$A$ thin converging lens of focal length $f=25 \,cm$ forms the image of an object on a screen placed at a distance of $75 \,cm$ from the lens. The screen is moved closer to the lens by a distance of $25 \,cm$. The distance through which the object has to be shifted, so that its image on the screen is sharp again, is (in $\,cm$)

Find the velocity of the image of the given object in $cm/sec$.

The word $KVPY$ is written on a board and viewed through different lenses such that the board is at a distance beyond the focal length of the lens. Ignoring magnification effects,consider the following statements:
$(I)$ First image has been viewed from the planar side of a plano-convex lens and second image from the convex side of a plano-convex lens.
$(II)$ First image has been viewed from the concave side of a plano-concave lens and second image from the convex side of a plano-convex lens.
$(III)$ First image has been viewed from the concave side of a plano-concave lens and second image from the planar side of a plano-convex lens.
$(IV)$ First image has been viewed from the planar side of a plano-concave lens and second image from the convex side of a plano-convex lens.
Which of the above statements are correct?

$A$ lens of refractive index $n$ is placed in a liquid of refractive index $n'$. If the focal length of the lens in air is $f$,what will be its focal length in the liquid?

$A$ convex lens of focal length $f$ produces an image $\frac{1}{n}$ times the size of the object. The distance of the object from the lens is:

The distance between an object and the screen is $100 \ cm$. $A$ lens produces an image on the screen when placed at either of the positions $40 \ cm$ apart. The power of the lens is