AP EAMCET · Maths · Binomial Theorem
In the expansion of \((1+x)^n\) the coefficients of \(p\) th and \((p+1)\) th terms are respectively \(p\) and \(q\), then \(p+q\) is equal to
- A \(n\)
- B \(n+1\)
- C \(n+2\)
- D \(n+3\)
Answer & Solution
Correct Answer
(B) \(n+1\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} T_p & ={ }^n C_{p-1}=p \\ T_{p+1} & ={ }^n C_p=q \\ \therefore \quad \frac{p}{q} & =\frac{{ }^n C_{p-1}}{{ }^n C_p} \\ \Rightarrow \quad \frac{p}{q} & =\frac{p}{n-p+1} \Rightarrow p+q=n+1 \end{aligned} \]
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