A fish rising vertically up towards the surface of water with speed 3 observes a bird diving vertically down towards it with speed 9 . The actual velocity of bird is

The image of point P when viewed from top of the slabs will be

A cube of side 2 m is placed in front of a concave mirror focal length 1m with its face P at a distance of 3 m and face Q at a distance of 5 m from the mirror. The distance between the images of face P and Q and height of images of P and Q are

Two transparent slabs have the same thickness as shown. One is made of material A of refractive index 1.5. The other is made of two materials B and C with thickness in the ratio 1 : 2. The refractive index of C is 1.6. If a monochromatic parallel beam passing through the slabs has the same number of waves inside both, the refractive index of B is

We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 

If , then  by trapezoidal rule is

We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 

A wire of length L  and radius r is rigidly fixed at one end on stretching the other end of the wire a force F the increase in its lengths is L. If another wire of same material but of length 2 L and radius 2r, is stretched with a force of 2F, the increase in its length will he

Consider the situation shown in figure. Water is filled in a breaker upto a height of 10 cm. A plane mirror fixed at a height of 5 cm from the surface of water. Distance of image from the mirror after reflection from it of an object O at the bottom of the beaker is

One side of a glass slab is silvered as shown. A ray of light is incident on the other side at angle of incidence . Refractive index of glass is given as 1.5. The deviation of the ray of light from its initial path when it comes out of the slab is

A plane mirror is placed at the bottom of the tank containing a liquid of refractive index . P is a small object at a height h above the mirror. An observer O-vertically above P outside the liquid see P and its image in the mirror. The apparent distance between these two will be

If an object moves towards a plane mirror with a speed v at an angle to the perpendicular to the plane of the mirror, find the relative velocity between the object and the image

Figure shows a cubical room ABCD with the wall CD as a plane mirror. Each side of the room is 3m. We place a camera at the midpoint of the wall AB. At what distance should the camera be focussed to photograph an object placed at A

Two point white dots are 1mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which dots can be resolved by the eye ? [Take wavelength of light = 500 nm]

We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 

We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means