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They challenged them and opened fire resulting in the death of one intruder, he said adding, the deceased was in his thirties.
The other intruders managed to escape, he said.
The force also destroyed two Pakistani posts in retaliation for the killing of its jawan in unprovoked firing.
Two Pakistani mortar positions were "located, targeted and destroyed by BSF troopers yesterday (Wednesday) night only. The coordinated precision fire of BSF troopers silenced Pakistani guns," a BSF spokesman said.