If $0 < \alpha < \beta < \frac{\pi}{2}$, then

$\frac{\tan \alpha}{\tan \beta} < \frac{a}{\beta}$

$\frac{\tan \alpha}{\tan \beta} > \frac{\alpha}{\beta}$

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JEE • MATHEMATICS • INCREASING & DECREASING

Increasing & decreasing practice · Medium

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Analyzing +4 | -1

0 < \alpha < \beta < \frac{\pi}{2}

, then

View answer and explanation

Correct option: B

\frac{\tan \beta}{\tan \alpha} > \frac{\alpha}{\beta}

The correct answer is B (

\frac{{\tan \beta}}{{\tan \alpha}} > \frac{{\alpha}}{{\beta}}

) because the function

f(x) = x \tan x

is increasing on

(0, \pi/2)

92 Medium

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Analyzing +4 | -1

f(x)=x e^{x(1-x)}

, then

f(x)

View answer and explanation

Correct option: A

increasing in

[-1 / 2,1]

Option A is correct because the function's derivative is non-negative in the interval [-1/2, 1], indicating an increasing function.

Revision notes and key takeaways

Review INCREASING & DECREASING in your textbook or class notes, then use this set to check your understanding.

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