NaOH is not produced in:
A. Nelson cell method
B. Downs Process
C. Castner kellner's method
D. Causticizing process

Hint: It is the process in which in place of NaOH, Na and Chlorine gas is formed at output by the electrolysis of molten NaCl. It's an electrochemical method to extract the sodium.

Complete step by step solution:
From your chemistry lessons you know that Nelson cell method, Castner kellner's method and Causticizing process all produce NaOH but in Downs process in place of NaOH they produce Na as a product.
Now, let us see how downs process work and what is produced by it,
-In the commercial preparation of sodium, molten NaCl is electrolyzed in a specialized cell called the Downs cell. The electrolyte medium through which current flows is molten NaCl.
-Calcium chloride, $CaC{{l}_{2}}$ is added to lower the melting point of the cell medium from the normal melting point of NaCl, $800{}^\circ C$ to around $600{}^\circ C$. The Na(liquid) and $C{{l}_{2}}$ (gas) produced in the electrolysis are kept from coming in contact and forming NaCl again.
-In addition, the Na must be prevented from contact with oxygen because the metal would quickly oxidize under the high-temperature conditions of the cell reaction. The electrolysis reaction is:

\[2NaCl\to \,2Na(l)+C{{l}_{2}}(g)\]

The cell is designed to collect sodium at the cathode and chlorine at the anode without allowing these two products to react with each other. The melting point of sodium chloride is about $800{}^\circ C$ , so a mixture whose mole ratio is about one mole of NaCl to three moles of $CaC{{l}_{2}}$ is employed to reduce the melting point to about $600{}^\circ C$.
The cell does not produce calcium metal because the electrowinning of Na occurs at a less -ve cathode potential than does the electrowinning of Ca. (In the absence of NaCl, electrolysis of $CaC{{l}_{2}}$ would indeed produce calcium metal at the cathode, and calcium metal is produced in just this way.)

Thus the correct option will be (B).

Note: In the Castner kellner process and nelson cell process NaCL is used for the production of NaOH and in Causticizing method NaOH is produced by the evaporation of water while in Downs process electrolysis of Nacl is used to produce Na and $C{{L}_{2}}$ in place of NaOH.