The correct answer is option 4: Nagpur and Kolkata.

To understand why Nagpur and Kolkata will have the mid-day Sun exactly overhead only once a year, let`s first understand what it means for the Sun to be overhead. When the Sun is directly overhead, it means that it is positioned exactly at the zenith, or the highest point in the sky from the observer`s perspective.

The position of the mid-day Sun varies throughout the year due to the tilt of the Earth`s axis. The Earth`s axis is tilted at an angle of approximately 23.5 degrees with respect to its orbit around the Sun. As a result, different regions of the Earth receive varying levels of direct sunlight at different times of the year.

Nagpur and Kolkata are both located close to the Tropic of Cancer, which is at approximately 23.5 degrees North latitude. This means that during the summer solstice, which occurs around June 21st, the Sun is directly overhead at noon in these cities. However, during the rest of the year, the Sun`s position shifts away from the zenith, resulting in the mid-day Sun not being exactly overhead.

Therefore, Nagpur and Kolkata will have the mid-day Sun exactly overhead only once a year, during