An aluminium ring $B$ faces an electromagnet $A$. The current $I$ through $A$ can be altered. Which of the following statements is correct?

Which of the following allotropes of carbon is isomorphous with crystalline silicon?

The set of solutions of the system of equations
$
\begin{aligned}
x+y & =\frac{2 \pi}{3} \\
\text{and} \quad \cos x+\cos y & =\frac{3}{2},
\end{aligned}
$
where $x, y$ are real,is

An $L-$shaped glass tube is just immersed in flowing water as shown. If the speed of the water current is $V$,then the height $h$ up to which water rises in the tube will be

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?

$A$ rod of glass $(\mu = 1.5)$ with a square cross-section is bent into the shape shown in the figure. $A$ parallel beam of light falls on the plane flat surface $A$ as shown. If $d$ is the width of a side and $R$ is the radius of the inner circular arc, then for what maximum value of $\frac{d}{R}$ will light entering the glass slab through surface $A$ emerge from the glass through surface $B$?