Confusion regarding photosynthesis and respiration in plants

During 24 hours there is a time in i.e. twilight when plants neither give oxygen nor carbon dioxide why is it so?

This also suggests that neither of the two vital processes i.e. respiration or photosynthesis is being carried out.

Well, during twilight there is not enough sunlight so photosynthesis may slow down or even cease but what about respiration?

Answer

You haven't directed us to any evidence for your assertion, so it is difficult to evaluate.

I'm not a plant physiologist, so I will argue from first principles:

photosynthesis consumes CO₂ and produces O₂:

6CO₂ +6H₂O -> C₆H₁₂O₆ + 6O₂

respiration consumes O₂ and produces CO₂:

C₆H₁₂O₆ + 6O₂ -> 6CO₂ +6H₂O

Plants do both of these things at the same time for at least part of the day. During the day, in a growing plant, photosynthesis will exceed respiration: a lot of the fixed carbon is fed into anabolic processes to produce "plant stuff"; polysaccharides, proteins, nucleic acids. This means that the plant will be a net producer of O₂ and a net consumer of CO₂. At night there is, of course, no photosynthesis and respiration will dominate and the plant will be a net producer of CO₂ and a net consumer of O₂.

At certain times of the day, twilight for example, there will be a transition between these two states, and the plant will pass through a state where there will be no net flux in either of the gases.