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answer is 2.
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Detailed Solution
The lines represented by 15x2+31xy+14y2=0 are 5x+7y=0 and 3x+2y=0length of perpendicular from (2,3) on these lines are d1=3174,d2=1213∴d12+174−d22+113=96174+174−14413−113=13−11=2