NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

The coefficient of x 9 in the expansion of 1 + x + x 2 + x 3 3 1 - x 6 is

Options

A– 7
B7
C9
D– 9

Correct answer

D. – 9

Step-by-step solution

Since, 1 + x + x 2 + x 3 = 1 - x 4 1 - x ⇒ 1 + x + x 2 + x 3 1 - x = 1 - x 4 ⇒ 1 + x + x 2 + x 3 3 1 - x 3 1 - x 3 = 1 - x 4 3 1 - x 3 = 1 - 3 x 4 + 3 x 8 - x 12 1 - 3 x + 3 x 2 - x 3 Coefficient of x 9 in this product is = 3 – 3 = – 9

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