Answer: Option A
$$\eqalign{
& {\text{The}}\,{\text{given}}\,{\text{expression}}\,{\text{is}}\,{\text{in}}\,{\text{GP}}\,{\text{series}} \cr
& S = {3^0} + {3^1} + {3^2} + {3^3} + ........ + {3^{200}} \cr
& S = {\frac{{ {{3^0} \times \left( {{3^{201}} - 1} \right)} }}{{ {3 - 1} }}} \cr
& S = \frac{{ {{3^{201}} - 1} }}{2} \cr
& S = \frac{{ {{{\left( {{3^3}} \right)}^{67}} - {1^3}} }}{2} \cr
& S = \frac{{ {{{27}^{67}} - {1^3}} }}{2} \cr} $$
Since, (An - Bn) is divisible by (A - B), So, (2767 - 13) is divisible by (27 - 1) = 26
Hence, Expression is also divisible by 13 as it is divisible by 26
Thus given expression is divisible by 13 so the remainder will be 0