A 3 cm long object pin is kept vertical on the horizontal principal axis of a convex mirror in front of it. The distance of the object pin (standing above the principal axis) is 30 cm from the pole of the convex mirror. A plane mirror facing the pin is placed perpendicular to the principal axis at a distance of 10 cm from and in front of the same convex mirror covering just the lower half of it. The images of the object pin, formed by the two mirrors, are found to coincide. Then 

This is a multiple-correct question, and the correct options are (a), (b) and (d). The pin is 20 cm from the plane mirror, so its plane-mirror image is 20 cm behind it, i.e. 10 cm behind the convex mirror; this image is erect and stands above the axis. For the convex mirror $$u = -30$$ cm and $$v = +10$$ cm, so $$\frac{1}{f} = \frac{1}{10} - \frac{1}{30} = \frac{1}{15}$$ and $$f = 15$$ cm. The magnification is $$m = -\frac{v}{u} = \frac{1}{3}$$, and a convex mirror always forms a virtual, erect image, so (c) is wrong.