What is the molar conductivity of $CH_3COOH$ at infinite dilution if the molar conductivities of $H_2SO_4$, $K_2SO_4$, and $CH_3COOK$ at infinite dilution are respectively $x$, $y$, and $z$ $\Omega^{-1} \text{ cm}^2 \text{ mol}^{-1}$?

Given the following molar conductivities at $25\,\text{}^{\circ}C$: $HCl = 426\,\Omega^{-1}\,cm^{2}\,mol^{-1}$,$NaCl = 126\,\Omega^{-1}\,cm^{2}\,mol^{-1}$,and sodium crotonate $(NaC)$ = $83\,\Omega^{-1}\,cm^{2}\,mol^{-1}$. Calculate the ionization constant $(K_{a})$ of crotonic acid $(HC)$ if the conductivity of a $0.001\,M$ crotonic acid solution is $3.83 \times 10^{-5}\,\Omega^{-1}\,cm^{-1}$.

An aqueous solution of $X$ is added slowly to an aqueous solution of $Y$ as shown in List-$I$. The variation in conductivity of these reactions is given in List-$II$. Match List-$I$ with List-$II$ and select the correct answer using the code given below the lists :

List-$I$	List-$II$
$P$. $\underset{X}{(C_2H_5)_3N} + \underset{Y}{CH_3COOH}$	$1$. Conductivity decreases and then increases
$Q$. $\underset{X}{KI (0.1 \ M)} + \underset{Y}{AgNO_3 (0.01 \ M)}$	$2$. Conductivity decreases and then does not change much
$R$. $\underset{X}{CH_3COOH} + \underset{Y}{KOH}$	$3$. Conductivity increases and then does not change much
$S$. $\underset{X}{NaOH} + \underset{Y}{HI}$	$4$. Conductivity does not change much and then increases

Codes: $P \quad Q \quad R \quad S$

The molar conductivity of $0.02 \ M$ $KCl$ solution is $410 \ \Omega^{-1} \ cm^2 \ mol^{-1}$ at $25^{\circ} C$. Calculate its conductivity?

The specific conductance of a solution depends upon -

Resistance of a conductivity cell filled with $0.1 \ mol \ L^{-1}$ $NaCl$ is $100 \ \Omega$. If the resistance of the same cell when filled with $0.02 \ mol \ L^{-1}$ $NaCl$ solution is $258 \ \Omega$,the conductivity of $0.02 \ mol \ L^{-1}$ $NaCl$ solution is (Conductivity of $0.1 \ mol \ L^{-1}$ $NaCl$ is $1.29 \ S \ m^{-1}$) (in $S \ m^{-1}$)