Which of the following acids will have relatively strong conjugate bases? So remember a strong conjugate base comes from a weak acid. So basically we have to look and see which one here is a weak acid.
So here we have per bromic acid which is one of the strong acids. So this wouldn't work. Hydrocyanic acid is a weak acid so this would be an answer. Nitric acid is a strong acid so that wouldn't work. And then we have perchloric acid which is a strong acid so that wouldn't work.
Remember a weak acid would equate to stronger or strong conjugate basis. So here the only answer that works is option B.