A pendulum clock is set to give correct time at the sea level. This clock is moved to hill station at an altitude of 2500m above the sea level. In order to keep correct time of the hill station, the length of the pendulum.

The correct option is Has to be reduced.

Let's understand why the length of the pendulum needs to be reduced step-by-step:

Step 1: Formula for the Time Period of a Simple Pendulum
The time period $T$ of a simple pendulum (the time taken to complete one full oscillation) is given by the formula:
$T=2\pi \sqrt{\frac{l}{g}}$
where:
- $l$ is the length of the pendulum.
- $g$ is the acceleration due to gravity at that location.

Step 2: Effect of Altitude on Acceleration due to Gravity ($g$)
As we move higher above sea level to a hill station (an altitude of 2500m), the acceleration due to gravity decreases because we move further away from the center of the Earth.
Therefore, the acceleration due to gravity at the hill station is less than that at sea level:
$g_{\text{hill}}<g_{\text{sea}}$

Step 3: Adjusting the Pendulum to Keep Correct Time
For the clock to keep correct time at the hill station, its time period $T$ must remain unchanged (constant).
Looking at the formula, to keep $T$ constant, the ratio of the length of the pendulum to gravity must remain constant:
$\frac{l}{g}=\text{constant}$

Since the acceleration due to gravity $g$ decreases at the higher altitude, the length $l$ of the pendulum must be decreased proportionally to keep the ratio constant.
Thus, the length of the pendulum has to be reduced.