NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

The coefficient of x 4 in the expansion of 1 + x + x 2 6 is

Options

A72
B90
C96
D112

Correct answer

B. 90

Step-by-step solution

1 + x 1 + x 6 = 1 + 6 C 1 x 1 + x + 6 C 2 x 2 1 + x 2 + 6 C 3 x 3 ( 1 + x ) 3 + 6 C 4 x 4 ( 1 + x ) 4 + . . . . Coefficient of x 4 is 6 C 2 + 6 C 3 . 3 + 6 C 4 = 6 × 5 2 + 6 × 5 × 4 3 × 2 × 3 + 6 × 5 2 = 15 + 60 + 15 = 9 0

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