At room temperature $\left(27^{\circ} \mathrm{C}\right)$, the resistance of a heating element is $50 \Omega$. The temperature coefficient of the material is $2.4 \times 10^{-4}{ }^{\circ} \mathrm{C}^1$. The temperature of the element, when its resistance is $62 \Omega$, is $\qquad$ ${ }^{\circ} \mathrm{C}$.
JEE MAIN 2024, Diffcult
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$mathrm{R}=\mathrm{R}_0(1+\alpha \Delta \mathrm{T})$
$62=50\left\lfloor 1+2.4 \times 10^{-4} \Delta \mathrm{T}\right\rfloor$
$\Delta \mathrm{T}=1000^{\circ} \mathrm{C}$
$\Rightarrow \mathrm{T}-27^{\circ}=1000^{\circ} \mathrm{C}$
$\mathrm{T}=1027^{\circ} \mathrm{C}$
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