Binomial Theorem And Its Simple Applications Question 33
Question: The remainder when $ 27^{40} $ is divided by 12 is
Options:
A) 3
B) 7
C) 9
D) 11
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] $ 27^{40}=3^{120} $
$ 3^{119}={{(4-1)}^{119}}={{,}^{119}}C_04^{119}-{{,}^{119}}C_14^{118} $
$ {{+}^{119}}C_24^{117}-{{,}^{119}}C_34^{116}+…+(-1) $
$ \therefore 3^{119}=4k-1 $
$ \therefore 3^{120}=12k-3=12(k-1)+9 $
$ \therefore $ The required remainder is 9.
BETA
