The correct option is (a) 1 only.
Explanation
The geographical extent of India is defined by key latitudinal and longitudinal reference lines. The Tropic of Cancer ($23^\circ 30' N$) divides the country into roughly two halves, while the Standard Meridian of India ($82^\circ 30' E$) serves as the reference for Indian Standard Time (IST).
Statement 1: Correct
The Tropic of Cancer passes through eight Indian states. Moving from West to East, these are Gujarat, Rajasthan, Madhya Pradesh, Chhattisgarh, Jharkhand, West Bengal, Tripura, and Mizoram. It cuts across the central part of Madhya Pradesh.
Statement 2: Incorrect
The Standard Meridian of India ($82^\circ 30' E$) passes through five states: Uttar Pradesh, Madhya Pradesh, Chhattisgarh, Odisha, and Andhra Pradesh. It does not pass through Rajasthan, which is located significantly to the west of this longitude.
Key Takeaway:
The Tropic of Cancer intersects 8 states: Gujarat, Rajasthan, MP, Chhattisgarh, Jharkhand, WB, Tripura, and Mizoram.
The Standard Meridian intersects 5 states: UP, MP, Chhattisgarh, Odisha, and AP.