A coordination complex compound of cobalt has molecular formula containing five ammonia molecules, one nitro group and two chlorine atoms for one cobalt atom. One mole of this compound produces three mole ions in an aqueous solution. On reacting this solution with excess of silver nitrate solution, two moles of AgCl get precipitated. The formula of this compound would be

[Co(NH₃)₅(NO₂)]Cl₂

The correct answer is option 3. [Co(NH₃)₅(NO₂)]Cl₂

To find the formula of the coordination complex compound of cobalt, let us analyze the information given step by step:

1. The molecular formula of the compound contains five ammonia \((NH_3)\) molecules, one nitro group \((NO_2)\), and two chlorine atoms \((Cl)\) for one cobalt atom.

2. One mole of this compound produces three mole ions in an aqueous solution. This indicates that the compound dissociates into three ions in solution.

3. On reacting this solution with excess silver nitrate \((AgNO_3)\) solution, two moles of \(AgCl\) get precipitated. This suggests that the compound contains chloride ions \((Cl^-)\) since \(AgCl\) is formed by the reaction of \(Ag^+\) with \(Cl^-\).

Now, let us try to construct the formula based on the given information. We need to ensure that the formula accounts for the number of moles of ions produced in the solution and the formation of \(AgCl\) precipitate.

Considering the information provided, the correct formula of the compound is: (3) \([Co(NH_3)_5(NO_2)]Cl_2\)

The complex consists of five ammonia ligands, which is represented as \([Co(NH_3)_5]\).

The complex also contains one nitro ligand \((NO_2\)), making the complete complex \([Co(NH_3)_5(NO_2)]\).

The presence of two chloride ions \((Cl^-)\) is indicated by \(Cl_2\) in the formula, forming the final compound \([Co(NH_3)_5(NO_2)]Cl_2\).

This formula correctly explains the dissociation into three ions in solution, and the reaction with \(AgNO_3\) to precipitate two moles of \(AgCl\). Therefore, option (3) \([Co(NH_3)_5(NO_2)]Cl_2\) is the correct formula for the given coordination complex compound of cobalt.