One $kg$ of copper is drawn into a wire of $1 \ mm$ diameter and a wire of $2 \ mm$ diameter. The resistance of the two wires will be in the ratio:

$A$ uniform metal wire carries a current of $2 \, A$ when an ideal cell of $3.4 \, V$ is connected across it. The wire has mass $8.92 \times 10^{-3} \, kg$, density $8.92 \times 10^3 \, kg/m^3$ and resistivity $1.7 \times 10^{-8} \, \Omega m$. Then the length of the wire is (in $m$)

The resistance of a conductor is $5\,\Omega$ at $50\,^{\circ}C$ and $6\,\Omega$ at $100\,^{\circ}C$. Its resistance at $0\,^{\circ}C$ is ................ $\Omega$.

$A$ certain wire has a resistance $R$. The resistance of another wire identical with the first except having twice its diameter is (in $,R$)

The resistance of a wire is $5\, \Omega$ at $50\, ^\circ C$ and $6\, \Omega$ at $100\, ^\circ C$. The resistance of the wire at $0\, ^\circ C$ will be .............. $\Omega$.

Choose the correct alternative:
$(a)$ Alloys of metals usually have (greater/less) resistivity than that of their constituent metals.
$(b)$ Alloys usually have much (lower/higher) temperature coefficients of resistance than pure metals.
$(c)$ The resistivity of the alloy manganin is nearly independent of/ increases rapidly with increase of temperature.
$(d)$ The resistivity of a typical insulator (e.g.,amber) is greater than that of a metal by a factor of the order of $(10^{22}/10^{23}).$