2018-II-37

Ans: D
$\begin{array}{cl}
& \dfrac{2i^{12} + 3i^{13} + 4i^{14} + 5i^{15} + 6i^{16}}{1-i} \\
= & \dfrac{2i^{4\times 3} + 3i^{4\times 3 + 1} + 4i^{4\times 3 + 2} + 5i^{4\times 3 + 3} + 6i^{4\times 4}}{1 – i} \\
= & \dfrac{2 + 3i + 4i^2 + 5i^3 + 6}{1 – i} \\
= & \dfrac{2 + 3i – 4 – 5i + 6}{1 – i} \\
= & \dfrac{4 – 2i}{1 – i} \\
= & \dfrac{4-2i}{1-i} \times \dfrac{1+i}{1+i} \\
= & \dfrac{4 + 4i – 2i – 2i^2}{1 – i^2} \\
= & \dfrac{4 + 2 + 2i}{2} \\
= & \dfrac{6 + 2i}{2} \\
= & 3 + i
\end{array}$

Therefore, the real part is $3$.