The first blast took place inside the residential complex of Moinuddin Ahmed, MLA of All India Democratic United Front, at Jaleshwar in Goalpara district.
The people apprehended one suspected militant and beat him up, after which he reportedly died though there was no official confirmation of this.
Three motorcycles suspected to have been used by the militants were recovered from the area, the sources said.
One bomb is suspected to be concealed in the MLA's house and a bomb disposal squad of the police reached the place, they added.
Another IED went off at Jaleshwar High School.
The other explosions in Goalpara district took place at Moriakichi Bazar, Gaurnagar, Porahita and Jamadar Bazar areas.
In Dhubri, the areas hit by the blasts are Airketa, Sirajkuthi and Metarteri.