IIM-K (BMSAT) 2025 (QA) PYQs

Let $\dfrac{m}{n} = \dfrac{90^2+5 \times 90+4}{90^2+5\times 90+6} \times \dfrac{91^2+5\times 91+4}{91^2+5\times 91+6} \times .......\times \dfrac{98^2+5\times 98+4}{98^2+5\times 98+6}$ where m and n are co-primes.

What is the value of $|m - n|$ ?

It is given that the sequence {$x_n$} satisfies $x_1 = 0, x_{n+1} = x_n + 1 + 2√(1+x_n)$ for $n = 1,2,...$ Then $x_{31}$ is _______

A lift carrying 50 passengers from the ground floor of a 100-storeyed building is moving upwards. The lift stops at the 1st, 2nd, and 3rd floor, then skips the 4th floor, again stops at the 5th, 6th, and 7th, then skips the 8th floor, and so on. Passengers get discharged in a pattern. 2, 3, 3, 2, 3, 3..... On which floor does the lift become empty?