If $A$ is an invertible matrix of order $n$,then the determinant of $\operatorname{adj} A$ is equal to :

Two gaseous equilibria $SO_{2(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons SO_{3(g)}$ and $2 SO_{3(g)} \rightleftharpoons 2 SO_{2(g)} + O_{2(g)}$ have equilibrium constants $K_{1}$ and $K_{2}$ respectively at $298 \ K$. Which of the following relationships between $K_{1}$ and $K_{2}$ is correct?

Sulphur on boiling with $NaOH$ solution gives

If $a > 0$ and $\lim _{x \rightarrow a} \frac{a^x - x^a}{x^x - a^a} = -1$,then $a$ is equal to

Standard entropy of $X_2, Y_2$ and $XY_3$ are $60, 40$ and $50 \, J \, K^{-1} \, mol^{-1}$,respectively. For the reaction,$\frac{1}{2} X_2 + \frac{3}{2} Y_2 \to XY_3, \Delta H = -30 \, kJ$,to be at equilibrium,the temperature will be .....$K$.

Twelve cells,each having emf $E$ volts,are connected in series and are kept in a closed box. Some of these cells are wrongly connected with positive and negative terminals reversed. This $12$-cell battery is connected in series with an ammeter,an external resistance $R$ ohms,and a two-cell battery (two cells of the same type used earlier,connected perfectly in series). The current in the circuit when the $12$-cell battery and $2$-cell battery aid each other is $3 \text{ A}$,and it is $2 \text{ A}$ when they oppose each other. Then,the number of cells in the $12$-cell battery that are connected wrongly is: