An object is placed on the principal axis of a convex lens of focal length $10\,cm$ as shown. $A$ plane mirror is placed on the other side of the lens at a distance of $20\,cm$. The final image produced by the plane mirror is $5\,cm$ behind the mirror. The distance of the object from the lens is $............cm$.

Assertion : $A$ red object appears dark in the yellow light.
Reason : The red colour is scattered less.

Assertion : $A$ concave mirror and convex lens both have the same focal length in air. When they are submerged in water,they will have same focal length.
Reason : The refractive index of water is smaller than the refractive index of air.

$A$ small source of light is to be suspended directly above the centre of a circular table of radius $R$. What should be the height of the light source above the table so that the intensity of light is maximum at the edges of the table compared to any other height of the source?

$A$ concave mirror is placed at the bottom of an empty tank with its face upwards and axis vertical. When sunlight falls normally on the mirror,it is focused at a distance of $32 \, cm$ from the mirror. If the tank is filled with water $\left( \mu = \frac{4}{3} \right)$ up to a height of $20 \, cm$,then the sunlight will now be focused at:

$A$ convex lens forms an image of an object on a screen. The height of the image is $9 \, cm$. The lens is now displaced until an image is again obtained on the screen. The height of this image is $4 \, cm$. The distance between the object and the screen is $90 \, cm$.