Question

Assertion :Statement I: The function $f\left(x\right)=x\sin x$ and $f^{\prime }\left(x\right)=x\cos x+\sin x$ are both non-periodic. Reason: Statement II: The derivative of a differentiable non-periodic function is a non-periodic function.

• A. Statement I is true,Statement II is also true; Statement II is the correct explanation of Statement I
• B. Statement I is true,Statement II is also true; Statement II is not the correct explanation of Statement I
• C. Statement I is true,Statement II is false
• D. Statement I is false,Statement II is true

Answer 1

The correct option is C Statement I is true,Statement II is false

Reason is false:
Assertion:
If we take example of $x+\sin x$,

it is non-periodic whereas its derivative $1+\cos x$ is periodic.