The molar conductivities at infinite dilution for sodium acetate, HCl and NaCl are $91 \mathrm{~S} \mathrm{~cm}{ }^2$ $\mathrm{mol}^{-1}, 425.9 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ and $12.6 .4 \mathrm{~S} \mathrm{~cm}^2$ $\mathrm{mol}^{-1}$ respectively. The molar conductivity of acetic acid at infinite dilution is

The vector equation of the plane $\mathbf{r}=(2 \hat{\mathbf{i}}+\hat{\mathbf{k}})+\lambda(\hat{\mathbf{i}})+\mu(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}})$ in scalar product form is $\mathbf{r} \cdot(3 \hat{\mathbf{i}}+2 \hat{\mathbf{k}})=\alpha$, then $\alpha=\ldots$

. Area of the region bounded by $y=\cos x, x=0$, $x=\pi$ and $X$-axis is ... sq. units.

The length of the latusrectum of an ellipse is $\frac{18}{5}$ and eccentricity is $\frac{4}{5}$, then equation of the ellipse is .....