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JEE Mains · Maths · STD 11 - 7. binomial theoram
The coefficient of \(x^{-5}\) in the binomial expansion of \({\left( {\frac{{x + 1}}{{{x^{\frac{2}{3}}} - {x^{\frac{1}{3}}} + 1}} - \frac{{x - 1}}{{x - {x^{\frac{1}{2}}}}}} \right)^{10}}\) where \(x \ne 0, 1\) , is
- A \(1\)
- B \(4\)
- C \(-4\)
- D \(-1\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
\({\left[ {\frac{{\left( {{x^{1/3}} + 1\left( {{x^{2/3}}} \right) + {x^{1/3}} + 1} \right)}}{{\left( {{x^{2/3}} - {x^{\sqrt 3 }} + 1} \right)}} - \frac{{(\sqrt x - 1(\sqrt x ) + 1)}}{{\sqrt x (\sqrt x - 1)}}} \right]^{10}}\) \( = {({x^{1/3}} + 1 - 1 - 1/{x^{1/2}})^{10}}\)…
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