What is the conjugate base of $OH^{-}$?

Widal test is used for the diagnosis of

What are $X$ and $Y$ in the following reaction sequence?
$C_2H_5OH$ $\xrightarrow{Cl_2} \underline{X}$ $\xrightarrow{Cl_2} \underline{Y}$

The ends of a stretched wire of length $L$ are fixed at $x = 0$ and $x = L$. In one experiment,the displacement of the wire is $y_1 = A \sin(\pi x/L) \sin(\omega t)$ and the energy is $E_1$. In another experiment,its displacement is $y_2 = A \sin(2\pi x/L) \sin(2\omega t)$ and the energy is $E_2$. Then:

If the lines $2x - 3y = 5$ and $3x - 4y = 7$ are two diameters of a circle of radius $7$,then the equation of the circle is

The equivalent capacitance between $A$ and $B$ is