Two particles $A$ and $B$,initially at rest,move towards each other under a mutual force of attraction. At the instant when the speed of $A$ is $v$ and the speed of $B$ is $2v$,the speed of the center of mass of the system is:

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

What is the wavelength of light with a frequency of $100\; Hz$?

One of the endangered species of Indian medicinal plants is

The area (in square units) of the region enclosed by the two circles $x^2+y^2=1$ and $(x-1)^2+y^2=1$ is

$A$ block of $200 \text{ g}$ mass moves with a uniform speed in a horizontal circular groove with vertical side walls of radius $20 \text{ cm}$. If the block takes $40 \text{ s}$ to complete one round,the normal force exerted by the side walls of the groove is: