One of the attacks, on the home of a former Islamic militant in southern Doda on Thursday, killed a 15-year-old girl and injured five members of her family.
At least 13 people were wounded when a grenade missed a security patrol and exploded in a crowded street in the town of Sopore.
Two Indian soldiers and two civilians were injured in a third attack in Wuyan, on the outskirts of the Kashmiri capital, Srinigar.
Shabir Ahmad, the man whose home was attacked, had been a member of the Hizb-ul Mujahedeen group, but surrendered to the authorities last year.
The attacks come a day before the visit by the Indian president, APJ Abdul Kalam, to the region where more than 45,000 people have been killed since a separatist revolt against Indian rule broke out in 1989.
Kashmir's separatist leader, Syed Ali Shah Geelani, has called for general strike on Friday and Saturday to protest against the president's visit.
Indian security officials say separatist violence has increased in the state in recent months as mountain snow melts allowing militants to move more easily from Pakistani-held territory.