CAT (QA) PYQs

The average of a non-decreasing sequence of $N$ numbers $a_{1}, a_{2}, \ldots, a_{N}$ is $300$. If $a_{1}$ is replaced by $6 a_{1}$, the new average becomes $400$. Then, the number of possible values of $a_{1}$ is

A lab experiment measures the number of organisms at $8$ am every day. Starting with $2$ organisms on the first day, the number of organisms on any day is equal to $3$ more than twice the number on the previous day. If the number of organisms on nth day exceeds one million, then the lowest possible value of $n$ is

The number of common terms in the two sequences: $15, 19, 23, 27,......., 415$ and $14, 19, 24, 29,........,464$ is