One state official said the surge was a result of water being released from an upstream dam.
The students had reportedly left a bus to take photographs when the surge occurred
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Anger
The incident took place some 200km (125 miles) from the state capital, Shimla, as the students were travelling to the popular tourist resort of Manali
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The BBC's Baldev Chauhan in Shimla says angry locals and tourists have blocked traffic on the busy road, asking why there was no warning before the dam released the water.
Himachal Transport Minister G S Bali said: "Rescue teams are looking downstream for the missing in the dark. They are engineering students of the VNR college, Hyderabad.
"The students had got off the bus to take photographs at the edge of the river at around 1930 when the sudden rise of the water washed them away
Speed Date."
Rakesh Kanwar, a senior state government official, said: "The water was released by the Larji power project dam
Speed Date."