List of top Mathematics Questions on Real Analysis asked in IIT JAM MA

Find the radius of convergence of the series
\[ \sum_{n=0}^{\infty} \frac{\binom{n}{6}^2}{(2n)!} x^n \]

Find the number of automorphisms of the cyclic group $\mathbb{Z}_n$ for $n = 30$.

Determine whether the sequence \[ a_n = 1 - (-1)^n + \frac{1}{n} \] is convergent or divergent.

Let $G = P(N)$, where the operation is
\[ A \Delta B = A \cup B - A \cap B \] Which of the following is true?

Find the radius of convergence of the series \[ \sum_{n=0}^{\infty} \frac{(n!)^2}{(2n)!}\, x^n. \]