The number of solutions of the equation $2\theta - \cos^2\theta + \sqrt{2} = 0$ in $\mathbf{R}$ is equal to ____________.

JEE Main 2022 · MathsNumerical answerNumerical valueMediumApplication

JEE Main 29 June 2022, Shift 1, Maths Q25

Question 25 of 90 in this shift, Maths question 25 of 30, Section B.

The number of solutions of the equation

2\theta - \cos^2\theta + \sqrt{2} = 0

\mathbf{R}

is equal to ____________.

Official answer

NTA final key (2022 Session 1).

Chapter: Trigonometric Functions
Topic: General Solutions
Idea tested: Graphical Root Counting for Mixed Equations

Same idea in other shifts

Asked 4× in all

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
5 Apr 2024, Shift 2 · Q21The number of solutions of $\sin^2 x + (2+2x-x^2)\sin x - 3(x-1)^2 = 0$ , where $-\pi \leq x \leq \pi$ , is ________.HardNumerical value
17 Mar 2021, Shift 2 · Q79The number of solutions of the equation $x+2\tan x=\frac{\pi}{2}$ in the interval $[0, 2\pi]$ is :MediumSingle 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.