The value of c in Lagrange's Mean Value theorem for the function  in the interval [-1,1] is

The Coefficient of linear expansion of brass & steel are  If we take a brass rod of length & steel rod of length  at ,0°c, their difference in length  will remain the same at a temperature if

If m and are the mean and variance of the random variable X, whose distribution is given by: 

A random variable X has the following Distribution  The value of ‘K’ and P(X<3) are respectively equal to

A random variable X has the following probability distribution  then the mean value of X is

If a random variable X has the following probability distribution  then the mean value of X is

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