The resistivity of alloys is $\rho_{\text{alloy}}$ and the resistivity of constituent metals is $\rho_{\text{metal}}$. Then,usually:

The resistance of a wire is $R$. It is bent at the middle by $180^o$ and both the ends are twisted together to make a shorter wire. The resistance of the new wire is

$A$ uniform wire of resistance $R$ is uniformly compressed along its length,until its radius becomes $n$ times the original radius. Now,the resistance of the wire becomes:

This question contains statement-$1$ and statement-$2$. Of the four choices given after the statements,choose the one that best describes the two statements.
statement-$1$: The temperature dependence of resistance is usually given as $R=R_{0}(1+\alpha \Delta t)$. The resistance of a wire changes from $100 \; \Omega$ to $150 \; \Omega$ when its temperature is increased from $27^{\circ} C$ to $227^{\circ} C$. This implies that $\alpha=2.5 \times 10^{-3} /^{\circ} C$.
statement-$2$: $R=R_{0}(1+\alpha \Delta t)$ is valid only when the change in the temperature $\Delta t$ is small and $\Delta R=(R-R_{0}) << R_{0}$.

If the length of a wire is increased by $0.1\%$,what is the percentage increase in its resistance (in $\%$)?

Dimensions of a block are $1 \, cm \times 1 \, cm \times 100 \, cm$. If the specific resistance of its material is $3 \times 10^{-7} \, \Omega \cdot m$,the resistance between the square faces is: