An artificial satellite of mass $m$ is moving along an elliptical path around the Earth. The areal velocity of the satellite is proportional to

$A$ stretched wire of length $110 \ cm$ is divided into three segments whose frequencies are in the ratio $1 : 2 : 3$. Their lengths must be

The $T.V.$ transmission tower in Delhi has a height of $245 \ m$. The distance up to which the broadcast can be received (taking the radius of earth to be $6.4 \times 10^6 \ m$) is........$km$ :

Two circular coils $X$ and $Y$,having an equal number of turns,carry equal currents in the same sense and subtend the same solid angle at point $O$. If the smaller coil $X$ is midway between $O$ and $Y$,and if we represent the magnetic induction due to the bigger coil $Y$ at $O$ as $B_Y$ and that due to the smaller coil $X$ at $O$ as $B_X$,then $\frac{B_Y}{B_X}$ is

If $A(2,-1)$ and $B(6,5)$ are two points,the ratio in which the foot of the perpendicular from $P(4,1)$ to $AB$ divides $AB$ is:

$A$ ball is dropped from a height $h$ on a floor of coefficient of restitution $e$. The total distance covered by the ball just before the second hit is