Question

Coefficient of x²⁵ in expansion of expression

$\sum_{r = 0}^{50}{50C_{r}}$ (2x – 3)^r(2 – x)^{50 – r} is :

• A. ⁵⁰C₂₅
• B. – ⁵⁰C₃₀
• C. ⁵⁰C₃₀
• D. – ⁵⁰C₂₅

Answer 1

Answer: (D)

– ⁵⁰C₂₅

Answer 2

$\sum_{r = 0}^{50}{50C_{r}}$ (2x – 3)^r(2 – x)^{50 – r}

= ((2 – x) + (2x – 3))⁵⁰

= (x –1)⁵⁰

= (1 –x)⁵⁰

= ⁵⁰C₀ – ⁵⁰C₁x ...........– ⁵⁰C₂₅ x²⁵ + ......

coefficient of x²⁵ is – ⁵⁰C₂₅