JEE Mains · Maths · STD 11 - 7. binomial theoram
In the expansion of \(\left(\sqrt[3]{2}+\frac{1}{\sqrt[3]{3}}\right)^n, \mathrm{n} \in \mathrm{N}\), if the ratio of \(15^{\text {at }}\) term from the beginning to the \(15^{\text {th }}\) term from the end is \(\frac{1}{6}\), then the value of \({ }^n C_3\) is:
- A 4060
- B 1040
- C 2300
- D 4960
Answer & Solution
Correct Answer
(C) 2300
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathrm{T}_{\mathrm{r}+1}={ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}\left(2^{1 / 3}\right)^{\mathrm{n}-\mathrm{r}}\left(\frac{1}{3^{1 / 3}}\right)^{\mathrm{r}} \\ & \mathrm{r}=14 \\ & \mathrm{~T}_{15}={ }^{\mathrm{n}} \mathrm{C}_{14}\left(2^{1 /…
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