We present the first high-angular resolution survey for multiple systems among very low-mass stars and brown dwarfs in the Hyades open cluster. Using the Keck,II adaptive optics system, we observed a complete sample of 16 objects with estimated masses $lesssim$0.1 Msun. We have identified three close binaries with projected separation $lesssim$0.11, or $lesssim$5 AU. A number of wide, mostly faint candidate companions are also detected in our images, most of which are revealed as unrelated background sources based on astrometric and/or photometric considerations. The derived multiplicity frequency, 19+13/-6 % over the 2-350 AU range, and the rarity of systems wider than 10 AU are both consistent with observations of field very low-mass objects. In the limited 3-50 AU separation range, the companion frequency is essentially constant from brown dwarfs to solar-type stars in the Hyades cluster, which is also in line with our current knowledge for field stars. Combining the binaries discovered in this surveys with those already known in the Pleiades cluster reveals that very low-mass binaries in open clusters, as well as in star-forming regions, are skewed toward lower mass ratios ($0.6 lesssim q lesssim 0.8$) than are their field counterparts, a result that cannot be accounted for by selection effects. Although the possibility of severe systematic errors in model-based mass estimates for very low-mass stars cannot be completely excluded, it is unlikely to explain this difference. We speculate that this trend indicates that surveys among very low-mass field stars may have missed a substantial population of intermediate mass ratio systems, implying that these systems are more common and more diverse than previously thought.
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