Identify $A$ and $B$ in the following reaction:
$CH_3-CH_3 \xleftarrow{B} CH_3COOH \xrightarrow{A} CH_3CH_2OH$

$A$

$B$

$\sinh^{-1}(2^{3/2})$ is equal to :

An $AC$ source of angular frequency $\omega$ is fed across a resistor $R$ and a capacitor $C$ in series. The current registered is $I$. If now the frequency of the source is changed to $\omega/3$ (but maintaining the same voltage),the current in the circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency $\omega$.

If $1$ is a multiple root of order $3$ for the equation $x^4-2x^3+2x-1=0$,then the other root is

Pulses are obtained from which family?

$A$ random variate $X$ takes the values $0, 1, 2, 3$ and its mean is $1.3$. If $P(X=3) = 2 P(X=1)$ and $P(X=2) = 0.3$, then $P(X=0)$ is equal to: