$A$ block of metal is heated to a temperature much higher than the room temperature and allowed to cool in a room free from air currents. Which of the following curves correctly represents the rate of cooling?

$A$ particle moves with simple harmonic motion in a straight line. In the first $\tau \, s$,after starting from rest,it travels a distance $a$,and in the next $\tau \, s$,it travels $2a$ in the same direction. Then:

$A$ circle with center at $(2,4)$ is such that the line $x+y+2=0$ cuts a chord of length $6$. The radius of the circle is

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio $2 : 3$. The ratio of their partial pressures,when enclosed in a vessel kept at a constant temperature,is $4 : 3$. The ratio of their densities is :-

For an ellipse with eccentricity $e = \frac{1}{2}$,the centre is at the origin. If one directrix is $x = 4$,then the equation of the ellipse is: