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

The term independent of x in the expansion of
$$\left( {{1 \over {60}} - {{{x^8}} \over {81}}} \right).{\left( {2{x^2} - {3 \over {{x^2}}}} \right)^6}$$ 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 :