The species having tetrahedral shape is

The distance of the point $(1, 1, 9)$ from the point of intersection of the line $\frac{x-3}{1} = \frac{y-4}{2} = \frac{z-5}{2}$ and the plane $x+y+z=17$ is

$A$ circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of the discs touch. The centre of mass of the new disc is at a distance $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

The coefficient of $x^{10}$ in the expansion of $(2+3x)e^{-x}$ is

The value of $k$,if $(1,2)$ and $(k,-1)$ are conjugate points with respect to the ellipse $2x^2 + 3y^2 = 6$ is:

The ratio among most probable velocity,mean velocity and root mean square velocity is given by