The short-baseline neutrino oscillation experiments, the excess of radiation from the measurement of the cosmic microwave background radiation, the necessity of the nonbaryonic dark matter candidate, and the depletion of the neutrino flux in IceCube all seem to hint at new physics beyond the standard model. An economical way to address these issues is to invoke the existence of sterile neutrinos. We present simple extensions of the standard model with additionally three sterile neutrinos and discuss the corresponding PMNS like neutrino flavor mixing matrix. The noteworthy features of the sterile neutrino scenario advocated here are that the lightest one is almost degenerate with one of the active neutrinos, the second sterile has mass of order eV, and the heaviest one is in the keV range. In the present scenario, the short-baseline anomaly is explained through m 2 ∼ 1 eV 2 , the depletion of the muon neutrino flux in IceCube is explained through m 2 ∼ 4.0 × 10 −16 eV 2 , and the dark matter problem is addressed through m 2 ∼ 1 keV 2 . Our proposed mixing matrix is also compatible with the observed neutrino oscillation data. We show that the highenergy muon and the tau neutrino fluxes from Gamma Ray Bursts can be depleted in IceCube by as much as 38 and 43 %, respectively. These substantial depletions in both muon and tau neutrino fluxes are due to their small but sizable mixing with the sterile neutrinos.