Which of the following form$(s)$ a virtual and erect image for all positions of the object?

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 $0.33$

$A$ $2\,m$ long scale with a least count of $0.2\,cm$ is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at $80\,cm$ mark and $1\,m$ mark, respectively. The image of the object pin on the other side of the lens coincides with the image pin that is kept at $180\,cm$ mark. The $\%$ error in the estimation of focal length is

$A$ lamp is hanging along the axis of a circular table of radius $r$. At what height should the lamp be placed above the table,so that the illuminance at the edge of the table is $\frac{1}{8}$ of that at its center?

$A$ convex lens forms an image of an object on a screen. The height of the image is $9 \, cm$. The lens is now displaced until an image is again obtained on the screen. The height of this image is $4 \, cm$. The distance between the object and the screen is $90 \, cm$.

Answer the following questions:
$(a)$ You have learnt that plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances? Explain.
$(b)$ $A$ virtual image,we always say,cannot be caught on a screen. Yet when we 'see' a virtual image,we are obviously bringing it on to the 'screen' (i.e.,the retina) of our eye. Is there a contradiction?
$(c)$ $A$ diver under water,looks obliquely at a fisherman standing on the bank of a lake. Would the fisherman look taller or shorter to the diver than what he actually is?
$(d)$ Does the apparent depth of a tank of water change if viewed obliquely? If so,does the apparent depth increase or decrease?
$(e)$ The refractive index of diamond is much greater than that of ordinary glass. Is this fact of some use to a diamond cutter?