CAT (QA) PYQs

On day one, there are $100$ particles in laboratory experiment. On day $n$, where $n \geq 2$, one out of every $n$ particles produces another particle. If the total number of particles in the laboratory experiment increases to $1000$ on day $m$, then $m$ equals.

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

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