The integral $\int \frac{3x^{13} + 2x^{11}}{(2x^4 + 3x^2 + 1)^4} dx$ is equal to (where $C$ is a constant of integration)

$3$ moles of an ideal monoatomic gas perform an $A B C D A$ cyclic process as shown in the figure. The gas temperatures are $T_A=400 \, K$, $T_B=800 \, K$, $T_C=2400 \, K$, and $T_D=1200 \, K$. The work done by the gas is (approximately) $(R=8.314 \, J / mol K)$. (in $ \, kJ$)

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 ..... $V$.

The gas used in the hydrogenation of vegetable oils in the presence of nickel as catalyst is

If $s$ and $p$ are respectively the sum and the product of the slopes of the lines $3x^2 - 2xy - 15y^2 = 0$,then $s:p$ is equal to

Consider the following statements about Langmuir isotherm.
$I.$ The free gas and adsorbed gas are in dynamic equilibrium.
$II.$ All adsorption sites are equivalent.
$III.$ The initially adsorbed layer can act as a substrate for further adsorption.
$IV.$ The ability of a molecule to get adsorbed at a given site is independent of the occupation of neighboring sites.
The correct statements are