CAT (QA) PYQs

The natural numbers are divided into groups as (1), $(2,3,4),(5,6,7,8,9), \ldots .$. and so on. Then, the sum of the numbers in the 15th group is equal to

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

The average of all 3-digit terms in the arithmetic progression $38, 55, 72, \dots$, is