In the first attack a donkey cart went over a mine buried by the roadside on the outskirts of Peshawar, police said.
"Both the donkey cart owner and donkey were killed. Basically the mine was planted to target police," said Kalam Khan, a senior police official.
In the second incident a remote control bomb hit a police patrol pick-up, injuring 11, in the village of Darsamand, in Hangu district.
"Nine policemen and two passers-by were were wounded in this bomb blast. Militants are responsible for this attack," said Abdur Rashid Khan, district police chief.