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_001759 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 88 distinct elements? | {
"A": "19587876",
"B": "29381814",
"C": "39175753",
"D": "39175752"
} | D | 39175752 | Order does not matter, so the count is C(88,5)=88!/[5!(83)!]=39175752. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 39175752, not 19587876.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39175752, not 29381814.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39175752, not ... | [
"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_008517 | 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 1.36 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": "-0.7072 K",
"B": "0.7072 K",
"C": "1.07072 K",
"D": "-2.2928 K"
} | B | 0.7072 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.52×1.36=0.7072 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7072 K, not -0.7072 K.",
"B": "Correct. The worked calculation gives 0.7072 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7072 K, not 1.07072 K.",
"D": "Incorrect. Substituting the st... | [
"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_001214 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ -9x² -5x+7. Evaluate f′(-3). | {
"A": "147.2",
"B": "184",
"C": "186",
"D": "182"
} | B | 184 | Differentiate: f′(x)=3(5)x²+2(-9)x+(-5). At x=-3, f′(-3)=3(5)(-3)²+2(-9)(-3)+(-5)=184. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 184, not 147.2.",
"B": "Correct. The worked calculation gives 184.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 184, not 186.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_000621 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 0 and common difference 2. Find the sum of its first 8 terms. | {
"A": "-56",
"B": "42",
"C": "6.6",
"D": "56"
} | D | 56 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=0, d=2, n=8: Sₙ=8/2[2(0)+(8−1)(2)]=56. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 56, not -56.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 56, not 42.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 56, not 6.6.",
"D": "Correct. The w... | [
"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_008101 | 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 10 A for 24590 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": "121.35738 g",
"B": "79.90492 g",
"C": "81.90492 g",
"D": "80.90492 g"
} | D | 80.90492 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×10×24590/(2×96500)=80.90492 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 80.90492 g, not 121.35738 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 80.90492 g, not 79.90492 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 80.90... | [
"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_005921 | 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 0.9 atm at 396 K. What is its pressure at 713 K? | {
"A": "1.16205 atm",
"B": "1.21534 atm",
"C": "1.62045 atm",
"D": "0.62045 atm"
} | C | 1.62045 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.9)(713)/(396)=1.62045 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.62045 atm, not 1.16205 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.62045 atm, not 1.21534 atm.",
"C": "Correct. The worked calculation gives 1.62045 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_008128 | 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 5 A for 14547 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": "35.89642 g",
"B": "11.96547 g",
"C": "23.93095 g",
"D": "47.86189 g"
} | C | 23.93095 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×5×14547/(2×96500)=23.93095 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 23.93095 g, not 35.89642 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23.93095 g, not 11.96547 g.",
"C": "Correct. The worked calculation gives 23.93095 g.",
"D": "Incorrect. Substitutin... | [
"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_008161 | 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 14 A for 24035 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": "110.71044 g",
"B": "109.71044 g",
"C": "-110.71044 g",
"D": "111.71044 g"
} | A | 110.71044 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×24035/(2×96500)=110.71044 g. | {
"A": "Correct. The worked calculation gives 110.71044 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 110.71044 g, not 109.71044 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 110.71044 g, not -110.71044 g.",
"D": "Incorrect. Subst... | [
"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_004298 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.12. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "31.24 N",
"B": "60.48 N",
"C": "30.24 N",
"D": "28.24 N"
} | C | 30.24 N | Net force=mg(sinθ−μcosθ)=6×10×(0.6−0.12×0.8)=30.24 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 30.24 N, not 31.24 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30.24 N, not 60.48 N.",
"C": "Correct. The worked calculation gives 30.24 N.",
"D": "Incorrect. Substituting the stated va... | [
"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_008554 | 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 1.88 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.744 K",
"B": "-2.256 K",
"C": "5.256 K",
"D": "2.256 K"
} | D | 2.256 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.6×1.88=2.256 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.256 K, not -0.744 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.256 K, not -2.256 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.256 K, not 5.2... | [
"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_004094 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.31. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "24.64 N",
"B": "3.464 N",
"C": "36.96 N",
"D": "23.64 N"
} | A | 24.64 N | Net force=mg(sinθ−μcosθ)=7×10×(0.6−0.31×0.8)=24.64 N. | {
"A": "Correct. The worked calculation gives 24.64 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24.64 N, not 3.464 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24.64 N, not 36.96 N.",
"D": "Incorrect. Substituting the stated va... | [
"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_003620 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 18 m s⁻¹ at 20° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "20.82632 m",
"B": "15.61974 m",
"C": "22.82632 m",
"D": "21.82632 m"
} | A | 20.82632 m | Range R=u²sin(2θ)/g. Substituting u=18, θ=20° and g=10 gives R=(18)²sin(40°)/10=20.82632 m. | {
"A": "Correct. The worked calculation gives 20.82632 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20.82632 m, not 15.61974 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20.82632 m, not 22.82632 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_007128 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 19 mol of gas at 468 K and 1.84 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "395.54937 L",
"B": "396.54937 L",
"C": "198.27469 L",
"D": "398.54937 L"
} | B | 396.54937 L | PV=nRT, so V=nRT/P=(19)(0.082057)(468)/(1.84)=396.54937 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 396.54937 L, not 395.54937 L.",
"B": "Correct. The worked calculation gives 396.54937 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 396.54937 L, not 198.27469 L.",
"D": "Incorrect. Substi... | [
"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_006281 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 73 cm in front of a thin convex lens of focal length 16 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.2807",
"B": "0.21053",
"C": "0.42105",
"D": "1.2807"
} | A | 0.2807 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(73)(16)/(73−16)=20.49123 cm. Thus |m|=v/u=20.49123/73=0.2807. | {
"A": "Correct. The worked calculation gives 0.2807.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.2807, not 0.21053.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.2807, not 0.42105.",
"D": "Incorrect. Substituting the stated value... | [
"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_006765 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 3 mol H₂ and 3 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "3 mol",
"B": "5 mol",
"C": "2 mol",
"D": "1.3 mol"
} | A | 3 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 3 mol H₂O; O₂ can produce 6 mol H₂O. The limiting condition is H₂; product=3 mol. | {
"A": "Correct. The worked calculation gives 3 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3 mol, not 5 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3 mol, not 2 mol.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_004179 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 31 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.20. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "102.3 N",
"B": "136.4 N",
"C": "68.2 N",
"D": "137.4 N"
} | B | 136.4 N | Net force=mg(sinθ−μcosθ)=31×10×(0.6−0.20×0.8)=136.4 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 136.4 N, not 102.3 N.",
"B": "Correct. The worked calculation gives 136.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 136.4 N, not 68.2 N.",
"D": "Incorrect. Substituting the stated val... | [
"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_005290 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +4 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "33.06122 N",
"B": "67.12245 N",
"C": "66.12245 N",
"D": "65.12245 N"
} | C | 66.12245 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(4×10⁻⁶)/(7×10⁻²)²=66.12245 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 66.12245 N, not 33.06122 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 66.12245 N, not 67.12245 N.",
"C": "Correct. The worked calculation gives 66.12245 N.",
"D": "Incorrect. Substitutin... | [
"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_007184 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 4 mol of gas at 427 K and 2.74 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "51.15086 L",
"B": "6.11509 L",
"C": "76.72629 L",
"D": "-51.15086 L"
} | A | 51.15086 L | PV=nRT, so V=nRT/P=(4)(0.082057)(427)/(2.74)=51.15086 L. | {
"A": "Correct. The worked calculation gives 51.15086 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 51.15086 L, not 6.11509 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 51.15086 L, not 76.72629 L.",
"D": "Incorrect. Substituting... | [
"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_005873 | 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 atm at 433 K. What is its pressure at 485 K? | {
"A": "4.48037 atm",
"B": "1.68014 atm",
"C": "2.24018 atm",
"D": "3.24018 atm"
} | C | 2.24018 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2)(485)/(433)=2.24018 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.24018 atm, not 4.48037 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.24018 atm, not 1.68014 atm.",
"C": "Correct. The worked calculation gives 2.24018 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_004373 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 10 kg and radius 5 m is acted on by a constant torque of 39 N m about its central axis. Find its angular acceleration. | {
"A": "3.312 rad s⁻²",
"B": "0.156 rad s⁻²",
"C": "0.312 rad s⁻²",
"D": "1.0312 rad s⁻²"
} | C | 0.312 rad s⁻² | For a solid disc, I=½MR²=½(10)(5)²=125 kg m². Using τ=Iα, α=39/125=0.312 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.312 rad s⁻², not 3.312 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.312 rad s⁻², not 0.156 rad s⁻².",
"C": "Correct. The worked calculation gives 0.312 rad s⁻².",
"D": "Incorre... | [
"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_008837 | 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 0.79 mol L⁻¹ and initially B is absent. At equilibrium, 10% of A has dissociated at constant volume. Find K_c. | {
"A": "0.02633",
"B": "0.03511",
"C": "1.03511",
"D": "2.03511"
} | B | 0.03511 | Let α=0.1. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.79)(0.1)²/(1−0.1)=0.03511. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.03511, not 0.02633.",
"B": "Correct. The worked calculation gives 0.03511.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.03511, not 1.03511.",
"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_002348 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, 4], [4, -6]]. | {
"A": "-48",
"B": "-66",
"C": "-64",
"D": "-63"
} | C | -64 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(-6)−(4)(4)=-64. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -64, not -48.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -64, not -66.",
"C": "Correct. The worked calculation gives -64.",
"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_005936 | 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 259 K. What is its pressure at 349 K? | {
"A": "7.3332 atm",
"B": "4.7499 atm",
"C": "8.3332 atm",
"D": "6.3332 atm"
} | D | 6.3332 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.7)(349)/(259)=6.3332 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.3332 atm, not 7.3332 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.3332 atm, not 4.7499 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.3332... | [
"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_009108 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.66 V, transfers 2 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.68955 V",
"B": "0.34477 V",
"C": "1.03432 V",
"D": "-0.68955 V"
} | A | 0.68955 V | Apply the Nernst equation: E=0.66−(0.0591/2)(-1)=0.68955 V. | {
"A": "Correct. The worked calculation gives 0.68955 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.68955 V, not 0.34477 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.68955 V, not 1.03432 V.",
"D": "Incorrect. Substituting the... | [
"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_003737 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 2 m s⁻¹. A constant net force does 19 N of work over 10 m in the direction of motion. Find its final kinetic energy. | {
"A": "206 J",
"B": "312 J",
"C": "207 J",
"D": "208 J"
} | D | 208 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(2)²+(19)(10)=208 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 208 J, not 206 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 208 J, not 312 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 208 J, not 207 J.",
"D":... | [
"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_003276 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-5+6i)/(7+8i). What is Re(z), the real part of z? | {
"A": "0.11504",
"B": "0.23009",
"C": "0.08628",
"D": "2.11504"
} | A | 0.11504 | Multiply numerator and denominator by the conjugate (7-8i). Then Re(z)=(ac+bd)/(c²+d²)=((-5)(7)+(6)(8))/(7²+(8)²)=0.11504. | {
"A": "Correct. The worked calculation gives 0.11504.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.11504, not 0.23009.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.11504, not 0.08628.",
"D": "Incorrect. Substituting the stated va... | [
"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_007177 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 6 mol of gas at 598 K and 0.81 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "272.61159 L",
"B": "363.48212 L",
"C": "290.78569 L",
"D": "545.22318 L"
} | B | 363.48212 L | PV=nRT, so V=nRT/P=(6)(0.082057)(598)/(0.81)=363.48212 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 363.48212 L, not 272.61159 L.",
"B": "Correct. The worked calculation gives 363.48212 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 363.48212 L, not 290.78569 L.",
"D": "Incorrect. Substi... | [
"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_009428 | 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_17H_28N_2X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "1.5",
"B": "2",
"C": "1",
"D": "3"
} | D | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×17+2+2−28−4)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.",
"D": "Correct. The worked ... | [
"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_002026 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 5 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.17488",
"B": "1.34975",
"C": "0.34975",
"D": "0.52463"
} | C | 0.34975 | Favourable pairs = C(12,2)+C(5,2)+C(12,2)=142. Total pairs=C(29,2)=406. Therefore P=142/406=0.34975. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34975, not 0.17488.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34975, not 1.34975.",
"C": "Correct. The worked calculation gives 0.34975.",
"D": "Incorrect. Substituting the stated va... | [
"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_007977 | 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 96 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "1.0375 mmol L⁻¹",
"B": "0.1875 mmol L⁻¹",
"C": "2.375 mmol L⁻¹",
"D": "0.375 mmol L⁻¹"
} | D | 0.375 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=96/2^8=0.375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.375 mmol L⁻¹, not 1.0375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.375 mmol L⁻¹, not 0.1875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing rel... | [
"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_002990 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, 9, -2) and v=(4, 2, 9), calculate u·v. | {
"A": "2.6",
"B": "16",
"C": "24",
"D": "12"
} | B | 16 | The dot product is the sum of corresponding component products: (4)(4)+(9)(2)+(-2)(9)=16. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16, not 2.6.",
"B": "Correct. The worked calculation gives 16.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16, not 24.",
"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_008560 | 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 0.85 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.4352 K",
"B": "0.4352 K",
"C": "0.8704 K",
"D": "0.6528 K"
} | B | 0.4352 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.512×0.85=0.4352 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.4352 K, not -0.4352 K.",
"B": "Correct. The worked calculation gives 0.4352 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.4352 K, not 0.8704 K.",
"D": "Incorrect. Substituting the sta... | [
"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_000426 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -8 and common difference 3. Find the sum of its first 32 terms. | {
"A": "124.2",
"B": "1232",
"C": "1848",
"D": "1231"
} | B | 1232 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-8, d=3, n=32: Sₙ=32/2[2(-8)+(32−1)(3)]=1232. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1232, not 124.2.",
"B": "Correct. The worked calculation gives 1232.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1232, not 1848.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_000570 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -4 and common difference 3. Find the sum of its first 33 terms. | {
"A": "1161.6",
"B": "2904",
"C": "726",
"D": "1452"
} | D | 1452 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-4, d=3, n=33: Sₙ=33/2[2(-4)+(33−1)(3)]=1452. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1452, not 1161.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1452, not 2904.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1452, not 726.",
"D": "Cor... | [
"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_001958 | 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 12 distinct elements? | {
"A": "1584",
"B": "80.2",
"C": "792",
"D": "594"
} | C | 792 | Order does not matter, so the count is C(12,7)=12!/[7!(5)!]=792. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 792, not 1584.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 792, not 80.2.",
"C": "Correct. The worked calculation gives 792.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_006997 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 23 mol H₂ and 19 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "18.4 mol",
"B": "11.5 mol",
"C": "23 mol",
"D": "22 mol"
} | C | 23 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 23 mol H₂O; O₂ can produce 38 mol H₂O. The limiting condition is H₂; product=23 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 23 mol, not 18.4 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23 mol, not 11.5 mol.",
"C": "Correct. The worked calculation gives 23 mol.",
"D": "Incorrect. Substituting the stated val... | [
"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_008689 | 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 1.95 mol L⁻¹ and initially B is absent. At equilibrium, 61% of A has dissociated at constant volume. Find K_c. | {
"A": "6.442",
"B": "7.442",
"C": "8.442",
"D": "3.721"
} | B | 7.442 | Let α=0.61. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.95)(0.61)²/(1−0.61)=7.442. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.442, not 6.442.",
"B": "Correct. The worked calculation gives 7.442.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.442, not 8.442.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_009914 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(Cl)_6]^-3, each Cl ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "4.5",
"B": "3",
"C": "-3",
"D": "0"
} | B | 3 | Let the formal oxidation state of Cr be x. Charge balance gives x+(6)(−1)=-3; hence x=-3+6=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.5.",
"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 rel... | [
"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_005306 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +7 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "-18.9 N",
"B": "16.9 N",
"C": "19.9 N",
"D": "18.9 N"
} | D | 18.9 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(7×10⁻⁶)/(10×10⁻²)²=18.9 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18.9 N, not -18.9 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18.9 N, not 16.9 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18.9 N, not 19.9 N.",... | [
"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_005446 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 41 μF capacitor is charged to a potential difference of 32 V. Calculate the energy stored, expressed in μJ. | {
"A": "20992 μJ",
"B": "10496 μJ",
"C": "15744 μJ",
"D": "41984 μJ"
} | A | 20992 μJ | U=½CV². Since C=41 μF, U in μJ is ½×41×(32)²=20992 μJ. | {
"A": "Correct. The worked calculation gives 20992 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20992 μJ, not 10496 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20992 μJ, not 15744 μJ.",
"D": "Incorrect. Substituting the stat... | [
"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_008332 | 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 22610 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": "83.82946 g",
"B": "163.65891 g",
"C": "9.18295 g",
"D": "81.82946 g"
} | D | 81.82946 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×22610/(2×96500)=81.82946 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 81.82946 g, not 83.82946 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 81.82946 g, not 163.65891 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 81.82... | [
"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_004348 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 10 kg and radius 4 m is acted on by a constant torque of 61 N m about its central axis. Find its angular acceleration. | {
"A": "0.7625 rad s⁻²",
"B": "0.57187 rad s⁻²",
"C": "1.14375 rad s⁻²",
"D": "-0.7625 rad s⁻²"
} | A | 0.7625 rad s⁻² | For a solid disc, I=½MR²=½(10)(4)²=80 kg m². Using τ=Iα, α=61/80=0.7625 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.7625 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7625 rad s⁻², not 0.57187 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7625 rad s⁻², not 1.14375 rad s⁻².",
"D": "... | [
"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_005395 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 51 μF capacitor is charged to a potential difference of 12 V. Calculate the energy stored, expressed in μJ. | {
"A": "4406.4 μJ",
"B": "368.2 μJ",
"C": "3672 μJ",
"D": "2754 μJ"
} | C | 3672 μJ | U=½CV². Since C=51 μF, U in μJ is ½×51×(12)²=3672 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3672 μJ, not 4406.4 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3672 μJ, not 368.2 μJ.",
"C": "Correct. The worked calculation gives 3672 μJ.",
"D": "Incorrect. Substituting the stated... | [
"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_008085 | 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 13 A for 26194 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": "110.03703 g",
"B": "113.03703 g",
"C": "89.62962 g",
"D": "112.03703 g"
} | D | 112.03703 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×26194/(2×96500)=112.03703 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 112.03703 g, not 110.03703 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 112.03703 g, not 113.03703 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11... | [
"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_005474 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 19 μF capacitor is charged to a potential difference of 33 V. Calculate the energy stored, expressed in μJ. | {
"A": "1035.55 μJ",
"B": "15518.25 μJ",
"C": "12414.6 μJ",
"D": "10345.5 μJ"
} | D | 10345.5 μJ | U=½CV². Since C=19 μF, U in μJ is ½×19×(33)²=10345.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10345.5 μJ, not 1035.55 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10345.5 μJ, not 15518.25 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10345... | [
"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_006085 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 109 cm in front of a thin convex lens of focal length 23 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.26744",
"B": "0.20058",
"C": "0.13372",
"D": "1.02674"
} | A | 0.26744 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(109)(23)/(109−23)=29.15116 cm. Thus |m|=v/u=29.15116/109=0.26744. | {
"A": "Correct. The worked calculation gives 0.26744.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.26744, not 0.20058.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.26744, not 0.13372.",
"D": "Incorrect. Substituting the stated va... | [
"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_008467 | 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 1.76 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "4.80224 K",
"B": "2.70336 K",
"C": "-1.80224 K",
"D": "1.80224 K"
} | D | 1.80224 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×1.76=1.80224 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.80224 K, not 4.80224 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.80224 K, not 2.70336 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.80224 K,... | [
"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_008283 | 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 2 A for 19434 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": "15.78818 g",
"B": "9.78818 g",
"C": "19.18226 g",
"D": "12.78818 g"
} | D | 12.78818 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×2×19434/(2×96500)=12.78818 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.78818 g, not 15.78818 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.78818 g, not 9.78818 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.7881... | [
"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_003817 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 5 m s⁻¹. A constant net force does 7 N of work over 9 m in the direction of motion. Find its final kinetic energy. | {
"A": "113 J",
"B": "226 J",
"C": "-113 J",
"D": "115 J"
} | A | 113 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(5)²+(7)(9)=113 J. | {
"A": "Correct. The worked calculation gives 113 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 113 J, not 226 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 113 J, not -113 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_006921 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 27 mol H₂ and 18 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "25 mol",
"B": "27 mol",
"C": "28 mol",
"D": "-27 mol"
} | B | 27 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 27 mol H₂O; O₂ can produce 36 mol H₂O. The limiting condition is H₂; product=27 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 27 mol, not 25 mol.",
"B": "Correct. The worked calculation gives 27 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 27 mol, not 28 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_009179 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.56 V, transfers 1 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.9146 V",
"B": "-0.9146 V",
"C": "0.4573 V",
"D": "1.3719 V"
} | A | 0.9146 V | Apply the Nernst equation: E=0.56−(0.0591/1)(-6)=0.9146 V. | {
"A": "Correct. The worked calculation gives 0.9146 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9146 V, not -0.9146 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9146 V, not 0.4573 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_003467 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 78 m s⁻¹ at 35° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "686.05079 m",
"B": "857.56349 m",
"C": "571.70899 m",
"D": "457.36719 m"
} | C | 571.70899 m | Range R=u²sin(2θ)/g. Substituting u=78, θ=35° and g=10 gives R=(78)²sin(70°)/10=571.70899 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 571.70899 m, not 686.05079 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 571.70899 m, not 857.56349 m.",
"C": "Correct. The worked calculation gives 571.70899 m.",
"D": "Incorrect. Substi... | [
"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_006757 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 22 mol H₂ and 21 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "23 mol",
"B": "22 mol",
"C": "-22 mol",
"D": "24 mol"
} | B | 22 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 22 mol H₂O; O₂ can produce 42 mol H₂O. The limiting condition is H₂; product=22 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22 mol, not 23 mol.",
"B": "Correct. The worked calculation gives 22 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22 mol, not -22 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_008170 | 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 7 A for 15082 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": "26.05162 g",
"B": "17.36774 g",
"C": "52.10323 g",
"D": "34.73549 g"
} | D | 34.73549 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×7×15082/(2×96500)=34.73549 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 34.73549 g, not 26.05162 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 34.73549 g, not 17.36774 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 34.735... | [
"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_002748 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-4, 3, 6) and v=(2, 7, 7), calculate u·v. | {
"A": "41.25",
"B": "56",
"C": "110",
"D": "55"
} | D | 55 | The dot product is the sum of corresponding component products: (-4)(2)+(3)(7)+(6)(7)=55. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 55, not 41.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 55, not 56.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 55, not 110.",
"D": "Correct. The... | [
"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_008705 | 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 1.3 mol L⁻¹ and initially B is absent. At equilibrium, 38% of A has dissociated at constant volume. Find K_c. | {
"A": "1.81665",
"B": "3.2111",
"C": "1.12111",
"D": "1.2111"
} | D | 1.2111 | Let α=0.38. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.3)(0.38)²/(1−0.38)=1.2111. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.2111, not 1.81665.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.2111, not 3.2111.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2111, not 1.12111."... | [
"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_003108 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-15+15i)/(6+7i). What is Re(z), the real part of z? | {
"A": "-0.17647",
"B": "0.17647",
"C": "-0.82353",
"D": "-1.82353"
} | B | 0.17647 | Multiply numerator and denominator by the conjugate (6-7i). Then Re(z)=(ac+bd)/(c²+d²)=((-15)(6)+(15)(7))/(6²+(7)²)=0.17647. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.17647, not -0.17647.",
"B": "Correct. The worked calculation gives 0.17647.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.17647, not -0.82353.",
"D": "Incorrect. Substituting the stated ... | [
"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_009333 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.03 V, transfers 3 electrons, and has reaction quotient Q=10^1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.0103 V",
"B": "1.51545 V",
"C": "-1.9897 V",
"D": "1.0103 V"
} | D | 1.0103 V | Apply the Nernst equation: E=1.03−(0.0591/3)(1)=1.0103 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0103 V, not 2.0103 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0103 V, not 1.51545 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0103 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_003164 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-9-7i)/(2+6i). What is Re(z), the real part of z? | {
"A": "-1.125",
"B": "-3",
"C": "-1.5",
"D": "1.5"
} | C | -1.5 | Multiply numerator and denominator by the conjugate (2-6i). Then Re(z)=(ac+bd)/(c²+d²)=((-9)(2)+(-7)(6))/(2²+(6)²)=-1.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.5, not -1.125.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.5, not -3.",
"C": "Correct. The worked calculation gives -1.5.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_001256 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=7x³ +6x² +1x+7. Evaluate f′(-4). | {
"A": "144.5",
"B": "291",
"C": "289",
"D": "-289"
} | C | 289 | Differentiate: f′(x)=3(7)x²+2(6)x+(1). At x=-4, f′(-4)=3(7)(-4)²+2(6)(-4)+(1)=289. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 289, not 144.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 289, not 291.",
"C": "Correct. The worked calculation gives 289.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_008885 | 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 1.01 mol L⁻¹ and initially B is absent. At equilibrium, 79% of A has dissociated at constant volume. Find K_c. | {
"A": "18.00974",
"B": "13.0065",
"C": "12.0065",
"D": "6.00325"
} | C | 12.0065 | Let α=0.79. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.01)(0.79)²/(1−0.79)=12.0065. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.0065, not 18.00974.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.0065, not 13.0065.",
"C": "Correct. The worked calculation gives 12.0065.",
"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_004530 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 9 kg and radius 4 m is acted on by a constant torque of 71 N m about its central axis. Find its angular acceleration. | {
"A": "0.98611 rad s⁻²",
"B": "1.98611 rad s⁻²",
"C": "3.98611 rad s⁻²",
"D": "1.97222 rad s⁻²"
} | A | 0.98611 rad s⁻² | For a solid disc, I=½MR²=½(9)(4)²=72 kg m². Using τ=Iα, α=71/72=0.98611 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.98611 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.98611 rad s⁻², not 1.98611 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.98611 rad s⁻², not 3.98611 rad s⁻².",
"D"... | [
"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_003773 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block initially moves at 0 m s⁻¹. A constant net force does 25 N of work over 3 m in the direction of motion. Find its final kinetic energy. | {
"A": "60 J",
"B": "37.5 J",
"C": "75 J",
"D": "112.5 J"
} | C | 75 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(15)(0)²+(25)(3)=75 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 75 J, not 60 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 75 J, not 37.5 J.",
"C": "Correct. The worked calculation gives 75 J.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_005066 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +2 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "14.69388 N",
"B": "29.38776 N",
"C": "13.69388 N",
"D": "22.04082 N"
} | A | 14.69388 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(2×10⁻⁶)/(7×10⁻²)²=14.69388 N. | {
"A": "Correct. The worked calculation gives 14.69388 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14.69388 N, not 29.38776 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14.69388 N, not 13.69388 N.",
"D": "Incorrect. Substitutin... | [
"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_001292 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-3x³ +7x² -2x+7. Evaluate f′(5). | {
"A": "-188.4",
"B": "-155",
"C": "-157",
"D": "-156"
} | C | -157 | Differentiate: f′(x)=3(-3)x²+2(7)x+(-2). At x=5, f′(5)=3(-3)(5)²+2(7)(5)+(-2)=-157. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -157, not -188.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -157, not -155.",
"C": "Correct. The worked calculation gives -157.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_003083 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(15+7i)/(10+6i). What is Re(z), the real part of z? | {
"A": "1.41176",
"B": "-0.58824",
"C": "3.41176",
"D": "1.14118"
} | A | 1.41176 | Multiply numerator and denominator by the conjugate (10-6i). Then Re(z)=(ac+bd)/(c²+d²)=((15)(10)+(7)(6))/(10²+(6)²)=1.41176. | {
"A": "Correct. The worked calculation gives 1.41176.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.41176, not -0.58824.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.41176, not 3.41176.",
"D": "Incorrect. Substituting the stated v... | [
"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_001799 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 11 elements can be selected from a set of 84 distinct elements? | {
"A": "18574174153081",
"B": "18574174153079",
"C": "37148348306160",
"D": "18574174153080"
} | D | 18574174153080 | Order does not matter, so the count is C(84,11)=84!/[11!(73)!]=18574174153080. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18574174153080, not 18574174153081.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18574174153080, not 18574174153079.",
"C": "Incorrect. Substituting the stated values into the governing relat... | [
"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_008083 | 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 14 A for 14203 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": "65.42211 g",
"B": "63.42211 g",
"C": "-65.42211 g",
"D": "67.42211 g"
} | A | 65.42211 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×14203/(2×96500)=65.42211 g. | {
"A": "Correct. The worked calculation gives 65.42211 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 65.42211 g, not 63.42211 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 65.42211 g, not -65.42211 g.",
"D": "Incorrect. Substituti... | [
"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_008975 | 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 0.4 mol L⁻¹ and initially B is absent. At equilibrium, 80% of A has dissociated at constant volume. Find K_c. | {
"A": "10.24",
"B": "5.12",
"C": "7.68",
"D": "2.12"
} | B | 5.12 | Let α=0.8. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.4)(0.8)²/(1−0.8)=5.12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.12, not 10.24.",
"B": "Correct. The worked calculation gives 5.12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.12, not 7.68.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_001044 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ +4x² -2x+7. Evaluate f′(0). | {
"A": "0",
"B": "1",
"C": "-2",
"D": "-1.5"
} | C | -2 | Differentiate: f′(x)=3(4)x²+2(4)x+(-2). At x=0, f′(0)=3(4)(0)²+2(4)(0)+(-2)=-2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2, not 0.",
"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 rel... | [
"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_000605 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 15 and common difference 5. Find the sum of its first 23 terms. | {
"A": "1207.5",
"B": "-1610",
"C": "1610",
"D": "1609"
} | C | 1610 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=15, d=5, n=23: Sₙ=23/2[2(15)+(23−1)(5)]=1610. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1610, not 1207.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1610, not -1610.",
"C": "Correct. The worked calculation gives 1610.",
"D": "Incorrect. Substituting the stated values into th... | [
"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_004021 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 49 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.28. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "276.36 N",
"B": "186.24 N",
"C": "184.24 N",
"D": "183.24 N"
} | C | 184.24 N | Net force=mg(sinθ−μcosθ)=49×10×(0.6−0.28×0.8)=184.24 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 184.24 N, not 276.36 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 184.24 N, not 186.24 N.",
"C": "Correct. The worked calculation gives 184.24 N.",
"D": "Incorrect. Substituting the stat... | [
"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_004831 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 11 Ω are connected in series; this combination is connected in parallel with a 6 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "8 A",
"B": "5 A",
"C": "-8 A",
"D": "6 A"
} | A | 8 A | Series branch resistance=7+11=18 Ω. Parallel equivalent R_eq=(18×6)/(18+6)=4.5 Ω. Total current I=V/R_eq=36/4.5=8 A. | {
"A": "Correct. The worked calculation gives 8 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8 A, not 5 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8 A, not -8 A.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_005599 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 7 μF capacitor is charged to a potential difference of 22 V. Calculate the energy stored, expressed in μJ. | {
"A": "1692 μJ",
"B": "1693 μJ",
"C": "1355.2 μJ",
"D": "1694 μJ"
} | D | 1694 μJ | U=½CV². Since C=7 μF, U in μJ is ½×7×(22)²=1694 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1694 μJ, not 1692 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1694 μJ, not 1693 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1694 μJ, not 1355.... | [
"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_006718 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 23 mol H₂ and 11 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "26.4 mol",
"B": "33 mol",
"C": "3.2 mol",
"D": "22 mol"
} | D | 22 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 23 mol H₂O; O₂ can produce 22 mol H₂O. The limiting condition is O₂; product=22 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22 mol, not 26.4 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22 mol, not 33 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22 mol, not 3.2 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_007913 | 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 31 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "-15.5 mmol L⁻¹",
"B": "13.5 mmol L⁻¹",
"C": "15.5 mmol L⁻¹",
"D": "16.5 mmol L⁻¹"
} | C | 15.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=31/2^1=15.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15.5 mmol L⁻¹, not -15.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15.5 mmol L⁻¹, not 13.5 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 15.5 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_004607 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 2 m is acted on by a constant torque of 97 N m about its central axis. Find its angular acceleration. | {
"A": "19.4 rad s⁻²",
"B": "9.7 rad s⁻²",
"C": "8.7 rad s⁻²",
"D": "10.7 rad s⁻²"
} | B | 9.7 rad s⁻² | For a solid disc, I=½MR²=½(5)(2)²=10 kg m². Using τ=Iα, α=97/10=9.7 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.7 rad s⁻², not 19.4 rad s⁻².",
"B": "Correct. The worked calculation gives 9.7 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.7 rad s⁻², not 8.7 rad s⁻².",
"D": "Incorrect. Subst... | [
"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_008614 | 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 1.05 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "6.2 K",
"B": "4.2 K",
"C": "3.2 K",
"D": "8.4 K"
} | B | 4.2 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×1.0×1.05=4.2 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.2 K, not 6.2 K.",
"B": "Correct. The worked calculation gives 4.2 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.2 K, not 3.2 K.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_001709 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 2 elements can be selected from a set of 19 distinct elements? | {
"A": "172",
"B": "205.2",
"C": "171",
"D": "128.25"
} | C | 171 | Order does not matter, so the count is C(19,2)=19!/[2!(17)!]=171. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 171, not 172.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 171, not 205.2.",
"C": "Correct. The worked calculation gives 171.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_007940 | 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 97 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "58.2 mmol L⁻¹",
"B": "47.5 mmol L⁻¹",
"C": "36.375 mmol L⁻¹",
"D": "48.5 mmol L⁻¹"
} | D | 48.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=97/2^1=48.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 48.5 mmol L⁻¹, not 58.2 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 48.5 mmol L⁻¹, not 47.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation ... | [
"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_004623 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 6 m is acted on by a constant torque of 14 N m about its central axis. Find its angular acceleration. | {
"A": "1.38889 rad s⁻²",
"B": "0.77778 rad s⁻²",
"C": "1.03889 rad s⁻²",
"D": "0.38889 rad s⁻²"
} | D | 0.38889 rad s⁻² | For a solid disc, I=½MR²=½(2)(6)²=36 kg m². Using τ=Iα, α=14/36=0.38889 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.38889 rad s⁻², not 1.38889 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.38889 rad s⁻², not 0.77778 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing r... | [
"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_009971 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(OH)_3]^-3, each OH ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "0",
"B": "-2",
"C": "1",
"D": "2"
} | A | 0 | Let the formal oxidation state of Cr be x. Charge balance gives x+(3)(−1)=-3; hence x=-3+3=+0. | {
"A": "Correct. The worked calculation gives 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_006172 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 33 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": "3.53846",
"B": "1.15385",
"C": "2.53846",
"D": "1.53846"
} | D | 1.53846 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(33)(20)/(33−20)=50.76923 cm. Thus |m|=v/u=50.76923/33=1.53846. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.53846, not 3.53846.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.53846, not 1.15385.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.53846, not 2.538... | [
"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_003626 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 100 m s⁻¹ at 70° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "642.78761 m",
"B": "65.27876 m",
"C": "514.23009 m",
"D": "771.34513 m"
} | A | 642.78761 m | Range R=u²sin(2θ)/g. Substituting u=100, θ=70° and g=10 gives R=(100)²sin(140°)/10=642.78761 m. | {
"A": "Correct. The worked calculation gives 642.78761 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 642.78761 m, not 65.27876 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 642.78761 m, not 514.23009 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_000825 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio 5. What is the sum of its first 11 terms? | {
"A": "109863279",
"B": "87890623.2",
"C": "131835934.8",
"D": "-109863279"
} | A | 109863279 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(5^11−1)/(5−1)=109863279. | {
"A": "Correct. The worked calculation gives 109863279.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 109863279, not 87890623.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 109863279, not 131835934.8.",
"D": "Incorrect. Substituting ... | [
"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_003610 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 88 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "774.4 m",
"B": "776.4 m",
"C": "387.2 m",
"D": "772.4 m"
} | A | 774.4 m | Range R=u²sin(2θ)/g. Substituting u=88, θ=45° and g=10 gives R=(88)²sin(90°)/10=774.4 m. | {
"A": "Correct. The worked calculation gives 774.4 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 774.4 m, not 776.4 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 774.4 m, not 387.2 m.",
"D": "Incorrect. Substituting the stated va... | [
"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_007315 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 12 mol of gas at 197 K and 0.79 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "243.54778 L",
"B": "122.77389 L",
"C": "245.54778 L",
"D": "196.43823 L"
} | C | 245.54778 L | PV=nRT, so V=nRT/P=(12)(0.082057)(197)/(0.79)=245.54778 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 245.54778 L, not 243.54778 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 245.54778 L, not 122.77389 L.",
"C": "Correct. The worked calculation gives 245.54778 L.",
"D": "Incorrect. Substi... | [
"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_001478 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (1x² -1x +7) dx. | {
"A": "27.5",
"B": "25.5",
"C": "20.4",
"D": "19.125"
} | B | 25.5 | An antiderivative is (1/3)x³+(-1/2)x²+(7)x. Evaluating between 0 and 3 gives (1/3)(3)³+(-1/2)(3)²+(7)(3)=25.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 25.5, not 27.5.",
"B": "Correct. The worked calculation gives 25.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 25.5, not 20.4.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_009294 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.94 V, transfers 1 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.7645 V",
"B": "1.2355 V",
"C": "-0.7645 V",
"D": "4.2355 V"
} | B | 1.2355 V | Apply the Nernst equation: E=0.94−(0.0591/1)(-5)=1.2355 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.2355 V, not -1.7645 V.",
"B": "Correct. The worked calculation gives 1.2355 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2355 V, not -0.7645 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_005281 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +1 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "71 N",
"B": "-70 N",
"C": "72 N",
"D": "70 N"
} | D | 70 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(1×10⁻⁶)/(3×10⁻²)²=70 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 70 N, not 71 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 70 N, not -70 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 70 N, not 72 N.",
"D": "Cor... | [
"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_001607 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (0x² +2x -2) dx. | {
"A": "-1",
"B": "-1.5",
"C": "-4",
"D": "1"
} | A | -1 | An antiderivative is (0/3)x³+(2/2)x²+(-2)x. Evaluating between 0 and 1 gives (0/3)(1)³+(2/2)(1)²+(-2)(1)=-1. | {
"A": "Correct. The worked calculation gives -1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1, not -1.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1, not -4.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"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_007325 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 6 mol of gas at 616 K and 2.18 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "141.12049 L",
"B": "166.94459 L",
"C": "139.12049 L",
"D": "-139.12049 L"
} | C | 139.12049 L | PV=nRT, so V=nRT/P=(6)(0.082057)(616)/(2.18)=139.12049 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 139.12049 L, not 141.12049 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 139.12049 L, not 166.94459 L.",
"C": "Correct. The worked calculation gives 139.12049 L.",
"D": "Incorrect. Substi... | [
"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_005344 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 39 μF capacitor is charged to a potential difference of 2 V. Calculate the energy stored, expressed in μJ. | {
"A": "78 μJ",
"B": "8.8 μJ",
"C": "76 μJ",
"D": "-78 μJ"
} | A | 78 μJ | U=½CV². Since C=39 μF, U in μJ is ½×39×(2)²=78 μJ. | {
"A": "Correct. The worked calculation gives 78 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 78 μJ, not 8.8 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 78 μJ, not 76 μJ.",
"D": "Incorrect. Substituting the stated values into... | [
"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_008822 | 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 0.43 mol L⁻¹ and initially B is absent. At equilibrium, 35% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.67585",
"B": "3.32415",
"C": "0.32415",
"D": "-0.32415"
} | C | 0.32415 | Let α=0.35. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.43)(0.35)²/(1−0.35)=0.32415. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32415, not -0.67585.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32415, not 3.32415.",
"C": "Correct. The worked calculation gives 0.32415.",
"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_009896 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(CN)_4]^+2, each CN ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "9",
"B": "12",
"C": "6",
"D": "1.6"
} | C | 6 | Let the formal oxidation state of Co be x. Charge balance gives x+(4)(−1)=+2; hence x=2+4=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 12.",
"C": "Correct. The worked calculation gives 6.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_009295 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.09 V, transfers 3 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.0282 V",
"B": "0.9718 V",
"C": "3.9718 V",
"D": "1.4577 V"
} | B | 0.9718 V | Apply the Nernst equation: E=1.09−(0.0591/3)(6)=0.9718 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9718 V, not -0.0282 V.",
"B": "Correct. The worked calculation gives 0.9718 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9718 V, not 3.9718 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_003476 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 52 m s⁻¹ at 65° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "207.13842 m",
"B": "-207.13842 m",
"C": "248.5661 m",
"D": "310.70763 m"
} | A | 207.13842 m | Range R=u²sin(2θ)/g. Substituting u=52, θ=65° and g=10 gives R=(52)²sin(130°)/10=207.13842 m. | {
"A": "Correct. The worked calculation gives 207.13842 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 207.13842 m, not -207.13842 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 207.13842 m, not 248.5661 m.",
"D": "Incorrect. Substi... | [
"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_001251 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-1x³ +10x² -11x+7. Evaluate f′(-1). | {
"A": "-40.8",
"B": "-34",
"C": "-33",
"D": "-27.2"
} | B | -34 | Differentiate: f′(x)=3(-1)x²+2(10)x+(-11). At x=-1, f′(-1)=3(-1)(-1)²+2(10)(-1)+(-11)=-34. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -34, not -40.8.",
"B": "Correct. The worked calculation gives -34.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -34, not -33.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_004103 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.24. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "44.88 N",
"B": "33.66 N",
"C": "42.88 N",
"D": "89.76 N"
} | A | 44.88 N | Net force=mg(sinθ−μcosθ)=11×10×(0.6−0.24×0.8)=44.88 N. | {
"A": "Correct. The worked calculation gives 44.88 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 44.88 N, not 33.66 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 44.88 N, not 42.88 N.",
"D": "Incorrect. Substituting the stated va... | [
"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_009620 | 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_5H_5N_3X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "2",
"B": "6",
"C": "4.5",
"D": "3"
} | D | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×5+2+3−5−4)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.5.",
"D": "Correct. The worked ... | [
"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 |
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