COMEDK · Maths · 7. Binomial Theorem
The coefficient of \(x^{20}\) in the expansion of \(\left(1+3 x+3 x^2+x^3\right)^{20}\) is
- A \({ }^{60} C_{40}\)
- B \({ }^{30} C_{20}\)
- C \({ }^{15} \mathrm{C}_2\)
- D None of these
Answer & Solution
Correct Answer
(A) \({ }^{60} C_{40}\)
Step-by-step Solution
Detailed explanation
The given expression is \((1 + 3x + 3x^2 + x^3)^{20}\). Observe that \(1 + 3x + 3x^2 + x^3 = (1 + x)^3\). Substituting this into the expression, we get \(((1 + x)^3)^{20} = (1 + x)^{60}\). The general term in the binomial expansion of \((1 + x)^{60}\) is given by…
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