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reformulated_problem
stringlengths 154
1.14k
| ground_truth
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| combined_translation
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1.14k
| problem
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1.03k
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dict | response
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⌀ | math_verify_ii
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"On a water surface, two coherent sources of waves, A and B, which oscillate in phase at a distance (...TRUNCATED) | \boxed{5} | "On a water surface, two coherent sources of waves, A and B, which oscillate in phase at a distance (...TRUNCATED) | "Ở mặt nước, tại hai điểm A và B cách nhau 19 cm, có hai nguồn kết hợp dao đ(...TRUNCATED) | {'A': '7.', 'B': '4.', 'C': '5.', 'D': '6.'} | {"bytes":"iVBORw0KGgoAAAANSUhEUgAABDQAAAGyCAYAAAAbP5QYAAAMPWlDQ1BJQ0MgUHJvZmlsZQAASImVVwdYU8kWnltSIb(...TRUNCATED) | ["Solution Explanation (Step by Step)\n\n1) Geometry Setup \n • Let the two coherent sources be(...TRUNCATED) | 5 | 1 | {"decision":"TRUE","explanation":"I compared the substance of the Predicted Answer and the Ground Tr(...TRUNCATED) |
"A single-phase alternating current generator has an armature consisting of four identical coils con(...TRUNCATED) | \boxed{100} | "A single-phase alternating current generator has an armature consisting of four identical coils con(...TRUNCATED) | "Một máy phát điện xoay chiều một pha có phần ứng gồm bốn cuộn dây giống nh(...TRUNCATED) | {'A': '400 vòng.', 'B': '100 vòng.', 'C': '71 vòng.', 'D': '200 vòng.'} | {"bytes":"iVBORw0KGgoAAAANSUhEUgAAB24AAAJ0CAYAAADasgOsAAAMPWlDQ1BJQ0MgUHJvZmlsZQAASImVVwdYU8kWnltSIb(...TRUNCATED) | ["Solution Explanation Step by Step:\n\n1) Let N be the number of turns per coil, and let Φ(t) = Φ(...TRUNCATED) | 100 | 1 | {"decision":"TRUE","explanation":"I compared the provided 'Predicted Answer' and 'Ground Truth Answe(...TRUNCATED) |
"A voltage defined by \\( u = 200\\sqrt{2}\\cos(100\\pi t) \\) V (with time \\( t \\) measured in se(...TRUNCATED) | \(\boxed{1}\) | "A voltage defined by $u = 200\\sqrt{2}\\cos(100\\pi t)$ V (with time $t$ measured in seconds) is ap(...TRUNCATED) | "Đặt điện áp $u = 200\\sqrt{2}cos(100\\pi t) (V)$( t tính bằng s) vào hai đầu đoạn (...TRUNCATED) | {'A': '$\\sqrt{2} A$.', 'B': '$1A$.', 'C': '$2\\sqrt{2} A$.', 'D': '$2A$. '} | {"bytes":"iVBORw0KGgoAAAANSUhEUgAABU4AAAKMCAYAAAA0QiLJAAAMPWlDQ1BJQ0MgUHJvZmlsZQAASImVVwdYU8kWnltSIb(...TRUNCATED) | ["Solution Explanation (Step by Step)\n\n1) Identify the Source Voltage (Amplitude and RMS Value) \(...TRUNCATED) | null | 0 | {"decision":"FALSE","explanation":"I evaluated the Predicted Answer and the Ground Truth Answer to d(...TRUNCATED) |
"According to Bohr's atomic model for the hydrogen atom, consider the electron moving in a circular (...TRUNCATED) | \boxed{2} | "According to Bohr's atomic model for the hydrogen atom, consider the electron moving in a circular (...TRUNCATED) | "Theo mẫu nguyên tử Bo về nguyên tử hiđrô, coi êlectron chuyển động tròn đều q(...TRUNCATED) | {'A': '2.', 'B': '0,25.', 'C': '4', 'D': '0,5.'} | {"bytes":"iVBORw0KGgoAAAANSUhEUgAABqIAAAIQCAYAAADq2n8PAAAMPWlDQ1BJQ0MgUHJvZmlsZQAASImVVwdYU8kWnltSIb(...TRUNCATED) | ["Step-by-step Solution:\n\n1) Start with Bohr’s quantization condition for the angular momentum o(...TRUNCATED) | null | 0 | {"decision":"FALSE","explanation":"The Predicted Answer is None, and thus does not convey or attempt(...TRUNCATED) |
"A harmonic voltage \\( u = U\\sqrt{2} \\cos 2\\pi ft \\) (where \\( f \\) can vary, and \\( U \\) i(...TRUNCATED) | \(\boxed{80}\) | "A harmonic voltage $u = U\\sqrt{2} \\cos 2\\pi ft$ (where $f$ can vary, and $U$ is proportional to (...TRUNCATED) | "Đặt điện áp $u = U\\sqrt{2} cos 2\\pi ft$ (f thay đổi được, U tỉ lệ thuận với(...TRUNCATED) | {'A': '60 Hz.', 'B': '80 Hz.', 'C': '50 Hz.', 'D': '120 Hz.'} | {"bytes":"iVBORw0KGgoAAAANSUhEUgAAA4YAAAVkCAYAAACILwG+AAAMPWlDQ1BJQ0MgUHJvZmlsZQAASImVVwdYU8kWnltSIb(...TRUNCATED) | ["Solution Sketch:\n\n1) Label the impedances. \n • Let the (“AM”) section be the series c(...TRUNCATED) | f_{1} \;=\; \frac{180}{\sqrt{5}} \,\text{Hz}\,\approx 80\,\text{Hz}. | 1 | {"decision":"TRUE","explanation":"The evaluation involved confirming the semantic consistency betwee(...TRUNCATED) |
"A three-phase alternating current generator is operating normally. In the three windings of the sta(...TRUNCATED) | \boxed{40} | "A three-phase alternating current generator is operating normally. In the three windings of the sta(...TRUNCATED) | "Một máy phát điện xoay chiều ba pha đang hoạt động bình thường. Trong ba cuộn (...TRUNCATED) | {'A': '50 V.', 'B': '40 V.', 'C': '45 V.', 'D': '35 V.'} | {"bytes":"iVBORw0KGgoAAAANSUhEUgAABe4AAAEiCAYAAACP5EIbAAAMPWlDQ1BJQ0MgUHJvZmlsZQAASImVVwdYU8kWnltSIb(...TRUNCATED) | ["Solution Explanation (step by step):\n\n1) Label the phase voltages. \n In a balanced three‐p(...TRUNCATED) | null | 0 | {"decision":"FALSE","explanation":"The predicted answer is 'None', which does not contain any inform(...TRUNCATED) |
"A small object belonging to a spring pendulum oscillates harmonically along the horizontal directio(...TRUNCATED) | \boxed{3} | "A small object belonging to a spring pendulum oscillates harmonically along the horizontal directio(...TRUNCATED) | "Vật nhỏ của một con lắc lò xo dao động điều hòa theo phương ngang, mốc thế (...TRUNCATED) | {'A': '\\frac{1}{2}', 'B': '3', 'C': '2', 'D': '\\frac{1}{3}'} | {"bytes":"iVBORw0KGgoAAAANSUhEUgAACO4AAARkCAYAAADPScnKAAAMPWlDQ1BJQ0MgUHJvZmlsZQAASImVVwdYU8kWnltSIb(...TRUNCATED) | ["Solution Explanation (Step by Step):\n\n1) Identify relevant physical quantities: \n • Let th(...TRUNCATED) | \frac{K}{U} = 3 | 1 | {"decision":"TRUE","explanation":"I evaluated the representation and intent of both answers to the p(...TRUNCATED) |
"The nucleus ${}_{6}^{13}C$ has a mass of 13.0001u. Given the mass of a proton is 1.0073u and the ma(...TRUNCATED) | \boxed{7.49} | "The nucleus ${}_{6}^{13}C$ has a mass of 13.0001u. Given the mass of proton and neutron are 1.0073u(...TRUNCATED) | "Hạt nhân ${}_{6}^{13}C$ có khối lượng 13,0001u. Cho khối lượng prôtôn và nơtron l(...TRUNCATED) | "{'A': '7,49MeV/ nuclôn.', 'B': '16,2MeV/ nuclôn.', 'C': '8,12MeV/ nuclôn.', 'D': '97,4MeV/ nucl(...TRUNCATED) | {"bytes":"iVBORw0KGgoAAAANSUhEUgAABqAAAAHGCAYAAAAboEqdAAAMPWlDQ1BJQ0MgUHJvZmlsZQAASImVVwdYU8kWnltSIb(...TRUNCATED) | ["Solution Steps:\n\n1. Identify the relevant masses and constants: \n • Mass of the ¹³C nucl(...TRUNCATED) | null | 0 | {"decision":"FALSE","explanation":"To evaluate the presence of meaningful content, comparing the pre(...TRUNCATED) |
"A tuning circuit in a radio receiver consists of an electromagnetic coil and a capacitor with varia(...TRUNCATED) | \boxed{2\lambda_0} | "A tuning circuit in a radio receiver consists of an electromagnetic coil and a capacitor with varia(...TRUNCATED) | "Một mạch chọn sóng ở một máy thu thanh là mạch dao động gồm cuộn cảm và t(...TRUNCATED) | "{'A': '$\\\\frac{\\\\lambda_0}{4}$.', 'B': '$4\\\\lambda_o$.', 'C': '$2\\\\lambda_o$.', 'D': '$\\\\(...TRUNCATED) | {"bytes":"iVBORw0KGgoAAAANSUhEUgAAA5gAAAFACAYAAADZOtPWAAAMPWlDQ1BJQ0MgUHJvZmlsZQAASImVVwdYU8kWnltSIb(...TRUNCATED) | ["Solution Explanation:\n\n1) The resonance condition in an LC (inductor-capacitor) circuit occurs a(...TRUNCATED) | "\\lambda = \\lambda_0 \\sqrt{\\frac{C}{C_0}} \\quad\\text{and}\\quad \\lambda(4 C_0) = 2\\,\\lambda(...TRUNCATED) | 0 | {"decision":"TRUE","explanation":"I compared the Ground Truth Answer against the Predicted Answer, f(...TRUNCATED) |
"Determine the number of electrically neutral nucleons (neutrons) in the nucleus ${}_{86}^{222}Rn$. (...TRUNCATED) | \boxed{136} | "The number of electrically neutral nucleons in the nucleus ${}_{86}^{222}Rn$ is. {\"A\": \"222.\", (...TRUNCATED) | Số nuclon không mang điện có trong một hạt nhân $_{86}^{222}Rn$ là | {'A': '222.', 'B': '86.', 'C': '308.', 'D': '136.'} | {"bytes":"iVBORw0KGgoAAAANSUhEUgAABLoAAADOCAYAAAA5ZGukAAAMPWlDQ1BJQ0MgUHJvZmlsZQAASImVVwdYU8kWnltSIb(...TRUNCATED) | ["Step-by-step reasoning:\n\n1. The atomic number (86) tells us the number of protons in the nucleus(...TRUNCATED) | 136 | 1 | {"decision":"TRUE","explanation":"I compared the Predicted Answer ('136') with the Ground Truth Answ(...TRUNCATED) |
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