JEE Mains · Maths · STD 11 - 7. binomial theoram
If the sum of the coefficients of all the positive even powers of \(x\) in the binomial expansion of \(\left(2 x^{3}+\frac{3}{x}\right)^{10}\) is \(5^{10}-\beta \cdot 3^{9}\), then \(\beta\) is equal to
- A \(36\)
- B \(75\)
- C \(89\)
- D \(83\)
Answer & Solution
Correct Answer
(D) \(83\)
Step-by-step Solution
Detailed explanation
\(T_{r+1}={ }^{10} C_{r}\left(2 x^{3}\right)^{10-r}\left(\frac{3}{x}\right)^{r}\) \(={ }^{10} C_{r} 2^{10-r} 3^{r} x^{30-4 r}\) Put \(r=0,1,2, \ldots 7\) and we get \(\beta=83\)
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