JEE MAIN - Mathematics (2024 - 30th January Morning Shift - No. 25)
$$\text { Number of integral terms in the expansion of }\left\{7^{\left(\frac{1}{2}\right)}+11^{\left(\frac{1}{6}\right)}\right\}^{824} \text { is equal to _________. }$$
Answer
138
Explanation
General term in expansion of $$\left((7)^{1 / 2}+(11)^{1 / 6}\right)^{824}$$ is $$\mathrm{t}_{\mathrm{r}+1}={ }^{824} \mathrm{C}_{\mathrm{r}}(7)^{\frac{824-\mathrm{r}}{2}}(11)^{\mathrm{r} / 6}$$
For integral term, $$r$$ must be multiple of 6.
Hence $$r=0,6,12, ....... 822$$
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