The positive charge present in 1.00 mol of neutral molecular hydrogen gas ($H_2$) is [[1]] X 10⁶ C.

The avogadro number of entities are present in one mole of any material. We have the Avogadro number of hydrogen molecules if one mole of hydrogen atoms and another mole of hydrogen atom combine to make one mole of hydrogen molecule.
Each hydrogen molecule will consist of two distinct hydrogen atoms since it is described as a hydrogen molecule. There are literally Avogadro number of hydrogen atoms in a mole, which translates to Avogadro number of protons and Avogadro number of electrons in a mole. We are unconcerned about neutrons because hydrogen atoms lack them.

The Avogadro number has a value of $6.022\times {10}^{23}$.
This indicates that there are $2\times 6.022\times {10}^{23}$ protons in a mole of hydrogen.
A proton's charge will be equivalent to the magnitude of an electron's charge. Hence The proton will have a charge of $1.6\times {10}^{19}$ coulombs.
Therefore, a neutral hydrogen molecule contains a total of coulombs of charge.

$2\times 6.022\times {10}^{23}\times 1.6\times {10}^{-19}$ coulombs

$\Rightarrow 19.27\times {10}^4$ coulombs
We know that 1 megacoulomb (1MC) is equal to ${10}^6$ coulombs.
$1\mathrm{MC}={10}^6$ coulombs
$\Rightarrow 1$ coulomb $=\frac{1}{{10}^6}\mathrm{MC}$
$\Rightarrow 19.27\times {10}^4$ coulombs $=19.27\times {10}^4\times \frac{1}{{10}^6}\mathrm{MC}$
$\Rightarrow 19.27\times {10}^4$ coulombs $=0.1927\mathrm{MC}$

Hence A mole of neutral hydrogen has a positive charge of 0.1927 mega coulombs in it.

Hence, the correct answer is 0.1927.