This paper studies the performance of single-input multiple-output (SIMO) systems under receive antenna selection (RAS) and BPSK/QPSK modulations. At the receiver, a subset of branches are selected and combined using maximal-ratio combining (MRC) to maximize the instantaneous Signal to Noise Ratio (SNR). By assuming independent and identical distributed (i.i.d.) Rayleigh flat fading, a closed-form expression, with considerably high precision, is developed to approximate the average input-output mutual information, also termed as symmetric capacity, of the whole system. Later, this approximated expression is further utilized to investigate the efficient capacity and energy efficiency of the SIMO system under BPSK/QPSK modulations and RAS. Besides analytical derivations, simulations are provided to demonstrate the approximation precision, feasibility and validity of the derived results.