$\underset{}{PbCr{O}_4}\stackrel{NaOH}{\to }Complex$ Complex is

The correct option is Dianionic with CN = 4.

Step 1: Understand the reaction
Lead chromate (represented as ${\mathrm{PbCrO}}_4$) is a bright yellow precipitate. When it is treated with an excess of sodium hydroxide ($\mathrm{NaOH}$), the precipitate dissolves to form a soluble coordination complex along with sodium chromate.

The balanced chemical equation for this reaction is:
$${\mathrm{PbCrO}}_4+4\mathrm{NaOH}\to {\mathrm{Na}}_2\left[\mathrm{Pb}{\left(\mathrm{OH}\right)}_4\right]+{\mathrm{Na}}_2{\mathrm{CrO}}_4$$

Step 2: Identify and analyze the complex ion
In the solution, the sodium salt of the complex dissociates to yield sodium cations (${\mathrm{Na}}^{+}$) and the tetrahydroxoplumbate(II) complex anion:
$${\left[\mathrm{Pb}{\left(\mathrm{OH}\right)}_4\right]}^{2-}$$

Step 3: Determine the ionic nature (charge) of the complex
The central metal atom is Lead in its +2 oxidation state (${\mathrm{Pb}}^{2+}$). It is coordinated to four hydroxide (${\mathrm{OH}}^{-}$) ligands, each carrying a charge of -1.
The net charge of the complex is calculated as follows:
$$\text{Net Charge}=\text{Charge on Pb}+(4\times \text{Charge on OH})$$
$$\text{Net Charge}=(+2)+4\times (-1)=-2$$
Because the overall charge on the coordination sphere is -2, the complex is classified as dianionic (an anion with a double negative charge).

Step 4: Determine the coordination number (CN)
The coordination number is defined as the total number of coordinate bonds formed between the central metal ion and the ligands. Hydroxide (${\mathrm{OH}}^{-}$) is a monodentate ligand, meaning each hydroxide ion donates one lone pair of electrons to form a single coordinate bond with the lead ion.
Since there are four hydroxide ligands bound to the central lead ion, the coordination number (CN) is:
$$\text{CN}=4$$

Conclusion
Combining these evaluations, the resulting complex is dianionic and has a coordination number of 4.