JEE Mains · Maths · STD 11 - 6. permutation and combination
If \(a, b\) and \(c\) are the greatest value of \(^{19} \mathrm{C}_{\mathrm{p}},^{20} \mathrm{C}_{\mathrm{q}}\) and \(^{21 }\mathrm{C}_{\mathrm{r}}\) respectively, then
- A \(\frac{a}{11}=\frac{b}{22}=\frac{c}{21}\)
- B \(\frac{\mathrm{a}}{10}=\frac{\mathrm{b}}{11}=\frac{\mathrm{c}}{21}\)
- C \(\frac{\mathrm{a}}{10}=\frac{\mathrm{b}}{11}=\frac{\mathrm{c}}{42}\)
- D \(\frac{a}{11}=\frac{b}{22}=\frac{c}{42}\)
Answer & Solution
Correct Answer
(D) \(\frac{a}{11}=\frac{b}{22}=\frac{c}{42}\)
Step-by-step Solution
Detailed explanation
\(a=^{19} \mathrm{C}_{10}, \mathrm{b}=^{20} \mathrm{C}_{10}\) and \(\mathrm{c}= ^{21} \mathrm{C}_{10}\) \(\Rightarrow \mathrm{a}=^{19} \mathrm{C}_{9}, \mathrm{b}=2\left(^{19} \mathrm{C}_{9}\right)\) and \(\mathrm{c}=\frac{21}{11}\left(^{20} \mathrm{C}_{10}\right)\)…
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