IPMAT Indore (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 $3^{\text {rd }}, 14^{\text {th }}$ and $69^{\text {th }}$ terms of an arithmetic progression form three distinct and consecutive terms of a geometric progression. If the next term of the geometric progression is the $n^{\text {th }}$ term of the arithmetic progression, then $n$ equals ________.

The terms of a geometric progression are real and positive. If the $p$-th term of the progression is $q$ and the $q$-th term is $p$, then the logarithm of the first term is