IPMAT Indore 2024 (MCQ) PYQs

There are numbers $a_1, a_2, a_3, \ldots, a_n$ each of them being $+1$ or $-1$. If it is known that $a_1 a_2 + a_2 a_3 + a_3 a_4 + \ldots a_{n-1} a_n + a_n a_1 = 0$ then

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

Let $S_n$ be sum of the first $n$ terms of an A.P. If $S_5 = S_9$, what is the ratio of $a_3 : a_5$