If c₀, c₁, c₂, ......, c₁₅ are the binomial coefficients in the expansion

of (1 + x)¹⁵, then the value of $${{{c_1}} \over {{c_0}}} + 2{{{c_2}} \over {{c_1}}} + 3{{{c_3}} \over {{c_2}}} + ... + 15{{{c_{15}}} \over {{c_{14}}}}$$ is

The number of irrational terms in the expansion of $${\left( {{3^{{1 \over 8}}} + {5^{{1 \over 4}}}} \right)^{84}}$$ is

The number (101)¹⁰⁰ $$-$$ 1 is divisible by

If n is even positive integer, then the condition that the greatest term in the expansion of (1 + x)ⁿ may also have the greatest coefficient, is