Which one of the following Indian cities will never receive the vertical rays of the Sun at any time of the year?

Introduction / Context:
The vertical rays of the Sun fall only between the Tropic of Cancer and the Tropic of Capricorn, and never north or south of these lines. This question checks whether you can apply that principle to identify an Indian city that will never receive the Sun directly overhead. Understanding the geographic range of vertical Sun rays is a basic concept in earth science and climatology.

Given Data / Assumptions:

• The cities listed are Srinagar, Thiruvananthapuram, Kolkata and Mumbai.
• The Tropic of Cancer is at approximately 23 and a half degrees north, and the Tropic of Capricorn is in the southern hemisphere.
• We assume standard approximate latitudes for these cities, with Srinagar well north of the Tropic of Cancer.
• Cities situated north of the Tropic of Cancer can never have the Sun at the zenith.

Concept / Approach:
Only places between the two tropics ever see the Sun directly overhead at noon. Cities located below the Tropic of Cancer within India, such as Mumbai and Thiruvananthapuram, can receive vertical rays once or twice a year. Cities close to the Tropic of Cancer, like Kolkata in many exam treatments, may experience vertical Sun conditions as well. However, a city such as Srinagar in Jammu and Kashmir lies far to the north and therefore never receives vertical rays.

Step-by-Step Solution:
Step 1: Identify the approximate latitudes of the cities Thiruvananthapuram lies close to eight degrees north, Mumbai around nineteen degrees north, Kolkata in the low twenties, and Srinagar above thirty degrees north.Step 2: Note that the band where vertical rays can occur extends only from the Equator to the Tropic of Cancer in the northern hemisphere.Step 3: Since Srinagar lies well north of the Tropic of Cancer, it falls outside this band and thus cannot have the Sun directly overhead at any time.Step 4: Therefore, Srinagar is the only city among the options that never receives vertical rays of the Sun.

Verification / Alternative check:
Climatology diagrams showing the apparent path of the Sun and the latitude bands for overhead Sun events clearly restrict such events to the tropical zone. Looking up the latitude of Srinagar confirms that it lies outside this zone, while checking for Mumbai or Thiruvananthapuram shows that they are inside it. Kolkata is often treated as near the Tropic of Cancer in exam materials, reinforcing the idea that it can have overhead Sun conditions.

Why Other Options Are Wrong:
Thiruvananthapuram lies well south of the Tropic of Cancer and therefore can receive the Sun overhead twice a year as the vertical rays move north and south. Mumbai also lies within the tropical belt and similarly experiences overhead Sun conditions during the year. Kolkata is close to the Tropic of Cancer and is treated in many exam settings as being effectively on or near it, meaning it can experience vertical Sun at least once a year.

Common Pitfalls:
Some students may incorrectly assume that only cities near the Equator receive vertical rays, leading them to overlook the full range of the tropical zone. Others may misread the map and think that Mumbai or Kolkata are too far north, forgetting the actual position of the Tropic of Cancer. Establishing a clear mental picture of where the key parallels are drawn relative to India's outline helps avoid these errors.

Final Answer:
The city that will never get the vertical rays of the Sun is Srinagar, because it lies north of the Tropic of Cancer.