Question

Assertion$\left(A\right)$: A sine function whose period is $\frac{2}{3}$ is $\pm \sin 3\pi x$.
Reason$\left(R\right)$: $\sin x$ is a periodic function with period $\frac{2\pi }{3}$.

• A. $A$ is true, $R$ is true
• B. $A$ is false, $R$ is true
• C. Both $A$ and $R$ are false
• D. $A$ is true, $R$ is false

Answer 1

Answer: (D)

$A$ is true, $R$ is false

Assertion (A) : A sine function whose period $\frac{2}{3}$ is $\pm \sin \left(3\pi x\right)$
Period of $\sin \left(3\pi x\right)=\frac{2\pi }{3\pi }=\frac{2}{3}\Rightarrow$ True.
Reason (R) : $\sin x$ is periodic function with period $\frac{2\pi }{3}$
Period of $sinx=2\pi \Rightarrow$ R is False
$\therefore$ $A$ is true, $R$ is false.