NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

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

Options

A144
B– 144
C154
D– 154

Correct answer

D. – 154

Step-by-step solution

1 - x 1 + 2 x 8 = 1 - 8 C 1 x 1 + 2 x + 8 C 2 x 2 1 + 2 x 2 - 8 C 3 x 3 1 + 2 x 3 + 8 C 4 x 4 1 + 2 x 4 . . . . . . . . . The coefficient of x 4 is 8 C 2 ⋅ 2 2 - 8 C 3 ⋅ 2 ⋅ 3 + 8 C 4 = 8 × 7 2 × 2 2 - 8 × 7 × 6 3 × 2 . 3.2 + 8 × 7 × 6 × 5 4 × 3 × 2 = 112 - 336 + 70 = – 154

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