Question

Assertion :

Let $f\left(x\right)=\sin x$

Statement I $f$ is not a polynomial function Reason: Statement II $n$th derivative of $f\left(x\right)$, w.r.t. $x$ is not a zero function for any positive integer $n$

• 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 A Statement I is true,Statement II is also true; Statement II is the correct explanation of Statement I

If $f\left(x\right)=a_0+a_{1}x+a_2{x}^2+...+a_n{x}^n,a_n\ne 0$
Then, $f^{n+1}\left(x\right)=0$, for all $x$ while any derivative of $\sin x$ is never a zero function.
Hence, $\sin x$ is not polynomial function.