CAT (QA) PYQs

Consider two sets $A = \{2, 3, 5, 7, 11, 13\}$ and $B = \{1, 8, 27\}$. Let $f$ be a function from $A$ to $B$ such that for every element $b$ in $B$, there is at least one element $a$ in $A$ such that $f(a) = b$. Then, the total number of such functions $f$ is

If $f(x + y) = f (x) f (y)$ and $f(5) = 4$, then $f (10) - f (-10)$ is equal to

For any real number x, let [x] be the largest integer less than or equal to x. If $\sum_{n=1}^{N} [\frac{1}{5} + \frac{n}{25}] = 25$ then N is