If \( f(x) \) satisfies the relation P \[ f\left(\frac{5 x-3 y}{2}\...

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If \( f(x) \) satisfies the relation
P
\[
f\left(\frac{5 x-3 y}{2}\right)=\frac{5 f(x)-3 f(y)}{2} \forall x, y \in R \text {. }
\]
W and \( f(0)=3 \) and \( f^{\prime}(0)=2 \), then the period of \( \sin (f(x)) \) is
(1) \( 2 \pi \)
(2) \( \pi \)
(3) \( 3 \pi \)
(4) \( 4 \pi \)
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