TS EAMCET · Maths · Binomial Theorem
If \(5|b| < 2|a|\). then the 4 th term in the expansion of \((2 a+5 b)^{-4}\) is
- A \({ }^4 C_3 2^5 5^3 a^5 b^3\)
- B \(-{ }^6 C_3 \frac{5^3}{2^7} \frac{b^3}{a^7}\)
- C \(-{ }^6 C_3 \frac{5^4}{2^8} \frac{b^4}{a^8}\)
- D \({ }^4 C_3 2^4 5^4 a^4 b^4\)
Answer & Solution
Correct Answer
(B) \(-{ }^6 C_3 \frac{5^3}{2^7} \frac{b^3}{a^7}\)
Step-by-step Solution
Detailed explanation
Given, binomial can be written as \((2 a)^{-4}\left(1+\frac{5 b}{2 a}\right)^{-4}\), where \(\left|\frac{5 b}{2 a}\right| < 1\) So, 4 th term will be \((2 a)^{-4}\left[\frac{(-4)(-5)(-6)}{3 !}\left(\frac{5 b}{2 a}\right)^3\right]\)…
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