Coefficient of x11 in the expansion of (1 + x2)4 (1 + x3)7 (1 + x4)12 is

Engineering

Mathematics

Properties of Binomial Coefficients

Question

Coefficient of x¹¹ in the expansion of (1 + x²)⁴ (1 + x³)⁷ (1 + x⁴)¹² is

1120

1113

1051

1106

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Coefficient of x¹¹ in (1 + x²)⁴ (1 + x³)⁷ (1 + x⁴)¹²

= (1 + ⁴C₁ x² + ⁴C₂ x⁴ + ⁴C₃ x⁶ + ⁴C₄ x⁸ ) (1 + ⁷C₁ x³ + ⁷C₂ x⁶ + ⁷C₃ x⁹)(1 + ¹²C₁ x⁴ + ¹²C₂ x⁸)

Coefficient of x¹¹ is 1 × ⁷C₁ × ¹²C₂ + ⁴C₁ × ⁷C₃ × 1 + ⁴C₂ × ⁷C₁ × ¹²C₁ + ⁴C₄ × ⁷C₁

= 462 + 140 + 504 + 7 = 1113