CAT (QA) PYQs

If $a_{1}, a_{2} \ldots .$. are in A.P., then, $\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\ldots .+\frac{1}{\sqrt{a_{n}}+\sqrt{a_{n+1}}}$ is equal to

Let $a_n$ and $b_n$ be two sequences such that $a_n = 13 + 6 (n - 1)$ and $b_n = 15 + 7 (n - 1)$ for all natural numbers $n$. Then, the largest three digit integer that is common to both these sequences, 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