To solve this problem, we need to identify the type of isomerism exhibited by the complex $[CoCl_2(en)_2]. \newline$The complex $[CoCl_2(en)_2]$ consists of a cobalt ion coordinated with two chloride ions and two ethylenediamine (en) ligands.$\newline$Ethylenediamine is a bidentate ligand, meaning it can form two bonds with the central metal ion.$\newline$Let's analyze the possible types of isomerism:$\newline •$Ionization isomerism occurs when the counter ions outside the coordination sphere can be exchanged with ligands inside the sphere.$\newline •$Coordination isomerism occurs in complexes with more than one type of metal ion, where ligands can be exchanged between the metal centers.$\newline •$Geometrical isomerism occurs due to different spatial arrangements of ligands around the central metal ion, typically in square planar or octahedral complexes.$\newline •$Linkage isomerism occurs when a ligand can coordinate to the metal in different ways, such as through different donor atoms.$\newline$In the complex $[CoCl_2(en)_2],$ the cobalt ion is in an octahedral environment with two bidentate en ligands and two chloride ions.$\newline$This arrangement allows for geometrical isomerism, specifically cis-trans isomerism.$\newline$• In the cis isomer, the two chloride ions are adjacent to each other.$\newline$• In the trans isomer, the two chloride ions are opposite each other.$\newline$Therefore, the type of isomerism shown by the complex $[CoCl_2(en)_2]$ is geometrical isomerism.$\newline$This corresponds to Option 3.