List of top Computer Science & Information Technology Questions on Functions asked in AP PGECET

What is the coefficient of $ x^{10} $ in the expansion of the generating function $$ \left( 1 + x + x^2 + x^3 + \cdots \right)^2? $$
What is the generating function for $ a_r $, where $ a_r $ is the number of integral solutions for the equation $$ a + b + c = r \quad \text{with} \quad 0 \leq a, b, c \leq 3? $$
What is the value of $ f(5) $ where $ f(n) $ is recursively defined as $ f(n) = n \times (n-1) $ for $ n>1 $ and $ f(1) = 2 $?