JEE Mains · Maths · STD 11 - 7. binomial theoram
If the coefficient of \(x ^7\) in \(\left(a x-\frac{1}{b x^2}\right)^{13}\) and the coefficient of \(x^{-5}\) in \(\left(a x+\frac{1}{b x^2}\right)^{13}\) are equal, then \(a^4 b^4\) is equal to :
- A \(44\)
- B \(22\)
- C \(11\)
- D \(33\)
Answer & Solution
Correct Answer
(B) \(22\)
Step-by-step Solution
Detailed explanation
\(T_{r+1}={ }^{13} C_r(a x)^{13-r}\left(-\frac{1}{b x^2}\right)^r\) \(={ }^{13} C_r(a)^{13-r}\left(-\frac{1}{b}\right)^r x^{13-3 r}\) \(1 3 - 3 r = 7 \Rightarrow r=2\) Coefficient of \(x^7={ }^{13} C_2(a)^{11} \cdot \frac{1}{b^2}\) In the other expansion…
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