Which princely state signed the "Standstill Agreement" with India in 1947?

Hyderabad

The correct answer is Option 1- Hyderabad

Hyderabad was the largest Princely state & was surrounded entirely by Indian territory. It was ruled by the Nizam (one of the world’s richest men), Mir Osman Ali Khan. Hyderabad had a majority Hindu population but was ruled by a Muslim ruler. The Nizam wanted an independent status for Hyderabad. He entered into Standstill Agreement with India in November 1947 for a year while negotiations with the Indian government were going on.

Junagadh:
A plebiscite was conducted, and most of Junagadh's population voted to join India.
The Government of India accepted the accession of Junagadh & Junagadh officially became a part of India on February 20, 1948.

Manipur:
Manipur was a princely state with its own monarch, Maharaja Bodhchandra Singh, and a distinct political and administrative system.
It enjoyed a measure of autonomy under the British colonial rule.
Maharaja Bodhachandra Singh of Manipur signed the Instrument of Accession with the Indian government shortly before Independence.

Jammu and Kashmir:
In October 1947, armed tribesmen from Pakistan invaded Kashmir with the aim to annex Kashmir to Pakistan.
Faced with the invasion and deteriorating security situation, Maharaja Hari Singh signed the Instrument of Accession on October 26, 1947, acceding to India.
Following the accession, India sent troops to Kashmir to repel the invading tribesmen.