The equation of the circle of radius $3$ that lies in the fourth quadrant and touches the lines $x=0$ and $y=0$ is

$A$ child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal floor. If the child starts running towards the other end of the trolley with a speed $u$,the centre of mass of the system (trolley + child) will move with a speed.

Which electron is associated with the least energy?

The equation of the hyperbola whose directrix is $2x + y = 1$,focus is $(1, 1)$,and eccentricity $e = \sqrt{3}$ is:

Which of the following is an incorrect pair?

Three waves of equal frequency having amplitudes $10 \mu m,$ $4 \mu m,$ and $7 \mu m$ arrive at a given point with a successive phase difference of $\frac{\pi}{2}.$ The amplitude of the resulting wave in $\mu m$ is given by