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Differentiation question

2024 · 30 Jan · Shift 2 · Q36

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PYQ Library
JEE Main
Mathematics
Differentiation
2024 · 30 Jan · Shift 2 · Q36

Differentiation question

2024 · 30 Jan · Shift 2 · Q36

JEE MainMathematicsDifferentiationMCQ+4 / −1

Let

f: \mathbb{R}-\{0\} \rightarrow \mathbb{R}

be a function satisfying

f\left(\frac{x}{y}\right)=\frac{f(x)}{f(y)}

for all

x, y, f(y) eq 0

. If

f^{\prime}(1)=2024

, then

A
$x f^{\prime}(x)+2024 f(x)=0$
B
$x f^{\prime}(x)-2023 f(x)=0$
C
$x f^{\prime}(x)-2024 f(x)=0$
D
$x f^{\prime}(x)+f(x)=2024$

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