id string | subject string | topic string | subtopic string | difficulty string | difficulty_labeling_method string | question_type string | question string | options dict | correct_answer string | correct_answer_value string | solution string | option_explanations dict | concepts_required list | reasoning_steps int64 | answer_type string | language string | origin string | generator string | generator_template_id string | verification_status string | verification_note string | difficulty_note string | source_type string | answer_validation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
openstem_005643 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 70 μF capacitor is charged to a potential difference of 2 V. Calculate the energy stored, expressed in μJ. | {
"A": "105 μJ",
"B": "112 μJ",
"C": "210 μJ",
"D": "140 μJ"
} | D | 140 μJ | U=½CV². Since C=70 μF, U in μJ is ½×70×(2)²=140 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 140 μJ, not 105 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 140 μJ, not 112 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 140 μJ, not 210 μJ.",
... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005195 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +5 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "75 N",
"B": "150 N",
"C": "148 N",
"D": "300 N"
} | B | 150 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(5×10⁻⁶)/(3×10⁻²)²=150 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 150 N, not 75 N.",
"B": "Correct. The worked calculation gives 150 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 150 N, not 148 N.",
"D": "Incorrect. Substituting the stated values into t... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001716 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 3 elements can be selected from a set of 53 distinct elements? | {
"A": "28111.2",
"B": "35139",
"C": "46852",
"D": "23426"
} | D | 23426 | Order does not matter, so the count is C(53,3)=53!/[3!(50)!]=23426. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 23426, not 28111.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23426, not 35139.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23426, not 46852.",
"D... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009484 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_3H_5N_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "-2",
"B": "1",
"C": "2",
"D": "5"
} | C | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×3+2+1−5−0)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"C": "Correct. The worked calculation gives 2.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006967 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 40 mol H₂ and 15 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "22.5 mol",
"B": "-30 mol",
"C": "60 mol",
"D": "30 mol"
} | D | 30 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 40 mol H₂O; O₂ can produce 30 mol H₂O. The limiting condition is O₂; product=30 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 30 mol, not 22.5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30 mol, not -30 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30 mol, not 60 mol.... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004069 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 27 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.27. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "11.368 N",
"B": "124.416 N",
"C": "102.68 N",
"D": "103.68 N"
} | D | 103.68 N | Net force=mg(sinθ−μcosθ)=27×10×(0.6−0.27×0.8)=103.68 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 103.68 N, not 11.368 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 103.68 N, not 124.416 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 103.68 N, not... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004272 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.36. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "56.16 N",
"B": "37.44 N",
"C": "29.952 N",
"D": "39.44 N"
} | B | 37.44 N | Net force=mg(sinθ−μcosθ)=12×10×(0.6−0.36×0.8)=37.44 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 37.44 N, not 56.16 N.",
"B": "Correct. The worked calculation gives 37.44 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 37.44 N, not 29.952 N.",
"D": "Incorrect. Substituting the stated v... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000792 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 5. What is the sum of its first 10 terms? | {
"A": "36621090",
"B": "24414060",
"C": "2441407",
"D": "24414058"
} | B | 24414060 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(5^10−1)/(5−1)=24414060. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24414060, not 36621090.",
"B": "Correct. The worked calculation gives 24414060.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24414060, not 2441407.",
"D": "Incorrect. Substituting the state... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002559 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 0], [7, 1]]. | {
"A": "3",
"B": "4",
"C": "5",
"D": "7"
} | B | 4 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(1)−(0)(7)=4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 3.",
"B": "Correct. The worked calculation gives 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 5.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007950 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 75 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "1.58594 mmol L⁻¹",
"B": "1.17188 mmol L⁻¹",
"C": "0.58594 mmol L⁻¹",
"D": "3.58594 mmol L⁻¹"
} | C | 0.58594 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=75/2^7=0.58594 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.58594 mmol L⁻¹, not 1.58594 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.58594 mmol L⁻¹, not 1.17188 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.58594 mmol L⁻¹.",
... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002542 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 6], [5, 1]]. | {
"A": "-28",
"B": "-27",
"C": "-32.4",
"D": "-29"
} | B | -27 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(1)−(6)(5)=-27. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -27, not -28.",
"B": "Correct. The worked calculation gives -27.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -27, not -32.4.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007040 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 9 mol of gas at 320 K and 0.43 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "412.1933 L",
"B": "274.79553 L",
"C": "439.67286 L",
"D": "549.59107 L"
} | D | 549.59107 L | PV=nRT, so V=nRT/P=(9)(0.082057)(320)/(0.43)=549.59107 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 549.59107 L, not 412.1933 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 549.59107 L, not 274.79553 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 549... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009029 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.78 V, transfers 3 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.7012 V",
"B": "0.3506 V",
"C": "-0.7012 V",
"D": "-0.2988 V"
} | A | 0.7012 V | Apply the Nernst equation: E=0.78−(0.0591/3)(4)=0.7012 V. | {
"A": "Correct. The worked calculation gives 0.7012 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7012 V, not 0.3506 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7012 V, not -0.7012 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007656 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 50 mL of 0.10 M HCl is mixed with 42 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.0607",
"B": "-0.9393",
"C": "3.0607",
"D": "1.54552"
} | A | 2.0607 | Excess H⁺ moles=0.10×(50−42)/1000=0.000800 mol. Total volume=0.092 L, so [H⁺]=0.008696 M and pH=−log₁₀[H⁺]=2.0607. | {
"A": "Correct. The worked calculation gives 2.0607.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.0607, not -0.9393.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.0607, not 3.0607.",
"D": "Incorrect. Substituting the stated values... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008693 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.84 mol L⁻¹ and initially B is absent. At equilibrium, 75% of A has dissociated at constant volume. Find K_c. | {
"A": "8.28",
"B": "16.56",
"C": "12.42",
"D": "2.656"
} | B | 16.56 | Let α=0.75. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.84)(0.75)²/(1−0.75)=16.56. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16.56, not 8.28.",
"B": "Correct. The worked calculation gives 16.56.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16.56, not 12.42.",
"D": "Incorrect. Substituting the stated values into t... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008034 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 9 A for 1644 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "5.86811 g",
"B": "3.65109 g",
"C": "3.86811 g",
"D": "4.86811 g"
} | D | 4.86811 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×9×1644/(2×96500)=4.86811 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.86811 g, not 5.86811 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.86811 g, not 3.65109 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.86811 g,... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001579 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (4x² +7x -3) dx. | {
"A": "883.66667",
"B": "89.26667",
"C": "882.66667",
"D": "441.33333"
} | C | 882.66667 | An antiderivative is (4/3)x³+(7/2)x²+(-3)x. Evaluating between 0 and 8 gives (4/3)(8)³+(7/2)(8)²+(-3)(8)=882.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 882.66667, not 883.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 882.66667, not 89.26667.",
"C": "Correct. The worked calculation gives 882.66667.",
"D": "Incorrect. Substituting the ... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004927 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 4 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.75 A",
"B": "-0.25 A",
"C": "1.75 A",
"D": "5.75 A"
} | A | 2.75 A | Series branch resistance=10+8=18 Ω. Parallel equivalent R_eq=(18×4)/(18+4)=3.27273 Ω. Total current I=V/R_eq=9/3.27273=2.75 A. | {
"A": "Correct. The worked calculation gives 2.75 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.75 A, not -0.25 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.75 A, not 1.75 A.",
"D": "Incorrect. Substituting the stated values... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001706 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 7 elements can be selected from a set of 31 distinct elements? | {
"A": "2629574",
"B": "2629575",
"C": "-2629575",
"D": "2629577"
} | B | 2629575 | Order does not matter, so the count is C(31,7)=31!/[7!(24)!]=2629575. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2629575, not 2629574.",
"B": "Correct. The worked calculation gives 2629575.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2629575, not -2629575.",
"D": "Incorrect. Substituting the stated v... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007501 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 71 mL of 0.10 M HCl is mixed with 42 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.59068",
"B": "-0.40932",
"C": "1.15907",
"D": "-1.40932"
} | A | 1.59068 | Excess H⁺ moles=0.10×(71−42)/1000=0.002900 mol. Total volume=0.113 L, so [H⁺]=0.025664 M and pH=−log₁₀[H⁺]=1.59068. | {
"A": "Correct. The worked calculation gives 1.59068.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.59068, not -0.40932.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.59068, not 1.15907.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003334 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-10+1i)/(9+6i). What is Re(z), the real part of z? | {
"A": "-0.53846",
"B": "-0.71795",
"C": "-1.07692",
"D": "0.71795"
} | B | -0.71795 | Multiply numerator and denominator by the conjugate (9-6i). Then Re(z)=(ac+bd)/(c²+d²)=((-10)(9)+(1)(6))/(9²+(6)²)=-0.71795. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.71795, not -0.53846.",
"B": "Correct. The worked calculation gives -0.71795.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.71795, not -1.07692.",
"D": "Incorrect. Substituting the stat... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003882 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 7 m s⁻¹. A constant net force does 12 N of work over 12 m in the direction of motion. Find its final kinetic energy. | {
"A": "389 J",
"B": "194.5 J",
"C": "466.8 J",
"D": "391 J"
} | A | 389 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(7)²+(12)(12)=389 J. | {
"A": "Correct. The worked calculation gives 389 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 389 J, not 194.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 389 J, not 466.8 J.",
"D": "Incorrect. Substituting the stated values i... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000709 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio -2. What is the sum of its first 11 terms? | {
"A": "5466",
"B": "10928",
"C": "5464",
"D": "8196"
} | C | 5464 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(-2^11−1)/(-2−1)=5464. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5464, not 5466.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5464, not 10928.",
"C": "Correct. The worked calculation gives 5464.",
"D": "Incorrect. Substituting the stated values into the ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003418 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 34 m s⁻¹ at 70° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "76.30625 m",
"B": "74.30625 m",
"C": "75.30625 m",
"D": "59.445 m"
} | B | 74.30625 m | Range R=u²sin(2θ)/g. Substituting u=34, θ=70° and g=10 gives R=(34)²sin(140°)/10=74.30625 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 74.30625 m, not 76.30625 m.",
"B": "Correct. The worked calculation gives 74.30625 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 74.30625 m, not 75.30625 m.",
"D": "Incorrect. Substitutin... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006174 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 64 cm in front of a thin convex lens of focal length 14 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.56",
"B": "0.21",
"C": "0.28",
"D": "-1.72"
} | C | 0.28 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(64)(14)/(64−14)=17.92 cm. Thus |m|=v/u=17.92/64=0.28. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.28, not 0.56.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.28, not 0.21.",
"C": "Correct. The worked calculation gives 0.28.",
"D": "Incorrect. Substituting the stated values into the g... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002353 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, -2], [5, 4]]. | {
"A": "15",
"B": "-14",
"C": "14",
"D": "17"
} | C | 14 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(4)−(-2)(5)=14. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14, not 15.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14, not -14.",
"C": "Correct. The worked calculation gives 14.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005745 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.8 atm at 256 K. What is its pressure at 528 K? | {
"A": "2.7125 atm",
"B": "7.425 atm",
"C": "3.7125 atm",
"D": "1.37125 atm"
} | C | 3.7125 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.8)(528)/(256)=3.7125 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.7125 atm, not 2.7125 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.7125 atm, not 7.425 atm.",
"C": "Correct. The worked calculation gives 3.7125 atm.",
"D": "Incorrect. Substituting... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009368 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_9H_16N_1X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "2",
"B": "4",
"C": "5",
"D": "3"
} | A | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×9+2+1−16−1)/2=2. | {
"A": "Correct. The worked calculation gives 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 5.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001897 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 4 elements can be selected from a set of 45 distinct elements? | {
"A": "111746.25",
"B": "148995",
"C": "119196",
"D": "148994"
} | B | 148995 | Order does not matter, so the count is C(45,4)=45!/[4!(41)!]=148995. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 148995, not 111746.25.",
"B": "Correct. The worked calculation gives 148995.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 148995, not 119196.",
"D": "Incorrect. Substituting the stated valu... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002750 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(6, 3, 3) and v=(-5, -3, 3), calculate u·v. | {
"A": "-2",
"B": "-30",
"C": "-15",
"D": "-22.5"
} | B | -30 | The dot product is the sum of corresponding component products: (6)(-5)+(3)(-3)+(3)(3)=-30. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -30, not -2.",
"B": "Correct. The worked calculation gives -30.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -30, not -15.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009099 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.23 V, transfers 1 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.14073 V",
"B": "1.4073 V",
"C": "2.11095 V",
"D": "0.4073 V"
} | B | 1.4073 V | Apply the Nernst equation: E=1.23−(0.0591/1)(-3)=1.4073 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.4073 V, not 1.14073 V.",
"B": "Correct. The worked calculation gives 1.4073 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.4073 V, not 2.11095 V.",
"D": "Incorrect. Substituting the st... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009962 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(OH)_3]^-2, each OH ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "-1",
"B": "2",
"C": "1.5",
"D": "1"
} | D | 1 | Let the formal oxidation state of Pd be x. Charge balance gives x+(3)(−1)=-2; hence x=-2+3=+1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not -1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.5.",
"D": "Correct. The worked... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003497 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 40 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "138.56406 m",
"B": "103.92305 m",
"C": "207.8461 m",
"D": "110.85125 m"
} | A | 138.56406 m | Range R=u²sin(2θ)/g. Substituting u=40, θ=60° and g=10 gives R=(40)²sin(120°)/10=138.56406 m. | {
"A": "Correct. The worked calculation gives 138.56406 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 138.56406 m, not 103.92305 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 138.56406 m, not 207.8461 m.",
"D": "Incorrect. Substit... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005677 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.7 atm at 203 K. What is its pressure at 692 K? | {
"A": "18.02167 atm",
"B": "16.02167 atm",
"C": "8.01084 atm",
"D": "19.22601 atm"
} | B | 16.02167 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.7)(692)/(203)=16.02167 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16.02167 atm, not 18.02167 atm.",
"B": "Correct. The worked calculation gives 16.02167 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16.02167 atm, not 8.01084 atm.",
"D": "Incorrect. Su... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003466 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 98 m s⁻¹ at 65° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "367.85454 m",
"B": "588.56727 m",
"C": "736.70908 m",
"D": "735.70908 m"
} | D | 735.70908 m | Range R=u²sin(2θ)/g. Substituting u=98, θ=65° and g=10 gives R=(98)²sin(130°)/10=735.70908 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 735.70908 m, not 367.85454 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 735.70908 m, not 588.56727 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 73... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006602 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 7 kg is attached to an ideal spring of force constant 102 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.47606 s",
"B": "1.04787 s",
"C": "1.05239 s",
"D": "0.52394 s"
} | D | 0.52394 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(7/102)=0.52394 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.52394 s, not -2.47606 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.52394 s, not 1.04787 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.52394 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004647 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 3 kg and radius 5 m is acted on by a constant torque of 90 N m about its central axis. Find its angular acceleration. | {
"A": "0.4 rad s⁻²",
"B": "1.2 rad s⁻²",
"C": "-0.6 rad s⁻²",
"D": "2.4 rad s⁻²"
} | D | 2.4 rad s⁻² | For a solid disc, I=½MR²=½(3)(5)²=37.5 kg m². Using τ=Iα, α=90/37.5=2.4 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.4 rad s⁻², not 0.4 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.4 rad s⁻², not 1.2 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003148 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-12-1i)/(1+11i). What is Re(z), the real part of z? | {
"A": "2.81148",
"B": "-0.37705",
"C": "-0.18852",
"D": "-0.09426"
} | C | -0.18852 | Multiply numerator and denominator by the conjugate (1-11i). Then Re(z)=(ac+bd)/(c²+d²)=((-12)(1)+(-1)(11))/(1²+(11)²)=-0.18852. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.18852, not 2.81148.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.18852, not -0.37705.",
"C": "Correct. The worked calculation gives -0.18852.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005768 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.6 atm at 277 K. What is its pressure at 774 K? | {
"A": "1.7265 atm",
"B": "10.89747 atm",
"C": "7.26498 atm",
"D": "5.44874 atm"
} | C | 7.26498 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.6)(774)/(277)=7.26498 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.26498 atm, not 1.7265 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.26498 atm, not 10.89747 atm.",
"C": "Correct. The worked calculation gives 7.26498 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006008 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 59 cm in front of a thin convex lens of focal length 20 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "2.51282",
"B": "-2.48718",
"C": "1.02564",
"D": "0.51282"
} | D | 0.51282 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(59)(20)/(59−20)=30.25641 cm. Thus |m|=v/u=30.25641/59=0.51282. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.51282, not 2.51282.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.51282, not -2.48718.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.51282, not 1.02... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001727 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 12 elements can be selected from a set of 58 distinct elements? | {
"A": "1783589578680",
"B": "668846092005",
"C": "891794789340",
"D": "891794789339"
} | C | 891794789340 | Order does not matter, so the count is C(58,12)=58!/[12!(46)!]=891794789340. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 891794789340, not 1783589578680.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 891794789340, not 668846092005.",
"C": "Correct. The worked calculation gives 891794789340.",
"D": "Incorrect. ... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002079 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 8 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.48039",
"B": "3.32026",
"C": "1.32026",
"D": "0.32026"
} | D | 0.32026 | Favourable pairs = C(6,2)+C(8,2)+C(4,2)=49. Total pairs=C(18,2)=153. Therefore P=49/153=0.32026. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32026, not 0.48039.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32026, not 3.32026.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32026, not 1.320... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005815 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.7 atm at 379 K. What is its pressure at 741 K? | {
"A": "1.91892 atm",
"B": "-9.18918 atm",
"C": "7.18918 atm",
"D": "9.18918 atm"
} | D | 9.18918 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.7)(741)/(379)=9.18918 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.18918 atm, not 1.91892 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.18918 atm, not -9.18918 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001761 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 7 elements can be selected from a set of 66 distinct elements? | {
"A": "778789440",
"B": "1168184160",
"C": "778789439",
"D": "934547328"
} | A | 778789440 | Order does not matter, so the count is C(66,7)=66!/[7!(59)!]=778789440. | {
"A": "Correct. The worked calculation gives 778789440.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 778789440, not 1168184160.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 778789440, not 778789439.",
"D": "Incorrect. Substituting th... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005212 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +8 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "52.89796 N",
"B": "5.40816 N",
"C": "33.06122 N",
"D": "44.08163 N"
} | D | 44.08163 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(8×10⁻⁶)/(7×10⁻²)²=44.08163 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 44.08163 N, not 52.89796 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 44.08163 N, not 5.40816 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 44.0816... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001102 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ -7x² -4x+7. Evaluate f′(-1). | {
"A": "28",
"B": "14",
"C": "30",
"D": "-28"
} | A | 28 | Differentiate: f′(x)=3(6)x²+2(-7)x+(-4). At x=-1, f′(-1)=3(6)(-1)²+2(-7)(-1)+(-4)=28. | {
"A": "Correct. The worked calculation gives 28.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28, not 14.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28, not 30.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000983 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio 4. What is the sum of its first 6 terms? | {
"A": "18018",
"B": "15015",
"C": "15013",
"D": "30030"
} | B | 15015 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(4^6−1)/(4−1)=15015. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15015, not 18018.",
"B": "Correct. The worked calculation gives 15015.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15015, not 15013.",
"D": "Incorrect. Substituting the stated values into ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005618 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 50 μF capacitor is charged to a potential difference of 2 V. Calculate the energy stored, expressed in μJ. | {
"A": "100 μJ",
"B": "150 μJ",
"C": "-100 μJ",
"D": "120 μJ"
} | A | 100 μJ | U=½CV². Since C=50 μF, U in μJ is ½×50×(2)²=100 μJ. | {
"A": "Correct. The worked calculation gives 100 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 100 μJ, not 150 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 100 μJ, not -100 μJ.",
"D": "Incorrect. Substituting the stated values... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007952 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 62 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "15.5 mmol L⁻¹",
"B": "18.6 mmol L⁻¹",
"C": "23.25 mmol L⁻¹",
"D": "11.625 mmol L⁻¹"
} | A | 15.5 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=62/2^2=15.5 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 15.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15.5 mmol L⁻¹, not 18.6 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15.5 mmol L⁻¹, not 23.25 mmol L⁻¹.",
"D": "Incorr... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002285 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 5 blue and 8 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.48529",
"B": "2.32353",
"C": "-2.67647",
"D": "0.32353"
} | D | 0.32353 | Favourable pairs = C(4,2)+C(5,2)+C(8,2)=44. Total pairs=C(17,2)=136. Therefore P=44/136=0.32353. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32353, not 0.48529.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32353, not 2.32353.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32353, not -2.67... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000337 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 12 and common difference 8. Find the sum of its first 20 terms. | {
"A": "1761",
"B": "1760",
"C": "880",
"D": "1758"
} | B | 1760 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=12, d=8, n=20: Sₙ=20/2[2(12)+(20−1)(8)]=1760. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1760, not 1761.",
"B": "Correct. The worked calculation gives 1760.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1760, not 880.",
"D": "Incorrect. Substituting the stated values into the go... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003661 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 12 m s⁻¹ at 35° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "13.53157 m",
"B": "14.53157 m",
"C": "20.29736 m",
"D": "12.53157 m"
} | A | 13.53157 m | Range R=u²sin(2θ)/g. Substituting u=12, θ=35° and g=10 gives R=(12)²sin(70°)/10=13.53157 m. | {
"A": "Correct. The worked calculation gives 13.53157 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13.53157 m, not 14.53157 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13.53157 m, not 20.29736 m.",
"D": "Incorrect. Substitutin... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005788 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.7 atm at 351 K. What is its pressure at 639 K? | {
"A": "1.12744 atm",
"B": "1.91154 atm",
"C": "1.27436 atm",
"D": "-0.72564 atm"
} | C | 1.27436 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.7)(639)/(351)=1.27436 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.27436 atm, not 1.12744 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.27436 atm, not 1.91154 atm.",
"C": "Correct. The worked calculation gives 1.27436 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006390 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 18 kg is attached to an ideal spring of force constant 588 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "3.34993 s",
"B": "0.52489 s",
"C": "0.34993 s",
"D": "-0.34993 s"
} | C | 0.34993 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(18/588)=0.34993 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34993 s, not 3.34993 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34993 s, not 0.52489 s.",
"C": "Correct. The worked calculation gives 0.34993 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008715 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.34 mol L⁻¹ and initially B is absent. At equilibrium, 79% of A has dissociated at constant volume. Find K_c. | {
"A": "-4.04179",
"B": "3.04179",
"C": "4.04179",
"D": "5.04179"
} | C | 4.04179 | Let α=0.79. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.34)(0.79)²/(1−0.79)=4.04179. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.04179, not -4.04179.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.04179, not 3.04179.",
"C": "Correct. The worked calculation gives 4.04179.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000177 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 +0x -2=0, let its roots be α and β. What is α²+β²? | {
"A": "1.2",
"B": "4",
"C": "0",
"D": "2"
} | D | 2 | By Vieta's relations, α+β = 0/2 and αβ = -2/2. Then α²+β²=(α+β)²−2αβ = (0/2)²−2(-2/2) = 2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 0.",
"D": "Correct. The worked ... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009483 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_6H_7X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "1.5",
"B": "2",
"C": "0",
"D": "1"
} | B | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+0−7−3)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.5.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 0.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009070 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.26 V, transfers 1 electrons, and has reaction quotient Q=10^1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.2009 V",
"B": "0.90068 V",
"C": "1.12009 V",
"D": "1.2009 V"
} | D | 1.2009 V | Apply the Nernst equation: E=1.26−(0.0591/1)(1)=1.2009 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.2009 V, not 0.2009 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.2009 V, not 0.90068 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2009 V, not... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005042 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +2 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "44 N",
"B": "22.5 N",
"C": "45 N",
"D": "54 N"
} | C | 45 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(2×10⁻⁶)/(4×10⁻²)²=45 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45 N, not 44 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 45 N, not 22.5 N.",
"C": "Correct. The worked calculation gives 45 N.",
"D": "Incorrect. Substituting the stated values into the... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003569 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 105 m s⁻¹ at 70° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "708.67334 m",
"B": "-708.67334 m",
"C": "1417.34668 m",
"D": "1063.01001 m"
} | A | 708.67334 m | Range R=u²sin(2θ)/g. Substituting u=105, θ=70° and g=10 gives R=(105)²sin(140°)/10=708.67334 m. | {
"A": "Correct. The worked calculation gives 708.67334 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 708.67334 m, not -708.67334 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 708.67334 m, not 1417.34668 m.",
"D": "Incorrect. Subs... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008898 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.57 mol L⁻¹ and initially B is absent. At equilibrium, 51% of A has dissociated at constant volume. Find K_c. | {
"A": "3.33353",
"B": "4.33353",
"C": "1.66676",
"D": "5.00029"
} | A | 3.33353 | Let α=0.51. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.57)(0.51)²/(1−0.51)=3.33353. | {
"A": "Correct. The worked calculation gives 3.33353.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.33353, not 4.33353.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.33353, not 1.66676.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006904 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 35 mol H₂ and 26 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "34 mol",
"B": "4.5 mol",
"C": "35 mol",
"D": "28 mol"
} | C | 35 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 35 mol H₂O; O₂ can produce 52 mol H₂O. The limiting condition is H₂; product=35 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 35 mol, not 34 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 35 mol, not 4.5 mol.",
"C": "Correct. The worked calculation gives 35 mol.",
"D": "Incorrect. Substituting the stated values... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009678 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(Cl)_4]^+3, each Cl ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "7",
"B": "5",
"C": "4",
"D": "5.25"
} | A | 7 | Let the formal oxidation state of Fe be x. Charge balance gives x+(4)(−1)=+3; hence x=3+4=+7. | {
"A": "Correct. The worked calculation gives 7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 4.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002268 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 9 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.64",
"B": "-1.64",
"C": "0.36",
"D": "2.36"
} | C | 0.36 | Favourable pairs = C(12,2)+C(9,2)+C(4,2)=108. Total pairs=C(25,2)=300. Therefore P=108/300=0.36. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.36, not -0.64.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36, not -1.64.",
"C": "Correct. The worked calculation gives 0.36.",
"D": "Incorrect. Substituting the stated values into the... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000784 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio -3. What is the sum of its first 6 terms? | {
"A": "728",
"B": "-546",
"C": "-728",
"D": "-364"
} | C | -728 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(-3^6−1)/(-3−1)=-728. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -728, not 728.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -728, not -546.",
"C": "Correct. The worked calculation gives -728.",
"D": "Incorrect. Substituting the stated values into the go... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009813 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(Cl)_2]^+2, each Cl ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "4",
"B": "2",
"C": "1",
"D": "1.4"
} | A | 4 | Let the formal oxidation state of Cu be x. Charge balance gives x+(2)(−1)=+2; hence x=2+2=+4. | {
"A": "Correct. The worked calculation gives 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008456 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.22 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.2196 K",
"B": "3.196 K",
"C": "0.196 K",
"D": "2.196 K"
} | D | 2.196 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.6×1.22=2.196 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.196 K, not 1.2196 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.196 K, not 3.196 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.196 K, not 0.19... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005721 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.6 atm at 351 K. What is its pressure at 687 K? | {
"A": "0.88077 atm",
"B": "-1.82564 atm",
"C": "2.34872 atm",
"D": "1.17436 atm"
} | D | 1.17436 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.6)(687)/(351)=1.17436 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.17436 atm, not 0.88077 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.17436 atm, not -1.82564 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001730 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 81 distinct elements? | {
"A": "32164253551",
"B": "48246380325",
"C": "32164253550",
"D": "24123190162.5"
} | C | 32164253550 | Order does not matter, so the count is C(81,8)=81!/[8!(73)!]=32164253550. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 32164253550, not 32164253551.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 32164253550, not 48246380325.",
"C": "Correct. The worked calculation gives 32164253550.",
"D": "Incorrect. Substi... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008979 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.47 mol L⁻¹ and initially B is absent. At equilibrium, 47% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.54926",
"B": "2.45074",
"C": "4.90148",
"D": "1.45074"
} | B | 2.45074 | Let α=0.47. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.47)(0.47)²/(1−0.47)=2.45074. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.45074, not -0.54926.",
"B": "Correct. The worked calculation gives 2.45074.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.45074, not 4.90148.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009420 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_16H_30N_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "2.25",
"B": "3",
"C": "-3",
"D": "6"
} | B | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×16+2+2−30−0)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not -3.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001211 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ -8x² -6x+7. Evaluate f′(4). | {
"A": "-248",
"B": "-310",
"C": "-30",
"D": "-308"
} | B | -310 | Differentiate: f′(x)=3(-5)x²+2(-8)x+(-6). At x=4, f′(4)=3(-5)(4)²+2(-8)(4)+(-6)=-310. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -310, not -248.",
"B": "Correct. The worked calculation gives -310.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -310, not -30.",
"D": "Incorrect. Substituting the stated values into the go... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002357 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, 5], [5, -3]]. | {
"A": "-40",
"B": "-60",
"C": "-39",
"D": "-30"
} | A | -40 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(-3)−(5)(5)=-40. | {
"A": "Correct. The worked calculation gives -40.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -40, not -60.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -40, not -39.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001981 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 4 elements can be selected from a set of 54 distinct elements? | {
"A": "-316251",
"B": "379501.2",
"C": "237188.25",
"D": "316251"
} | D | 316251 | Order does not matter, so the count is C(54,4)=54!/[4!(50)!]=316251. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 316251, not -316251.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 316251, not 379501.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 316251, not 237188.... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003698 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block initially moves at 12 m s⁻¹. A constant net force does 25 N of work over 10 m in the direction of motion. Find its final kinetic energy. | {
"A": "395 J",
"B": "394 J",
"C": "40.4 J",
"D": "788 J"
} | B | 394 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(2)(12)²+(25)(10)=394 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 394 J, not 395 J.",
"B": "Correct. The worked calculation gives 394 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 394 J, not 40.4 J.",
"D": "Incorrect. Substituting the stated values into... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001560 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (1x² +1x -4) dx. | {
"A": "170.66667",
"B": "-170.66667",
"C": "341.33333",
"D": "168.66667"
} | A | 170.66667 | An antiderivative is (1/3)x³+(1/2)x²+(-4)x. Evaluating between 0 and 8 gives (1/3)(8)³+(1/2)(8)²+(-4)(8)=170.66667. | {
"A": "Correct. The worked calculation gives 170.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 170.66667, not -170.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 170.66667, not 341.33333.",
"D": "Incorrect. Substituting th... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007366 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 80 mL of 0.10 M HCl is mixed with 80 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "8",
"B": "14",
"C": "7",
"D": "5"
} | C | 7 | Equal moles of strong acid and base are present. They neutralize completely, so at 25°C pH=7.00. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 14.",
"C": "Correct. The worked calculation gives 7.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001604 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (-4x² +8x +0) dx. | {
"A": "-427.66667",
"B": "-213.33333",
"C": "-426.66667",
"D": "-424.66667"
} | C | -426.66667 | An antiderivative is (-4/3)x³+(8/2)x²+(0)x. Evaluating between 0 and 8 gives (-4/3)(8)³+(8/2)(8)²+(0)(8)=-426.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -426.66667, not -427.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -426.66667, not -213.33333.",
"C": "Correct. The worked calculation gives -426.66667.",
"D": "Incorrect. Substitutin... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005265 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +3 μC are separated by 5 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "21.6 N",
"B": "43.2 N",
"C": "-43.2 N",
"D": "34.56 N"
} | B | 43.2 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(3×10⁻⁶)/(5×10⁻²)²=43.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 43.2 N, not 21.6 N.",
"B": "Correct. The worked calculation gives 43.2 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 43.2 N, not -43.2 N.",
"D": "Incorrect. Substituting the stated values... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000734 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio 3. What is the sum of its first 5 terms? | {
"A": "605",
"B": "607",
"C": "-605",
"D": "606"
} | A | 605 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(3^5−1)/(3−1)=605. | {
"A": "Correct. The worked calculation gives 605.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 605, not 607.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 605, not -605.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003722 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block initially moves at 5 m s⁻¹. A constant net force does 25 N of work over 18 m in the direction of motion. Find its final kinetic energy. | {
"A": "514.5 J",
"B": "512.5 J",
"C": "511.5 J",
"D": "1025 J"
} | B | 512.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(5)(5)²+(25)(18)=512.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 512.5 J, not 514.5 J.",
"B": "Correct. The worked calculation gives 512.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 512.5 J, not 511.5 J.",
"D": "Incorrect. Substituting the stated va... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003115 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(10-14i)/(11+11i). What is Re(z), the real part of z? | {
"A": "-0.18182",
"B": "-0.27273",
"C": "0.81818",
"D": "-2.18182"
} | A | -0.18182 | Multiply numerator and denominator by the conjugate (11-11i). Then Re(z)=(ac+bd)/(c²+d²)=((10)(11)+(-14)(11))/(11²+(11)²)=-0.18182. | {
"A": "Correct. The worked calculation gives -0.18182.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.18182, not -0.27273.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.18182, not 0.81818.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002605 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, 2], [7, -8]]. | {
"A": "-53",
"B": "-4.4",
"C": "-108",
"D": "-54"
} | D | -54 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(-8)−(2)(7)=-54. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -54, not -53.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -54, not -4.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -54, not -108.",
"D": "Correct.... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002809 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(6, 4, 1) and v=(3, 6, 5), calculate u·v. | {
"A": "47",
"B": "70.5",
"C": "45",
"D": "23.5"
} | A | 47 | The dot product is the sum of corresponding component products: (6)(3)+(4)(6)+(1)(5)=47. | {
"A": "Correct. The worked calculation gives 47.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 47, not 70.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 47, not 45.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005653 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 4 μF capacitor is charged to a potential difference of 10 V. Calculate the energy stored, expressed in μJ. | {
"A": "200 μJ",
"B": "100 μJ",
"C": "150 μJ",
"D": "160 μJ"
} | A | 200 μJ | U=½CV². Since C=4 μF, U in μJ is ½×4×(10)²=200 μJ. | {
"A": "Correct. The worked calculation gives 200 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 200 μJ, not 100 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 200 μJ, not 150 μJ.",
"D": "Incorrect. Substituting the stated values ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008260 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 11 A for 19587 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "53.16653 g",
"B": "8.08887 g",
"C": "70.8887 g",
"D": "106.33305 g"
} | C | 70.8887 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×19587/(2×96500)=70.8887 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 70.8887 g, not 53.16653 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 70.8887 g, not 8.08887 g.",
"C": "Correct. The worked calculation gives 70.8887 g.",
"D": "Incorrect. Substituting th... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006376 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 20 kg is attached to an ideal spring of force constant 689 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.65925 s",
"B": "2.34075 s",
"C": "-0.34075 s",
"D": "0.34075 s"
} | D | 0.34075 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(20/689)=0.34075 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34075 s, not -2.65925 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34075 s, not 2.34075 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34075 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009266 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.86 V, transfers 1 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.0373 V",
"B": "1.0373 V",
"C": "2.0373 V",
"D": "-1.0373 V"
} | B | 1.0373 V | Apply the Nernst equation: E=0.86−(0.0591/1)(-3)=1.0373 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0373 V, not 0.0373 V.",
"B": "Correct. The worked calculation gives 1.0373 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0373 V, not 2.0373 V.",
"D": "Incorrect. Substituting the stat... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000175 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 +3x +2=0, let its roots be α and β. What is α²+β²? | {
"A": "-0.41667",
"B": "2.58333",
"C": "0.41667",
"D": "-0.625"
} | A | -0.41667 | By Vieta's relations, α+β = -3/6 and αβ = 2/6. Then α²+β²=(α+β)²−2αβ = (-3/6)²−2(2/6) = -0.41667. | {
"A": "Correct. The worked calculation gives -0.41667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.41667, not 2.58333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.41667, not 0.41667.",
"D": "Incorrect. Substituting the stated... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007640 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 85 mL of 0.10 M HCl is mixed with 43 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.48396",
"B": "-1.51604",
"C": "1.11297",
"D": "-0.51604"
} | A | 1.48396 | Excess H⁺ moles=0.10×(85−43)/1000=0.004200 mol. Total volume=0.128 L, so [H⁺]=0.032813 M and pH=−log₁₀[H⁺]=1.48396. | {
"A": "Correct. The worked calculation gives 1.48396.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.48396, not -1.51604.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.48396, not 1.11297.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006529 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 9 kg is attached to an ideal spring of force constant 750 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.21909 s",
"B": "0.32863 s",
"C": "0.10954 s",
"D": "-0.21909 s"
} | A | 0.21909 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(9/750)=0.21909 s. | {
"A": "Correct. The worked calculation gives 0.21909 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.21909 s, not 0.32863 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.21909 s, not 0.10954 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007202 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 8 mol of gas at 270 K and 1.6 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "88.62156 L",
"B": "-110.77695 L",
"C": "111.77695 L",
"D": "110.77695 L"
} | D | 110.77695 L | PV=nRT, so V=nRT/P=(8)(0.082057)(270)/(1.6)=110.77695 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 110.77695 L, not 88.62156 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 110.77695 L, not -110.77695 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007548 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 13 mL of 0.10 M HCl is mixed with 33 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "15.63827",
"B": "9.63827",
"C": "12.63827",
"D": "25.27654"
} | C | 12.63827 | Excess OH⁻ moles=0.10×(33−13)/1000=0.002000 mol. Total volume=0.046 L, so [OH⁻]=0.043478 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.63827. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.63827, not 15.63827.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.63827, not 9.63827.",
"C": "Correct. The worked calculation gives 12.63827.",
"D": "Incorrect. Substituting the state... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000545 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -14 and common difference 4. Find the sum of its first 11 terms. | {
"A": "66",
"B": "132",
"C": "-66",
"D": "49.5"
} | A | 66 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-14, d=4, n=11: Sₙ=11/2[2(-14)+(11−1)(4)]=66. | {
"A": "Correct. The worked calculation gives 66.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 66, not 132.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 66, not -66.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008552 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.76 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.03952 K",
"B": "0.7904 K",
"C": "2.3952 K",
"D": "0.3952 K"
} | D | 0.3952 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.52×0.76=0.3952 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3952 K, not 1.03952 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3952 K, not 0.7904 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3952 K, not... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009114 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.89 V, transfers 3 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.7915 V",
"B": "1.18725 V",
"C": "0.59362 V",
"D": "0.7915 V"
} | D | 0.7915 V | Apply the Nernst equation: E=0.89−(0.0591/3)(5)=0.7915 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7915 V, not 1.7915 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7915 V, not 1.18725 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7915 V, not... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000292 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 +13x +2=0, let its roots be α and β. What is α²+β²? | {
"A": "4.87755",
"B": "5.7551",
"C": "1.87755",
"D": "2.87755"
} | D | 2.87755 | By Vieta's relations, α+β = -13/7 and αβ = 2/7. Then α²+β²=(α+β)²−2αβ = (-13/7)²−2(2/7) = 2.87755. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.87755, not 4.87755.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.87755, not 5.7551.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.87755, not 1.8775... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003972 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 3 kg block initially moves at 9 m s⁻¹. A constant net force does 13 N of work over 10 m in the direction of motion. Find its final kinetic energy. | {
"A": "201.2 J",
"B": "251.5 J",
"C": "301.8 J",
"D": "503 J"
} | B | 251.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(3)(9)²+(13)(10)=251.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 251.5 J, not 201.2 J.",
"B": "Correct. The worked calculation gives 251.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 251.5 J, not 301.8 J.",
"D": "Incorrect. Substituting the stated va... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001154 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ +4x² +3x+7. Evaluate f′(-3). | {
"A": "156",
"B": "-156",
"C": "-117",
"D": "-158"
} | B | -156 | Differentiate: f′(x)=3(-5)x²+2(4)x+(3). At x=-3, f′(-3)=3(-5)(-3)²+2(4)(-3)+(3)=-156. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -156, not 156.",
"B": "Correct. The worked calculation gives -156.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -156, not -117.",
"D": "Incorrect. Substituting the stated values into the go... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006789 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 20 mol H₂ and 14 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "10 mol",
"B": "15 mol",
"C": "21 mol",
"D": "20 mol"
} | D | 20 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 20 mol H₂O; O₂ can produce 28 mol H₂O. The limiting condition is H₂; product=20 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20 mol, not 10 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20 mol, not 15 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20 mol, not 21 mol.",
... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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