In the arrangement shown in the figure,the pulley is smooth and massless,and all the strings are light. Let $F_1$ be the force exerted on the pulley in case $(i)$ and $F_2$ be the force in case $(ii)$. Then:

The internal energy change in a system that has absorbed $2 \, kcal$ of heat and done $500 \, J$ of work is ........... $J$.

$A$ parallel plate capacitor with air between the plates has a capacitance of $9 \, pF$. The separation between its plates is $d$. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant $K_1 = 3$ and thickness $d/3$,while the other one has dielectric constant $K_2 = 6$ and thickness $2d/3$. The new capacitance of the capacitor is .... $pF$.

Which of the following halogen oxides is ionic?

Two unknown resistances are connected in two gaps of a meter-bridge. The null point is obtained at $40 \ cm$ from left end. A $30 \Omega$ resistance is connected in series with the smaller of the two resistances, the null point shifts by $20 \ cm$ to the right end. The value of smaller resistance in $\Omega$ is

Which one of the following oxides is reduced by water gas to obtain the metal during its extraction?