IIM-B (BBA-DBE) 2024 #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?

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