The potential energy of a particle of mass $m$ is given by $U(x) = \begin{cases} E_0; & 0 \le x \le 1 \\ 0; & x > 1 \end{cases}$. $\lambda_1$ and $\lambda_2$ are the de-Broglie wavelengths for $0 \le x \le 1$ and $x > 1$ respectively. If the total energy of the particle is $2E_0$,the ratio $\frac{\lambda_1}{\lambda_2}$ will be

When $25 \ g$ of a non-volatile solute is dissolved in $100 \ g$ of water,the vapour pressure is lowered by $0.225 \ mm$. If the vapour pressure of water at $20^{\circ}C$ is $17.5 \ mm$,what is the molecular weight of the solute?

$A$ thin semi-circular ring of radius $r$ has a positive charge $q$ distributed uniformly over it. The net electric field $\vec{E}$ at the center $O$ is:

As shown in the figure,two particles each of mass $m$ tied at the ends of a light string of length $2 a$ are kept on a frictionless horizontal surface. When the mid-point $(P)$ of the string is pulled vertically upwards with a small but constant force $F$,the particles move towards each other on the surface. The magnitude of acceleration of each particle,when the separation between them becomes $2 x$,is:

What is necessary for the maintenance of good health?

The common characteristics between tomato and potato will be maximum at the level of their . . . . . . .