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A pendulum clock loses \( 12 \mathrm{~s} \) a day if the temperature is \( 40^{\circ} \mathrm{C} \) and gains \( 4 \mathrm{~s} \) a day if the temperature is \( 20^{\circ} \mathrm{C} \). The temperature at which the clock will show correct time and the co-efficient of linear expansion \( (\alpha) \) of the metal of the pendulum shaft are respectively
[JEE (Main) 2016]
(a) \( 60^{\circ} \mathrm{C} ; \alpha=1.85 \times 10^{-4} /{ }^{\circ} \mathrm{C} \)
(b) \( 30^{\circ} \mathrm{C} ; \alpha=1.85 \times 10^{-3} /{ }^{\circ} \mathrm{C} \)
(c) \( 55^{\circ} \mathrm{C} ; \alpha=1.85 \times 10^{-2} /{ }^{\circ} \mathrm{C} \)
(d) \( 25^{\circ} \mathrm{C} ; \alpha=1.85 \times 10^{-5} /{ }^{\circ} \mathrm{C} \)
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