Where should an object be placed in front of a concave mirror to obtain a real and diminished image?

Sudha finds out that the sharp image of the window pane of her science laboratory is formed at a distance of $15\, cm$ from the lens. She now tries to focus the building visible to her outside the window instead of the window pane without disturbing the lens. In which direction will she move the screen to obtain a sharp image of the building? What is the approximate focal length of this lens?

One half of a convex lens of focal length $10\, cm$ is covered with a black paper. Can such a lens produce an image of a complete object placed at a distance of $30\, cm$ from the lens? Draw a ray diagram to justify your answer.
$A$ $4\, cm$ tall object is placed perpendicular to the principal axis of a convex lens of focal length $20\, cm$. The distance of the object from the lens is $15\, cm$. Find the nature,position and size of the image.

Where is the image formed when an object is placed anywhere in front of a concave lens?

What kind of image is formed when an object is placed between the principal focus $(F)$ and the optical center $(O)$ of a convex lens?

$A$ convex lens has a focal length of $25\, cm$. Calculate the distance of the object from the lens if the image is to be formed on the opposite side of the lens at a distance of $75\, cm$ from the lens. What will be the nature of the image?