JEE Mains · Maths · STD 11 - 7. binomial theoram
A possible value of \(^{\prime}x^{\prime}\), for which the ninth term in the expansion of \(\left\{3^{\log _{3} \sqrt{25^{x-1}+7}}+3^{\left(-\frac{1}{8}\right) \log _{3}\left(5^{x-1}+1\right)}\right\}^{10}\) in the increasing powers of \(3^{\left(-\frac{1}{8}\right) \log _{3}\left(5^{x-1}+1\right)}\) is equal to \(180\) , is:
- A \(2\)
- B \(1\)
- C \(0\)
- D \(-1\)
Answer & Solution
Correct Answer
(B) \(1\)
Step-by-step Solution
Detailed explanation
\({ }^{10} \mathrm{C}_{8}\left(25^{(x-1)}+7\right) \times\left(5^{(x-1)}+1\right)^{-1}=180\) \(\Rightarrow \frac{25^{x-1}+7}{5^{(x-1)}+1}=4\) \(\Rightarrow \frac{t^{2}+7}{t+1}=4\) \(\Rightarrow t=1,3=5^{x-1}\) \(\Rightarrow x-1=0 \text { (one of the possible value) }\)…
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