Binomial Theorem And Its Simple Applications Question 128
Question: if $ I{f^{n+1}}{C_{r+1}}{{:}^{n}}C_{r}{{:}^{n-1}}{C_{r-1}}=11:6:3 $ , then nr=
Options:
A) 20
B) 30
C) 40
D) 50
Show Answer
Answer:
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{nC_{r}}{^{n-1}{C_{r-1}}}=\frac{6}{3}or\frac{\frac{n}{r}{{\times }^{n-1}}{C_{r-1}}}{^{n-1}{C_{r-1}}}=\frac{6}{3}orn=2r $ (2) From (1) and (2), r=5 and n=10,
$ \therefore nr=50 $
BETA
