AP EAMCET · Maths · Binomial Theorem
The coefficient of \(x^4\) in the expansion of \(\frac{1}{(1-x)(1-2 x)(1-3 x)}\) is
- A 602
- B 301
- C \(\frac{601}{2}\)
- D 302
Answer & Solution
Correct Answer
(B) 301
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {Since, } \frac{1}{(1-x)(1-2 x)(1-3 x)} \\ & =(1-x)^{-1}(1-2 x)^{-1}(1-3 x)^{-1} \\ & =\left(1+x+x^2+x^3+x^4\right)\left(1+2 x+4 x^2+8 x^3+16 x^4\right) \\ & \left(1+3 x+9 x^2+27 x^3+81 x^4\right) \end{aligned}\) [Expand till \(x^4\)-term because…
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