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

For any non-zero real number x, let $f(x) + 2 f(\frac{1}{x}) = 3x$. Then, the sum of all possible values of $x$ for which $f(x) = 3$, is

Let $f$ be a function such that $f(mn) = f(m)f(n)$ for every positive integers m and n. If $f(1)$, $f(2)$ and $f(3)$ are positive integers, $f(1) < f(2)$, and $f(24) = 54$, then $f(18)$ equals