The resistance of a wire is $5\mathrm{\Omega }$ at 50^oC and $6\mathrm{\Omega }$ at 100^oC . The resistance of the wire at 0^oC will be

From , R_r = R₀(1+$\mathrm{\alpha }$t), we get
5 = R₀(1 + 50$\mathrm{\alpha }$) ---------------------------(i)
and 6 = R₀(1 + 100$\mathrm{\alpha }$)
$\therefore \frac{5}{6}=\frac{1+50\mathrm{\alpha }}{1+100\mathrm{\alpha }}\Rightarrow \mathrm{\alpha }=\frac{1}{200}$
putting the value of $\mathrm{\alpha }$ in (i) , we get
$\begin{array}{l}5=\left({\mathrm{R}}_0+50\times 1/200\right)=\frac{1}{200}\\ \Rightarrow {\mathrm{R}}_0=4\mathrm{\Omega }\end{array}$