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Correct explanation of molarity is,
A. The number of moles of solute dissolved in ${\text{1}}\,{\text{d}}{{\text{m}}^{\text{3}}}$of the solution.
B. The number of moles of solute dissolved in ${\text{1}}\,{\text{kg}}$of the solvent.
C. The number of moles of solute dissolved in ${\text{1}}\,{\text{d}}{{\text{m}}^{\text{3}}}$of the solvent.
D. The number of moles of solute dissolved in ${\text{100}}\,{\text{ml}}$of the solvent.

Answer
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Hint: Molarity is a way to express the concentration of a solution. The amount of solute dissolved in a given amount of the solvent is known as concentration.

Complete step by step answer:
Molarity is defined as the amount of solute dissolved in a volume of solution. The amount of solute is taken in the form of mole and the volume of the solution is taken as per litre.

So, the formula of molarity is as follows:

${\text{Molarity}}\,{\text{ = }}\,\dfrac{{{\text{Moles}}\,{\text{of}}\,{\text{solute}}}}{{{\text{Litter}}\,{\text{of}}\,{\text{solution}}}}$

So, the molarity is defined as the moles of solute dissolved in per litter of the solution.
The unit litre can be replaced with different volume units.

$1\,{\text{L}}$is equals to ${\text{1}}\,{\text{d}}{{\text{m}}^{\text{3}}}$.
So, the molarity can also be defined as the moles of solute dissolved in ${\text{1}}\,{\text{d}}{{\text{m}}^{\text{3}}}$of the solution.
So, option (A) is correct.
$1\,{\text{L}}$ is equal to ${\text{1}}\,{\text{kg}}$.

So, the molarity can also be defined as the moles of solute dissolved in ${\text{1}}\,{\text{kg}}$ of the solution.

Option B defines the molarity as the number of moles of solute dissolved in ${\text{1}}\,{\text{kg}}$ of the solvent whereas the molarity is defined in the form of the volume of the solution so, option B is incorrect.

Option C defines the molarity as the number of moles of solute dissolved in ${\text{1}}\,{\text{d}}{{\text{m}}^{\text{3}}}$ of the solvent so, option C is incorrect.

$1\,{\text{L}}$ is equal to ${\text{1000 ml}}$.

So, the molarity can also be defined as the moles of solute dissolved in ${\text{1000 ml}}$ of the solution.
Option D defines the molarity as the number of moles of solute dissolved in ${\text{100 ml}}$ of the solvent so, option D is incorrect.
Therefore, option (A) the number of moles of solute dissolved in ${\text{1}}\,{\text{d}}{{\text{m}}^{\text{3}}}$of the solution is the correct answer.

Note:
Concentration is also defined in some other terms as a molality, mole concentration, normality. Molality is defined as the moles of the solute dissolved in per kg of the solvent. Normality is defined as the gram equivalent of the solute dissolved in per liter of the solution.