Which of the following sols are correctly matched with their corresponding charges?

$\left(A\right)$	$\mathrm{Cr}\left(\mathrm{OH}\right)3\text{sol : negatively charged sol}$
$\left(B\right)$	${\mathrm{TiO}}_2\text{sol : positively charged sol}$
$\left(C\right)$	$\mathrm{CdS}\text{sol : positively charged sol}$
$\left(D\right)$	$\text{Gum : negatively charged sol}$
$\left(E\right)$	$\text{Silver sol : positively charged sol}$

$\text{Choose the correct answer from the options given below:}$

The correct answer is (B) and (D) only.

To understand why this is the correct choice, let us review the classification of colloidal solutions (sols) based on the charge present on their particles:

1. Positively Charged Sols:
- Hydrated metallic oxides such as ${\mathrm{Al}}_2{O}_3·x{H}_{2}O$, ${\mathrm{Fe}}_2{O}_3·x{H}_{2}O$, and $\mathrm{Cr}{\left(\mathrm{OH}\right)}_3$ are positively charged.
- Oxide sols such as ${\mathrm{TiO}}_2$ sol are also positively charged.
- Basic dyestuffs like methylene blue.

2. Negatively Charged Sols:
- Metallic sols like copper, silver, gold, and platinum sols.
- Metallic sulfide sols such as ${\mathrm{As}}_2{S}_3$, $\mathrm{Sb}{S}_3$, and $\mathrm{CdS}$ sols.
- Sols of natural starch, gum, gelatin, clay, charcoal, etc.
- Acidic dyestuffs like congo red.

Now, let us evaluate the given statements one by one:

- (A) $\mathrm{Cr}{\left(\mathrm{OH}\right)}_3$ sol : negatively charged sol
Incorrect: Being a hydrated metallic hydroxide, chromium hydroxide sol carries a positive charge, not a negative charge.

- (B) ${\mathrm{TiO}}_2$ sol : positively charged sol
Correct: Titanium dioxide is a metal oxide sol which carries a positive charge.

- (C) $\mathrm{CdS}$ sol : positively charged sol
Incorrect: Cadmium sulfide is a metallic sulfide, and all metallic sulfide sols are negatively charged.

- (D) Gum : negatively charged sol
Correct: Gum is a natural organic macromolecular colloid, which behaves as a negatively charged sol in aqueous media.

- (E) Silver sol : positively charged sol
Incorrect: Metal sols, including silver sol, are stabilized by acquiring a negative charge (usually due to the adsorption of anions).

Therefore, only statements (B) and (D) are correctly matched.