An aeroplane flying at a constant speed, parallel to the horizontal ground, $$\sqrt 3 $$ kmabove it, is obsered at an elevation of $${60^o}$$ from a point on the ground. If, after five seconds, its elevation from the same point, is $${30^o}$$, then the speed (in km / hr) of the aeroplane, is :

If (p $$ \wedge $$ $$ \sim $$ q) $$ \wedge $$ (p $$ \wedge $$ r) $$ \to $$ $$ \sim $$ p $$ \vee $$ q is false, then the truth values of $$p, q$$ and $$r$$ are, respectively :

A given object takes n times more time to slide down a $${45^ \circ }$$ rough inclined plane as it takes to slide down a perfectly smooth $${45^ \circ }$$ incline. The coefficient of kinetic friction between the object and the incline is :

A body of mass m is moving in a circular orbit of radius R about a planet of mass M. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius $${R \over 2},$$ and the other mass, in a circular orbit of radius $${3R \over 2}$$. The difference between the final and initial total energies is :