Exam 2017 Chemistry question bank (Chemistry)

Let $a, b, c \in R$. If $f(x) = ax^2 + bx + c$ is such that $a + b + c = 3$ and $f(x + y) = f(x) + f(y) + xy$ for all $x, y \in R$,then $\sum_{n=1}^{10} f(n)$ is equal to:

If for $x \in \left( 0, \frac{1}{4} \right)$,the derivative of $\tan^{-1} \left( \frac{6x\sqrt{x}}{1 - 9x^3} \right)$ is $\sqrt{x} \cdot g(x)$,then $g(x)$ equals: