Hello Saif
In IGMPv1, there is no election process for the active querier. However, if there are two IGMPv1 routers on the same subnet, then it is the Designated Router (DR) that will also perform the role of the querier. The designated router is elected exactly for the purpose of avoiding the duplication of multicast traffic for connected hosts.
More information about this can be found here:
I hope this has been helpful!
Laz