IIM-B (BBA-DBE) 2025 #1 (QA) PYQs

Let $a_{1}, a_{2}, a_{3}$ be three distinct real numbers in geometric progression. If the equations $a_{1} x ^ 2 + 2a_{2}x + a_{3} = 0$ and $b_{1} x ^ 2 + 2b_{2}x + b_{3} = 0$ have a common root, then which of the following is necessarily true?

Given $(A = 2^{65})$ and $(B = 2^{64} + 2^{63} + 2^{62} + ... + 2^0)$, which of the following is true?

A person standing at the centre of an open ground first walks 32 meters towards the east, takes a right turn and walks 16 meters, takes another right turn and walks 8 meters, and so on. How far will the person be from the original starting point after an infinite number of such walks in this pattern?