Correct answer: (c) 20.21.2¹⁸

Explanation:

(1 + x)²⁰ = C₀ + C₁x + C₂x₂ + ....+C₂₀x²⁰

Differentiate w.r.t. x

20(1 + x)¹⁹ = C₁ + 2C₂x+ .....20C₂₀x¹⁵

Multiply by x

20x(1 + x)¹⁵ = C₁x + 2C₂x² + 20C₂₀x²⁰

Differentiate w.r.t x

20(1 + x)¹⁹ + 20.x.19(1 + x)¹⁸ = C₁ + 2²C₂x + 20²C₂₀x¹⁹

Put x = 1

20.2¹⁵ + 20.19.2¹⁸ = C₁ + 2²C₂ + ....+ 20²C₂₀

⟹ Σr².²⁰Cr = 20.2¹⁹ + 20.19.2¹⁸

= 2¹⁸.20[2 + 19]

= 20.21.2¹⁸