1. Time period of a pendulum

For a simple pendulum, $T = 2\pi \sqrt{\frac{l}{g}}$ where $l$ is the length of the pendulum and $g$ is the acceleration due to gravity.

2. Effect of taking the pendulum to Mount Everest

At Mount Everest, the altitude is higher, so the distance from the Earth's center increases. Hence the value of $g$ decreases.

Therefore, from $T \propto \frac{1}{\sqrt{g}}$ if $g$ decreases, then $T$ increases.

So each oscillation takes more time, and the pendulum clock runs slow, not fast.

Thus, Assertion A is false.

3. Check the Reason R

Reason says: the value of $g$ is less at Mount Everest than its value on the surface of earth.

This is true, because with increase in altitude, $g_h = g\left(\frac{R}{R+h}\right)^2$ which is less than $g$ at the Earth's surface.

Thus, Reason R is true.

4. Evaluate the options

• A: Both A and R are correct but R is NOT the correct explanation of A — false
• B: A is correct but R is not correct — false
• C: Both A and R are correct and R is the correct explanation of A — false
• D: A is not correct but R is correct — true

Hence, the correct option is: $\boxed{D}$