The equation $\sqrt{3} \sin x + \cos x = 4$ has

The equations of the normals at the ends of the latus rectum of the parabola $y^2 = 4ax$ are given by

An ice ball melts at a rate proportional to the amount of ice present at that instant. Half the quantity of ice melts in $20 \text{ minutes}$. Let $x_0$ be the initial quantity of ice. If after $40 \text{ minutes}$ the amount of ice left is $k x_0$,then the value of $k$ 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 of the following organisms belongs to the Kingdom $Monera$?