JEE Mains · Maths · STD 11 - 7. binomial theoram
If the coefficient of \(x ^{10}\) in the binomial expansion of \(\left(\frac{\sqrt{x}}{5^{\frac{1}{4}}}+\frac{\sqrt{5}}{x^{\frac{1}{3}}}\right)^{60}\) is \(5^{ k } l\), where \(l, k \in N\) and \(l\) is coprime to \(5\) , then \(k\) is equal to
- A \(5\)
- B \(6\)
- C \(7\)
- D \(8\)
Answer & Solution
Correct Answer
(A) \(5\)
Step-by-step Solution
Detailed explanation
\(\left(\frac{\sqrt{x}}{5^{1 / 4}}+\frac{\sqrt{5}}{x^{1 / 3}}\right)^{60}\) \(T_{r+1}={ }^{60} C_{r}\left(\frac{x^{1 / 2}}{5^{1 / 4}}\right)^{60-r}\left(\frac{5^{1 / 2}}{x^{1 / 3}}\right) r\) \(={ }^{60} C_{r} 5 \frac{3 r-60}{4} x \frac{180-5 r}{6}\)…
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