If the magnitude of the coefficient of x⁷ in the expansion of $${\left( {a{x^2} + {1 \over {bx}}} \right)^8}$$, where a, b are positive numbers, is equal to the magnitude of the coefficient of x⁷ in the expansion of $${\left( {ax + {1 \over {b{x^2}}}} \right)^8}$$, then a and b are connected by the relation

If $${}^{16}{C_r} = {}^{16}{C_{r + 1}}$$, then the value of $${}^r{P_{r - 3}}$$ is

The coefficient of x^$$-$$10 in $${\left( {{x^2} - {1 \over {{x^3}}}} \right)^{10}}$$ is

If C₀, C₁, C₂, ......, C_n denote the coefficients in the expansion of (1 + x)ⁿ then the value of C₁ + 2C₂ + 3C₃ + ..... + nC_n is