A) 4
B) 8
C) 2
D) 6
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.
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