Which one of the following statements regarding lenses is not correct

Which one of the following statements regarding lenses is not correct ?

A convex lens produces both real and virtual images.
A concave lens produces virtual images.
A convex lens can produce images equal, greater and smaller than the size of the object.
A concave lens always produces images smaller than the size of the object.
This question was previously asked in
UPSC NDA-2 – 2019
Let’s analyze each statement regarding lenses, assuming standard behaviour with real objects, but considering the possibility of virtual objects as the word “always” appears in option D.
A) A convex lens produces both real and virtual images. This is correct. A convex lens produces real images for objects placed beyond its focal point (F) and virtual images for objects placed between F and the optical center (O).
B) A concave lens produces virtual images. This is correct. A concave lens produces virtual, erect, and diminished images for any real object position. It can also produce real images for virtual objects. The statement “produces virtual images” is true as it is capable of doing so.
C) A convex lens can produce images equal, greater and smaller than the size of the object. This is correct. For real objects, a convex lens produces diminished images (object beyond 2F), same-sized images (object at 2F), and magnified images (object between F and 2F). It also produces a magnified virtual image (object between F and O).
D) A concave lens always produces images smaller than the size of the object. This statement is incorrect. While a concave lens always produces smaller, virtual images for *real* objects, it can produce magnified *real* images for certain *virtual* object positions (specifically, when a virtual object is placed between the focal point F and the optical center O). Therefore, it does not *always* produce images smaller than the object size when considering all possible object types.
– Convex lenses can form both real and virtual, magnified, diminished, or same-sized images depending on the object position.
– Concave lenses always form virtual, erect, and diminished images for real objects.
– The word “always” in statement D makes it universally true or false. Considering virtual objects, a concave lens does not always produce smaller images.
For a concave lens, a virtual object placed between the optical center (O) and the focal point (F) forms a real, inverted, and magnified image beyond F. This contradicts statement D, making it incorrect in the most general sense. If the question were restricted to real objects, all other options would be correct, which suggests D is the intended incorrect statement due to the inclusion of “always”.