JEE Mains · Maths · STD 11 - 7. binomial theoram
If the greatest value of the term independent of \(^{\prime}x^{\prime}\) in the expansion of \(\left(x \sin \alpha+a \frac{\cos \alpha}{x}\right)^{10}\) is \(\frac{10 !}{(5 !)^{2}}\), then the value of \(' a^{\prime}\) is equal to:
- A \(2\)
- B \(-1\)
- C \(1\)
- D \(-2\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
\(T_{r+1}={ }^{10} C_{r}(x \sin \alpha)^{10-t}\left(\frac{a \cos \alpha}{x}\right)^{r}\) \(r=0,1,2, \ldots, 10\) \(T_{r+1}\) will be independent of \(x\) When \(10-2 r=0 \Rightarrow r=5\) \(T_{6}={ }^{10} C_{5}(x \sin \alpha)^{5} \times\left(\frac{a \cos \alpha}{x}\right)^{5}\)…
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