If two solutions have the same osmolarity,they are said to be

$x = \frac{1-\sqrt{y}}{1+\sqrt{y}} \Rightarrow \frac{dy}{dx}$ is equal to

Four smooth steel balls of equal mass at rest are free to move along a straight line without friction. The first ball is given a velocity of $0.4 \, m/s$. It collides head-on with the second elastically,the second one similarly with the third,and so on. The velocity of the last ball is .......... $m/s$.

The correct order of reactivity of $PhMgBr$ with: $(I)$ $Ph-CO-Ph$,$(II)$ $CH_3-CHO$,$(III)$ $CH_3-CO-CH_3$ 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

$A$ $0.001 \, \text{molal}$ solution of $[Pt(NH_3)_4Cl_4]$ in water shows a freezing point depression of $0.0054 \, ^\circ C$. If $K_f$ for water is $1.80$,the correct formulation of the above compound is?