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# The resistance of a wire is $5\: ohm \: at\: 50^{\circ}C$ and $6\: ohm \: at\: 100^{\circ}C$. The resistance of the wire at $0^{\circ}C$ will be

$\begin {array} {1 1} (A)\;1\: ohm & \quad (B)\;2\: ohms \\ (C)\;3\: ohms & \quad (D)\;4\: ohms \end {array}$

$\large\frac{5}{6}$ $= \large\frac{1+50 \alpha}{1+ 100 \alpha}$
we get $\alpha=1/200$
substituting for $\alpha$ in
$5 = R_0( 1+ \alpha \times 50)$  we get
$R_0=4$
Ans : (D)

edited Sep 10, 2014