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JEE Main202125 Jul 2021Morning ShiftMathematicsBinomial TheoremActual

The ratio of the coefficient of the middle term in the expansion of ( 1 + x ) 20 and the sum of the coefficients of two middle terms in expansion of ( 1 + x ) 19 is .

Correct answer

1

Step-by-step solution

In 1 + x n , if n is even, then the middle term is n 2 + 1 t h term. So, Coefficient of middle term in ( 1 + x ) 20 = C 10 20 In 1 + x n , if n is odd, then the middle term is n + 1 2 t h   &   n + 3 2 t h term. So, Sum of Coefficient of two middle terms in ( 1 + x ) 19 = C 9 19 + C 10 19 So required ratio = C 10 20 C 9 19 + C 10 19 = C 10 20 C 10 20 = 1

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