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JEE Main202228 Jul 2022Evening ShiftMathematicsBinomial TheoremActual

If 1 + 2 + C 1 49 + C 2 49 + … . + C 49 49 C 2 50 + C 4 50 + … . . + C 50 50 is equal to 2 n . m , where m is odd, then n + m is equal to _____ .

Correct answer

0

Step-by-step solution

Let I = 1 + 1 + C 0 49 + C 1 49 + … + C 49 49 C 2 50 + C 4 50 + … + C 50 50 As C 0 49 + C 1 49 + … + C 49 49 = 2 49 and C 0 50 + C 2 50 + … + C 50 50 = 2 49 ⇒ C 2 50 + C 4 50 + … . + C 50 50 = 2 49 - 1 ∴   I = 1 + 2 49 + 1 2 49 - 1 = 2 98 Now comparing I = 2 n m we get, m = 1 and n = 98 So, m + n = 99

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