A) 11
B) 10
C) 12
D) 13
Correct Answer: A
Solution :
\[^{n}{{C}_{5}}\,+{{\,}^{n}}{{C}_{6}}\,\,>\,{{\,}^{n+1}}{{C}_{5}}\] Þ \[^{n+1}{{C}_{6}}\,\,>\,{{\,}^{n+1}}{{C}_{5}}\] Þ \[\frac{(n+1)!}{6!\,.\,(n-5)!}\,.\,\frac{5!\,.\,(n-4)!}{(n+1)!}\,\,>\,\,1\] Þ \[\frac{(n-4)}{6}\,\,>\,\,1\] Þ \[n-4\,\,>\,\,6\,\,\,\,\Rightarrow \,\,\,n\,\,\,>\,\,10\] Hence according to options n = 11.
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