AP EAMCET · Maths · Binomial Theorem
The greatest term in the expansion of \((1+x)^{15}\), when \(x=\frac{1}{2}\) is
- A \(\frac{1}{32}{ }^{15} \mathrm{C}_5\)
- B \(\frac{1}{64}{ }^{15} \mathrm{C}_6\)
- C \(\frac{1}{32}{ }^{15} \mathrm{C}_6\)
- D \(\frac{1}{64}{ }^{15} \mathrm{C}_5\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{32}{ }^{15} \mathrm{C}_5\)
Step-by-step Solution
Detailed explanation
Let \(T_{r+1}\) and \(T_r\) denotes the \((\mathrm{r}+1)\) th and \(r\) th term in the expansion of \((1+x)^{15}\) \[ \therefore \quad T_{r+1}={ }^n C_r x^r \text { and } T_r={ }^n C_{r-1} x^{r-1} \text {, where } n=15 \] For greatest term in the expansion…
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