Two long parallel wires are at a distance $2d$ apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field $B$ along the line $XX'$ is given by

The value of $c$ in the Lagrange's mean value theorem for $f(x)=\sqrt{x-2}$ in the interval $[2,6]$ is

Which of the following sulfates is insoluble in water?

$A$ $Ge$ specimen is doped with $Al$. The concentration of acceptor atoms is $\sim 10^{21} \text{ atoms}/m^3$. Given that the intrinsic concentration of electron-hole pairs is $\sim 10^{19} /m^3$,the concentration of electrons in the specimen is:

Charge $q$ is uniformly distributed over a thin half ring of radius $R$. The electric field at the centre of the ring is

$A$ flask of volume $10^3 \text{ cc}$ is completely filled with mercury at $0 \ ^\circ\text{C}$. The coefficient of cubical expansion of mercury is $180 \times 10^{-6} / ^\circ\text{C}$ and that of glass is $40 \times 10^{-6} / ^\circ\text{C}$. If the flask is now placed in boiling water at $100 \ ^\circ\text{C}$,how much mercury (in $\text{cc}$) will overflow?