Step 1: Understand the question.
The question asks which kingdom was ruled by Jarasandha, a strong king in the Mahabharata. We need to recall his home kingdom and then check the four choices.
Step 2: Recall who Jarasandha was.
Jarasandha was the son of King Brihadratha. His capital was Girivraja, also called Rajagriha, in the old Magadha region (today's south Bihar). He was known for his great strength and for his many wars against the Yadavas.
Step 3: Check option 1, Magadha.
Magadha is the kingdom of Jarasandha. His strength and his army made Magadha the leading power of his time. So option 1 is correct.
Step 4: Check option 2, Hastinapur.
Hastinapur was the capital of the Kuru kingdom, ruled by the Kauravas and Pandavas. Jarasandha was not its king. So option 2 is wrong.
Step 5: Check option 3, Gandhar.
Gandhar was the kingdom of Shakuni and Gandhari, in the north-west. It has no link with Jarasandha. So option 3 is wrong.
Step 6: Check option 4, Kashi.
Kashi was a separate kingdom around Varanasi. Jarasandha only married his daughters to Kansa, not to a Kashi throne. So option 4 is wrong.
Final Answer:
Jarasandha ruled Magadha from Girivraja, so option 1 is right.
\[ \boxed{\text{Magadha (option 1)}} \]