What is the molar conductivity of $0.005 \ M$ $NaI$ solution if its conductivity is $6.065 \times 10^{-4} \ \Omega^{-1} \ cm^{-1}$?

When a certain conductivity cell was filled with $0.1 \ M \ KCl$,it had a resistance of $85 \ \Omega$ at $25 \ ^oC$. When the same cell was filled with an aqueous solution of $0.052 \ M$ unknown electrolyte,the resistance was $96 \ \Omega$. Calculate the molar conductivity of the unknown electrolyte at this concentration ............. $\Omega^{-1} \ cm^2 \ mol^{-1}$ (Given: Specific conductance of $0.1 \ M \ KCl = 1.29 \times 10^{-2} \ \Omega^{-1} \ cm^{-1}$)

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

An electrolyte of a polymer-salt complex of poly(ethylene oxide)-LiCF$_{3}$SO$_{3}$ is shaped into a free standing circular film of $20 \ mm$ diameter and a thickness of $20 \ \mu m$. When it is sandwiched between $2$ stainless steel circular electrodes of the same diameter, this cell exhibits a conductance of $\frac{314}{5} \ S$. What is the specific conductivity of the electrolyte?

The ionic conductivity of $Ba^{2+}$ and $Cl^{-}$ at infinite dilution are $127$ and $76 \ ohm^{-1} cm^2 eq^{-1}$ respectively. The equivalent conductivity of $BaCl_2$ at infinite dilution (in $ohm^{-1} cm^2 eq^{-1}$) would be $:-$

Given below are two statements :
Statement $I :$ The limiting molar conductivity of $KCl$ (strong electrolyte) is higher compared to that of $CH_{3}COOH$ (weak electrolyte).
Statement $II :$ Molar conductivity decreases with decrease in concentration of electrolyte.
In the light of the above statements,choose the most appropriate answer from the options given below: