NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

The coefficient of x 2 in the expansion of 1 - x + 2 x 2 x + 1 x 10 is

Options

A210
B714
C504
D240

Correct answer

B. 714

Step-by-step solution

The required coefficient is the coefficient of x 12 in 1 - x + 2 x 2 x 2 + 1 10 = 1 - x + 2 x 2 1 + 10 C 1 x 2 + 10 C 2 x 4 + . . . . . . . + 10 C 9 x 18 + x 20 Coefficient of x 12 is 1 × 10 C 6 + 2 × 10 C 5 = 10 × 9 3 × 8 × 7 4 × 3 × 2 + 2 × 10 × 9 3 × 8 2 × 7 × 6 5 × 4 × 3 × 2 = 210 + 50 4 = 71 4

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