CAT (QA) PYQs

For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which $\{(a_1)^1 \times (a_2)^2 \times \ldots \times (a_{20})^{20}\} < \{a_{21} \times a_{22} \times \ldots \times a_{(20+m)}\}$, is

If the population of a town is $p$ in the beginning of any year then it becomes $3+2 p$ in the beginning of the next year. If the population in the beginning of $2019$ is $1000$ then the population in the beginning of $2034$ will be

Let $a_1, a_2, a_3, a_4, a_5$ be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with $2a_3$.

If the sum of the numbers in the new sequence is $450$, then $a_5$ is