$A$ body is sliding down a rough inclined plane. The coefficient of friction between the body and the plane is $0.5$. The ratio of the net force required for the body to slide down and the normal reaction on the body is $1:2$. Then the angle of the inclined plane is: (in $^{\circ}$)

With an increase in atomic number,the melting point of alkali metals .......

$A$ transverse wave propagating on a stretched string of linear density $3 \times 10^{-4} ~kg ~m^{-1}$ is represented by the equation $y=0.2 \sin (1.5 x+60 t)$,where $x$ is in metres and $t$ is in seconds. The tension in the string (in newton) is

Match the following columns.

Column-$I$	Column-$II$
$A.$ $500$ million years ago	$1.$ Invertebrates
$B.$ $350$ million years ago	$2.$ Jawless fishes
$C.$ $320$ million years ago	$3.$ Sea weeds and few plants

The general formula of a cycloalkane is

In the arrangement shown in the figure,the masses of blocks $B$ and $A$ are $2m$ and $m$ respectively. The surface between $B$ and the floor is smooth. Block $B$ is connected to block $C$ by means of a string-pulley system. If the whole system is released,find the minimum value of the mass of block $C$ so that block $A$ remains stationary with respect to $B$. The coefficient of friction between $A$ and $B$ is $\mu$.