JEE Mains · Maths · STD 11 - 6. permutation and combination
\({ }^{n-1} C_r=\left(k^2-8\right){ }^n C_{r+1}\) if and only if :
- A \(2 \sqrt{2}<\mathrm{k} \leq 3\)
- B \(2 \sqrt{3}<\mathrm{k} \leq 3 \sqrt{2}\)
- C \(2 \sqrt{3}<\mathrm{k}<3 \sqrt{3}\)
- D \(2 \sqrt{2}<\mathrm{k}<2 \sqrt{3}\)
Answer & Solution
Correct Answer
(A) \(2 \sqrt{2}<\mathrm{k} \leq 3\)
Step-by-step Solution
Detailed explanation
\( { }^{n-1} C_r=(k^2-8){ }^n C_{T+1} \) \(\underbrace{r+1 \geq 0, \quad r \geq 0}_{r \geq 0}\) \(\frac{{ }^{n-1} C_{\mathrm{r}}}{{ }^n C_{\mathrm{r}+1}}=\mathrm{k}^2-8\) \(\frac{\mathrm{r}+1}{\mathrm{n}}=\mathrm{k}^2-8\) \(\Rightarrow \mathrm{k}^2-8>0\)…
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