$A$ double convex lens $(R_1 = R_2 = 10\,cm)$ with refractive index $(\mu = 1.5)$ has a focal length equal to the focal length of a concave mirror. The radius of curvature of the concave mirror is.......$cm$.

$A$ point object $O$ is moving towards a concave mirror as shown in the figure. Choose the correct option representing the direction of the velocity of the image ($F$ is the focus and $C$ is the centre of curvature).

An object is placed in front of a convex mirror at a distance of $50 \ cm$. $A$ plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is $30 \ cm$,it is found that there is no gap between the images formed by the two mirrors. The radius of the convex mirror is .......$cm$.

An object is placed at a distance of $50 \, cm$ in front of a convex mirror. $A$ plane mirror is inserted covering half of the convex mirror. If the distance between the object and the plane mirror is $30 \, cm$,it is observed that there is no parallax between the images formed by the two mirrors. The radius of curvature of the convex mirror is ..... $cm$.

Match List $I$ with List $II$ and select the correct answer using the codes given below the lists:

List $I$ (Position of the object)	List $II$ (Magnification)
$(I)$ An object is placed at focus before a convex mirror	$(A)$ Magnification is $-\infty$
$(II)$ An object is placed at centre of curvature before a concave mirror	$(B)$ Magnification is $0.5$
$(III)$ An object is placed at focus before a concave mirror	$(C)$ Magnification is $+1$
$(IV)$ An object is placed at centre of curvature before a convex mirror	$(D)$ Magnification is $-1$
	$(E)$ Magnification is $0.33$

The exposure time of a camera lens at the $f/2.8$ setting is $1/200$ second. The correct time of exposure at $f/5.6$ is......$sec$