Molecular Orbital Theory (MOT) builds molecular orbitals by linear combination of atomic orbitals. For O_2^{2-} (peroxide ion), oxygen has 8 electrons, so two oxygen atoms contribute 16 electrons, and the 2^- charge adds 2 more, giving 18 total electrons. The MO filling sequence for the second-period homonuclear diatomics is: \sigma(1s)^2, \sigma^(1s)^2, \sigma(2s)^2, \sigma^(2s)^2, \sigma(2p_z)^2, \pi(2p_x)^2, \pi(2p_y)^2, \pi^(2p_x)^2, \pi^(2p_y)^2. With 18 electrons, both \pi^(2p_x) and \pi^(2p_y) are completely filled (two electrons each). Bond order = (bonding electrons - antibonding electrons)/2 = (10 - 8)/2 = 1. Since all 18 electrons are paired (no unpaired electrons remain), O_2^{2-} is diamagnetic. Option '2, paramagnetic' describes neutral O_2 (16 electrons, two unpaired electrons in degenerate \pi^* orbitals). Option '1, paramagnetic' would imply unpaired electrons at bond order 1, which contradicts the completely filled \pi^* orbitals. Option '2, diamagnetic' overestimates the bond order for 18 electrons. This is a frequently tested NCERT MOT concept in JEE. Plausibility check: bond order of 1 is consistent with the known O-O single bond in H_2O_2, where the peroxide unit also has bond order 1.