JEE Mains · Maths · STD 11 - 7. binomial theoram
Let the coefficients of third, fourth and fifth terms in the expansion of \(\left(x+\frac{a}{x^{2}}\right)^{n}, x \neq 0,\) be in the ratio \(12: 8: 3 .\) Then the term independent of \(x\) in the expansion, is equal to ...... .
- A \(5\)
- B \(3\)
- C \(4\)
- D \(6\)
Answer & Solution
Correct Answer
(C) \(4\)
Step-by-step Solution
Detailed explanation
\(T _{ r +1} ={ }^{ n } C _{ r }( x )^{ n - r }\left(\frac{ a }{ x ^{2}}\right)^{ r }\) \(={ }^{n} C _{ r } a ^{ r } x ^{ n -3 r }\) \({ }^{ n } C _{2} a ^{2}:{ }^{ n } C _{3} a ^{3}:{ }^{ n } C _{4} a ^{4}=12: 8: 3\) After solving \(n =6, a =\frac{1}{2}\) For term independent…
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