Will the aqueous solution of titanium(II) chloride and beryllium chloride be colored or colorless?

TiCl2 probably. BeCl2 probably not.

By the way, an aqueous TiCl2 is NOT stable as it reacts with H2O quite strongly. You can read about it here.
http://en.wikipedia.org/wiki/Titanium%28II%29_chloride

The aqueous solution of titanium(II) chloride and beryllium chloride will be colorless.

To determine the color of the aqueous solution of titanium(II) chloride and beryllium chloride, we need to examine the properties of the individual compounds.

Titanium(II) chloride, TiCl2, is a transition metal compound. Transition metals often exhibit various colors due to the presence of partially filled d orbitals, which can result in absorption of certain wavelengths of light. In the case of titanium(II) chloride, it is typically a pale green color.

Beryllium chloride, BeCl2, on the other hand, is a compound of a non-transition metal. Non-transition metal compounds generally do not exhibit vivid colors, and are often colorless or very pale in solution.

Considering this, when these two compounds are dissolved in an aqueous solution together, the presence of titanium(II) chloride as a pale green colored compound may dominate the color of the solution. Thus, it is likely that the mixture will have a pale green color when dissolved in water.