b
(b) Since there is no parallex, it means that both images (By plane mirror and convex mirror) coinciding each other.

According to property of plane mirror it will form image at a distance of \(30 cm\) behind it. Hence for convex mirror \(u = -50 cm, \,\,v = + 10 cm\)

By using \(\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\)

\( \Rightarrow \,\,\,\frac{1}{f} = \frac{1}{{ + 10}} + \frac{1}{{ - 50}} = \frac{4}{{50}}\)

\( \Rightarrow \) \(f = \frac{{25}}{2}cm\)

\( \Rightarrow \,\,\,R = 2f = 25cm.\)