The vapour pressure of a solvent decreases by $10 \ mm$ of mercury when a non-volatile solute is added to the solvent. The mole fraction of the solute in the solution is $0.2$. What should be the mole fraction of the solute if the decrease in the vapour pressure is to be $20 \ mm$ of mercury?

The equation $\frac{1}{r} = \frac{1}{8} + \frac{3}{8} \cos \theta$ represents

Which of the following forms a stable $+4$ oxidation state?

Two polaroids are placed in the path of an unpolarized beam of intensity $I_0$ such that no light is emitted from the second polaroid. If a third polaroid,whose polarization axis makes an angle $\theta$ with the polarization axis of the first polaroid,is placed between these polaroids,then the intensity of light emerging from the last polaroid will be:

If $(2,3,-3)$ is one end of a diameter of the sphere $x^2+y^2+z^2-6x-12y-2z+20=0$, then the other end of the diameter is

Half-life of a radioactive substance $A$ is two times the half-life of another radioactive substance $B$. Initially,the number of nuclei of $A$ and $B$ are $N_A$ and $N_B$ respectively. After three half-lives of $A$,the number of nuclei of both are equal. Then the ratio $\frac{N_A}{N_B}$ is