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JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Binomial Theorem

Number of integral terms in the expansion of

{7^{(\frac{1}{2})} + 1 1^{(\frac{1}{6})}}^{824}

is equal to ______.

Answer: 138

Solution

General term:

t_{r + 1} = (r 824) 7^{(824 - r) /2} 1 1^{r /6}

.

Both exponents are integers exactly when

r

is a multiple of

6

(which also makes

824 - r

even automatically).

r = 0, 6, 12, \dots, 822

gives

\frac{822}{6} + 1 = 138

integral terms.

JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Integer answer

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