If for some positive integer n, the coefficients
of three consecutive terms in the binomial
expansion of (1 + x)^{n + 5} are in the ratio
5 : 10 : 14, then the largest coefficient in this expansion is :

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 :