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We report a search for the standard model (SM) Higgs boson based on data collected by the D0 experiment at the Fermilab Tevatron Collider, corresponding to an integrated luminosity of 260 pb-1. We study events with missing transverse energy and two acoplanar b jets, which provide sensitivity to the ZH production cross section in the νν̅bb̅ channel, and to WH production when the lepton from the W → ℓν decay is undetected. The data are consistent with the SM background expectation, and we set 95% C.L. upper limits on σ(pp̅ → ZH/WH) ×B(H → bb̅) from 3.4/8.3 to 2.5/6.3 pb, for Higgs-boson masses between 105 and 135 GeV.