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Alums purify water by-
(a). Dialysis
(b). Absorption
(c). Coagulation
(d). Forming true solution

Answer
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Hint: The purification of water by using potash alum is the phenomenon of agglomeration of suspended particles in the solution and further settling of these particles in the bottom of the container.

Complete step by step solution:
First of all, let us understand what the coagulation is. It is the process of accumulation to form aggregates, precipitate under the gravity and settling down of these aggregates at the bottom of the container.
The technique of coagulation can be carried out in the following ways.
By electrophoresis: In this method, the colloidal particles are forced to move towards the oppositely charged particles and then they are discharged and collected at the bottom
By mixing two oppositely charged sols: In this type of coagulation equal amounts of oppositely charged particles are mixed, they cancel out their charges and then precipitate.
Potassium alum is also known as potash alum or tawas. It is aluminum potassium sulfate. This remains in the crystallised form. It is also used in leather tanning, as a flocculant in water purification, as an ingredient in aftershave and as a treatment to fireproof textiles
Potash alum uses the 2nd technique of coagulation of mixing two oppositely charged sols as mentioned above. Muddy water is negative sol. $ \text{A}{{\text{l}}^{3+}} $ has a high +3 positive charge. Therefore, $\text{A}{{\text{l}}^{3+}}$ will coagulate impurities present in muddy water. When potash alum is added to water, it reacts with the bicarbonate alkalinities present in water and forms a gelatinous precipitate. The floc attracts other fine particles and suspended material in water and settles down at the bottom of the container.
Hence, Alums purify water by coagulation and the correct option is (c).

Note: The chemical formula of Potash Alum is $K_2SO_4.Al_2(SO_4)_3$. It should be noted that dialysis is also a purification process in which spontaneous separation process of suspended colloidal particles from dissolved ions or molecules of small dimensions through a semipermeable membrane. However, Alum uses a coagulation process.