Consider the two statements :

Statement-1 : A capillary tube is first dipped in hot water and then dipped in cold water. The rise is higher in hot water.

Statement-2 : Capillary tube is first dipped in cold water and then dipped in hot water. The rise is higher in cold water.

The height of the liquid column in a capillary tube is given by the formula:

$h=\frac{2Tcos\theta }{r\rho g}$

where:
$h$ is the height of the capillary rise,
$T$ is the surface tension of the liquid,
$\theta$ is the angle of contact,
$r$ is the radius of the capillary tube,
$\rho$ is the density of the liquid, and
$g$ is the acceleration due to gravity.

When the temperature of a liquid increases, the kinetic energy of its molecules increases, which weakens the intermolecular cohesive forces. Consequently, the surface tension ($T$) of water decreases significantly as the temperature rises. Although the density of water ($\rho$) also decreases with an increase in temperature, the relative decrease in surface tension is much larger and dominates the capillary rise relationship.

Since the height of the capillary rise ($h$) is directly proportional to the surface tension ($T$), the rise is lower at higher temperatures (hot water) and higher at lower temperatures (cold water).

Let us evaluate the two statements:
- Statement-1 claims that the rise is higher in hot water. This is false.
- Statement-2 claims that the rise is higher in cold water. This is true.

Therefore, Statement-1 is false and statement-2 is true.