Which of the following Indian cities will never receive the vertical rays of the sun directly overhead at any time of the year?

Introduction / Context:
Earth sun geometry is an important concept in geography. The vertical rays of the sun, meaning the sun appearing exactly overhead at noon, occur only between the Tropic of Cancer and the Tropic of Capricorn. Any place outside this tropical zone never experiences the sun at the zenith. This question asks you to apply that concept to Indian cities by identifying which city lies outside the tropics and therefore never receives the sun's vertical rays.

Given Data / Assumptions:
• The question lists several Indian cities at different latitudes. • The condition is never receiving the sun directly overhead. • We know that the Tropic of Cancer passes through India at about 23 and a half degrees north. • Cities significantly north of this latitude will not have the sun at the zenith.

Concept / Approach:
Any place between approximately 23 and a half degrees north and 23 and a half degrees south can experience the vertical rays of the sun on at least two days of the year, as the declination of the sun moves between the two tropics. In India, cities such as Mumbai, Kolkata, Ranchi, and Thiruvananthapuram lie within this tropical belt, with latitudes south of or near the Tropic of Cancer. Srinagar, on the other hand, lies in Jammu and Kashmir at a latitude of about 34 degrees north, well outside the tropical zone. Therefore, Srinagar never receives the sun directly overhead, while the other cities can.

Step-by-Step Solution:
Step 1: Recall that the vertical rays of the sun occur only between the Tropic of Cancer and the Tropic of Capricorn. Step 2: Compare approximate latitudes: Thiruvananthapuram around 8 degrees north, Mumbai around 19 degrees north, Kolkata around 22 degrees north, Ranchi near the Tropic of Cancer, all within the tropics. Step 3: Note that Srinagar is far to the north at about 34 degrees north, outside the tropical belt. Step 4: Conclude that Srinagar is the city that will never have the sun's rays vertically overhead. Step 5: Choose Srinagar as the correct answer.

Verification / Alternative check:
If you check a map or atlas with latitude lines, you will see that the Tropic of Cancer crosses India roughly through states like Gujarat, Rajasthan, Madhya Pradesh, Jharkhand, and West Bengal. Cities south of this line, such as Mumbai and Thiruvananthapuram, and cities very close to it, such as Kolkata and Ranchi, fall within or near the tropical zone. Astronomical tables and school level geography texts state that such locations can observe the sun at the zenith on specific days. In contrast, Srinagar, located in the Kashmir Valley, lies well north of the Tropic of Cancer and thus never experiences vertical rays from the sun. This confirms Srinagar as the correct option.

Why Other Options Are Wrong:
• Mumbai is at about 19 degrees north, within the tropics, so the sun can be overhead there on two days each year. • Thiruvananthapuram lies close to 8 degrees north and definitely experiences the vertical rays of the sun. • Kolkata, near 22 and a half degrees north, is just south of or close to the Tropic of Cancer and can also receive overhead sun. • Ranchi is near the Tropic of Cancer and thus lies within the zone where overhead sun is possible.

Common Pitfalls:
• Assuming that only cities very close to the equator can receive overhead sun and forgetting that the entire tropical belt qualifies. • Relying on a rough mental picture of India without checking which parts fall outside the tropical latitudes. • Ignoring the latitude clue and guessing based on temperature alone, which can be misleading.

Final Answer:
Among the given cities, Srinagar will never receive the vertical rays of the sun directly overhead at any time of the year.