By increasing the temperature, the specific resistance of a conductor and a semiconductor
A. Increasing for both
B. Decreases for both
C. Increases, decreases
D. Decreases, increases

Hint: Resistance of a material is defined as the obstruction to the path of current passing through that material. Specific resistance is defined as the resistance offered by a material of unit length and unit cross-sectional area.

Detailed step by step solution:
The specific resistance of a material is defined as the resistance offered by a unit length of that material across a unit cross-sectional area. It is also called resistivity of the material. The resistivity of a material depends on temperature by the following relation:
$\rho = {\rho _0}\left[ {1 + {\alpha _t}\left( {T - {T_0}} \right)} \right]$
where $\rho $ and ${\rho _0}$ represent the value of resistivity at temperatures $T$ and ${T_0}$ respectively and ${\alpha _t}$ is known as the temperature coefficient of resistivity which basically tells whether the resistivity of the material increases or decreases with temperature.
For conductors, the value of temperature coefficient is negative because in conductors, the resistance increases with temperature as thermal agitations increase, obstructing the motion of charge carriers. Therefore the resistivity of conductors decreases with temperature.
For semiconductors, the value of temperature coefficient is positive because in semiconductors, the resistance decreases with temperature as energy required to cross the band gap is readily available at higher temperature. Therefore the resistivity of semiconductors increases with temperature.
Hence, the correct answer is option C.

Note: In the terms of band theory, we can differentiate between conductors and semiconductors on the basis of the fact that for conductors, the valence band overlaps the conduction band and free motion of charge carriers is possible. For the case of semiconductors, there is a small gap between the conduction band and valence band which means that charge carriers can flow freely only when supplied some energy to cross the energy gap between valence band and conduction band.