If $f(1)=0$ and $f(n+1)-f(n)=5n$ for all $n \in N$,then $f(n)=$

If $f: R \rightarrow R$ is defined by $f(x+y)=f(x)+f(y)$ for all $x, y \in R$ and $f(1)=7$,then $\sum_{r=1}^n f(r)=$

If $f: R \setminus \{0\} \rightarrow R$ is such that $2 f(x) + f\left(\frac{1}{x}\right) = 4x$ and $S = \{x \in R : f(x) = f(-x)\}$,then the number of elements in $S$ is

If $f(0)=0, f(1)=1, f(2)=2$ and $f(x)=f(x-2)+f(x-3)$ for $x=3, 4, 5, \ldots$,then $f(9)$ is equal to

If $(f(x))^2 = f(x^2) + f(1)$ holds good,then find $f(x)$.

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 $\sum_{k=1}^{10} f(k)=$