1. Find $X$: number of acidic oxides

We examine each oxide:

• $VO_2$ : vanadium is in $+4$ oxidation state. This oxide is amphoteric.
• $V_2O_3$ : vanadium is in $+3$ oxidation state. Lower oxidation state metal oxides are generally basic.
• $CrO_3$ : chromium is in $+6$ oxidation state. This is an acidic oxide.
• $V_2O_5$ : vanadium is in $+5$ oxidation state. This is an acidic oxide.
• $Mn_2O_7$ : manganese is in $+7$ oxidation state. This is the anhydride of permanganic acid, so it is acidic.

Hence, acidic oxides are: $CrO_3,\ V_2O_5,\ Mn_2O_7$ So, $X=3$

2. Find $Y$: primary valency of cobalt in $[Co(H_2NCH_2CH_2NH_2)_3]_2(SO_4)_3$

Here, $H_2NCH_2CH_2NH_2$ is ethylenediamine (en), which is a neutral ligand.

Let oxidation state of Co be $x$.

For one complex cation: $[Co(en)_3]^{n+}$ Since $en$ is neutral, charge on complex equals oxidation state of Co.

The full compound is: $[Co(en)_3]_2(SO_4)_3$ Each sulfate ion has charge $-2$, so total negative charge is: $3\times(-2)=-6$ Thus total positive charge of the two complex ions must be $+6$. So each complex ion has charge: $+3$ Therefore cobalt is in oxidation state: $Y=3$

Since primary valency = oxidation state, we get $Y=3$

3. Calculate $X+Y$

$X+Y=3+3=6$

4. Compare with given options

The computed value is: $6$ But the options are $2,3,4,5$ only. So none of the listed options matches.

5. Compare with stored correct answer

Stored correct answer is D = 5, but our derived answer is 6.

Therefore, the stored answer appears to be incorrect.