When \(1\) kg of ice at \(0^{\circ}\) C melts into the water at \(0^{\circ}\) C, the resulting change in its entropy, taking the latent heat of ice to be \(80\) cal/gm, is:
1. \(8\times 10^4\) cal/K
2. \(80\) cal/K
3. \(293\) cal/K
4. \(273\) cal/K

A planet moving along an elliptical orbit is closest to the sun at a distance r₁ and farthest away at a distance of r₂. If v₁ and v₂ are the linear velocities at these points respectively, then the ratio $\frac{{\mathrm{v}}_1}{{\mathrm{v}}_2}$ is:

1.  ${\mathrm{r}}_2/{\mathrm{r}}_1$

2.  ${\left({\mathrm{r}}_2/{\mathrm{r}}_1\right)}^2$

3.  ${\mathrm{r}}_1/{\mathrm{r}}_2$

4.  ${\left({\mathrm{r}}_1/{\mathrm{r}}_2\right)}^2$

A nucleus \({ }_{{n}}^{{m}} \mathrm{X}\) emits one $\mathrm{}$\(\alpha\text -\text{particle}\) and two \(\beta\text- \text{particle}\) The resulting nucleus is:

During an isothermal expansion, a confined ideal gas does \(-150\text{ J}\) of work against its surrounding. This implies that: