JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 7 April 2025, Shift 1, Maths Q1

Question 1 of 75 in this shift, Maths question 1 of 25, Section A.

If for

\theta \in \left[-\frac{\pi}{3}, 0\right]

, the points

(x, y) = \left(3\tan\left(\theta+\frac{\pi}{3}\right), 2\tan\left(\theta+\frac{\pi}{6}\right)\right)

lie on

xy + \alpha x + \beta y + \gamma = 0

, then

\alpha^2 + \beta^2 + \gamma^2

is equal to

(1) $75$ Official answer
(2) $80$
(3) $96$
(4) $72$

Official answer

Option 1

NTA final key.

Chapter: Trigonometric Functions
Topic: Trigonometric Identities
Idea tested: Elimination of Trigonometric Parameters

Same topic in other shifts

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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.