Let $f(x+y)=f(x)f(y)$ for all $x, y$ where $f(0) \neq 0$. If $f(5) = 2$ and $f'(0) = 3$,then $f'(5)$ is equal to

Let $f: N \rightarrow N$ be a function such that $f(x+y)=f(x)+f(y)+xy$ for every $x, y \in N$. If $f(1)=2$,then $\sum_{k=1}^{10} f(k)=$

If $f(10-x)=3x^2+4x-5$ and $f(x)=px^2+qx+r$,then find the value of $p+q+r$.

If $f: R \rightarrow R$ is defined as $f(x+y)=f(x)+f(y)$,$\forall x, y \in R$ and $f(1)=5$,then find the value of $\sum_{r=1}^n f(r)$.

Let $R$ be the set of all real numbers and let $f$ be a function from $R$ to $R$ such that $f(x) + (x + \frac{1}{2}) f(1 - x) = 1$,for all $x \in R$. Then $2 f(0) + 3 f(1)$ is equal to

Suppose $f$ is a function satisfying $f(x + y) = f(x) + f(y)$ for all $x, y \in \mathbb{N}$ and $f(1) = \frac{1}{5}$. If $\sum_{n=1}^m \frac{f(n)}{n(n+1)(n+2)} = \frac{1}{12}$,then $m$ is equal to $...............$.