IPMAT Indore (SA) PYQs

The number of terms common to both the arithmetic progressions $2, 5, 8, 11, ..., 179$ and $3, 5, 7, 9, ..., 101$ is

The sum of a given infinite geometric progression is 80 and the sum of its first two terms is 35. Then the value of $n$ for which the sum of its first $n$ terms is closest to 100, is

Let $S$ denote an arithmetic progression whose first term is either 132 or 158, and the common difference is an even integer less than 10. If the $n^{\text{th}}$ term of $S$ is 174, then the number of possible distinct values of $n$ is ___