Binomial Theorem And Its Simple Applications Question 127
Question: If the $ 6^{th} $ term in the expansion of $ {{( \frac{1}{{x^{8/3}}}+x^{2}{\log_{10}}x )}^{8}} $ is 5600, then x equals
Options:
A) 1
B) $ {\log_{e}}10 $
C) 10
D) x does not exist
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] It is given that $ 6^{th} $ term in the expansion of $ {{( \frac{1}{{x^{8/3}}}+x^{2}{\log_{10}}x )}^{8}} $
$ ^{8}C_5{{(x^{2}log_{10}x)}^{5}}{{( \frac{1}{{x^{8/3}}} )}^{3}}=5600 $
Or $ 56x^{10}{{(log_{10}x)}^{5}}\frac{1}{x^{8}}=5600 $ Or $ x^{2}{{(log_{10}x)}^{5}}=100 $ Or
$ x^{2}{{(log_{10}x)}^{5}}=10^{2}{{(log_{10}10)}^{5}} $ Or $ x=10 $
BETA
