JEE Mains · Maths · STD 11 - 7. binomial theoram
The coefficient of \(t^4\) in the expansion of \({\left( {\frac{{1 - {t^6}}}{{1 - t}}} \right)^3}\) is
- A \(12\)
- B \(15\)
- C \(10\)
- D \(14\)
Answer & Solution
Correct Answer
(B) \(15\)
Step-by-step Solution
Detailed explanation
\(\left(1-t^{6}\right)^{3}(1-t)^{-3}\) \(\left(1-t^{18}-3 t^{6}+3 t^{12}\right)(1-t)^{-3}\) \(\Rightarrow\) coefficient of \(t^{4}\) in \((1-t)^{-3}\) is \(^{3+1-1} C_{4}=^{6} C_{2}=15\)
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