Let 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 $\alpha+i\beta$, $i=\sqrt{-1}$. Let p and q be the maximum and the minimum values of $\alpha+\beta$ respectively. Then $p+q$ is equal to :

JEE Main 2025 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 4 April 2025, Shift 2, Maths Q3

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

Let the product of

\omega_1=(8+i)\sin\theta+(7+4i)\cos\theta

and

\omega_2=(1+8i)\sin\theta+(4+7i)\cos\theta

\alpha+i\beta

i=\sqrt{-1}

. Let p and q be the maximum and the minimum values of

\alpha+\beta

respectively. Then

p+q

is equal to :

(1)130Official answer
(2)140
(3)150
(4)160

Official answer

Option 1

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Trigonometric Identities
Idea tested: Extrema of Quadratic Trigonometric Forms

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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.