Suppose that two stars are separated in the sky by 0.01 arcsecond, and you observe them with a telescope that has an angular resolution of 1 arcsecond. What will you see?

The light from the two stars will be blended together so that they look like one star.

Explanation:

Given that;

two stars are separated in the sky by 0.01 arcsecond.

and we are told that a telescope that has an angular resolution of 1 arcsecond.

Therefore the maximum limit of the telescope to be visible to the stars is 1 arcsecond, That implies that since the separating  distance between the two stars is less than that of the telescope, then the telescope will see lesser than the original distinct images. As such, the light emerging from the two stars will be blended together so that they look like one star.