If the range of $f(\theta)=\frac{\sin^4\theta+3\cos^2\theta}{\sin^4\theta+\cos^2\theta}$, $\theta\in\mathbb{R}$ is $[\alpha,\beta]$, then the sum of the infinite G.P., whose first term is 64 and the common ratio is $\frac{\alpha}{\beta}$, is equal to ____________.

JEE Main 2024 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 8 April 2024, Shift 1, Maths Q21

Question 21 of 90 in this shift, Maths question 21 of 30, Section B.

If the range of

f(\theta)=\frac{\sin^4\theta+3\cos^2\theta}{\sin^4\theta+\cos^2\theta}

\theta\in\mathbb{R}

[\alpha,\beta]

, then the sum of the infinite G.P., whose first term is 64 and the common ratio is

\frac{\alpha}{\beta}

, is equal to ____________.

Official answer

NTA final key.

Chapter: Trigonometric Functions
Topic: Functions and Domain
Idea tested: Range of Quadratic Rational Functions

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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.