The intrinsic semiconductor becomes an insulator at
(A) $0^\circ C$
(B) 0K
(C) 300K
(D) $ - 100^\circ C$

Hint
The property of conduction of any material depends on the number of the free electrons present. At very high temperatures, the electrons break free of their bond and become free and can conduct heat or electricity. But at very low temperatures the electrons cannot jump from the valence band to the conduction band, and therefore, they behave as an insulator.

Complete step by step answer
Intrinsic semiconductors are also called doped or i-type semiconductors. They are pure semiconductors without the presence of any significant foreign species. There is a small energy gap in a semiconductor between the conduction band and the valence band, unlike the conductors where the two bands are overlapping. So the free electrons in an intrinsic semiconductor come from the electrons that leave the valence band and jump to the conduction band, due to thermal excitation, leaving behind holes in the valence band.
These electrons in the conduction band are responsible for the conduction of heat or electrical energy.
So, at a higher temperature, the electrons get the required amount of heat to cross the energy gap to move to the conduction band.
In room-temperature also, the intrinsic semiconductors have some electrons to conduct energy.
But at absolute zero temperature 0K , the electrons get no external thermal energy to cross the energy gap and move to the conduction band. Hence there are no electrons present in the conduction band at the absolute zero temperature. So, at 0K, the semiconductor behaves as an insulator.
Therefore, the correct answer is option (B).

Note
The intrinsic semiconductors conduct electricity or heat energy with the help of the electrons that move from the valence band to the conduction band leaving behind holes in the valence band. But in the case of extrinsic semiconductor, the electrons are provided by the foreign species that is used to dope the semiconductor.