Image Formation for Virtual Object in Concave Lens

Two diverging lenses are kept as shown in the figure. The final image formed will be:

In the figure shown an object $O$ is placed in front of a thin lens of small aperture. The dotted curves represent the extensions of the respective curves in the figure. How many images will be formed finally.

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$

The position of the optic axis $\mathrm{OO}\text{'}$path of incident ray $\mathrm{AB}$ and emergent ray $\mathrm{BC}$are known. Find by construction, the position of lens and position of main foci.

The following figure shows a beam of light converging at point $P\mathit{.}$ When a concave lens of focal length $16 \mathrm{cm}$ is introduced in the path of the beam at a place $O$ shown by dotted line, such that $OP$ becomes the axis of the lens, the beam converges at a distance $x$ from the lens. The value of $x$ will be equal to

A diverging lens of focal length $20 \mathrm{cm}$ and a converging mirror of focal length $10 \mathrm{cm}$are placed coaxially at a separation of $5 \mathrm{cm}$. Where should an object be placed so that a real image is formed at the object itself?

A diverging lens of focal length $10 \mathrm{cm}$ is placed $10 \mathrm{cm}$ in front of a plane mirror as shown in the figure. Light from a very far away source falls on the lens. The final image is at a distance

An object is placed at a distance of $20 \mathrm{cm}$ from a concave lens, the image formed is small. Which statement is certainly correct?