NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

The coefficient of x 6 in the expansion of 1 + x + x 2 6 is

Options

A131
B141
C151
D167

Correct answer

B. 141

Step-by-step solution

Coefficient of x 6 in 1 + x 1 + x 6 = 1 + C 1 x 6 1 + x + C 2 x 6 2 1 + x 2 + C 3 6 x 3 1 + x 3 + C 4 6 x 4 1 + x 4 + C 5 6 x 5 1 + x 5 + C 6 6 x 6 1 + x 6 ⇒ The coefficient of x 6 is C 3 6 × C 3 3 + C 4 6 × C 2 4 + C 5 6 × C 1 5 + C 6 6 × C 0 6 = 6 × 5 × 4 3 × 2 × 1 + 6 × 5 2 × 4 × 3 2 + 6 × 5 + 1 × 1 = 20 + 90 + 30 + 1 = 141

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