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 ______. [8 Apr 2024 Shift 1]

JEE Main 8 Apr 2024 Shift 1 Solved Paper

Section: Mathematics

Question : 26 of 90

Marks: +1, -0

If the range of f(θ)=‌

sin‌4θ+3cos2θ

sin‌4θ+cos2θ

,θ∈ℝ is [α,β], then the sum of the infinite G.P., whose first term is 64 and the common ratio is ‌

, is equal to ______.

[8 Apr 2024 Shift 1]

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