Which has more luminous efficiency?

An object $O$ is placed in front of a small plane mirror $M_1$ and a large convex mirror $M_2$ of focal length $f$. The distance between $O$ and $M_1$ is $x$,and the distance between $M_1$ and $M_2$ is $y$. The images of $O$ formed by $M_1$ and $M_2$ coincide. The magnitude of $f$ is

$A$ small object is placed $50 \ cm$ to the left of a thin convex lens of focal length $30 \ cm$. $A$ convex spherical mirror of radius of curvature $100 \ cm$ is placed to the right of the lens at a distance of $50 \ cm$. The mirror is tilted such that the axis of the mirror is at an angle $\theta=30^{\circ}$ to the axis of the lens,as shown in the figure. If the origin of the coordinate system is taken to be at the centre of the lens,the coordinates (in $cm$) of the point $(x, y)$ at which the image is formed are

$A$ small source of light is to be suspended directly above the centre of a circular table of radius $R$. What should be the height of the light source above the table so that the intensity of light is maximum at the edges of the table compared to any other height of the source?

An optical component and an object $S$ placed along its optic axis are given in Column $I$. The distance between the object and the component can be varied. The properties of images are given in Column $II$. Match all the properties of images from Column $II$ with the appropriate components given in Column $I$.

Column $I$	Column $II$
$A$. Concave Mirror	$(p)$ Real image
$B$. Convex Mirror	$(q)$ Virtual image
$C$. Convex Lens	$(r)$ Magnified image
$D$. Concave Lens	$(s)$ Image at infinity

$A$ finite size object is placed normal to the principal axis at a distance of $30 \ cm$ from a convex mirror of focal length $30 \ cm$. $A$ plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is (in $cm$)