ISI 2010,. Utility function question

[Spiti]

[Dreyfus]

I think we can do this question by taking three different types of preferences ie perfect substitutes, perfect complement, and x^a + y^a where 0<a<1 in all three cases utility function is symmetric and optimal Solution will be x1*=x2*
But I m not sure if this is the right approach to solve this question by taking examples as ISI may not award the marks for it!