AP EAMCET · Maths · Binomial Theorem
If the ratio of the terms equidistant from the middle term in the expansion of \((1+x)^{12}\) is \(\frac{1}{256}(x \in N)\) then sum of all the terms of the expansion \((1+x)^{12}\) is
- A \(4^{12}\) or \(6^{12}\)
- B \(3^{12}\) or \(5^{12}\)
- C \(6^{12}\) or \(7^{12}\)
- D \(12^{12}\)
Answer & Solution
Correct Answer
(B) \(3^{12}\) or \(5^{12}\)
Step-by-step Solution
Detailed explanation
Middle term \(\left(\frac{n}{2}+1\right)^{\text {th }}\) term i.e., \(7^{\text {th }}\) term \(T_7={ }^{12} C_6 x^6\) Now, \(\frac{{ }^{12} C_8 x^4}{{ }^{12} C_4 x^8}=\frac{1}{256} \Rightarrow x=4\) and…
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