NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

Number of integral terms in the expansion of 5 + 7 8 1024 is

Correct answer

129

Step-by-step solution

We have, T r = 1 = 1024 C r 5 1024 - r 2 7 r 8 This is an integer, if 1024 - r is an even number and r is a multiple of 8 i.e. when r is a multiple of 8 since 0 ≤ r ≤ 1024 The number of multiples of 8 which lies between 0 and 1024 is 1024 = 0 + n - 1 8 ⇒ n - 1 = 1024 8 = 128 ⇒ n = 129

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