Question

Statement 1: $f:R\to R,f\left(x\right)=\sin x$ is a one-one function.
Statement 2: The period of $\sin x$ is $2\pi$ and $2\pi$ is an irrational number

• A. Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1
• B. Both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1
• C. STATEMENT 1 is TRUE and STATEMENT 2 is FALSE
• D. STATEMENT 1 is FALSE and STATEMENT 2 is TRUE

Answer 1

The correct option is D STATEMENT 1 is FALSE and STATEMENT 2 is TRUE

$f\left(x\right)=\sin \left(x\right)$ is not a one-to-one function as
$f\left(a\right)=f\left(b\right)$
Implies $a=b$ and $a=\pi -b$.
However the period of $f\left(x\right)$ is $2\pi$ which is an irrational number.