Step 1: Link the name to a place.
Think of the story where Bhima fights a long wrestling duel and kills a mighty king near Rajagriha. That king was Jarasandha. The place of the story gives us the kingdom.
Step 2: Use the Mahabharata story.
Krishna, Bhima and Arjuna went to Girivraja in disguise. Bhima fought Jarasandha for many days and finally split his body. Girivraja was the capital of Magadha, so the kingdom is Magadha.
Step 3: Use the family link.
Jarasandha's father Brihadratha founded the Brihadratha dynasty of Magadha. The ruler of this line is the one who held Magadha, so Jarasandha belongs to Magadha.
Step 4: Eliminate the other kingdoms.
Hastinapur is the Kuru capital, Gandhar is Shakuni's land, and Kashi is a separate Janapada. None of these had Jarasandha as king, so only Magadha is left.
Step 5: Cross-check with the sixteen Mahajanapadas.
Magadha later grew into the strongest of all the Mahajanapadas. Its early fame in the epic age through Jarasandha fits this record of a powerful kingdom in the east.
Final Answer:
The answer is Magadha, so the correct choice is option 1.
\[ \boxed{\text{Option 1: Magadha}} \]