The value of the coefficient of volume expansion of glycerine is $5\times10^{-4}~\text{K}^{-1}.$ The fractional change in the density of glycerine for a rise of $40^\circ \text{C}$ in its temperature is:

On observing light from three different stars $P,$ $Q,$ and $R,$ it was found that the intensity of the violet colour is maximum in the spectrum of $P,$ the intensity of the green colour is maximum in the spectrum of $R$ and the intensity of the red colour is maximum in the spectrum of $Q.$ If $T_P,$ $T_Q,$ and $T_R$ are the respective absolute temperatures of $P,$ $Q,$ and $R,$ then it can be concluded from the above observations that:
1. $T_P>T_Q>T_R$
2. $T_P>T_R>T_Q$
3. $T_P<T_R<T_Q$
4. $T_P<T_Q<T_R$

The two ends of a metal rod are maintained at temperatures $100~^\circ\text{C}$ and $110~^\circ\text{C}.$ The rate of heat flow in the rod is found to be $4.0$ J/s. If the ends are maintained at temperatures $200~^\circ \text{C}$ and $210 ~^\circ \text{C},$ the rate of heat flow will be:
1. $44.0$ J/s
2. $16.8$ J/s
3. $8.0$ J/s
4. $4.0$ J/s

Steam at $100~^{\circ}\text{C}$ is passed into $20~\text{g}$ of water at $10~^{\circ}\text{C}.$ When water acquires a temperature of $80~^{\circ}\text{C},$ the mass of water present will be: 
[Take specific heat of water $= 1~\text{cal g}^{-1}~^\circ\text{C}^{-1}$ and latent heat of steam $= 540~\text{cal g}^{-1}$]
1. $24~\text{g}$
2. $31.5~\text{g}$
3. $42.5~\text{g}$
4. $22.5~\text{g}$

A certain quantity of water cools from $70~^{\circ}\text{C}$ to $60~^{\circ}\text{C}$ in the first $5$ minutes and to $54~^{\circ}\text{C}$ in the next $5$ minutes. The temperature of the surroundings is:
1. $45~^{\circ}\text{C}$
2. $20~^{\circ}\text{C}$
3. $42~^{\circ}\text{C}$
4. $10~^{\circ}\text{C}$

If the radius of a star is $R$ and it acts as a black body, what would be the temperature of the star at which the rate of energy production is $Q?$
$\left(\sigma~ \text{is Stefan-Boltzmann constant}\right)$
1. $\dfrac{Q}{4\pi R^2\sigma}$

2. $\left(\dfrac{Q}{4\pi R^2\sigma}\right )^{\dfrac{-1}{2}}$

3. $\left(\dfrac{4\pi R^2 Q}{\sigma}\right )^{\dfrac{1}{4}}$

4. $\left(\dfrac{Q}{4\pi R^2 \sigma}\right)^{\dfrac{1}{4}}$

Liquid oxygen at $50~\text K$ is heated up to $300~\text K$ at a constant pressure of $1~\text{atm}.$ The rate of heating is constant. Which one of the following graphs represents the variation of temperature with time?

1.		2.
3.		4.