TS EAMCET · Maths · Binomial Theorem
The expansion of \((a+x)^n\) contains 15 terms. When \(x=1\) the ratio of the neighbouring terms to the middle term in this expansion is 16 . Then the positive integral value of ' \(a\) ' is
- A 1
- B 3
- C 4
- D 2
Answer & Solution
Correct Answer
(C) 4
Step-by-step Solution
Detailed explanation
Since, given expansion contains 15 terms hence \(n=\) 14 for expansion \((1+a)^{14}\) \[ \begin{aligned} & \mathrm{T}_7=\mathrm{T}_{6+1}=14_{\mathrm{C}_6}(\mathrm{a})^8 \\ & \mathrm{~T}_{\mathrm{g}}=\mathrm{T}_{8+1}=14_{\mathrm{C}_8}(\mathrm{a})^6 \end{aligned} \] Ratio…
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