If ²⁰C₁ + (2²) ²⁰C₂ + (3²) ²⁰C₃ + ..... + (20² ) ²⁰C₂₀ = A(2^{$$\beta $$}), then the ordered pair (A, $$\beta $$) is equal to :

The coefficient of x¹⁸ in the product
(1 + x) (1 – x)¹⁰ (1 + x + x²)⁹ is :

The smallest natural number n, such that the coefficient of x in the expansion of $${\left( {{x^2} + {1 \over {{x^3}}}} \right)^n}$$ is ⁿC₂₃, is :

If the coefficients of x² and x³ are both zero, in the expansion of the expression (1 + ax + bx² ) (1 – 3x)¹⁵ in powers of x, then the ordered pair (a,b) is equal to :