NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

The coefficient of x 10 in the expansion of 1 + x 15 + 1 + x 16 + 1 + x 17 + . . . + 1 + x 30 is

Options

A31 C 10 - 15 C 10
B31 C 11 - 15 C 11
C30 C 10 - 15 C 10
D31 C 10 - 14 C 11

Correct answer

B. 31 C 11 - 15 C 11

Step-by-step solution

Coefficient of x 10 in the given expansion = 15 C 10 + 16 C 10 + 17 C 10 + . . . 30 C 10 = 10 C 10 + 11 C 10 + . . . + 14 C 10 + 15 C 10 + . . . + 30 C 10 - 10 C 10 + 11 C 10 + . . . + 14 C 10 = 31 C 11 - 15 C 11

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