Binomial Theorem And Its Simple Applications Question 141
Question: If $ x\in {1,2,3….9} $ and $ f_{n}(x)=x,x,x…x $ (n digits), then $ f^2_{n}(3)+f_{n}(2)= $
Options:
A) $ 2f_{2n}(1) $
B) $ f^2_{n}(1) $
C) $ f_{2n}(1) $
D) $ -f_{2n}(4) $
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ f_{n}(3)=333…3 $ (n digits) and $ f_n^{2}(3)=999…9 $ (n digits), $ f_{n}(2)=222…2 $ (n digits)
$ \therefore $ $ f_n^{2}(3)+f_{n}(2)=12…2221((n+1)digits) $
Answer cannot be (1), (3) or (4)
$ f_{n}(1)=111…1 $ (n digits)
$ \therefore $ $ f_n^{2}(3)(1)=122…21((n+1)digits). $
BETA
