CAT (QA) PYQs

Let the $m^{th}$ and $n^{th}$ terms of a geometric progression be $3 / 4$ and $12$, respectively, where $m<n$. If the common ratio of the progression is an integer $r$, then the smallest possible value of $r+n-m$ is

Let both the series $a_1, a_2, a_3, \dots$ and $b_1, b_2, b_3 \dots$ be in arithmetic progression such that the common differences of both the series are prime numbers. If $a_5 = b_9$, $a_{19} = b_{19}$ and $b_2 = 0$, then $a_{11}$ equals

If $\mathrm{a}_{1}=\frac{1}{2 \times 5}, \mathrm{a}_{2}=\frac{1}{5 \times 8}, \mathrm{a}_{3}=\frac{1}{8 \times 11}$, then $\mathrm{a}_{1,}+\mathrm{a}_{2,}+\mathrm{a}_{3,}+\ldots . . \mathrm{a}_{100}$ is