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 \(-{ }^{45} C_{16}\)
- B \({ }^{45} C_{28}\)
- C \({ }^{45} C_{30}\)
- D \({ }^{45} C_{29}\)
Answer & Solution
Correct Answer
(A) \(-{ }^{45} C_{16}\)
Step-by-step Solution
Detailed explanation
The given expression is \(\left(1 - 3x + 3x^2 - x^3\right)^{15}\). Observe that \(1 - 3x + 3x^2 - x^3 = (1 - x)^3\). Substituting this into the expression, we get \(((1 - x)^3)^{15} = (1 - x)^{45}\). The general term in the binomial expansion of \((1 - x)^{n}\) is given by…
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