Four security personnel are among the scores of people injured.
On Saturday, in the state's summer capital Srinagar, a youth was killed and about 40 people, including women and children wounded when a time bomb hidden in a fruit-seller's pushcart triggered a massive explosion at a thoroughfare during morning rush hour.
One person later died in a government-run hospital in Srinagar while many of the others are "battling for life", according to Rauf Husain, a doctor who is treating the injured.
After a lull, violence is creeping
back into the life of Kashmiris
Government officials said armed separatist fighters were behind the attack, adding that the target of the blast was most likely security personnel who often use the road on their way to the nearby Drugjan market.
Besides, due to its proximity to the Kashmir chief minister's residence and other important government officials, police and paramilitary forces make frequent rounds of the area, the officials said.
Later in the day, 23 more people were wounded, including four Indian security personnel, when suspected separatist fighters tossed a hand grenade at a passing military vehicle in Anantnag, 55km south of Srinagar.
Attacks on security forces often
also kill civilians
A second grenade attack killed one police officer and wounded another at Mardha, a remote village in Poonch district, which lies close to the de facto border that splits Kashmir between Indian and Pakistani control.
None of the separatist groups battling Indian security forces in Kashmir have claimed responsibility for Saturday's attacks.
Thousands of people – civilians, Indian security personnel and armed fighters - have been killed in the 15-year-old conflict.
Last week, in the same Poonch area, suspected infiltrators mowed down 12 nomadic herdsmen, including seven members of a village-defence committee.
Following the killing, the Indian federal government decided to equip the committees with latest weapons in place of the small arms they had been provided earlier.