Binomial Theorem And Its Simple Applications Question 2
Question: The value of x in the expression $ {{[x+{x^{{\log_{10}}}}^{(x)}]}^{5}} $ , if the third term in the expansion is 10,00,000 [Roorkee 1992]
Options:
A) 10
B) 11
C) 12
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- $ T_3={{,}^{5}}C_2.x^{2}{{({x^{{\log_{10}}x}})}^{3}}=10^{6} $ Put $ ^{5}C_2=10,[\because {\log_{10}}10=1] $ . If $ x=10 $ ,then $ 10^{3}{{.10}^{2.1}}=10^{5} $ is satisfied.
Hence x =10.
BETA
