JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 April 2026, Shift 1, Maths Q11

Question 11 of 75 in this shift, Maths question 11 of 25, Section A.

\sin\left(\frac{\pi}{18}\right)\sin\left(\frac{5\pi}{18}\right)\sin\left(\frac{7\pi}{18}\right)=K

, then the value of

\sin\left(\frac{10K\pi}{3}\right)

is :

(1) $\frac{\sqrt3+1}{2\sqrt2}$ Official answer
(2) $\frac{\sqrt3-1}{\sqrt2}$
(3) $\frac{\sqrt3}{2}$
(4) $\frac12$

Official answer

Option 1

NTA final key.

Chapter: Trigonometric Functions
Topic: Trigonometric Identities
Idea tested: Sine Product Identity with 60 Degrees

Same topic in other shifts

All Trigonometric Identities questions

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4 Apr 2026, Shift 1 · Q23If $A=\frac{\sin 3^\circ}{\cos 9^\circ}+\frac{\sin 9^\circ}{\cos 27^\circ}+\frac{\sin 27^\circ}{\cos 81^\circ}$ and…MediumNumerical value
5 Apr 2026, Shift 1 · Q6Let $\tan A$ , $\tan B$ , where $A, B \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ , be the roots of the quadratic equation…MediumSingle correct
8 Apr 2026, Shift 2 · Q22If…HardNumerical value
4 Apr 2025, Shift 2 · Q3Let the product of $\omega_1=(8+i)\sin\theta+(7+4i)\cos\theta$ and $\omega_2=(1+8i)\sin\theta+(4+7i)\cos\theta$ be $\alpha+i\beta$ ,…HardSingle correct
7 Apr 2025, Shift 1 · Q1If for $\theta \in \left[-\frac{\pi}{3}, 0\right]$ , the points…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.