The sum of the coefficients of all odd degree terms in the expansion of $$\left(x+\sqrt{x^3-1}\right)^5 +\left(x-\sqrt{x^3-1}\right)^5, x>1$$ is

$$\sum_\limits{\substack{i, j=0 \\ i \neq j}}^n{ }^n C_i{ }^n C_j$$ is equal to

The number of terms in the expansion of $${(1 + 5\sqrt {2x} )^9} + {(1 - 5\sqrt {2x} )^9}$$ is

If the sum of the coefficients in the expansion of (x + y)ⁿ is 1024, then the value of the greatest coefficient in the expansion is

$${{{C_1}} \over {{C_0}}} + 2{{{C_2}} \over {{C_1}}} + 3{{{C_3}} \over {{C_2}}} + 4{{{C_4}} \over {{C_3}}} + ....20{{{C_{20}}} \over {{C_{19}}}} = $$

The value of $${}^{47}{C_4} + \sum\limits_{r = 1}^5 {{}^{52 - r}{C_3}} $$ is equal to

The coefficient of x⁸ in the polynomial (x $$-$$ 1) (x $$-$$ 2) ..... (x $$-$$ 10)