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We observe a striking difference in the behavior of the Seebeck coefficient, S in the vicinity of the Quantum Critical Point (QCP) in the two systems. As the critical field is approached, S/T enhances in beta-YbAlB4 but is drastically reduced in YbRh2Si2. While in the former system, the ratio of thermopower-to-specific heat remains constant, it drastically drops near the QCP in YbRh2Si2. 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