question_index
int64 0
86
| question
stringlengths 27
2.28k
| options
stringlengths 101
2.62k
| category
stringclasses 14
values | correct_answer
stringclasses 10
values | samples
sequencelengths 100
100
| GRMLlama32_scores
sequencelengths 100
100
| GRMLlama32_scores_normalized
sequencelengths 100
100
| OffsetBias_scores
sequencelengths 100
100
| OffsetBias_scores_normalized
sequencelengths 100
100
| GRM_scores
sequencelengths 100
100
| GRM_scores_normalized
sequencelengths 100
100
| Skyworks_scores
sequencelengths 100
100
| Skyworks_scores_normalized
sequencelengths 100
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sequencelengths 100
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| URM_scores_normalized
sequencelengths 100
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sequencelengths 100
100
| QRM_scores_normalized
sequencelengths 100
100
| GPM_scores
sequencelengths 100
100
| GPM_scores_normalized
sequencelengths 100
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sequencelengths 100
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sequencelengths 100
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sequencelengths 100
100
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sequencelengths 100
100
| InternLM2Reward7B_scores
sequencelengths 100
100
| InternLM2Reward7B_scores_normalized
sequencelengths 100
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sequencelengths 100
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sequencelengths 100
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|
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0
|
Which of the following was not cited as evidence for life in the martian meteorite ALH84001?
| "{\"A\": \"Amino acids with a preferred orientation or \\\"chirality\\\"\", \"B\": \"Magnetite grain(...TRUNCATED)
|
physics
|
A
| ["Here's the step-by-step justification for the likely correct answer:\n\n1. The question asks which(...TRUNCATED)
| [-8.203125,-2.28125,-3.533203125,-0.76904296875,-3.26953125,-2.3828125,-1.6162109375,-3.189453125,-3(...TRUNCATED)
| [null,0.7805008292198181,0.6092821359634399,0.9873121976852417,0.645342230796814,0.7666110396385193,(...TRUNCATED)
| [-5.0625,-3.5,-3.109375,-3.90625,-3.671875,-2.65625,-3.6875,-3.71875,-3.65625,-2.6875,-3.3125,-5.281(...TRUNCATED)
| [0.0,0.6622516512870789,0.8278145790100098,0.4900662302970886,0.5894039869308472,null,0.582781434059(...TRUNCATED)
| [-13.125,-11.9375,-6.48046875,-8.1171875,-10.265625,-5.3828125,-9.6484375,-7.4375,-11.5234375,-7.882(...TRUNCATED)
| [0.009846827015280724,0.17614880204200745,0.9403719902038574,0.7111597657203674,0.41028445959091187,(...TRUNCATED)
| [-10.9375,4.4375,6.90625,5.34375,3.0625,7.125,8.25,3.03125,0.193359375,6.71875,1.5,-9.6875,1.9296875(...TRUNCATED)
| [null,0.7732341885566711,0.9200743436813354,0.8271375298500061,0.6914498209953308,0.9330855011940002(...TRUNCATED)
| [3.78564453125,7.8828125,8.48291015625,8.7294921875,8.0615234375,9.84716796875,8.2470703125,9.642089(...TRUNCATED)
| [null,0.5975390076637268,0.7204881906509399,0.7710084319114685,0.6341536641120911,1.0,0.672168850898(...TRUNCATED)
| [0.610440194606781,0.8455281853675842,0.8638948202133179,0.8532167077064514,0.8277403116226196,0.837(...TRUNCATED)
| [null,0.8382554650306702,0.941804051399231,0.8816023468971252,0.7379698157310486,0.7944909334182739,(...TRUNCATED)
| [0.99609375,1.0,0.99609375,1.0,1.0,1.0,0.99609375,1.0,1.0,0.99609375,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED)
| [0.0,1.0,0.0,1.0,1.0,1.0,0.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,1.0,0.0,1.0,0.0(...TRUNCATED)
| [-1.403821587562561,2.501441717147827,2.5467419624328613,2.729806423187256,1.5680263042449951,3.0758(...TRUNCATED)
| [null,0.5589416027069092,0.5656800866127014,0.5929113030433655,0.42009419202804565,0.644390583038330(...TRUNCATED)
| [0.12255859375,0.15234375,0.1884765625,0.1806640625,0.1787109375,0.203125,0.1689453125,0.1884765625,(...TRUNCATED)
| [null,0.2950819730758667,0.9016393423080444,0.7704917788505554,0.7377049326896667,null,0.57377046346(...TRUNCATED)
| [-0.52978515625,0.7626953125,1.396484375,1.47265625,1.3515625,1.275390625,0.387451171875,0.926269531(...TRUNCATED)
| [null,0.47499412298202515,0.779760479927063,0.8163888454437256,0.7581592202186584,0.7215308547019958(...TRUNCATED)
| [1.4382991790771484,3.0954952239990234,3.3312766551971436,3.3165245056152344,3.1267266273498535,3.22(...TRUNCATED)
| [null,0.7645683884620667,0.931788444519043,0.9213259816169739,0.7867181897163391,0.8547337651252747,(...TRUNCATED)
|
1
| "For the two linear equations $2 * x + 3 * y = 10$ and $4 * x + 4 * y = 12$ iwth variables x and y. (...TRUNCATED)
| "{\"A\": \"[4, 1]\", \"B\": \"[-1, 4]\", \"C\": \"[2, 2]\", \"D\": \"[3, 2]\", \"E\": \"[1, 2]\", \"(...TRUNCATED)
|
math
|
B
| ["To solve this problem using Cramer's rule, we need to follow these steps:\n\n1. Calculate the dete(...TRUNCATED)
| [1.8134765625,2.64453125,5.5546875,1.9765625,0.20166015625,2.4921875,4.6796875,1.2880859375,5.425781(...TRUNCATED)
| [0.5059441328048706,0.590251624584198,0.8854765295982361,0.5224885940551758,0.3424311578273773,0.574(...TRUNCATED)
| [-1.625,-2.5,-1.515625,-2.484375,-2.46875,-2.28125,-1.3046875,-2.703125,-2.125,-1.5078125,-1.5,-2.85(...TRUNCATED)
| [0.8421052694320679,0.4736842215061188,0.8881579041481018,0.4802631437778473,0.4868420958518982,0.56(...TRUNCATED)
| [-4.05859375,-7.6640625,-2.86328125,-5.90625,-7.62890625,-4.53125,-4.3359375,-6.18359375,-6.2421875,(...TRUNCATED)
| [0.5917558670043945,0.28053611516952515,0.6949338316917419,0.4322684109210968,0.2835707664489746,0.5(...TRUNCATED)
| [1.96875,-1.6640625,8.75,1.6796875,-3.5,-1.21875,3.0625,-3.28125,6.25,9.6875,0.6953125,-5.625,10.062(...TRUNCATED)
| [0.6525885462760925,0.49420979619026184,0.9482288956642151,0.6399863958358765,0.41416892409324646,0.(...TRUNCATED)
| [5.40185546875,5.8974609375,5.92919921875,5.3408203125,4.931640625,5.0908203125,6.38818359375,5.6977(...TRUNCATED)
| [0.4310685992240906,0.5267150402069092,0.5328401923179626,0.4192894697189331,0.3403222858905792,0.37(...TRUNCATED)
| [0.783957839012146,0.7508915066719055,0.7718150615692139,0.7604230642318726,0.6858876943588257,0.716(...TRUNCATED)
| [0.8591219186782837,0.7392129302024841,0.8150883913040161,0.7737773656845093,0.5034886002540588,0.61(...TRUNCATED)
| [1.0,1.0,1.0,0.99609375,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.99609375,1(...TRUNCATED)
| [1.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0(...TRUNCATED)
| [5.747735023498535,3.261308193206787,6.034763336181641,2.6712751388549805,2.683863878250122,4.682403(...TRUNCATED)
| [0.7881371378898621,0.4642467498779297,0.8255264163017273,0.3873870372772217,0.3890269100666046,0.64(...TRUNCATED)
| [0.09765625,0.08544921875,0.09765625,0.091796875,0.07958984375,0.095703125,0.095703125,0.08447265625(...TRUNCATED)
| [0.7543859481811523,0.31578946113586426,0.7543859481811523,0.5438596606254578,0.10526315867900848,0.(...TRUNCATED)
| [0.72119140625,0.00733184814453125,0.61572265625,0.2705078125,-0.1370849609375,0.85302734375,1.01562(...TRUNCATED)
| [0.7584728598594666,0.4599868655204773,0.7143732309341431,0.5700286030769348,0.39960187673568726,0.8(...TRUNCATED)
| [2.9088449478149414,2.6879186630249023,2.8527374267578125,2.762754201889038,2.2532613277435303,2.435(...TRUNCATED)
| [0.8363644480705261,0.7137706875801086,0.8052299618721008,0.7552975416183472,0.47257593274116516,0.5(...TRUNCATED)
|
2
| "This question refers to the following information.\nAn Act to place certain restrictions on Immigra(...TRUNCATED)
| "{\"A\": \"Iron smelting\", \"B\": \"Fertilizer harvesting\", \"C\": \"Coal mining\", \"D\": \"Fur t(...TRUNCATED)
|
history
|
I
| ["To answer this question, let's analyze the context and the specific information provided in the pa(...TRUNCATED)
| [-2.2890625,-4.4375,-3.58984375,2.080078125,-1.689453125,-0.5224609375,-2.638671875,-3.982421875,2.1(...TRUNCATED)
| [0.32963740825653076,0.0,0.1300569325685501,1.0,0.4216361939907074,0.6006892323493958,0.275996416807(...TRUNCATED)
| [-4.21875,-4.46875,-4.71875,-3.703125,-4.5,-4.0625,-5.15625,-5.03125,-2.90625,-4.4375,-3.875,-4.8437(...TRUNCATED)
| [0.6545454263687134,0.5575757622718811,0.46060606837272644,0.8545454740524292,0.5454545617103577,0.7(...TRUNCATED)
| [-12.4140625,-9.828125,-10.9375,-8.890625,-10.84375,-11.1796875,-10.9453125,-11.3828125,-6.77734375,(...TRUNCATED)
| [0.1915966421365738,0.5624650120735168,0.40336135029792786,0.696918785572052,0.41680672764778137,0.3(...TRUNCATED)
| [1.359375,-0.71875,9.75,6.28125,-2.0,-7.71875,-4.78125,0.458984375,16.5,8.5,11.5,-4.5625,3.484375,10(...TRUNCATED)
| [0.3807339370250702,0.29357796907424927,0.7326343655586243,0.5871559381484985,0.2398427277803421,0.0(...TRUNCATED)
| [7.9306640625,7.70068359375,8.9169921875,8.208984375,8.146484375,6.48876953125,6.4072265625,7.774902(...TRUNCATED)
| [0.5219907164573669,0.4800569713115692,0.7018340229988098,0.5727385878562927,0.5613425970077515,0.25(...TRUNCATED)
| [0.7609701752662659,0.732041597366333,0.7681005001068115,0.7910037040710449,0.7239270806312561,0.694(...TRUNCATED)
| [0.5295865535736084,0.39756643772125244,0.562126874923706,0.6666492819786072,0.36053457856178284,0.2(...TRUNCATED)
| [1.0,1.0,1.0,1.0,0.99609375,1.0,1.0,1.0,1.0,1.0,0.99609375,1.0,0.99609375,0.99609375,1.0,1.0,1.0,1.0(...TRUNCATED)
| [1.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0,0.0,1.0,0.0,0.0,1.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0,0.0,0.0,1.0(...TRUNCATED)
| [2.508190870285034,2.7670819759368896,2.4646568298339844,4.917096138000488,4.333746910095215,3.16188(...TRUNCATED)
| [0.3094806969165802,0.34019267559051514,0.30431631207466125,0.5952465534210205,0.526044487953186,0.3(...TRUNCATED)
| [0.1083984375,0.1279296875,0.1318359375,0.1298828125,0.142578125,0.1171875,0.115234375,0.1279296875,(...TRUNCATED)
| [0.23232322931289673,0.6363636255264282,0.7171717286109924,0.6767676472663879,0.939393937587738,0.41(...TRUNCATED)
| [0.327880859375,0.32275390625,0.783203125,0.373046875,0.36328125,-0.1583251953125,-0.1365966796875,0(...TRUNCATED)
| [0.5525968074798584,0.5486307740211487,0.9048158526420593,0.5875353813171387,0.5799810886383057,0.17(...TRUNCATED)
| [2.589278221130371,2.455235242843628,2.8866777420043945,2.922701835632324,2.0632457733154297,2.03047(...TRUNCATED)
| [0.4689018130302429,0.39301320910453796,0.6372749209403992,0.6576700210571289,0.1710878610610962,0.1(...TRUNCATED)
|
3
|
Which of the following is a consequence of removal of a protective tariff on imported steel?
| "{\"A\": \"The quality of imported steel decreases.\", \"B\": \"Domestic steel producers lose their (...TRUNCATED)
|
economics
|
E
| ["To analyze this question, we need to consider the effects of removing a protective tariff on impor(...TRUNCATED)
| [-8.546875,-7.79296875,-4.953125,-9.6484375,-10.46875,-4.88671875,-9.5390625,-7.9140625,-7.203125,-6(...TRUNCATED)
| [0.28416380286216736,0.37937837839126587,0.7380365133285522,0.14504192769527435,0.04144055396318436,(...TRUNCATED)
| [-4.34375,-4.34375,-3.25,-5.0,-5.40625,-3.234375,-4.8125,-4.5,-4.46875,-2.875,-5.5,-3.734375,-3.2187(...TRUNCATED)
| [0.4236453175544739,0.4236453175544739,0.7684729099273682,0.21674877405166626,0.08866994827985764,0.(...TRUNCATED)
| [-10.0390625,-6.94140625,-7.140625,-12.0,-12.1015625,-3.931640625,-13.53125,-9.1953125,-7.7109375,-8(...TRUNCATED)
| [0.3788321316242218,0.668248176574707,0.6496350169181824,0.19562043249607086,0.18613138794898987,0.9(...TRUNCATED)
| [-9.75,0.1435546875,6.0,-14.6875,-11.25,1.265625,-8.0625,-1.46875,4.46875,5.03125,-14.75,-0.15625,-9(...TRUNCATED)
| [0.16532258689403534,0.4844695031642914,0.6733871102333069,0.006048386916518211,0.11693548411130905,(...TRUNCATED)
| [4.89111328125,7.591796875,8.07763671875,3.673828125,3.10009765625,7.93505859375,4.79345703125,5.424(...TRUNCATED)
| [0.2825668156147003,0.7086511254310608,0.7853015661239624,0.09051690995693207,0.0,0.7628071904182434(...TRUNCATED)
| [0.6753570437431335,0.7933770418167114,0.8147945404052734,0.524854838848114,0.5941703915596008,0.736(...TRUNCATED)
| [0.41878587007522583,0.7617642283439636,0.8240057229995728,null,0.18284903466701508,0.59792596101760(...TRUNCATED)
| [1.0,0.99609375,1.0,0.99609375,1.0,1.0,1.0,1.0,0.99609375,1.0,0.99609375,1.0,1.0,0.99609375,1.0,1.0,(...TRUNCATED)
| [1.0,0.0,1.0,0.0,1.0,1.0,1.0,1.0,0.0,1.0,0.0,1.0,1.0,0.0,1.0,1.0,0.0,1.0,0.0,1.0,0.0,1.0,1.0,1.0,1.0(...TRUNCATED)
| [-4.385854721069336,-1.0855481624603271,-0.5663106441497803,-2.4039273262023926,-5.098751068115234,-(...TRUNCATED)
| [0.023822778835892677,0.40564286708831787,0.46571463346481323,0.25311651825904846,null,0.30891606211(...TRUNCATED)
| [0.1494140625,0.1826171875,0.1904296875,0.1474609375,0.1142578125,0.189453125,0.1416015625,0.1796875(...TRUNCATED)
| [0.3964497148990631,0.7988165616989136,0.8934911489486694,0.37278106808662415,null,0.88165682554245,(...TRUNCATED)
| [-0.3056640625,-0.69482421875,0.197509765625,-0.74609375,-0.98046875,0.630859375,-0.1175537109375,-0(...TRUNCATED)
| [0.3937804400920868,0.24447359144687653,0.5868302583694458,0.22480329871177673,0.13488197326660156,0(...TRUNCATED)
| [2.137941598892212,3.1204535961151123,3.3709640502929688,1.4480208158493042,1.628314733505249,2.9226(...TRUNCATED)
| [0.34421196579933167,0.764098048210144,0.8711560964584351,0.04936762526631355,0.12641797959804535,0.(...TRUNCATED)
|
4
| "suppose $-\\pi<x<\\pi$. what is the value of $(\\sum_{n=1}^{\\infty}(-1)^{n-1} \\frac{cos(nx)}{n})/(...TRUNCATED)
| "{\"A\": \"-1.0\", \"B\": \"2.5\", \"C\": \"1.5\", \"D\": \"2.0\", \"E\": \"0.25\", \"F\": \"3.0\", (...TRUNCATED)
|
math
|
H
| ["To solve this problem, we can break it down into steps:\n\n1. We are given the series $\\sum_{n=1(...TRUNCATED)
| [3.41796875,-3.03515625,-0.08197021484375,1.783203125,-2.212890625,-3.490234375,2.478515625,-4.10546(...TRUNCATED)
| [null,0.193446084856987,0.5930315256118774,0.8454017043113708,0.3047040104866028,0.1318710297346115,(...TRUNCATED)
| [-3.453125,-7.34375,-5.96875,-5.96875,-4.84375,-6.5,-6.1875,-6.4375,-6.90625,-6.25,-6.0625,-7.125,-7(...TRUNCATED)
| [null,null,0.5194805264472961,0.5194805264472961,0.9870129823684692,0.29870128631591797,0.4285714328(...TRUNCATED)
| [0.34716796875,-9.3125,-10.4921875,-5.14453125,-7.03515625,-13.859375,-5.41015625,-12.1015625,-13.86(...TRUNCATED)
| [null,0.4334941506385803,0.3294279873371124,0.801171600818634,0.6343900561332703,0.03239145502448082(...TRUNCATED)
| [-1.390625,-25.25,-18.125,-18.75,-12.0625,-23.875,-15.625,-18.375,-19.875,-20.25,-18.5,-16.125,-19.0(...TRUNCATED)
| [null,null,0.40466925501823425,0.3657587468624115,0.7821011543273926,0.046692606061697006,0.56031125(...TRUNCATED)
| [5.2783203125,1.224609375,1.71484375,2.5859375,2.81494140625,0.782470703125,2.5966796875,1.51953125,(...TRUNCATED)
| [null,0.28226906061172485,0.4173491895198822,0.6573720574378967,0.7204722166061401,0.160441294312477(...TRUNCATED)
| [0.7257901430130005,0.4463624656200409,0.5471139550209045,0.4954816699028015,0.5972116589546204,0.47(...TRUNCATED)
| [null,null,0.4282267987728119,0.18235401809215546,0.6667919158935547,0.09245271235704422,0.379967689(...TRUNCATED)
| [1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.99609375,1.0,1.0078125,1.0,1.0,1.0,1.0,0.99609375,1.0,0.99609375,1.0,(...TRUNCATED)
| [1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,1.0,null,1.0,1.0,1.0,1.0,0.0,1.0,0.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0,1.(...TRUNCATED)
| [1.1825506687164307,-2.524963855743408,-1.591982126235962,-1.1486361026763916,-4.160987854003906,-3.(...TRUNCATED)
| [null,0.5676809549331665,0.8112720847129822,0.927024781703949,0.14053331315517426,0.2840994298458099(...TRUNCATED)
| [0.1494140625,0.11279296875,0.10791015625,0.12890625,0.12353515625,0.09423828125,0.1162109375,0.0952(...TRUNCATED)
| [null,0.6020408272743225,0.5,0.9387755393981934,0.8265306353569031,0.2142857164144516,0.673469364643(...TRUNCATED)
| [0.057281494140625,-1.6884765625,-0.9326171875,-0.974609375,-0.1531982421875,-1.4765625,-1.47265625,(...TRUNCATED)
| [null,0.13388606905937195,0.6092430353164673,0.5828343033790588,null,0.26715800166130066,0.269614607(...TRUNCATED)
| [2.615055561065674,0.9049346446990967,1.2839235067367554,1.0992810726165771,1.6389517784118652,0.987(...TRUNCATED)
| [null,0.06949086487293243,0.34510400891304016,0.21082596480846405,0.6032922267913818,0.1294964849948(...TRUNCATED)
|
5
| "A marine research facility uses a towing basin to test models of proposed ship hull configurations.(...TRUNCATED)
| "{\"A\": \"18 m/s\", \"B\": \"20 m/s\", \"C\": \"12 m/s\", \"D\": \"14 m/s\", \"E\": \"10 m/s\", \"F(...TRUNCATED)
|
engineering
|
D
| ["To solve this problem, we can use Froude's Law of Similitude, which states that for geometrically (...TRUNCATED)
| [7.5546875,6.40234375,-0.9599609375,7.55859375,2.291015625,2.693359375,5.75390625,3.412109375,1.1884(...TRUNCATED)
| [0.9237757325172424,0.7930423021316528,null,0.9242189526557922,0.3266119956970215,0.3722579181194305(...TRUNCATED)
| [-1.5859375,-1.953125,-4.46875,-2.140625,-3.125,-3.25,-3.15625,-3.375,-2.75,-3.015625,-1.5625,-3.031(...TRUNCATED)
| [null,0.9470587968826294,0.0,0.8764705657958984,0.5058823823928833,0.4588235318660736,0.494117647409(...TRUNCATED)
| [3.8671875,1.4990234375,-9.3828125,0.4423828125,-0.5244140625,-5.9921875,0.004486083984375,-1.546875(...TRUNCATED)
| [0.9860464930534363,0.8098110556602478,0.0,0.7311773300170898,0.6592296361923218,0.2523255944252014,(...TRUNCATED)
| [13.1875,14.6875,-14.5,7.84375,12.4375,1.8828125,12.8125,9.625,-8.6875,15.1875,15.0625,8.875,9.8125,(...TRUNCATED)
| [0.7483108043670654,0.7888513803482056,0.0,0.6038851141929626,0.7280405163764954,0.44277870655059814(...TRUNCATED)
| [8.90625,9.379150390625,2.63818359375,7.83544921875,7.430908203125,7.4912109375,7.68896484375,8.7006(...TRUNCATED)
| [0.8077648878097534,0.868707537651062,0.0,0.6697709560394287,0.6176378130912781,0.6254090070724487,0(...TRUNCATED)
| [0.8729190230369568,0.8827284574508667,0.516610324382782,0.8480284214019775,0.8974416255950928,0.776(...TRUNCATED)
| [0.9315972924232483,0.957244873046875,0.0,0.8665188550949097,0.9957135915756226,0.6799725890159607,0(...TRUNCATED)
| [1.0,1.0078125,1.0,1.0,0.99609375,1.0,1.0,1.0,1.0,1.0,0.99609375,0.99609375,1.0,1.0,1.0,1.0,0.996093(...TRUNCATED)
| [1.0,null,1.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0,0.0,0.0,1.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,0.0,0.0,1.0,0.(...TRUNCATED)
| [8.588591575622559,8.091537475585938,-1.6308650970458984,6.955060005187988,2.2903547286987305,1.9844(...TRUNCATED)
| [null,0.9535519480705261,null,0.8314225077629089,0.3301386833190918,0.2972632348537445,0.86730861663(...TRUNCATED)
| [0.1943359375,0.1982421875,0.1396484375,0.1865234375,0.171875,0.15234375,0.1796875,0.1640625,0.17382(...TRUNCATED)
| [0.9333333373069763,1.0,0.0,0.800000011920929,0.550000011920929,0.21666666865348816,0.68333333730697(...TRUNCATED)
| [2.005859375,1.3037109375,0.278076171875,1.5908203125,0.822265625,0.5869140625,1.6630859375,1.326171(...TRUNCATED)
| [0.9820359349250793,0.7129490971565247,0.31989145278930664,0.8229790329933167,0.5284430980682373,0.4(...TRUNCATED)
| [3.5181260108947754,3.575953722000122,1.150828242301941,3.341289520263672,3.4997053146362305,2.81214(...TRUNCATED)
| [0.9664449095726013,0.9900529384613037,0.0,0.8942517638206482,0.9589247107505798,0.6782276034355164,(...TRUNCATED)
|
6
| "The cost of making the correct decisions for the given binary channel is zero, i.e., c(d_1/x_1) = c(...TRUNCATED)
| "{\"A\": \"(a) Decision made is d_1, (b) Decision d_1\", \"B\": \"(a) Decision made is d_2, (b) Deci(...TRUNCATED)
|
engineering
|
H
| ["To determine the correct answer, we need to analyze the given probabilities and costs.\n\nGiven:\n(...TRUNCATED)
| [0.0469970703125,-3.19921875,-2.458984375,0.82568359375,-0.31396484375,-6.30078125,-2.46875,2.492187(...TRUNCATED)
| [0.8907331228256226,0.4352175295352936,0.5390887260437012,1.0,0.8400822281837463,0.0,0.5377184152603(...TRUNCATED)
| [-4.46875,-4.1875,-4.625,-4.5,-3.890625,-5.15625,-4.375,-4.5,-5.125,-4.75,-4.40625,-5.125,-4.03125,-(...TRUNCATED)
| [0.5857142806053162,0.7142857313156128,0.5142857432365417,0.5714285969734192,0.8500000238418579,0.27(...TRUNCATED)
| [-8.40625,-11.4765625,-11.375,-8.8046875,-8.28125,-13.5234375,-12.421875,-7.75,-9.421875,-10.6953125(...TRUNCATED)
| [0.8672286868095398,0.453108549118042,0.46680715680122375,0.8134878873825073,0.8840885162353516,0.17(...TRUNCATED)
| [-1.3828125,-10.3125,-11.9375,-6.53125,-5.09375,-13.8125,-10.6875,4.28125,-13.875,-15.75,-9.625,-9.0(...TRUNCATED)
| [1.0,0.5668814182281494,0.48806366324424744,0.7502841949462891,0.8200075626373291,0.3971201181411743(...TRUNCATED)
| [6.89111328125,4.56689453125,4.950927734375,6.50341796875,6.394775390625,2.1903076171875,4.258789062(...TRUNCATED)
| [null,0.5510146617889404,0.6400532126426697,1.0,0.9748110771179199,0.0,0.47957998514175415,null,0.39(...TRUNCATED)
| [0.757157564163208,0.6150215268135071,0.6179036498069763,0.7349032759666443,0.6535599827766418,0.606(...TRUNCATED)
| [null,0.542494535446167,0.5526766777038574,0.9660203456878662,0.6786456108093262,0.5136821866035461,(...TRUNCATED)
| [1.0,1.0,1.0,0.99609375,1.0,1.0,0.99609375,0.99609375,0.99609375,1.0,1.0,1.0,1.0,1.0,1.0078125,1.0,1(...TRUNCATED)
| [0.3333333432674408,0.3333333432674408,0.3333333432674408,0.0,0.3333333432674408,0.3333333432674408,(...TRUNCATED)
| [0.8417044281959534,-0.5957123637199402,-0.7497966289520264,1.452514410018921,0.9995710253715515,-3.(...TRUNCATED)
| [0.7263269424438477,0.4683310091495514,0.4406750798225403,0.8359586596488953,0.7546617388725281,0.02(...TRUNCATED)
| [0.11865234375,0.11181640625,0.10888671875,0.11865234375,0.1328125,0.09423828125,0.11474609375,0.125(...TRUNCATED)
| [0.6499999761581421,0.5099999904632568,0.44999998807907104,0.6499999761581421,0.9399999976158142,0.1(...TRUNCATED)
| [0.06024169921875,-0.67431640625,-0.455810546875,-0.2274169921875,0.00127410888671875,-0.748046875,-(...TRUNCATED)
| [0.8539782166481018,0.42877331376075745,0.5552572011947632,0.6874646544456482,0.8198443651199341,0.3(...TRUNCATED)
| [2.4902963638305664,1.7665001153945923,1.5531193017959595,2.3951311111450195,2.1448490619659424,1.47(...TRUNCATED)
| [0.9962615370750427,0.6106612682342529,0.4969833195209503,0.9455625414848328,0.8122255206108093,0.45(...TRUNCATED)
|
7
| "Ringlet Wholesalers discounted its old line of dining-room sets at a chain discount of 30% and 10%.(...TRUNCATED)
| "{\"A\": \"List price: $560.57, Net price: $392.40\", \"B\": \"List price: $992.00, Net price: $671.(...TRUNCATED)
|
business
|
F
| ["Let's break down the problem step by step:\n\nLet the list price of the dining-room set be x.\n\nF(...TRUNCATED)
| [0.2413330078125,-2.568359375,-0.5,-1.3505859375,-1.162109375,-0.281982421875,-2.89453125,-0.9350585(...TRUNCATED)
| [0.7329849004745483,0.34865081310272217,0.6315789222717285,0.5152284502983093,0.5410099029541016,0.6(...TRUNCATED)
| [-2.046875,-2.0625,-2.4375,-2.59375,-3.0,-2.625,-4.5625,-3.5625,-2.1875,-2.421875,-4.96875,-2.421875(...TRUNCATED)
| [0.9235127568244934,0.9178470373153687,0.7818697094917297,0.7252124547958374,0.577903687953949,0.713(...TRUNCATED)
| [-4.7109375,-8.6484375,-7.0,-6.3984375,-8.1328125,-7.1328125,-12.3984375,-8.0546875,-8.3984375,-5.92(...TRUNCATED)
| [0.758820116519928,0.3701561689376831,0.5328706502914429,0.592249870300293,0.42105263471603394,0.519(...TRUNCATED)
| [1.359375,-7.03125,-0.0152587890625,-2.953125,-1.875,-2.46875,-15.75,-5.46875,-5.4375,1.3984375,-18.(...TRUNCATED)
| [0.7099999785423279,0.39411765336990356,0.6582490801811218,0.5476470589637756,0.5882353186607361,0.5(...TRUNCATED)
| [4.3603515625,3.0146484375,4.85546875,2.796142578125,3.3426513671875,2.31298828125,0.99493408203125,(...TRUNCATED)
| [0.739879310131073,0.4716815948486328,0.8385558724403381,0.4281335175037384,0.53705233335495,0.33184(...TRUNCATED)
| [0.707942545413971,0.5979933738708496,0.6290352940559387,0.6640326976776123,0.636929988861084,0.6503(...TRUNCATED)
| [0.8495885133743286,0.5817146897315979,0.6573434472084045,0.7426090836524963,0.676577627658844,0.709(...TRUNCATED)
| [1.0,1.0,1.0,1.0,1.0,0.99609375,1.0,0.99609375,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1(...TRUNCATED)
| [1.0,1.0,1.0,1.0,1.0,0.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED)
| [2.006531238555908,-1.9118092060089111,0.6372783184051514,0.5329081416130066,-0.9321526885032654,-0.(...TRUNCATED)
| [0.9218378663063049,0.39234331250190735,0.7368075251579285,0.7227036952972412,0.5247265696525574,0.5(...TRUNCATED)
| [0.1142578125,0.11279296875,0.109375,0.10205078125,0.11083984375,0.1015625,0.09375,0.099609375,0.111(...TRUNCATED)
| [0.6811594367027283,0.6376811861991882,0.5362318754196167,0.3188405930995941,0.5797101259231567,0.30(...TRUNCATED)
| [-0.56591796875,0.0028171539306640625,-0.348388671875,-0.33154296875,-0.6201171875,-0.75830078125,-0(...TRUNCATED)
| [0.48615917563438416,0.774040937423706,0.5962679386138916,0.6047948598861694,0.4587246775627136,0.38(...TRUNCATED)
| [2.623067617416382,1.9879422187805176,2.2602250576019287,2.3103904724121094,2.1235814094543457,2.251(...TRUNCATED)
| [0.8554682731628418,0.5880515575408936,0.7026950716972351,0.723816990852356,0.6451618671417236,0.699(...TRUNCATED)
|
8
| "Under which of the following situations would bootstrapping be preferred to pure simulation?\n\ni) (...TRUNCATED)
| "{\"A\": \"(i) and (ii) only\", \"B\": \"(ii) and (iii) only\", \"C\": \"(i) and (iii) only\", \"D\"(...TRUNCATED)
|
economics
|
C
| ["To determine the correct answer, let's analyze the characteristics of bootstrapping and pure simul(...TRUNCATED)
| [-0.92578125,-4.01953125,1.001953125,-7.23828125,-5.33203125,-5.84765625,-2.52734375,-3.0625,-3.5585(...TRUNCATED)
| [0.8995581269264221,0.45868560671806335,null,0.0,0.27164873480796814,0.1981699913740158,0.6713286638(...TRUNCATED)
| [-3.140625,-2.828125,-2.359375,-4.75,-2.8125,-2.90625,-1.953125,-2.5625,-3.03125,-2.15625,-1.8671875(...TRUNCATED)
| [0.5219941139221191,0.6392961740493774,0.8152492642402649,null,0.6451612710952759,0.6099706888198853(...TRUNCATED)
| [-8.2421875,-12.71875,-4.78125,-11.1640625,-12.8046875,-12.2734375,-6.46875,-10.15625,-10.8671875,-7(...TRUNCATED)
| [0.6458643078804016,0.07825656235218048,null,0.275383859872818,0.06736008077859879,0.134720161557197(...TRUNCATED)
| [-5.09375,-5.90625,18.25,-13.3125,-3.953125,-3.890625,2.6875,1.3359375,8.1875,11.8125,11.6875,-4.25,(...TRUNCATED)
| [0.23549884557724,0.20533642172813416,null,null,0.2778422236442566,0.28016242384910583,0.52436196804(...TRUNCATED)
| [6.61376953125,7.265625,11.1636962890625,3.92822265625,5.1123046875,6.82080078125,7.8828125,7.490722(...TRUNCATED)
| [0.3459702134132385,0.47345301508903503,null,null,0.05233002454042435,0.3864591419696808,0.594155848(...TRUNCATED)
| [0.7002556920051575,0.7559373378753662,0.907067060470581,0.6221395134925842,0.7230359315872192,0.763(...TRUNCATED)
| [0.12932224571704865,0.38213080167770386,null,null,0.23275020718574524,0.4180913269519806,0.61152827(...TRUNCATED)
| [0.99609375,1.0,1.0,1.0,1.0,1.0,1.0,0.99609375,1.0,0.99609375,1.0078125,0.99609375,1.0,1.0,1.0078125(...TRUNCATED)
| [0.0,0.3333333432674408,0.3333333432674408,0.3333333432674408,0.3333333432674408,0.3333333432674408,(...TRUNCATED)
| [6.007296562194824,1.8269898891448975,6.578876972198486,-1.402024745941162,3.7311320304870605,1.6574(...TRUNCATED)
| [0.907707691192627,0.35274195671081543,0.9835891127586365,null,0.6055305004119873,0.3302362263202667(...TRUNCATED)
| [0.1376953125,0.111328125,0.142578125,0.11767578125,0.10986328125,0.1142578125,0.126953125,0.1220703(...TRUNCATED)
| [0.9259259104728699,0.25925925374031067,null,0.4197530746459961,0.2222222238779068,0.333333343267440(...TRUNCATED)
| [0.54638671875,-1.15625,-0.43798828125,-1.6259765625,-0.462646484375,-0.763671875,-0.2310791015625,-(...TRUNCATED)
| [null,0.12325674295425415,0.5140124559402466,null,0.5005977153778076,0.33683091402053833,0.626577258(...TRUNCATED)
| [2.272648811340332,2.3331902027130127,3.8358006477355957,1.505295991897583,2.242269992828369,2.43470(...TRUNCATED)
| [0.2353820502758026,0.26756760478019714,null,null,0.21923178434371948,0.32153457403182983,0.63409876(...TRUNCATED)
|
9
|
Scarcity is best defined as
| "{\"A\": \"the opportunity cost of not pursuing a given course of action.\", \"B\": \"the difference(...TRUNCATED)
|
economics
|
B
| ["Here's the step-by-step justification for the likely correct answer:\n\n1. **Understanding Scarcit(...TRUNCATED)
| [-7.69140625,-8.3984375,-5.91796875,-7.94921875,-7.24609375,-6.18359375,-7.6015625,-6.90625,-8.15625(...TRUNCATED)
| [0.30046510696411133,0.13209302723407745,0.7227907180786133,0.23906977474689484,0.4065116345882416,0(...TRUNCATED)
| [-5.9375,-5.84375,-5.0,-6.0625,-5.34375,-4.6875,-5.59375,-5.59375,-5.875,-6.0625,-5.46875,-4.78125,-(...TRUNCATED)
| [0.06896551698446274,0.12068965286016464,0.5862069129943848,0.0,0.3965517282485962,0.758620679378509(...TRUNCATED)
| [-12.2109375,-11.8203125,-8.9765625,-13.1953125,-11.3125,-10.3203125,-11.96875,-10.9765625,-13.96093(...TRUNCATED)
| [0.25772517919540405,0.32347139716148376,0.8021038770675659,0.09204471111297607,0.40894147753715515,(...TRUNCATED)
| [-5.40625,-14.375,-7.25,-14.0,-12.1875,-3.59375,-9.9375,-10.0,-17.875,-9.3125,-2.8125,-12.3125,-11.8(...TRUNCATED)
| [0.5716180205345154,0.1909814327955246,0.4933687150478363,0.2068965584039688,0.28381961584091187,0.6(...TRUNCATED)
| [6.3798828125,4.8330078125,5.140625,3.955078125,4.90771484375,6.17724609375,3.73095703125,5.12158203(...TRUNCATED)
| [0.6677364110946655,0.4313008487224579,0.47831928730010986,0.29711171984672546,0.44271960854530334,0(...TRUNCATED)
| [0.745646059513092,0.6963297128677368,0.7144533395767212,0.6492956280708313,0.6945730447769165,0.758(...TRUNCATED)
| [0.6671126484870911,0.43164145946502686,0.5181764960289001,0.20706745982170105,0.4232538938522339,0.(...TRUNCATED)
| [1.0,1.0,1.0,1.0,1.0,1.0,0.99609375,1.0,1.0,1.0,1.0,1.0078125,0.99609375,1.0,0.99609375,1.0,1.0,1.0,(...TRUNCATED)
| [1.0,1.0,1.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,null,0.0,1.0,0.0,1.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0,0.0,1.(...TRUNCATED)
| [-0.7946221232414246,-2.7494096755981445,0.3561249375343323,-2.239683151245117,0.9801698923110962,-2(...TRUNCATED)
| [0.43824100494384766,0.10982716828584671,0.6315721273422241,0.19546370208263397,0.7364147305488586,0(...TRUNCATED)
| [0.08203125,0.08740234375,0.091796875,0.0888671875,0.09326171875,0.0947265625,0.078125,0.0927734375,(...TRUNCATED)
| [0.3285714387893677,0.48571428656578064,0.6142857074737549,0.5285714268684387,0.6571428775787354,0.6(...TRUNCATED)
| [-0.1397705078125,-0.038177490234375,0.7998046875,1.01953125,0.372802734375,1.208984375,-0.050933837(...TRUNCATED)
| [0.1690414547920227,0.21804344654083252,0.6222326755523682,0.7282148003578186,0.41627413034439087,0.(...TRUNCATED)
| [2.3922717571258545,1.9350411891937256,2.129549741744995,1.598385214805603,1.8072962760925293,2.5513(...TRUNCATED)
| [0.6430643200874329,0.3787742555141449,0.49120479822158813,0.1841791570186615,0.30493468046188354,0.(...TRUNCATED)
|
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