JEE Mains · Maths · STD 11 - 7. binomial theoram
If the fourth term in the binomial expansion of \(\left(\sqrt{\frac{1}{x^{1+\log _{10} x}}}+x^{\frac{1}{12}}\right)^{6}\) is equal to \(200\), and \(x > 1\), then the value of \(x\) is
- A \(10^4\)
- B \(100\)
- C \(10^3\)
- D None of these
Answer & Solution
Correct Answer
(D) None of these
Step-by-step Solution
Detailed explanation
\(^{6} \mathrm{C}_{3} \times x^{- \frac{3}{2}(1+\operatorname{log} x)} \cdot \mathrm{x}^{\frac{1}{4}}=200\) \(x^{\frac{1}{4}- \frac{3}{2}(1+\operatorname{log} x)}=10\) \(\Rightarrow \frac{1}{4}-\frac{3}{2}\left(1+\log _{10} x\right) \cdot \log _{10} x=1\)…
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