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(D) The rate of heat absorption is given by $R = \frac{dq}{dt} = m C \frac{dT}{dt}$. Since the temperature is increased at a constant rate,$\frac{dT}{

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$(B, C, D)$

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(D) The rate of heat absorption is given by $R = \frac{dq}{dt} = m C \frac{dT}{dt}$. Since the temperature is increased at a constant rate,$\frac{dT}{dt} = k$ (constant). Thus,$R \propto C$.$(A)$ In the range $0-100 \ K$,the graph of $C$ vs $T$ is non-linear (curved),so the rate of heat absorption $R$ does not vary linearly with $T$. Statement $(A)$ is incorrect.$(B)$ The heat absorbed is $\Delta Q = \int m C dT$,which is proportional to the area under the $C-T$ curve. The area under the curve from $0-100 \ K$ is clearly smaller than the area under the curve from $400-500 \ K$ (where $C$ is nearly constant at its maximum value). Statement $(B)$ is correct.$(C)$ In the range $400-500 \ K$,the graph of $C$ vs $T$ is a horizontal line,meaning $C$ is constant. Since $R \propto C$,the rate of heat absorption remains constant. Statement $(C)$ is correct.$(D)$ In the range $200-300 \ K$,the graph of $C$ vs $T$ has a positive slope,meaning $C$ is increasing. Since $R \propto C$,the rate of heat absorption increases. Statement $(D)$ is correct.Therefore,statements $(B, C, D)$ are correct.

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