Rumours of greased cartridges spread like wildfire across cantonments as:

Cantonments were connected through telegraphic lines

Late in the afternoon of 10 May 1857, the sepoys in the cantonment of Meerut broke out in mutiny. It began in the lines of the native infantry, spread very swiftly to the cavalry and then to the city. The ordinary people of the town and surrounding villages joined the sepoys. The sepoys captured the bell of arms where the arms and ammunition were kept and proceeded to attack white people, and to ransack and burn their bungalows and property. Government buildings – the record office, jail, court, post office, treasury, etc. – were destroyed and plundered. The telegraph line to Delhi was cut. As darkness descended, a group of sepoys rode off towards Delhi.

It is a previous year's question.

Per the text in NCERT,  neither it is mentioned that the cantonments published their own newspapers nor that the news was broadcasted on television (even if it was, most of the Indians did not have access to television). Moreover, the British officials would not spread any rumour or news to make things worse for themselves. The only logical answer is 'Option 1- Cantonments were connected through telegraphic lines' as telegraphs were a means of mass communication, they existed during the British era and as they were used to disseminate information, the telegraphic line to Delhi was cut.