Test sequencing is a binary identification problem wherein one needs to develop a minimal expected cost test procedure to determine which one of a finite number of possible failure states, if any, is present. In this paper, we consider a multimode test sequencing (MMTS) problem, in which tests are distributed among multiple modes and additional transition costs will be incurred if a test sequence involves mode changes. The multimode test sequencing problem can be solved optimally via dynamic programming or AND/OR graph search methods. However, for large systems, the associated computation with dynamic programming or AND/OR graph search methods is substantial due to the rapidly increasing number of OR nodes (denoting ambiguity states and current modes) and AND nodes (denoting next modes and tests) in the search graph. In order to overcome the computational explosion, we propose to apply three heuristic algorithms based on information gain: information gain heuristic (IG), mode capability evaluation (MC), and mode capability evaluation with limited exploration of depth and degree of mode Isolation (MCLEI). We also propose to apply rollout strategies, which are guaranteed to improve the performance of heuristics, as long as the heuristics are sequentially improving. We show computational results, which suggest that the information-heuristic based rollout policies are significantly better than traditional information gain heuristic. We also show that among the three information heuristics proposed, MCLEI achieves the best tradeoff between optimality and computational complexity.