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JEE Main202431 Jan 2024Morning ShiftMathematicsBinomial TheoremActual

In the expansion of 1 + x 1 − x 2 1 + 3 x + 3 x 2 + 1 x 3 5 , x ≠ 0 , the sum of the coefficient of x 3 and x - 13 is equal to ______

Correct answer

0

Step-by-step solution

Given, 1 + x 1 - x 2 1 + 3 x + 3 x 2 + 1 x 3 5 = 1 + x 2 1 - x x 3 + 3 x 2 + 3 x + 1 x 3 5 = 1 + x 2 1 - x 1 + x 3 x 3 5 = 1 + x 17 1 - x x 15 = 1 + x 17 x 15 - 1 + x 17 x 14 Now for coefficient of x 3 , we will find coefficient of x 18 in expansion of 1 + x 17 which is not possible and x 17 in expansion of - 1 + x 17 which will be - C 17 17 = - 1 And for coefficient of x - 13 we will coefficient of x 2 in expansion of 1 + x 17 which will be C 2 17 and coefficient of x in expansion of - 1 + x 17 which will be - C 1

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