Let n $$\ge$$ 5 be an integer. If 9ⁿ $$-$$ 8n $$-$$ 1 = 64$$\alpha$$ and 6ⁿ $$-$$ 5n $$-$$ 1 = 25$$\beta$$, then $$\alpha$$ $$-$$ $$\beta$$ is equal to

If the constant term in the expansion of

$${\left( {3{x^3} - 2{x^2} + {5 \over {{x^5}}}} \right)^{10}}$$ is 2^k.l, where l is an odd integer, then the value of k is equal to:

The term independent of x in the expansion of

$$(1 - {x^2} + 3{x^3}){\left( {{5 \over 2}{x^3} - {1 \over {5{x^2}}}} \right)^{11}},\,x \ne 0$$ is :

If

$$\sum\limits_{k = 1}^{31} {\left( {{}^{31}{C_k}} \right)\left( {{}^{31}{C_{k - 1}}} \right) - \sum\limits_{k = 1}^{30} {\left( {{}^{30}{C_k}} \right)\left( {{}^{30}{C_{k - 1}}} \right) = {{\alpha (60!)} \over {(30!)(31!)}}} } $$,

where $$\alpha$$ $$\in$$ R, then the value of 16$$\alpha$$ is equal to