AP EAMCET · Maths · Binomial Theorem
If the coefficients of \((2 r+6)^{\text {th }}\) and \((r-1)^{\text {th }}\) terms in the expansion of \((1+x)^{21}\) are equal, then the value of \(r=\)
- A \(7\)
- B \(5\)
- C \(6\)
- D \(8\)
Answer & Solution
Correct Answer
(C) \(6\)
Step-by-step Solution
Detailed explanation
General term of \((1+x)^{21}\) is \(\mathrm{T}_{\mathrm{r}+1}={ }^{21} \mathrm{C}_{\mathrm{r}} x^{\mathrm{r}}\) Coefficient of \((2 r+6)^{\text {th }}\) term \(=\) Coeff. of \((r-1)^{\text {th }}\) term \(\Rightarrow 2 r+5=21-(r-2) \Rightarrow \mathrm{r}=6\)
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