Binomial Theorem And Its Simple Applications Question 84
Question: When $ 2^{301} $ is divided by 5, the least positive remainder is
Options:
A) 4
B) 8
C) 2
D) 6
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] $ 2^{4}\equiv 1(mod5)\Rightarrow {{(2^{4})}^{75}}\equiv {{(1)}^{75}}(mod5) $ i.e., $ 2^{300}\equiv 1(mod5)\Rightarrow 2^{300}\times 2\equiv (1.2)(mod5) $
$ \Rightarrow 2^{301}\equiv 2(mod5) $
$ \therefore $ Least positive remainder is 2.
BETA
