If $u(x, y)=y \log x+x \log y$, then $u_x u_y-u_x \log x-u_y \log y+\log x \log y$ is equal to :

If the area of the auxiliary circle of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ $(a > b)$ is twice the area of the ellipse,then the eccentricity of the ellipse is

Name the method of asexual reproduction in lichens.

Which of the following is a basic salt?

The molecular formula of compound $A$ is $C_2Cl_3OH$. It reduces Fehling's solution and on oxidation gives a monocarboxylic acid $B$. Compound $A$ is obtained by the reaction of chlorine with ethyl alcohol. What is $A$?

The minimum value of $27 \tan ^2 \theta + 3 \cot ^2 \theta$ is