Gravitation-3

at a very large distance(d=∞) body is at rest and thus relative velocity should be zero...therefore option a) and d) can't be the answer...
to choose between b and c simply dimensional analysis would suffice...so the answer i think is c....

We can do this using the concept of reduced mass.

M=(m1*m2)/(m1+m2)
Now conserving energy....

G*m1*m2 /d = 1/2*M*v²

Solving for v, we get option c as the correct answer.