What is necessary for the maintenance of good health?

$A$ 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

If $\frac{2 x^3+x^2-5}{x^4-25}=\frac{A x+B}{x^2-5}+\frac{C x+1}{x^2+5}$,then $(A, B, C)$ equals to

If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$,then the angle between them is

Which of the following criteria is $NOT$ associated with the Five Kingdom classification system?

The angle between the lines represented by $\cos \theta(\cos \theta+1) x^2 - (2 \cos \theta + \sin^2 \theta) xy + (1 - \cos \theta) y^2 = 0$ is