IPMAT Indore 2020 (MCQ) PYQs

Let $A=\{1,2,3\}$ and $B=\{a, b\}$. Assuming all relations from set $A$ to set $B$ are equally likely, what is the probability that a relation from $A$ to $B$ is also a function?

If $f\left(x^{2}+f(y)\right)=x f(x)+y$ for all non-negative integers $x$ and $y$, then the value of $[f(0)]^{2}+f(0)$ equals _________.

Let $f$ and $g$ be two functions defined by $f(x) = |x + |x||$ and $g(x) = \frac{1}{x}$ for $x \neq 0$. If $f(a) + g(f(a)) = \frac{13}{6}$ for some real $a$, then the maximum possible value of$f(g(a))$ is: