What is the amount of charge possessed by $1\text{kg}$ of electrons ?

The correct option is A $1.76\times {10}^{11}\text{C}$
Given:
Mass of electrons $\left(m\right)=1\text{kg}$
We know that, mass of 1 electron is $m_e=9.1\times {10}^{-31}\text{kg}$

Total number of electrons in given mass,
$\Rightarrow n=\frac{m}{m_e}$
$\Rightarrow n=\frac{1}{9.1\times {10}^{-31}}=\frac{{10}^{31}}{9.1}$

Total amount of charge possessed by $1\text{kg}$ of electrons is
$q_{\text{total}}=ne$

$\Rightarrow q_{\text{total}}=\frac{{10}^{31}}{9.1}\times 1.6\times {10}^{-19}$

$\therefore q_{\text{total}}=1.76\times {10}^{11}\text{C}$

Hence, option $\left(a\right)$ is correct.

$\begin{array}{c}\text{Why this question ?}\\ \text{Bottom line: In this question, total charge asked, shouldn't}\\ \text{be confused with quantization principle.}\end{array}$