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

If the coefficients of x² and x³ in the expansion of (3 + ax)⁹ be same, then the value of a is