The correct answer is option (c) - (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv).
The Chalukyas were associated with Vatapi (which is now called Badami) and hence option (ii) corresponds to option (a).
The Hoysalas were associated with Dwarasamudra (which is now called Halebidu) and hence option (iv) corresponds to option (b).
The Rashtrakutas were associated with Malkhed and hence option (i) corresponds to option (c).
The Kakatiyas were associated with Warangal and hence option (iii) corresponds to option (d).
Therefore, the correct mapping is as follows:
(a) Chalukyas - (i) Malkhed
(b) Hoysalas - (ii) Vatapi
(c) Rashtrakutas - (iii) Warangal
(d) Kakatiyas - (iv) Dwarasamudra