JEE Mains · Maths · STD 11 - 7. binomial theoram
Number of integral terms in the expansion of \(\left\{7^{\left(\frac{1}{2}\right)}+11^{\left(\frac{1}{6}\right)}\right\}^{824}\) is equal to ...........
- A \(142\)
- B \(138\)
- C \(421\)
- D \(456\)
Answer & Solution
Correct Answer
(B) \(138\)
Step-by-step Solution
Detailed explanation
General term in expansion of \(\left((7)^{1 / 2}+(11)^{1 / 6}\right)^{824}\) is \(t_{I+1}={ }^{824} C_{\mathrm{r}}(7)^{\frac{824-\mathrm{I}}{2}}(11)^{\mathrm{I} / 6}\) For integral term, \(r\) must be multiple of \(6\) . Hence \(r=0,6,12, \ldots \ldots \ldots........ .822\)
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