Which of the following is not a fat-soluble vitamin?

$A$ frictionless track $ABCDE$ ends in a circular loop of radius $R$. $A$ body slides down the track from point $A$ which is at a height $h = 5 \, cm$. The maximum value of $R$ for the body to successfully complete the loop is .................. $cm$.

Which sample contains a greater number of nuclei: a $5.00 \, \mu Ci$ sample of $^{240}Pu$ (half-life $6560 \, y$) or a $4.45 \, \mu Ci$ sample of $^{243}Am$ (half-life $7370 \, y$)?

The network shown in the figure is a part of a complete circuit. If at a certain instant the current $i$ is $5 \ A$ and is decreasing at the rate of $10^3 \ A/s$,then $V_A - V_B$ is ..... $V$.

$\left|\begin{array}{ccc} \log e & \log e^2 & \log e^3 \\ \log e^2 & \log e^3 & \log e^4 \\ \log e^3 & \log e^4 & \log e^5 \end{array}\right|$ is equal to :

$A$ Carnot engine having an efficiency of $1/10$ as a heat engine is used as a refrigerator. If the work done on the system is $10 \, J$,the amount of energy absorbed from the reservoir at a lower temperature is .......... $J$.