What is the value of

C(51, 21) - C(51, 22) + C(51, 23) - C(51, 24) + C(51, 25) - C(51, 26) + C(51, 27) - C(51, 28) + C(51, 29) - C(51, 30) ?

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?