If $f(f(0)) = 0$,where $f(x) = x^2 + ax + b$ and $b \neq 0$,then $a + b =$

Let $f(x)$ be a differentiable function which satisfies the equation $f(xy) = f(x) + f(y)$ for all $x > 0, y > 0$. Then $f'(x)$ is equal to:

Let $\sum\limits_{k = 1}^{10} {f(a + k)} = 16(2^{10} - 1),$ where the function $f$ satisfies $f(x + y) = f(x)f(y)$ for all natural numbers $x, y$ and $f(1) = 2.$ Then the natural number $a$ is

If $f(x) = x - \frac{1}{x}$, $x \neq 0$, then $3f(x) =$

If $f(x + y) = f(x)f(y)$ for all $x$ and $y$ and $f(5) = 2$,$f'(0) = 3$,then $f'(5)$ will be

Let $f$ be a function defined on the set of all positive integers such that $f(xy) = f(x) + f(y)$ for all positive integers $x, y$. If $f(12) = 24$ and $f(8) = 15$,then the value of $f(48)$ is: