IPMAT Indore 2021 (SA) PYQs

Suppose that a real-valued function $f(x)$ of real numbers satisfies $f(x + xy) = f(x) + f(xy$) for all real $x, y,$ and that $f(2020) = 1$. Compute $f(2021)$.

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?

The function $f(x) = \dfrac{x^3 - 5x^2 - 8x}{3}$ is