Question

In the expansion of \((2^\frac{1}{4}+3^{-\frac{1}{4}})^n\), the ratio of \(5^{th}\) term from start and \(5^{th}\) term form end is \(\sqrt 6 : 1\) , then find \(3^{rd}\) term

• A. 30\(\sqrt 3\)
• B. 60\(\sqrt 3\)
• C. 30
• D. 50\(\sqrt 3\)

Answer 1

The Correct Option is B

\(\frac{^nC_4 (2^\frac{1}{4})^{n-4}(3^{\frac{-1}{4}})^4}{^nC_4 (2^\frac{-1}{4})^{n-4}(3^{\frac{1}{4}})^4}\) = \(\sqrt 6\)
\((\frac{2^\frac{1}{4}}{3^\frac{-1}{4}})^{(n-8)}\) = \(\sqrt 6\)
\((6)^\frac{n-8}{4}\) = \(\sqrt 6\)
\(n-8=2\)
\(n=10\)
\(T_3 = {^{10}}C_2(2^{\frac{1}{4}})^8 (3^\frac{-1}{4})^2\)
\(= {^{10}}C_2\times(\sqrt2)^4\times\frac{1}{\sqrt3} = 60\sqrt3\)

So, the correct answer is (B): \(60\sqrt 3\)