TS EAMCET · Maths · Binomial Theorem
If the coefficient of \(3^{\text {rd }}\) term from the beginning in the expansion of \(\left(a x^2-\frac{8}{b x}\right)^9\) is equal to the coefficient of \(3^{\text {rd }}\) term from the end in the expansion of \(\left(a x-\frac{2}{b x^2}\right)^9\) then the relation between \(a\) and \(b\) is
- A \(a b=-1\)
- B \(a b=1\)
- C \(a^5 b^5=-2\)
- D \(a^5 b^5=2\)
Answer & Solution
Correct Answer
(C) \(a^5 b^5=-2\)
Step-by-step Solution
Detailed explanation
Coefficient of \(3^{\text{rd}}\) term in \(\left(a x^2-\frac{8}{b x}\right)^9\): \(C_1 = \binom{9}{2} (a)^7 \left(-\frac{8}{b}\right)^2 = 36 \cdot \frac{64 a^7}{b^2}\) \(3^{\text{rd}}\) term from end in \(\left(a x-\frac{2}{b x^2}\right)^9\) is \((9-3+1)^{th} = 7^{th}\) term…
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