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The coefficient of the 2 m + 1 t h and 4 m + 5 t h terms in the expansion of 1 + x 100 are equal, then the value of m 2 is equal to

Correct answer

8

Step-by-step solution

T 2 m + 1 = C 100 2 m x 2 m T 4 m + 5 = C 100 4 m + 4 x 4 m + 4 Coefficients of T 2 m + 1 and T 4 m + 5 are equal ⇒ C 100 2 m = C 100 4 m + 4 ⇒ 2 m + 4 m + 4 = 100 ⇒ 6 m = 96 ⇒ m = 16 Hence, m 2 = 8

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