$$\text { Number of integral terms in the expansion of }\left\{7^{\left(\frac{1}{2}\right)}+11^{\left(\frac{1}{6}\right)}\right\}^{824} \text { is equal to _________. }$$
Answer (integer)
138
Solution
<p>General term in expansion of $\left((7)^{1 / 2}+(11)^{1 / 6}\right)^{824}$ is $$\mathrm{t}_{\mathrm{r}+1}={ }^{824} \mathrm{C}_{\mathrm{r}}(7)^{\frac{824-\mathrm{r}}{2}}(11)^{\mathrm{r} / 6}$$</p>
<p>For integral term, $r$ must be multiple of 6.</p>
<p>Hence $r=0,6,12, ....... 822$</p>
About this question
Subject: Mathematics · Chapter: Binomial Theorem · Topic: Binomial Expansion
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