A) 4
B) 8
C) 2
D) 6
Correct Answer: C
Solution :
\[{{2}^{4}}\equiv 1\](mod 5);\[\Rightarrow {{({{2}^{4}})}^{75}}\equiv {{(1)}^{75}}\](mod5) i.e. \[{{2}^{300}}\equiv 1\] (mod 5) \[\Rightarrow {{2}^{300}}\times 2\equiv (1.2)\](mod 5) \[\Rightarrow {{2}^{301}}\equiv 2\] (mod 5), \[\therefore \] Least positive remainder is 2.
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