Question

You can only see stars whose peak intensity of radiation is in the visible band.
true or false

Answer 1

I would argue False.

The peak intensity of radiation will definitely be the wavelength at which the object looks the brightest.

However, stars are modeled as black bodies, so they emit continuous radiation. There will be radiation emitted at all wavelengths.

So if you look at a star with your naked eye (which can only see visible wavelengths), even a star whose peak radiation is not in the visible region, there may still be enough radiation from the visible region to see the star.

Answer 2

Not to mention the impact of red-shift.

A star could emit its peak radiation at a short wavelength and then have that light be red-shifted on its way to Earth. By the time it arrives, its in the visible spectrum.