$f(x)=ax^2+bx+c$ is an even function and $g(x)=px^3+qx^2+rx$ is an odd function. If $h(x)=f(x)+g(x)$ and $h(-2)=0$, then $8p+4q+2r=$

If a function $f: R \rightarrow R$ is defined by $f(x)=x^3-x$,then $f$ is

Let $f: R \rightarrow R$ be a function defined by
$f(x) = \begin{cases} x^2 \sin \left(\frac{\pi}{x^2}\right) & \text{if } x \neq 0 \\ 0 & \text{if } x = 0 \end{cases}$
Then which of the following statements is $TRUE$?

$A$ function $f$ from the set of natural numbers $\mathbb{N}$ to the set of integers $\mathbb{Z}$ is defined by $f(n) = \begin{cases} \frac{n-1}{2}, & \text{if } n \text{ is odd} \\ -\frac{n}{2}, & \text{if } n \text{ is even} \end{cases}$. The function $f$ is:

Function $f: R \rightarrow R$ defined by $f(x) = x^3$ is . . . . . . .

Let $A$ be the set of all $3 \times 3$ scalar matrices with real entries. If $f: A \rightarrow R$ is defined by $f(M) = \operatorname{det}(M)$ for all $M \in A$,then $f$ is