The explosions, suspected to have been triggered by ULFA (Independent) insurgents, took place at two places in the district.
Two blasts occurred within a gap of a few minutes in a drain near the Jagun police station, and the other at the Tirap colliery near the Ledo police station, police said.
Director General of Police Mukesh Sahay told reporters here that the explosions were of low-intensity and was carried out by ULFA (Independent) to prove its existence.
In Dima Hasao, the indefinite curfew in Maibang, which was clamped yesterday after clashes between the police and a mob during a bandh, continued today.
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The bandh was extended by groups opposing the proposed inclusion of Dima Hasao in Greater Nagalim after two people, injured allegedly in police firing during the clashes, died today.
"While one person died on the way to a hospital in Guwahati, the other succumbed at a hospital this morning," a senior government official told PTI.
The Republic Day function at the Haflong, the district's headquarters, was cut short after hoisting of the tricolour as there was hardly any people present.
Chakradharpur Sub-Divisional Police Officer Sakaldeo Ram said that a CPI (Maoists) squad led by its 'area commander' Jeevan Kandulana fired on police and CRPF personnel around 9.40 am.
The personnel retaliated and the exchange of fire lasted for over half an hour, forcing the ultras to retreat, the officer said.
In a search operation a .303 rifle, which was looted from the police, was recovered along with 100 rounds of ammunition, six powerful bombs, over 20 detonators, cordex wire and explosive-attached arrows.
In Guwahati, Assam Governor Jagdish Mukhi said that the government was working on a Rs 1,500-crore project for protection measures against flood and erosion.
In neighbouring Meghalaya, Governor Ganga Prasad said that the state had evolved as one of the most preferred tourists destinations in the northeast.
On the occasion, Sikkim Governor N Sriniwas Patil paid homage to those who laid down their lives for India's freedom, while his counterpart in Manipur, Najma Heptulla, in an event in Imphal, awarded medals to police and fire brigade personnel for their services.
The day was also celebrated in the other north eastern states of Tripura, Mizoram and Arunachal Pradesh.
In Kolkata, West Bengal Governor K N Tripathi presided over an hour-long march past of the armed and police forces.
The state's 'Unity in Brotherhood' tableau, which was rejected by the Centre for the Republic Day procession in Delhi, was also included in the parade.
Bihar Governor Satya Pal Malik in Patna said the state was working for the development of all sections of the society.