The angle of elevation of the top of a vertical tower from a point A, due east of it is 45^o. The angle of elevation of the top of the same tower from a point B, due south of A is 30^o. If the distance between A and B is $$54\sqrt 2 \,m,$$ then the height of the tower (in metres), is :

The contrapositive of the following statement,

“If the side of a square doubles, then its area increases four times”, is :

A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by n² R t² where n is a constant. The power delivered to the particle by the force acting on it, is :

A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation AD = C ln (BD) holds true. Then which of the combination is not a meaningful quantity ?