Binomial Theorem And Its Simple Applications Question 31
Question: If the second term in the expansion $ {{( \sqrt[13]{a}+\frac{a}{\sqrt{{a^{-1}}}} )}^{n}} $ is $ 14{a^{5/2}} $ , then $ \frac{^{n}C_3}{^{n}C_2}= $
Options:
A) 4
B) 3
C) 12
D) 6
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] We have $ T_2=14,{a^{\frac{5}{2}}} $
$ \Rightarrow {{,}^{n}}C_1{{({a^{\frac{1}{13}}})}^{n-1}}({a^{\frac{3}{2}}})=14{a^{\frac{5}{2}}} $
$ \Rightarrow n{a^{\frac{n-1}{13}+\frac{3}{2}}}=14{a^{\frac{5}{2}}}\Rightarrow n=14 $
$ \Rightarrow \frac{^{n}C_3}{^{n}C_2}=\frac{^{14}C_3}{^{14}C_2}=\frac{12}{3}=4 $
BETA
