JEE Mains · Maths · STD 11 - 7. binomial theoram
If the fourth term in the Binomial expansion of \({\left( {\frac{2}{x} + {x^{{{\log }_e}x}}} \right)^6}(x > 0)\) is \(20\times 8^7,\) then a value of \(x\) is
- A \(8^3\)
- B \(8^{-2}\)
- C \(8\)
- D \(8^2\)
Answer & Solution
Correct Answer
(D) \(8^2\)
Step-by-step Solution
Detailed explanation
\({T_4} = {T_{3 + 1}} = \left( {\frac{6}{3}} \right){\left( {\frac{2}{x}} \right)^3} \cdot {\left( {{x^{{{\log }_8}x}}} \right)^3}\) \(20 \times 8^{7}=\frac{160}{x^{3}} \cdot x^{3000} x\) \(8^{6}=x^{\log _{2} x}-3\) \(2^{18}=x^{\log _{2} x-3}\)…
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