Var (K) =0 where k is a constant

E(K) =K where K is a constant .TRUE or FALSE

From the definition of definite integral as the limit of a sum, evaluate: int_(a)^(b)kdx , where k is a constant

The pressure p and the volume v of a gas are connected by the relation pv^(1.4)=k , where k is a constant. Then a decrease of 0.5 % in the volume of the gas corresponds to an increase of pressure by-

A particle of mass m is rotated in a circular path of radius r under the influence of a force F=-k/(r^2) , where k is a constant. Find the total energy of the particle.

If X and Y are two independent variables, then prove that var(aX+bY)=a^2var(X)+b^2var(Y) , where a and b are constants.

answer any one question : (ii) if X and Y are two independent variables , then rove that var(aX+bY ) =a^2 var (X) +b^2 var (Y) , where a and b are constants

The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.

The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.