The kinetic energy needed to project a body of mass $m$ from the earth's surface (radius $R$) to infinity is

In a triangle $ABC$,if the midpoints of sides $AB, BC, CA$ are $(3,0,0), (0,4,0), (0,0,5)$ respectively,then $AB^2 + BC^2 + CA^2 = $

Green glands,present in some arthropods,help in

If $x^2 y - x^3 \frac{dy}{dx} = y^4 \cos x$, then $x^3 y^{-3}$ is equal to

$A$ magnetized wire of magnetic moment $M$ and length $l$ is bent into the form of a semicircle of radius $r$. Then its new magnetic moment is:

$A$ rectangle $ABCD$ is inscribed in a circle whose center lies on the line $3y = x + 10$. If $A$ and $B$ are the points $(-6, 7)$ and $(4, 7)$ respectively,find the area of the rectangle.