When did $R.H. Whittaker$ propose the five-kingdom classification system?

The equation of the circle concentric with the circle $x^2+y^2-6x+12y+15=0$ and having double its area is

The equation of the line joining the centres of the circles belonging to the coaxial system of circles $4x^2 + 4y^2 - 12x + 6y - 3 + \lambda(x + 2y - 6) = 0$ is

If $S_n = 1^3 + 2^3 + \ldots + n^3$ and $T_n = 1 + 2 + \ldots + n$,then

$A$ block of mass $1\,kg$ lies on a horizontal surface in a truck. The coefficient of static friction between the block and the surface is $0.6$. If the acceleration of the truck is $5\,m\,s^{-2}$,the frictional force acting on the block is ........ $N$.

The direction ratios of the two lines $AB$ and $AC$ are $1, -1, -1$ and $2, -1, 1$. The direction ratios of the normal to the plane $ABC$ are