JEE Main · 2021 · 16 Mar 2021 · Shift 1 · Sequences and Series

From the given set, $11,16,21,26$ are four terms of an arithmetic progression with common difference $5$, and $4,8,16,32$ are four terms of a geometric progression with ratio $2$.
Every term of the arithmetic progression leaves remainder $1$ on division by $5$, and the largest four digit number of that form is $9996$, so the progression is $11,16,21,\dots ,9996$. The geometric progression is $4,8,16,\dots ,8192$, since $4\cdot 2^{11}=8192$ while the next term has five digits.
The geometric terms are

and those leaving remainder $1$ on division by $5$ are $16$, $256$ and $4096$; each exceeds $11$ and is at most $9996$, so each belongs to the arithmetic progression as well.
The two series have $3$ terms in common.