JEE Main 2025 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 8 April 2025, Shift 2, Maths Q3

Question 3 of 75 in this shift, Maths question 3 of 25, Section A.

Let

A = \left\{\theta \in [0, 2\pi] : 1 + 10\,\mathrm{Re}\left(\frac{2\cos\theta + i\sin\theta}{\cos\theta - 3i\sin\theta}\right) = 0\right\}

. Then

\sum_{\theta \in A} \theta^2

is equal to

(1) $8\pi^2$
(2) $\frac{27}{4}\pi^2$
(3) $6\pi^2$
(4) $\frac{21}{4}\pi^2$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: General Solutions
Idea tested: Cosine General Solution

Same topic in other shifts

All General Solutions questions

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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

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.