One set of a plant was grown at 12 hours day and 12 hours night period cycles and it flowered while in the other set night phase was interrupted by flash of light and it did not produce flower. Under which one of the following categories will you place this plant ?

Photoperiodism is the response of plants to the relative lengths of day and night. What really matters is the length of the uninterrupted dark period.
Short day plants (long night plants) flower only when they get a continuous dark period longer than a critical length.
If the long night is interrupted even by a brief flash of light, the dark period is broken into two short nights, and a short day plant does not flower.
Here the plant flowered with a 12 hour uninterrupted night, but failed to flower when the night was interrupted by a flash of light. This is the typical behaviour of a short day plant.
A long day plant would be promoted (not inhibited) by a night break, and a day neutral plant would not respond to it at all.
So the plant is a short day plant.