In a semiconductor,

The temperature dependence of resistances of $Cu$ and undoped $Si$ in the temperature range $300-400 \ K$ is best described by:

The energy band gap is maximum in

Match the List $I$ with List $II$:

$LIST$ $I$	$LIST$ $II$
$A$. Intrinsic Semiconductor	$I$. Fermi-level near conduction band
$B$. $n$-type semiconductor	$II$. Fermi-level at middle
$C$. $p$-type semiconductor	$III$. Fermi-level near valence band
$D$. Metals	$IV$. Fermi-level inside conduction band

Choose the correct answer from the options given below:

In a semiconductor,which of the following statements are correct?
$(i)$ There are no free electrons at $0\, K$.
$(ii)$ There are no free electrons at any temperature.
$(iii)$ The number of free electrons increases with temperature.
$(iv)$ The number of free electrons is less than that in a conductor.

Carbon, silicon, and germanium atoms have four valence electrons each. Their valence and conduction bands are separated by energy band gaps represented by $(E_g)_C$, $(E_g)_{Si}$, and $(E_g)_{Ge}$ respectively. Which one of the following relationships is true in their case?