Intelligence officers on Thursday blamed the blasts on the United Liberation Front of Asom (ULFA), a group fighting for Assam's independence since the late 1970s, which claimed responsibility for a blast last week that killed 22 people.
"Militant activities are definitely on the rise and the situation has turned for the worse," Khogen Sharma, the state's Inspector General of Police, told reporters.
Two soldiers and a daughter of one of them were killed when the vehicle in which they were travelling hit a crude landmine
at Goalpara, 100 km west of Guwahati, Assam's main city.
Six soldiers were wounded in the blast.
Another person was killed and at least 37 wounded when a time bomb exploded in Gossaigaon town, west of Guwahati.
Police said ULFA armed fighters also threw a grenade outside a crowded cinema on Wednesday night in Dibrugarh, the biggest town in eastern Assam, wounding seven people.
The ULFA had called for a boycott of Indian movies and there have been several attacks on cinemas in the past. Another bomb exploded on a railway track late on Wednesday but no one was hurt, police said.
About 10,000 people have been killed in 25 years of insurgency in Assam, an oil and tea-producing state that the rebels say is exploited and neglected by the central government.
The separatist rebels claimed responsibility for a bomb attack on 15 August in Dhemaji town in which 22 people were killed, including about a dozen children.