d
We know that 

\(R_{t}=R_{0}(1+\alpha t)\)

where \(R_{t}\) is the resistance of the wire at \(t\,^{o} \mathrm{C}\)

\(R_{0}\) is the resistance of the wire at \(0\,^{o} \mathrm{C}\)

and \(\alpha\) is the temperature coefficient of resistance. 

\(\Rightarrow R_{50}=R_{0}(1+50 \alpha)\)         ......\((i)\)

\(R_{100}=R_{0}(1+100 \alpha)\)       .......\((ii)\)

From \((i),\) \(R_{50}-R_{0}=50 \alpha R_{0}\)        .....\((iii)\)

From \((ii),\) \(R_{100}-R_{0}=100 \alpha R_{0}\)        ....\((iv)\)

Dividing \((iii)\) by \((iv),\) we get

\(\frac{R_{50}-R_{0}}{R_{100}-R_{0}}=\frac{1}{2}\)

Here, \(R_{50}=5\, \Omega\) and \(R_{100}=6\, \Omega\)

\(\therefore \frac{5-R_{0}}{6-R_{0}}=\frac{1}{2}\)

or, \(6-R_{0}=10-2 R_{0}\) or, \(R_{0}=4\, \Omega\)