Find the potential difference across the $24\,\Omega$ resistor in the given circuit.

The $pH$ of a buffer solution decreases by $0.02$ units when $0.12 \ g$ of acetic acid is added to $250 \ mL$ of a buffer solution of acetic acid and potassium acetate at $27^{\circ} C$. The buffer capacity of the solution is

If $A = \begin{bmatrix} -2 & 2 \\ -3 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$,then $(B^{-1} A^{-1})^{-1}$ is equal to

The lines $2x + 3y = 6$ and $2x + 3y = 8$ cut the $X$-axis at $A$ and $B$,respectively. $A$ line $L$ drawn through the point $(2, 2)$ meets the $X$-axis at $C$ in such a way that the abscissae of $A, B,$ and $C$ are in arithmetic progression. Then,the equation of the line $L$ is

The coefficients of apparent expansion of a liquid when determined using two different vessels $A$ and $B$ are $\gamma_1$ and $\gamma_2$,respectively. If the coefficient of linear expansion of the vessel $A$ is $\alpha$,the coefficient of linear expansion of the vessel $B$ is

If $u=\sin ^{-1}\left(\frac{x^4+y^4}{x+y}\right)$, then $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}$ is equal to