If X is a random variable with the following probability distribution  then the variance of X, V(x)=

A random variable X has the probability distribution given below. Its variance is 

If the probability distribution of a random variable X is  then k =

If the probability distribution of a random variable X is  then second moment about 0 i.e.,

X is a random variable with distribution given below Then the value of k and variance are 

We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or 

When the rectangular metal tank is filled to the top with an unknown liquid, as observer with eyes level with the top of the tank can just see the corner E; a ray that refracts towards the observer at the top surface of the liquid is shown. The refractive index of the liquid will be

Following figure shows the multiple reflections of a light ray along a glass corridor where the walls are either parallel or perpendicular to one another. If the angle of incidence at point P is 30°, what are the angles of reflection of the light ray at points Q, R, S and T respectively

Which of the following ray diagram show physically possible refraction

A water drop in air refractes the light ray as

A small fish 0.4 m below the surface of a lake, is viewed through a simple converging lens of focal length 3 m. The lens is kept at 0.2 m above the water surface such that fish lies on the optical axis of the lens. The image of the fish seen by observer will be at

In a thin spherical fish bowl of radius 10 cm filled with water of refractive index 4/3 there is a small fish at a distance of 4 cm from the centre C as shown in figure. Where will the image of fish appears, if seen from E

An object is placed at a point distant x from the focus of a convex lens and its image is formed at I as shown in the figure. The distances x, x' satisfy the relation

Three lenses are placed co-axially as shown in figure. Focal length's of lenses are given 30 cm, 10 cm and 5 cm respectively. If a parallel beam of light falling on lens , emerging as a convergent beam such that it converges at the focus of . Distance between and will be