After what period (in seconds) will the identifiers generated by a host wrap around?
IDs generated per second by a host = 1000
Total IDs possible = $2^{50}$
So, in $\frac{2^{50}}{1000}$ seconds, a host will exhaust all IDs, and will have to wrap-around. This number is too high, and not in the options.
So, assume that the question means: every host generates 1000 IDs per second, after what time a random host will accidentally produce a duplicate ID?
IDs generated per second by a host = 1000
Total IDs possible = $2^{50}$
Total hosts possible with IPv4 = $2^{32}$ since IPv4 is a 32 bit address.
So, when all the hosts generate 1000 IDs each second, in how much time would they exhaust the total IDs =
$\frac{2^{50}}{2^{32}*1000}$; which is roughly equal to
$\frac{2^{50}}{2^{32}*2^{10}}$
$= \frac{2^{50}}{2^{42}}$
$= 2^{8}$