A.) Simply, when the temperature decreases the motion of electrons decreases and at 0K their motion tends to cease due. Thus, no conduction or free electrons are possible a 0K.

Therefore, option A is correct.

B.) At any temperature above 0K, in semiconductors the bonds are continuously breaking and producing electron-hole pairs. Thus, there will always be some conducting electrons present for conduction.

Therefore, option B is incorrect.

C.) As the temperature increases the heat energy tends to break the covalent bonds between the atoms which leads to the creation of free electrons. Thus, more temperature means more breaking of covalent bonds and more free electrons.

Therefore, option C is correct.

D.) The energy band gap of a conductors is very less than that of a semiconductor.

Therefore, option D is correct.