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Definite Integration question

2023 · Shift 1 · Q21

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PYQ Library
JEE Advanced
Mathematics
Definite Integration
2023 · Shift 1 · Q21

Definite Integration question

2023 · Shift 1 · Q21

JEE AdvancedMathematicsDefinite IntegrationMCQ+3 / −1

Let

f:(0,1) \rightarrow \mathbb{R}

be the function defined as

f(x)=\sqrt{n}

if

x \in\left[\frac{1}{n+1}, \frac{1}{n}\right)

where

n \in \mathbb{N}

. Let

g:(0,1) \rightarrow \mathbb{R}

be a function such that

\int\limits_{x^2}^x \sqrt{\frac{1-t}{t}} d t \lt g(x) \lt 2 \sqrt{x}

for all

x \in(0,1)

. Then

\lim\limits_{x \rightarrow 0} f(x) g(x)

A
does NOT exist
B
is equal to 1
C
is equal to 2
D
is equal to 3

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