The value of $$\sum\limits_{r = 0}^{20} {{}^{50 - r}{C_6}} $$ is equal to:

If the term independent of x in the expansion of
$${\left( {{3 \over 2}{x^2} - {1 \over {3x}}} \right)^9}$$ is k, then 18 k is equal to :

If the number of integral terms in the expansion
of (3^1/2 + 5^1/8)ⁿ is exactly 33, then the least value of n is :

Let $$\alpha $$ > 0, $$\beta $$ > 0 be such that
$$\alpha $$³ + $$\beta $$² = 4. If the maximum value of the term independent of x in
the binomial expansion of $${\left( {\alpha {x^{{1 \over 9}}} + \beta {x^{ - {1 \over 6}}}} \right)^{10}}$$ is 10k,
then k is equal to :