CAT (QA) PYQs

Let the $m^{th}$ and $n^{th}$ terms of a geometric progression be $3 / 4$ and $12$, respectively, where $m<n$. If the common ratio of the progression is an integer $r$, then the smallest possible value of $r+n-m$ is

If $\mathrm{x}_{0}=1, \mathrm{x}_{1}=2$, and $\mathrm{x}_{\mathrm{n}+2}=\frac{1+x_{n+1}}{x_{n}}, n=0,1,2,3 \ldots \ldots$., then $x_{2021}$ is

Consider a sequence of real number $x_1, x_2, x_3, ...$ such that $x_{n+1} = x_n + n - 1$ for all $n \ge 1$. If $x_1 = -1$ then $x_{100}$ is equal to