COMEDK · Maths · 7. Binomial Theorem
The coefficient of \(x^{29}\) in the expansion of \(\left(1-3 x+3 x^2-x^3\right)^{15}\) is
- A \({ }^{45} C_{29}\)
- B \({ }^{45} C_{28}\)
- C \(-{ }^{45} C_{16}\)
- D \({ }^{45} C_{30}\)
Answer & Solution
Correct Answer
(C) \(-{ }^{45} C_{16}\)
Step-by-step Solution
Detailed explanation
\(\left(1-3 x+3 x^2-x^3\right)^{15}=\left[(1-x)^3\right]^{15}\) \(=(1-x)^{45}\) So, \(T_{r+1}={ }^{45} C_r(1)^{45-r}(-x)^r\) For coefficient of \(x^{29}\), put \(r=29\) Then, \(T_{30}={ }^{45} C_{29}(1)^{45-29}(-x)^{29}=-{ }^{45} C_{29} x^{29}\) Hence, coefficient of…
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