An object is placed 21 cm in front of a concave mirror of radius of curvature 10 cm. A glass slab of thickness 3 cm and refractive index 1.5 is then placed close to the mirror in the space b/w the object and the mirror. Find the pos. of the image formed.

The slab just makes your optical path bigger by (n-1)*d (d is the thickness) so 1.5cm in this case (1.5-1)*3

so the optical distance to the mirror is not 21cm but instead 22.5cm 21+1.5.
the focal distance of a concave mirror is positive so f=R/2=10cm

so calculation goes very simply

1/v'+1/22.5=1/10

v'=10*22.5/(22.5-10)

v'=18cm

now this is the optical distance not the distance it self

remember the glass is actually between cm 10 and 13 from the mirror
First you realise that this distance is bigger then the 10 cm so it might be on the other side of the glass lets try cheking this out by subtracting the total optical path introduced by the slab

18-1.5=16.5cm it's the actual distance from the mirror of the image.