Let's analyze each statement carefully:

Statement (I): When an object is placed at the centre of curvature of a concave lens, image is formed at the centre of curvature of the lens on the other side.

To understand this statement, let's recall the nature of images formed by concave lenses. A concave lens (diverging lens) always forms images that are virtual, erect, and smaller than the object, regardless of the object's position. The term "centre of curvature" is typically associated with mirrors rather than lenses. Therefore, this statement is incorrect because a concave lens does not form a real image that could be said to be at the centre of curvature on the other side.

Statement (II): Concave lens always forms a virtual and erect image.

Now, considering the second statement, a concave lens (diverging lens) indeed always forms virtual, erect, and diminished images. This is a fundamental property of concave lenses.

Given this analysis:

The correct answer is Option A: Statement I is false but Statement II is true.