The value of $E_1^{\circ}$ is (in $V$)

For a saturated solution of $Ag_{2}CrO_{4}$ at infinite dilution,$\lambda_{m}^{\infty}(Ag^{+}) = 127 \ \Omega^{-1} \ cm^{2} \ mol^{-1}$ and $\lambda_{m}^{\infty}(CrO_{4}^{2-}) = 246 \ \Omega^{-1} \ cm^{2} \ mol^{-1}$. If the specific conductance of the solution is $2 \times 10^{-2} \ \Omega^{-1} \ cm^{-1}$,calculate the solubility product $(K_{sp})$ of $Ag_{2}CrO_{4}$.

The molar conductivity of a solution of a weak acid $HX$ $(0.01 \ M)$ is $10$ times smaller than the molar conductivity of a solution of a weak acid $HY$ $(0.10 \ M)$. If $\lambda_{X^{-}}^0 \approx \lambda_{Y^{-}}^0$,the difference in their $pK_a$ values,$pK_a(HX) - pK_a(HY)$,is (consider degree of ionization of both acids to be $\ll 1$)

For lead storage battery,pick the correct statements:
$A.$ During charging of battery,$PbSO_4$ on anode is converted into $Pb$.
$B.$ During charging of battery,$PbSO_4$ on cathode is converted into $PbO_2$.
$C.$ Lead storage battery consists of a grid of lead packed with $PbO_2$ as cathode.
$D.$ Lead storage battery has $\sim 38\%$ solution of sulphuric acid as an electrolyte.
Choose the correct answer from the options given below:

Identify the correct statements from the following:
$(A)$ At $298 \ K$,the potential of a hydrogen electrode placed in a solution of $pH = 10$ is $-0.59 \ V$.
$(B)$ The limiting molar conductivity of $Ca^{2+}$ and $Cl^{-}$ are $119$ and $76 \ S \ cm^2 \ mol^{-1}$ respectively. The limiting molar conductivity of $CaCl_2$ is $195 \ S \ cm^2 \ mol^{-1}$.
$(C)$ The correct relationship between $K_{c}$ and $E_{cell}^{0}$ is $E_{cell}^{0} = \frac{2.303 RT}{nF} \log K_{c}$.

Given:
$\lambda _{ClCH_2COONa} = 224 \ \Omega ^{-1} \ cm^2 \ gmeq^{-1}$
$\lambda _{NaCl} = 38.2 \ \Omega ^{-1} \ cm^2 \ gmeq^{-1}$
$\lambda _{HCl} = 203 \ \Omega ^{-1} \ cm^2 \ gmeq^{-1}$
What is the value of $\lambda _{ClCH_2COOH}$ in $\Omega ^{-1} \ cm^2 \ gmeq^{-1}$?