JEE Mains · Maths · STD 11 - 7. binomial theoram
In the expansion of \(\left(\frac{\mathrm{x}}{\cos \theta}+\frac{1}{\mathrm{x} \sin \theta}\right)^{16},\) if \(\ell_{1}\) is the least value of the term independent of \(x\) when \(\frac{\pi}{8} \leq \theta \leq \frac{\pi}{4}\) and \(\ell_{2}\) is the least value of the term independent of \(x\) when \(\frac{\pi}{16} \leq \theta \leq \frac{\pi}{8},\) then the ratio \(\ell_{2}: \ell_{1}\) is equal to
- A \(1 : 8\)
- B \(1 : 16\)
- C \(8 : 1\)
- D \(16 : 1\)
Answer & Solution
Correct Answer
(D) \(16 : 1\)
Step-by-step Solution
Detailed explanation
\(\mathrm{T}_{\mathrm{r}+1}=16 \mathrm{C}_{\mathrm{r}}\left(\frac{\mathrm{x}}{\cos \theta}\right)^{16-\mathrm{r}}\left(\frac{1}{\mathrm{x} \sin \theta}\right)^{\mathrm{r}}\)…
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