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JEE Main202429 Jan 2024Morning ShiftMathematicsBinomial TheoremActual

If C 1 11 2 + C 2 11 3 + … . . + C 9 11 10 = n m with gcd ( n , m ) = 1 , then n + m is equal to

Correct answer

0

Step-by-step solution

Given, C 1 11 2 + C 2 11 3 + C 3 11 4 . . . . . . . . . + C 9 11 10 = m n Now, we know that, 1 + x 11 = C 0 11 + C 1 11 x + C 2 11 x 2 + . . . . . . . . . . C 11 11 x 11 Now integrating the above expression both side we get, ∫ 0 1 1 + x 11 d x = ∫ 0 1 C 0 11 + C 1 11 x + C 2 11 x 2 + . . . . . . . . . . C 11 11 x 11 d x ⇒ 1 + x 12 12 0 1 = C 0 11 x + C 1 11 x 2 2 + C 2 11 x 3 3 + . . . . . . . . . . C 11 11 x 12 12 0 1 ⇒ 2 12 - 1 12 = 1 + C 1 11 2 + C 2 11 3 + C 3 11 4 . . . . . . . . . + C 9 11 10 + 11 11 + 1 12 ​

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