A concave lens of refractive index 1.5 is immersed in a medium of refractive index 1.65. What is the nature of the lens?

A concave lens with refractive index 1.5 (with respect to air) is a diverging lens when surrounded by air.

However, if this lens is placed in a medium (suppose a liquid) of refractive index 1.65 (with respect to air), it behaves like a converging lens. When a ray of light is incident on the lens, since the lens is surrounded by liquid, the ray bends away from the normal as it is moving from a denser to a rarer medium. When this ray emerges out of the lens, it bends towards the normal as it is moving from a rarer to a denser medium.

So, the concave lens behaves like a convex lens when put in a denser medium from its rarer medium (such as from air to a liquid).