In the expansion of $\left(x + \frac{1}{x}\right)^{2n} $, what is the (n + 1)th term from the end (when arranged in descending powers of x) ?

How many terms are there in the expansion of $\rm \left(\frac{a^2}{b^2}+\frac{b^2}{a^2}+2\right)^{21}$ where a ≠ 0, b ≠ 0? 

Consider the expansion of (1 + x)ⁿ. Let p, q, r and s be the coefficients of first, second, nth and (n + 1)th terms respectively. What is (ps + qr) equal to?

What is the sum of the coefficients of first and last terms in the expansion of (1 + x)²ⁿ, where n is a natural number?