Which of the following statements is correct for any thermodynamic system?

When a $J$-shaped conducting rod is rotating in its own plane with constant angular velocity $\omega$,about one of its ends $P$,in a uniform magnetic field $\vec B$ (directed normally into the plane of the paper),then the magnitude of the emf induced across it will be:

$A$ vertical $U-$tube of uniform inner cross-section contains mercury in both sides of its arms. $A$ glycerin (density $= 1.3 \ g/cm^3$) column of length $10 \ cm$ is introduced into one of its arms. Oil of density $0.8 \ g/cm^3$ is poured into the other arm until the upper surfaces of the oil and glycerin are in the same horizontal level. Find the length of the oil column. (Density of mercury $= 13.6 \ g/cm^3$) (in $cm$)

$\cos ^{-1}\left(\frac{-1}{2}\right)-2 \sin ^{-1}\left(\frac{1}{2}\right)+3 \cos ^{-1}\left(\frac{-1}{\sqrt{2}}\right)-4 \tan ^{-1}(-1)$ equals:

What will happen if the stretch receptors of the urinary bladder wall are completely removed?

The utility of a microorganism like $Trichoderma$ $harzianum$ has been proven in which of the following?