Cell constant of a conductivity cell is $0.9 \ cm^{-1}$ and resistance shown by $AgNO_3$ solution is $6530 \ \Omega$. What is the conductivity of $AgNO_3$ solution?

The equivalent conductance of a monobasic acid at infinite dilution is $348 \ ohm^{-1} \ cm^2 \ eq^{-1}$. If the resistivity of the solution containing $15 \ g$ of the acid (molecular weight $49$) in $1 \ L$ is $18.5 \ ohm \ cm$,what is the degree of dissociation of the acid? (Answer in percentage)

Match List-$I$ with List-$II$:

List-$I$ (Parameter)	List-$II$ (Unit)
$a$. Cell constant	$i$. $S\, cm^{2}\, mol^{-1}$
$b$. Molar conductivity	$ii$. Dimensionless
$c$. Conductivity	$iii$. $m^{-1}$
$d$. Degree of dissociation of electrolyte	$iv$. $\Omega^{-1}\, m^{-1}$

Choose the most appropriate answer from the options given below:

At $298 \ K$ the molar conductivities at infinite dilution $(\Lambda_m^{\circ})$ of $NH_4Cl, KOH$ and $KCl$ are $152.8, 272.6$ and $149.8 \ S \ cm^2 \ mol^{-1}$ respectively. The $\Lambda_m^{\circ}$ of $NH_4OH$ in $S \ cm^2 \ mol^{-1}$ and $\%$ dissociation of $0.01 \ M \ NH_4OH$ with $\Lambda_m = 25.1 \ S \ cm^2 \ mol^{-1}$ at the same temperature are

The values of $\mu^{\infty}$ for $NH_4Cl$,$NaOH$,and $NaCl$ are $129.8$,$248.1$,and $126.4 \ \Omega^{-1} \ cm^{2} \ mol^{-1}$ respectively. Calculate $\mu^{\infty}$ for $NH_4OH$ solution.

The molar conductivity of $0.007 \ M$ acetic acid is $20 \ S \ cm^{2} \ mol^{-1}$. What is the dissociation constant of acetic acid? (In $\times 10^{-5} \ mol \ L^{-1}$)
$[\Lambda_{H^{+}}^{\circ}=350 \ S \ cm^{2} \ mol^{-1}, \Lambda_{CH_{3}COO^{-}}^{\circ}=50 \ S \ cm^{2} \ mol^{-1}]$