NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

The coefficient of x 8 in the expansion of 1 + x + x 2 + x 3 4 is

Options

Correct answer

B. 31

Step-by-step solution

We have, 1 + x + x 2 + x 3 4 = 1 + x 1 + x 2 4 = 1 + x 4 1 + x 2 4 = 1 + 4 x + 6 x 2 + 4 x 3 + x 4 1 + 4 x 2 + 6 x 4 + 4 x 6 + x 8 Therefore, the coefficient of x 8 = 1 × 1 + 6 × 4 + 1 × 6 = 31

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