NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

The number of integral terms in the expansion of 5 1 6 + 7 1 9 1824 is

Options

A84
B96
C91
D102

Correct answer

D. 102

Step-by-step solution

T r + 1 = 1824 C r 5 1 6 1824 - r 7 1 9 r = 1824 C r 5 1824 - r 6 7 r 9 = 1824 C r 5 304 - r 6 7 r 9 Both r 6 and r 9 are integers, if r is a multiple of 18 ⇒ r = 0,18,36 , . . . . . . , 181 8 Let, the number of terms be n ⇒ 1818 = 0 + n - 1 18 ⇒ n = 102 .

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