JEE Main Maths · Trigonometric Functions

General Solutions in JEE Main

Name: General Solutions: JEE Main previous year questions
Creator: Lumi

General Solutions (Maths, Trigonometric Functions) came 17 times in 16 of the 42 JEE Main shifts Lumi analysed, across 11 distinct ideas. 11 of them came in 2024–26; it was last asked in 2026.

Questions: 17; in 16 shifts
Ideas asked: 11; 2 asked more than once
Numerical answer: 3; 18% of its questions
Pattern: Asked most years; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 1Medium 11Hard 5

Format

Single correct14 Q
Numerical value3 Q

Ideas inside the topic

11 ideas

Quadratic Substitution in Trigonometry6 Q
Graphical Root Counting for Mixed Equations2 Q
Boundedness and Range Analysis1 Q
Cosine General Solution1 Q
Domain Restricted Solutions1 Q
Linear Combination Solution1 Q
Modulus Trigonometric Equations1 Q
Multiple Angle Equating1 Q
Product-to-Sum Transformation1 Q
Sine General Solution1 Q
Sum-to-Product Factorization1 Q

Where it sits

Part of Trigonometric Functions, which had 41 questions in all. General Solutions accounts for 41% of them. In Lumi's JEE taxonomy it belongs to Trigonometry.

Some questions sit in other chapters too: Complex Numbers and Quadratic Equations.

Every question

All 17 General Solutions questions

Newest first, each with its options and official answer.

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
3 Apr 2025, Shift 2 · Q13The number of solutions of the equation…HardSingle correct
7 Apr 2025, Shift 2 · Q14The number of solutions of the equation $\cos 2\theta\cos\frac{\theta}{2}+\cos\frac{5\theta}{2}=2\cos^3\frac{5\theta}{2}$ in…HardSingle correct
8 Apr 2025, Shift 2 · Q3Let…HardSingle correct
29 Jan 2024, Shift 1 · Q20If $\alpha,-\frac{\pi}{2}<\alpha<\frac{\pi}{2}$ is the solution of $4\cos\theta+5\sin\theta=1$ , then the value of $\tan\alpha$ isMediumSingle 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
25 Jul 2022, Shift 1 · Q18The number of solutions of $|\cos x|=\sin x$ , such that $-4\pi\le x\le4\pi$ is :EasySingle correct
24 Jun 2022, Shift 1 · Q19Let $S=\left\{\theta\in[-\pi, \pi]-\left\{\pm\frac{\pi}{2}\right\}: \sin\theta\tan\theta+\tan\theta=\sin 2\theta\right\}$ . If…MediumSingle 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
29 Jun 2022, Shift 1 · Q25The number of solutions of the equation $2\theta - \cos^2\theta + \sqrt{2} = 0$ in $\mathbf{R}$ is equal to ____________.MediumNumerical value
25 Jul 2021, Shift 1 · Q80The sum of all values of $x$ in $[0,2\pi]$ , for which $\sin x+\sin2x+\sin3x+\sin4x=0$ , is equal to :MediumSingle correct