$f(x)=ax^2+bx+c$ 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 $8p+4q+2r=$

Let $A = \{1, 2, 3, 4, 5, 6\}$. The number of functions $f: A \to A$ such that $f(m) + f(n) = 7$ whenever $m + n = 7$ is:

If $f: R \to R$ is a continuous function such that $|f(x) - f(y)| \geqslant |e^x - e^y|$ for all $x, y \in R$,then $f(x)$ is:

Show that $f: N \rightarrow N$,given by $f(x) = \begin{cases} x+1, & \text{if } x \text{ is odd} \\ x-1, & \text{if } x \text{ is even} \end{cases}$ is both one-one and onto.

If the function $f: R \rightarrow R$ is defined by $f(x)=x|x|$,then:

Which of the following is an even function?