JEE Mains · Maths · STD 11 - 7. binomial theoram
If \(\left(\frac{3^{6}}{4^{4}}\right) \mathrm{k}\) is the term, independent of \(\mathrm{x}\), in the binomial expansion of \(\left(\frac{\mathrm{x}}{4}-\frac{12}{\mathrm{x}^{2}}\right)^{12}\), then \(\mathrm{k}\) is equal to ...... .
- A \(22\)
- B \(11\)
- C \(55\)
- D \(99\)
Answer & Solution
Correct Answer
(C) \(55\)
Step-by-step Solution
Detailed explanation
\(\left(\frac{x}{4}-\frac{12}{x^{2}}\right)^{12}\) \(T_{r+1}=(-1)^{r} \cdot{ }^{12} C_{r}\left(\frac{x}{4}\right)^{12-\mathrm{r}}\left(\frac{12}{x^{2}}\right)^{r}\) \(T_{r+1}=(-1)^{r} \cdot{ }^{12} C_{r}\left(\frac{1}{4}\right)^{12-r}(12)^{r} \cdot(x)^{12-3 r}\) Term independent…
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