The main objective of Internet of Things (IoT) is to connect almost all the devices anywhere and everywhere in the world. IoT network is heterogeneous in nature, hence routing the data packets in this network is a big challenge. Routing Protocol for Low Power Lossy Network (RPL), has been designed by Internet Engineering Task Force (IETF) for such type of network. The existing design of RPL Objective Function (OF) is insufficient to cover all the issues of IoT applications. In this paper, the proposed OFs designs using various routing metrics are used to enhance the performance of the IoT applications. The analysis for various scenarios for these designs shows that only traditional hop and Expected Transmission Count (ETX) routing parameters will not fit for the smart applications need. The routing metric selection according to the application requirement is the principal idea of the proposed design. Three metrics ETX, Content and Energy, single and combination with each other are used to enhance the design of objective function of RPL for IoT applications. The enhanced triggering technique is added in these designs for the improvement of RPL. This technique will eliminate the cumulative effect of the short-listen problem of default trickle timer. The result analysis done using Cooja simulator along with Contiki Operating System (OS) states that, all the designs are performing well in one or other manner than the traditional OF. Energy combined with Content (EC) and aggregation with Enhanced timer (EC_En_Timer) design gives better result for Packet Delivery Ratio (PDR) and Latency Delay (LD) as compared to default OF design. Residual Energy (RE) combined with ETX (EE) and conjunction with Enhanced timer (EE_En_Timer) design works well for energy consumption. Overhead is very less in RE and ETX design. Conversion time is reduced by almost 50% in an En_Timer design. Higher PDR and low delay values of EC and EC_En_Timer design encourages its use in health monitoring application where reliability is essential. Low energy consumption results of RE, EE and EE_En_Timer designs are comfortable for forest monitoring application, as energy is a crucial aspect. This comparative result outcome will help to fulfill the IoT application requirements.