A) \[\frac{a}{10}=\frac{b}{11}=\frac{c}{42}\]
B) \[\frac{a}{11}=\frac{b}{22}=\frac{c}{42}\]
C) \[\frac{a}{10}=\frac{b}{11}=\frac{c}{21}\]
D) \[\frac{a}{11}=\frac{b}{22}=\frac{c}{21}\]
Correct Answer: B
Solution :
[b] \[a={}^{19}{{C}_{10}}\,\,\text{or}\,{{\,}^{19}}{{C}_{19}}\] \[b={}^{20}{{C}_{10}}\] \[c={}^{21}{{C}_{10}}\,\text{or}{{\,}^{21}}{{C}_{11}}\] \[\Rightarrow 1=\frac{a}{^{19}{{C}_{10}}}=\frac{b}{^{20}{{C}_{10}}}=\frac{c}{^{21}{{C}_{10}}}\] \[\Rightarrow \frac{a}{11}=\frac{b}{22}=\frac{c}{42}\]
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