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A beaker contains $200 \mathrm{gm}$ of water. The heat capacity of the beaker is equal to that of $20 \mathrm{gm}$ of water. The initial temperature of water in the beaker is $20^{\circ} \mathrm{C}$. If $440 \mathrm{gm}$ of hot water at $92^{\circ} \mathrm{C}$ is poured in it, the final temperature (neglecting radiation loss) will be nearest to
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$68^{\circ} \mathrm{C}$
Heat lost by hot water $=$ Heat gained by cold water in beaker + Heat absorbed by beaker
$\begin{aligned} & \Rightarrow 440(92-\theta)=200 \times(\theta-20)+20 \times(\theta-20) \\ & \Rightarrow \theta=68^{\circ} \mathrm{C}\end{aligned}$
$\begin{aligned} & \Rightarrow 440(92-\theta)=200 \times(\theta-20)+20 \times(\theta-20) \\ & \Rightarrow \theta=68^{\circ} \mathrm{C}\end{aligned}$
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