The color of the wool cloth dyed directly by dipping in hot solution of malachite green dye is fast. The color of cotton cloth dyed directly (without using mordant) by dipping in hot solution malachite green is not fast to washing and is of low intensity.

 Tannic acid is used to mordant cellulose fibres and fabrics before the alum mordant. Many dyestuffs contain tannin (black oak, pomegranate, cutch, fustic, etc) and do not need an additional tannin mordant. Tannins can be clear or they can add colour to the fibre

Basic dye is a stain that is cationic (+ve charged) and so will react with material that is (-ve) negatively charged. Alizarin prominent red dye is a basic dye. Some other examples of basic dyes are methylene blue, crystal violet, basic fuchsin safranin.

 Colour fastness is a professional word used in theprocess of dyeing for textile materials that characterize a material's color resistance to fading or running. The term is generally used for clothes. In different veryties of cloth, wool is the most easily dyed fiber and the resulting color will change the least. 

Sol is a colloidal suspension with solid particles as dispersed phase dissolve in a liquid i.e dispersion medium.

Methyl orange is the azo dye, which consists of azo $(-N=N-)$ structure in it. The other compounds do not contain this azo structure in them.

All other dyes are natural dyes. Basic dyes are water soluble and are cationic and act as bases. Malachite green is an organic compound. Malachite green is prepared by condensation of  benzaldehyde and dimethylaniline. Basic dyes display cationic functional groups like $-NR _3^+$ or $=NR _2^+$.

Adsorption is multilayer in case of physical adsorption. However, in the case of chemisorption, the absorption is unilayer as it involves the formation of a chemical bond between adsorbate and adsorbent molecules.

If a homogeneous solution is observed in the direction of light, it appears clear and when it is observed from a direction at right angles to the direction of the light beam, it appears perfectly dark. 

Auxochromes are commonly called as color helpers or color intensifiers. Dyes containing auxochromes are basically aromatic compounds and include the presence of aryl rings which have delocalized electron systems. These are responsible for the absorption of different radiations with different wavelengths based on the energy of the electron. If an auxochrome is present in the meta position of the chromophore, then there is no change in the color. Electrons present in the chromophore get excited from the ground level to the excited state.

When visible light falls on them. Chromophores also alter the energy in
the delocalized systems. A chromophore gives the dye the property of absorbing different radiations whereas auxochrome imparts it with the property of being colored.
Hence option A is correct.

Vat dyes are essentially insoluble in water and incapable of dyeing fibers directly. However, reduction in alkaline liquor produces the water-soluble alkali metal salt of the dye, which, in this leuco form, has an affinity for the textile fiber. Subsequent oxidation reforms the original insoluble dye. The color of denim is due to indigo, the original vat dye.

Hence option A Is correct.

Auxochrome is a Greek word arising from; Auxo meaning to increase and chrome meaning color. An auxochrome is a group of atoms which will impart a particular color when attached to a chromophore but when present alone, will fail to produce that color.
Chromophore is that part of the molecule which when exposed to visible
light will absorb and reflect a certain color.
Hence option A is correct.

Auxochrome is a Greek word arising from two-word roots; Auxo meaning to
increase and chrome meaning color. An auxochrome is a group of atoms
which will impart a particular color when attached to a
chromophore but when present alone, will fail to produce that color.

A chromophore is that part of the molecule which when exposed to visible light will absorb and reflect a certain color. Auxochrome increases the color of any organic substance.
Hence option B is correct.

Auxochrome is a Greek word arising from two-word roots; Auxo meaning to
increase and chrome meaning color. An auxochrome is a group of atoms
which will impart a particular color when attached to a chromophore but when present alone, will fail to produce that color.

The chromophore is that part of the molecule which when exposed to visible
light will absorb and reflect a certain color.
Hence option A is correct.

Dispersed dyes were originally developed for the dyeing of Cellulose acetate and are water-insoluble. The dyes are finely ground in the presence of a dispersing agent and sold as a paste, or spray-dried and sold as a powder.
Hence option A is correct.

An auxochrome (Greek auxnein: "to increase" and chrma: "colour") is a group of atoms attached to a chromophore which modifies the ability of that chromophore to absorb light. They themselves fail to produce the colour; but when present along with the chromophores in an organic compound intensifies the colour of the chromogen.[1] Examples include the hydroxyl group (-OH), the amino group (-NH2), the aldehyde group (-CHO), and the methyl mercaptan group (-SMe).[2]

 An auxochrome is a functional group with nonbonded electrons when attached to the chromophore, changes both the wavelength and intensity of absorption. If these groups are in direct conjugation with the pi-electron system of the chromophore, they may increase the wavelength of light
that  is being absorbed and as a result,t intensify the absorption. A feature of these auxochromes is the presence of at least one lone pair of electrons which can be viewed as extending the conjugated system by resonance.

Hence option B is correct.

A dye is a colored substance that has an affinity to the substrate to which it is being applied. The dye is generally applied in an aqueous solution and may require a mordant to improve the fastness of the dye on the fiber.
Hence option C is correct.

Basic dyes are water-soluble cationic dyes that are mainly applied to acrylic fibres but find some use for wool and silk. Usually acetic
acid is added to the dye bath to help the uptake of the dye onto the fiber.
Basic dyes are also used in the coloration of paper.
Hence option D is correct.

Vat dyes are not used to dye nylon and polyester fibres but used to dye cotton fibres. 

If more number of double bonds are present in the carotenoid system the intensity or the darkness of the pigment will increases.
Hence option C is correct.

Natural dyes are dyes derived from animal or plant material without any chemical treatment. They are obtained from sources like flowers,
leaves, insects, bark roots etc.; however, they are not readily
available and involve an extraction process.In th above question and the natural dyes are indigo, bixin and alizarin.
Hence option B is correct.

Vat dyes are essentially insoluble in water and incapable of dyeing fibers
directly. However, reduction in alkaline liquor produces the water-soluble
alkali metal salt of the dye, which, in this leuco form, has an affinity for
the textile fiber. Subsequent oxidation reforms the original insoluble dye. The
color of denim is due to indigo, the original vat dye
So a vat dye must be reduced to a soluble form so that it can dissolve in the dye bath and get trapped in the cellulose fiber.
Hence option D is correct

A mordant or dye fixative is a substance used to set dyes on fabrics or tissue sections by forming a coordination complex with the dye which is then attached to the fabric or tissue.

[1] It may be used for dyeing fabrics, or for intensifying stains in a cell or tissue preparations. 
it was thought that a mordant helped the dye bite onto the fibre so that it
would hold fast during washing. A mordant is often a polyvalent metal ion.

[2] The resulting coordination complex of dye and ion is colloidal and can be either acidic or alkaline. So a mordant is a metallic ion or salt added to the dye bath to make dyes more colourfast by forming a bridge between the dye and the fibre.

Hence option D is correct.

If more number of double bonds are present in the carotenoid system the intensity or the darkness of the pigment will increases.
Hence option C is correct.

(A) Mauveine

A colloidal solution can be purified by the following methods - Dialysis, Electro-dialysis and Ultrafiltration.

The dye is known as a coloured substance which has a great affinity towards the substrate on which it is applied. The basic difference in between dye and pigment is that dye is diffused into the interior of a given fabric from its water solution whereas pigment does not.

Vat dyes can applied directly on fibre and are generally insoluble in water. These can be used only on cotton but can not be used on silk and wool. In this case  dying is a continuous process and is carried out in a large vessel called vat. For this reason these dyes are Known as vat dyes, indigo is an example of vat dyes 

Direct Dye is a class of dyestuff's that are applied directly to the substrate in a neutral or alkaline bath. They produce full shades on cotton and linen without mordant and can also be applied to rayon, silk, and wool. Direct dyes give bright shades but exhibit poor wash fastness. Various after treatments are used to improve the wash fastness of direct dyes, and such dyes are referred to as 'after treated direct colors". Direct dyes are molecules that adhere to the fabric molecules without help from other chemicals.

 Indigo dye is an example of Vat dye, These dyes can be used only on cotton it is a long continuous process which is carried out in a large vessel known as Vat. These dyes are applied directly on the fibre and are generally insoluble in water.

Azo dyes are organic compounds, which contain the coloring azo function (N=M-). The azo function is often bound to an aromatic ring, and the dye can then be broken down to an aromatic amine, arylamine. This can take place either chemically, through reductive cleavage, or through the body's own enzyme system. Some azo dyes can also be broken down to arylamines during storage due to light and high temperature. Some arylamines have been judged to be carcinogenic.

When soap or detergent is added to water, this results in the formation of oil in water type emulsion.
The polar water-soluble ( hydrophilic) head is on the surface of the micelle whereas non-polar oil soluble (hydrophobic) tail is in the centre of the micelle. In the centre of the micelle, small oil droplets are present in which hydrophobic part of micelle dissolves.

The development step uses reducing chemicals, and the exposed silver-halide grains develop to pure silver. The oxidized developer is produced in this reaction, and the oxidized developer reacts with chemicals called couplers in each of the image-forming layers. This reaction causes the coupler to form a color, and this color varies depending on how the silver-halide grains were spectrally sensitized. A different color-forming coupler is used in the red, green, and blue sensitive layers. The latent image in the different layers forms a different colored dye when the film is developed.