Three lenses of focal lengths $+10 \ cm, -10 \ cm$ and $+30 \ cm$ are placed at distances of $30 \ cm, 35 \ cm$ and $45 \ cm$ respectively from an object. The distance between the object and the final image formed is: (in $cm$)

$A$ biconvex glass lens has a focal length $f$ and power $P$. It is cut into two symmetric parts along its principal axis. If these two parts are joined as shown in figure $(b)$,what is the new power of the combination?

$A$ convex lens of focal length $30\, cm$ and a concave lens of focal length $10\, cm$ are placed coaxially at a distance $d$ apart. Parallel rays are incident on the convex lens. The rays emerging from the concave lens are also parallel. Then $d = $ . . . . . . $cm$.

Two convex lenses of focal length $20\,cm$ each are placed coaxially with a separation of $60\,cm$ between them. The image of the distant object formed by the combination is at $...........\,cm$ from the first lens.

$A$ convex lens of focal length $30 \ cm$ is placed in contact with a concave lens of focal length $20 \ cm$. An object is placed at $20 \ cm$ to the left of this lens system. The distance of the image from the lens in $cm$ is . . . . . .

What is the power of the combination of a convex lens and a concave lens of equal focal length $25 \text{ cm}$?