{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"mmlu-pro","formal_name":"MMLU-Pro","introduction":"MMLU-Pro rebuilds MMLU with ten answer options instead of four and removes items that no longer separate models. Questions span fourteen academic and professional subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/TIGER-Lab/MMLU-Pro","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"264d409e-1f68-57ff-add9-2ca8b0728909","task_key":"default--test--12209","task_revision_id":"1","upstream_id":"12209","short_description":"a) The velocity profile for laminar flow between two parallel plates is given by…","config":"default","split":"test","body":"{\"category\":\"engineering\",\"options\":\"['(a) Average velocity = (5/7) u_m, beta = 1.18. (b) Average velocity = (41 / 60) u_m, beta = 1.008. (c) Average velocity = 7.5 m/s, beta = 1.185.', '(a) Average velocity = u_m, beta = 1.25. (b) Average velocity = (55 / 60) u_m, beta = 1.030. (c) Average velocity = 13.2 m/s, beta = 1.165.', '(a) Average velocity = (5/6) u_m, beta = 1.10. (b) Average velocity = (52 / 60) u_m, beta = 1.017. (c) Average velocity = 11.1 m/s, beta = 1.150.', '(a) Average velocity = (7/8) u_m, beta = 1.28. (b) Average velocity = (46 / 60) u_m, beta = 1.013. (c) Average velocity = 9.9 m/s, beta = 1.210.', '(a) Average velocity = (2/3) u_m, \\\\x08eta = 1.20. (b) Average velocity = (49 / 60) u_m, \\\\x08eta = 1.020. (c) Average velocity = 10.75 m/s, \\\\x08eta = 1.178.', '(a) Average velocity = (1/3) u_m, \\\\x08eta = 1.15. (b) Average velocity = (45 / 60) u_m, \\\\x08eta = 1.010. (c) Average velocity = 11.8 m/s, \\\\x08eta = 1.160', '(a) Average velocity = (3/5) u_m, beta = 1.22. (b) Average velocity = (42 / 60) u_m, beta = 1.012. (c) Average velocity = 8.6 m/s, beta = 1.190.', '(a) Average velocity = (3/4) u_m, \\\\x08eta = 1.30. (b) Average velocity = (50 / 60) u_m, \\\\x08eta = 1.025. (c) Average velocity = 9.4 m/s, \\\\x08eta = 1.200', '(a) Average velocity = (1/2) u_m, \\\\x08eta = 1.10. (b) Average velocity = (40 / 60) u_m, \\\\x08eta = 1.015. (c) Average velocity = 12.75 m/s, \\\\x08eta = 1.150', '(a) Average velocity = (1/4) u_m, beta = 1.05. (b) Average velocity = (56 / 60) u_m, beta = 1.022. (c) Average velocity = 14.3 m/s, beta = 1.170.']\",\"question\":\"a) The velocity profile for laminar flow between two parallel plates is given by u = u_m{1 - (b^2 / B^2)} where u_m is thecenterplanevelocity, B is the half-spacing between plates, and b is the normal distance from the center plane. (1) What is the average velocity in terms of u_m? (2) What is the momentum correction factor \\\\beta? b) The velocity profile for turbulent flow in a circular tube may be approximated by u = u_m(y/R)^1/7 = u_m {1 - (r/R)}^1/7 where u_m is the centerline velocity, R is the tube radius, and y is the radial distance from the tube wall (r = R - y). (1) What is the average velocity in terms of u_m? (2) What is the momentum flux factor \\\\beta? c) Velocities measured at the center of equal increments of (r/R)^2, representing equal increments of area, at the downstream end of a diffuser in acavitation-testing water tunnel are as follows: 18.2, 16.8, 14.9, 12.75, 10.9, 9.4, 7.9, 6.5, 5.6, and 4.5 m/s. (a) What is the average flow velocity? (b) What is the momentum flux factor \\\\beta?\",\"src\":\"stemez-FluidMechanics\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/TIGER-Lab/MMLU-Pro","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}