The angle between the lines whose direction cosines are $\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right)$ and $\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\right)$ is:

The area (in sq. units) of the region lying in the first quadrant and enclosed by the $X$-axis,the straight line $x-\sqrt{3} y=0$ and the circle $x^2+y^2=4$,is

The major product of the following reaction is

$A$ beam of electrons passes undeflected through mutually perpendicular electric and magnetic fields. If the electric field is switched off, and the same magnetic field is maintained, the electrons move

Which of the products is formed when acetone is reacted with barium hydroxide solution?

Two spherical bodies of mass $M$ and $5M$ and radii $R$ and $2R$ respectively are released in free space with an initial separation between their centres equal to $12\,R$. If they attract each other due to gravitational force only,then the distance covered by the smaller body just before collision is (in $, R$)