A) 20
B) 30
C) 40
D) 50
Correct Answer: D
Solution :
[d] Given, \[\frac{^{n+1}{{C}_{r+1}}}{^{n}{{C}_{r}}}=\frac{11}{6}\]or \[\frac{\frac{n+1}{r+1}{{\times }^{n}}{{C}_{r}}}{^{n}{{C}_{r}}}=\frac{11}{6}\] Or \[6n+6=11r+11\]or \[6n-11r=5\] (1) Also, \[\frac{n{{C}_{r}}}{^{n-1}{{C}_{r-1}}}=\frac{6}{3}\,\,or\text{ }\frac{\frac{n}{r}{{\times }^{n-1}}{{C}_{r-1}}}{^{n-1}{{C}_{r-1}}}=\frac{6}{3}\,\,or\text{ }n=2r\] (2) From (1) and (2), r=5 and n=10, \[\therefore nr=50\]
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