The Q/U Imaging ExperimenT (QUIET) has observed the cosmic microwave background (CMB) at 43 and 95 GHz. The 43 GHz results have been published in a previous paper, and here we report the measurement of CMB polarization power spectra using the 95 GHz data. This data set comprises 5337 hr of observations recorded by an array of 84 polarized coherent receivers with a total array sensitivity of 87 μK. Four low-foreground fields were observed, covering a total of 1000 deg2 with an effective angular resolution of 128, allowing for constraints on primordial gravitational waves and high signal-to-noise measurements of the E-modes across three acoustic peaks. The data reduction was performed using two independent analysis pipelines, one based on a pseudo-C ℓ (PCL) cross-correlation approach, and the other on a maximum-likelihood (ML) approach. All data selection criteria and filters were modified until a predefined set of null tests had been satisfied before inspecting any non-null power spectrum. The results derived by the two pipelines are in good agreement. We characterize the EE, EB, and BB power spectra between ℓ = 25 and 975 and find that the EE spectrum is consistent with ΛCDM, while the BB power spectrum is consistent with zero. Based on these measurements, we constrain the tensor-to-scalar ratio to r = 1.1+0.9 -0.8 (r < 2.8 at 95% C.L.) as derived by the ML pipeline, and r = 1.2+0.9 - 0.8 (r < 2.7 at 95% C.L.) as derived by the PCL pipeline. In one of the fields, we find a correlation with the dust component of the Planck Sky Model, though the corresponding excess power is small compared to statistical errors. Finally, we derive limits on all known systematic errors, and demonstrate that these correspond to a tensor-to-scalar ratio smaller than r = 0.01, the lowest level yet reported in the literature.
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