Step 1: Determine the acidic oxides among the given options.
The acidic character of transition metal oxides increases with the oxidation state of the metal.
\( VO_2 \): Oxidation state of V is +4 (amphoteric)
\( V_2O_3 \): Oxidation state of V is +3 (basic)
\( CrO_3 \): Oxidation state of Cr is +6 (acidic)
\( V_2O_5 \): Oxidation state of V is +5 (amphoteric, predominantly acidic)
\( Mn_2O_7 \): Oxidation state of Mn is +7 (highly acidic)
The acidic oxides are \( CrO_3 \) and \( Mn_2O_7 \). The number of acidic oxides, X = 2.
Step 2: Determine the primary valency of cobalt in the given complex.
The complex is \( [Co(H_2NCH_2CH_2NH_2)_3]_2 (SO_4)_3 \), which contains the complex ion \( [Co(en)_3]^{3+} \). The primary valency is the oxidation state of the central metal ion (Co).
Let the oxidation state of Co be \( y \). Ethylenediamine (en) is a neutral ligand.
\( y + 3(0) = +3 \)
\( y = +3 \)
The primary valency of cobalt (Y) is 3.
Step 3: Calculate the value of X + Y.
X = 2
Y = 3
X + Y = 2 + 3 = 5