqrt{3}},\ x \in \left[-2\pi, \frac{5\pi}{2}\right]

(1)5Official answer
(2)6
(3)3
(4)4

Official answer

Option 1

NTA final key.

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

Same idea in other shifts

Asked 6× 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
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
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 42 of the 174 JEE Main shifts held from 2017 to 2026.