Two thin lenses,one of focal length $+ 60 \ cm$ and the other of focal length $-20 \ cm$ are put in contact. The combined focal length is........$cm$.

In the given optical instrument,how can a third lens of the same focal length be inserted to increase the light-collecting efficiency without changing the positions of the object and the image? Calculate the position of that lens.

Concave and convex lenses are placed touching each other. The ratio of magnitudes of their power is $2:3$. The focal length of the system is $30 \ cm$. The focal lengths of individual lenses are

List-$I$ contains four combinations of two lenses ($1$ and $2$) whose focal lengths (in $cm$) are indicated in the figures. In all cases,the object is placed $20 \ cm$ from the first lens on the left,and the distance between the two lenses is $5 \ cm$. List-$II$ contains the positions of the final images.
Which one of the following options is correct?

An object is placed $30 \ cm$ away from a convex lens of focal length $10 \ cm$ and a sharp image is formed on a screen. Now,a concave lens is placed in contact with the convex lens. The screen now has to be moved by $45 \ cm$ to get a sharp image again. The magnitude of the focal length of the concave lens is (in $cm$):

Two lenses of power $3\,D$ and $-5\,D$ are combined to form a compound lens. An object is placed at a distance of $50\,cm$ from this combination. At what distance (in $cm$) will the image be formed?