🛠️ JEE➗ Maths

Let \(f: R -\{0\} \rightarrow R\) be a function satisfying \(f\left(\frac{x}{y}\right)=\frac{f(x)}{f(y)}\) for all \(x, …

Q1

Let \(f: R -\{0\} \rightarrow R\) be a function satisfying \(f\left(\frac{x}{y}\right)=\frac{f(x)}{f(y)}\) for all \(x, y, f(y) \neq 0\). If \(f^{\prime}(1)=2024\), then

[JEE Main 2024, 30 Jan (Shift 2)]

a

\(x f^{\prime}(x)+2024 f(x)=0\)

b

\(x f^{\prime}(x)-2024 f(x)=0\)

c

\(x f^{\prime}(x)-2023 f(x)=0\)

d

\(x f^{\prime}(x)+f(x)=2024\)

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