IPMAT Indore 2021 (MCQ) PYQs

Given that $1 + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + ... = \frac{\pi^2}{6}$, the value of $1 + \frac{1}{3^2} + \frac{1}{5^2} + \frac{1}{7^2} + ...$ is

Assume that all positive integers are written down consecutively from left to right as in 1234567891011...... The 6389th digit in this sequence is

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 _______