Correct Answer - Option 3 : 0.2 MΩ

__Concept:__

Insulation resistance is inversely proportional to length of the cable

\(R = \frac{\rho }{{2\pi l}}\log \frac{{{r_2}}}{{{r_1}}}\)

\(\Rightarrow R \propto \frac{1}{l}\)

where,

r2 = radius of cable, r1 = radius of core conductor, l = length of cable

__Calculation:__

Given

l1 = 10 km, R1 = 1 MΩ, l2 = 50 km

\(\Rightarrow \frac{{{R_1}}}{{{R_2}}} = \frac{{{l_2}}}{{{l_1}}}\)

\(\Rightarrow \frac{{1 }}{{{R_2}}} = \frac{50}{10} \Rightarrow {R_2} = 0.2\;M{\rm{Ω }}\)