COMEDK · Maths · 7. Binomial Theorem
The coefficient of \(x^{24}\) in the expansion of \(\left(1-x^5\right)^{10}\) is
- A 0
- B \({ }^{10} C_5\)
- C \({ }^{10} C_4\)
- D 110
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { } \because \text { General term of }(x+y)^n={ }^n C_r(x)^{n-r}(y)^r \\ & \Rightarrow \quad T_{r+1}={ }^{10} C_r(1)^{10-r}\left(-x^5\right)^r={ }_{}^{10} C_r(-1)^r(x)^{5 r} \\ & \therefore \quad 5 r=24 \Rightarrow r=4.8 \end{aligned}\) \(\therefore r\)…
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