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_007156 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 1 mol of gas at 424 K and 2.76 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "13.60586 L",
"B": "12.60586 L",
"C": "11.60586 L",
"D": "14.60586 L"
} | B | 12.60586 L | PV=nRT, so V=nRT/P=(1)(0.082057)(424)/(2.76)=12.60586 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.60586 L, not 13.60586 L.",
"B": "Correct. The worked calculation gives 12.60586 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.60586 L, not 11.60586 L.",
"D": "Incorrect. Substitutin... | [
"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_003000 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(3, -7, 5) and v=(0, 8, 5), calculate u·v. | {
"A": "-33",
"B": "31",
"C": "-24.8",
"D": "-31"
} | D | -31 | The dot product is the sum of corresponding component products: (3)(0)+(-7)(8)+(5)(5)=-31. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -31, not -33.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -31, not 31.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -31, not -24.8.",
"D": "Correct. ... | [
"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_002245 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 11 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-2.65368",
"B": "-0.34632",
"C": "0.34632",
"D": "-1.65368"
} | C | 0.34632 | Favourable pairs = C(5,2)+C(11,2)+C(6,2)=80. Total pairs=C(22,2)=231. Therefore P=80/231=0.34632. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34632, not -2.65368.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34632, not -0.34632.",
"C": "Correct. The worked calculation gives 0.34632.",
"D": "Incorrect. Substituting the stated ... | [
"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_006937 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 38 mol H₂ and 5 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "-10 mol",
"B": "2 mol",
"C": "10 mol",
"D": "8 mol"
} | C | 10 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 38 mol H₂O; O₂ can produce 10 mol H₂O. The limiting condition is O₂; product=10 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not -10 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 2 mol.",
"C": "Correct. The worked calculation gives 10 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_004870 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 3 Ω are connected in series; this combination is connected in parallel with a 19 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.07237 A",
"B": "1.38158 A",
"C": "-1.38158 A",
"D": "-0.61842 A"
} | B | 1.38158 A | Series branch resistance=13+3=16 Ω. Parallel equivalent R_eq=(16×19)/(16+19)=8.68571 Ω. Total current I=V/R_eq=12/8.68571=1.38158 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.38158 A, not 2.07237 A.",
"B": "Correct. The worked calculation gives 1.38158 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.38158 A, not -1.38158 A.",
"D": "Incorrect. Substituting th... | [
"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_008349 | 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 0.18 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.02765 K",
"B": "3.27648 K",
"C": "0.27648 K",
"D": "-1.72352 K"
} | C | 0.27648 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.512×0.18=0.27648 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.27648 K, not 1.02765 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.27648 K, not 3.27648 K.",
"C": "Correct. The worked calculation gives 0.27648 K.",
"D": "Incorrect. Substituting the... | [
"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_009980 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(CN)_4]^+0, each CN ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "4",
"B": "5",
"C": "8",
"D": "1"
} | A | 4 | Let the formal oxidation state of Fe be x. Charge balance gives x+(4)(−1)=+0; hence x=0+4=+4. | {
"A": "Correct. The worked calculation gives 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 8.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008126 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 9 A for 12434 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": "55.22822 g",
"B": "73.63763 g",
"C": "36.81881 g",
"D": "34.81881 g"
} | C | 36.81881 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×9×12434/(2×96500)=36.81881 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 36.81881 g, not 55.22822 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 36.81881 g, not 73.63763 g.",
"C": "Correct. The worked calculation gives 36.81881 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_003968 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 3 m s⁻¹. A constant net force does 26 N of work over 8 m in the direction of motion. Find its final kinetic energy. | {
"A": "198.8 J",
"B": "25.85 J",
"C": "248.5 J",
"D": "298.2 J"
} | C | 248.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(3)²+(26)(8)=248.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 248.5 J, not 198.8 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 248.5 J, not 25.85 J.",
"C": "Correct. The worked calculation gives 248.5 J.",
"D": "Incorrect. Substituting the stated va... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006685 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 45 mol H₂ and 31 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "47 mol",
"B": "45 mol",
"C": "44 mol",
"D": "90 mol"
} | B | 45 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 45 mol H₂O; O₂ can produce 62 mol H₂O. The limiting condition is H₂; product=45 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45 mol, not 47 mol.",
"B": "Correct. The worked calculation gives 45 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 45 mol, not 44 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_003820 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block initially moves at 2 m s⁻¹. A constant net force does 8 N of work over 20 m in the direction of motion. Find its final kinetic energy. | {
"A": "344 J",
"B": "129 J",
"C": "172 J",
"D": "137.6 J"
} | C | 172 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(6)(2)²+(8)(20)=172 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 172 J, not 344 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 172 J, not 129 J.",
"C": "Correct. The worked calculation gives 172 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_009795 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(Cl)_4]^+0, each Cl ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "6",
"B": "5",
"C": "-4",
"D": "4"
} | D | 4 | Let the formal oxidation state of Cu be x. Charge balance gives x+(4)(−1)=+0; hence x=0+4=+4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not -4.",
"D": "Correct. The worked c... | [
"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_004029 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 13 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.37. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "39.52 N",
"B": "47.424 N",
"C": "29.64 N",
"D": "41.52 N"
} | A | 39.52 N | Net force=mg(sinθ−μcosθ)=13×10×(0.6−0.37×0.8)=39.52 N. | {
"A": "Correct. The worked calculation gives 39.52 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39.52 N, not 47.424 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39.52 N, not 29.64 N.",
"D": "Incorrect. Substituting the stated v... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001610 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (4x² +8x +5) dx. | {
"A": "87",
"B": "104.4",
"C": "174",
"D": "89"
} | A | 87 | An antiderivative is (4/3)x³+(8/2)x²+(5)x. Evaluating between 0 and 3 gives (4/3)(3)³+(8/2)(3)²+(5)(3)=87. | {
"A": "Correct. The worked calculation gives 87.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 87, not 104.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 87, not 174.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_003814 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 4 m s⁻¹. A constant net force does 16 N of work over 14 m in the direction of motion. Find its final kinetic energy. | {
"A": "256 J",
"B": "204.8 J",
"C": "26.6 J",
"D": "128 J"
} | A | 256 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(4)²+(16)(14)=256 J. | {
"A": "Correct. The worked calculation gives 256 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 256 J, not 204.8 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 256 J, not 26.6 J.",
"D": "Incorrect. Substituting the stated values in... | [
"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_009341 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_16H_32X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "0",
"B": "1",
"C": "-1",
"D": "3"
} | A | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×16+2+0−32−2)/2=0. | {
"A": "Correct. The worked calculation gives 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not -1.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003880 | 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 17 N of work over 15 m in the direction of motion. Find its final kinetic energy. | {
"A": "382.5 J",
"B": "257 J",
"C": "255 J",
"D": "253 J"
} | C | 255 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(15)(0)²+(17)(15)=255 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 255 J, not 382.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 255 J, not 257 J.",
"C": "Correct. The worked calculation gives 255 J.",
"D": "Incorrect. Substituting the stated values int... | [
"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_006173 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 30 cm in front of a thin convex lens of focal length 15 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "4",
"B": "0.75",
"C": "2",
"D": "1"
} | D | 1 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(30)(15)/(30−15)=30 cm. Thus |m|=v/u=30/30=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"D": "Correct. The worked... | [
"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_002325 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 9 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "3.31481",
"B": "0.31481",
"C": "2.31481",
"D": "-0.31481"
} | B | 0.31481 | Favourable pairs = C(8,2)+C(9,2)+C(11,2)=119. Total pairs=C(28,2)=378. Therefore P=119/378=0.31481. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31481, not 3.31481.",
"B": "Correct. The worked calculation gives 0.31481.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31481, not 2.31481.",
"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_005288 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +1 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "11.25 N",
"B": "5.625 N",
"C": "7.5 N",
"D": "8.5 N"
} | C | 7.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(1×10⁻⁶)/(6×10⁻²)²=7.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.5 N, not 11.25 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.5 N, not 5.625 N.",
"C": "Correct. The worked calculation gives 7.5 N.",
"D": "Incorrect. Substituting the stated values i... | [
"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_007436 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 27 mL of 0.10 M HCl is mixed with 10 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.33775",
"B": "1.13378",
"C": "0.66888",
"D": "1.00331"
} | A | 1.33775 | Excess H⁺ moles=0.10×(27−10)/1000=0.001700 mol. Total volume=0.037 L, so [H⁺]=0.045946 M and pH=−log₁₀[H⁺]=1.33775. | {
"A": "Correct. The worked calculation gives 1.33775.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.33775, not 1.13378.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.33775, not 0.66888.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003606 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 81 m s⁻¹ at 65° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "500.60176 m",
"B": "402.08141 m",
"C": "503.60176 m",
"D": "502.60176 m"
} | D | 502.60176 m | Range R=u²sin(2θ)/g. Substituting u=81, θ=65° and g=10 gives R=(81)²sin(130°)/10=502.60176 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 502.60176 m, not 500.60176 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 502.60176 m, not 402.08141 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 50... | [
"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_002729 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-4, 9, 4) and v=(9, 0, 4), calculate u·v. | {
"A": "-20",
"B": "20",
"C": "-18",
"D": "-16"
} | A | -20 | The dot product is the sum of corresponding component products: (-4)(9)+(9)(0)+(4)(4)=-20. | {
"A": "Correct. The worked calculation gives -20.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -20, not 20.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -20, not -18.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007082 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 18 mol of gas at 443 K and 2.28 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "229.58685 L",
"B": "285.98356 L",
"C": "286.98356 L",
"D": "143.49178 L"
} | C | 286.98356 L | PV=nRT, so V=nRT/P=(18)(0.082057)(443)/(2.28)=286.98356 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 286.98356 L, not 229.58685 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 286.98356 L, not 285.98356 L.",
"C": "Correct. The worked calculation gives 286.98356 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_000181 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +10x -4=0, let its roots be α and β. What is α²+β²? | {
"A": "10.33333",
"B": "14.77778",
"C": "6.88889",
"D": "13.77778"
} | D | 13.77778 | By Vieta's relations, α+β = -10/3 and αβ = -4/3. Then α²+β²=(α+β)²−2αβ = (-10/3)²−2(-4/3) = 13.77778. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13.77778, not 10.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13.77778, not 14.77778.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13.77778, not ... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001183 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=2x³ +0x² +0x+7. Evaluate f′(-1). | {
"A": "12",
"B": "6",
"C": "4",
"D": "3"
} | B | 6 | Differentiate: f′(x)=3(2)x²+2(0)x+(0). At x=-1, f′(-1)=3(2)(-1)²+2(0)(-1)+(0)=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 12.",
"B": "Correct. The worked calculation gives 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_007334 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 7 mol of gas at 645 K and 0.22 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "2526.05015 L",
"B": "1686.03343 L",
"C": "1683.03343 L",
"D": "1684.03343 L"
} | D | 1684.03343 L | PV=nRT, so V=nRT/P=(7)(0.082057)(645)/(0.22)=1684.03343 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1684.03343 L, not 2526.05015 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1684.03343 L, not 1686.03343 L.",
"C": "Incorrect. Substituting the stated values into the governing relation give... | [
"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_005795 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.3 atm at 274 K. What is its pressure at 569 K? | {
"A": "-0.30036 atm",
"B": "2.02473 atm",
"C": "2.69964 atm",
"D": "3.69964 atm"
} | C | 2.69964 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.3)(569)/(274)=2.69964 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.69964 atm, not -0.30036 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.69964 atm, not 2.02473 atm.",
"C": "Correct. The worked calculation gives 2.69964 atm.",
"D": "Incorrect. Subst... | [
"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_004265 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 30 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.40. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "83 N",
"B": "63 N",
"C": "168 N",
"D": "84 N"
} | D | 84 N | Net force=mg(sinθ−μcosθ)=30×10×(0.6−0.40×0.8)=84 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 84 N, not 83 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 84 N, not 63 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 84 N, not 168 N.",
"D": "Cor... | [
"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_005379 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 48 μF capacitor is charged to a potential difference of 10 V. Calculate the energy stored, expressed in μJ. | {
"A": "2400 μJ",
"B": "1800 μJ",
"C": "2398 μJ",
"D": "2880 μJ"
} | A | 2400 μJ | U=½CV². Since C=48 μF, U in μJ is ½×48×(10)²=2400 μJ. | {
"A": "Correct. The worked calculation gives 2400 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2400 μJ, not 1800 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2400 μJ, not 2398 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"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_003510 | 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 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "31.90777 m",
"B": "47.86166 m",
"C": "25.52622 m",
"D": "63.81554 m"
} | A | 31.90777 m | Range R=u²sin(2θ)/g. Substituting u=18, θ=40° and g=10 gives R=(18)²sin(80°)/10=31.90777 m. | {
"A": "Correct. The worked calculation gives 31.90777 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 31.90777 m, not 47.86166 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 31.90777 m, not 25.52622 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_007723 | 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 49 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "7.125 mmol L⁻¹",
"B": "6.125 mmol L⁻¹",
"C": "8.125 mmol L⁻¹",
"D": "9.1875 mmol L⁻¹"
} | B | 6.125 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=49/2^3=6.125 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.125 mmol L⁻¹, not 7.125 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 6.125 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.125 mmol L⁻¹, not 8.125 mmol L⁻¹.",
"D": "In... | [
"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_007624 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 67 mL of 0.10 M HCl is mixed with 45 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "0.7068",
"B": "3.41359",
"C": "1.7068",
"D": "2.7068"
} | C | 1.7068 | Excess H⁺ moles=0.10×(67−45)/1000=0.002200 mol. Total volume=0.112 L, so [H⁺]=0.019643 M and pH=−log₁₀[H⁺]=1.7068. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.7068, not 0.7068.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.7068, not 3.41359.",
"C": "Correct. The worked calculation gives 1.7068.",
"D": "Incorrect. Substituting the stated values... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003254 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-12-6i)/(5+5i). What is Re(z), the real part of z? | {
"A": "0.2",
"B": "-4.8",
"C": "-1.8",
"D": "1.2"
} | C | -1.8 | Multiply numerator and denominator by the conjugate (5-5i). Then Re(z)=(ac+bd)/(c²+d²)=((-12)(5)+(-6)(5))/(5²+(5)²)=-1.8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.8, not 0.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.8, not -4.8.",
"C": "Correct. The worked calculation gives -1.8.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_008370 | 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 1.2 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": "1.48 K",
"B": "1.8 K",
"C": "-4.8 K",
"D": "4.8 K"
} | D | 4.8 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×1.0×1.2=4.8 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.8 K, not 1.48 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.8 K, not 1.8 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.8 K, not -4.8 K.",
"D... | [
"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_002594 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, -6], [8, -8]]. | {
"A": "-17",
"B": "-12.8",
"C": "-16",
"D": "-18"
} | C | -16 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(-8)−(-6)(8)=-16. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -16, not -17.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -16, not -12.8.",
"C": "Correct. The worked calculation gives -16.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008515 | 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 1.51 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-2.31936 K",
"B": "3.31936 K",
"C": "4.31936 K",
"D": "2.31936 K"
} | D | 2.31936 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.512×1.51=2.31936 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.31936 K, not -2.31936 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.31936 K, not 3.31936 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.31936 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_002830 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, 6, -2) and v=(5, 4, 6), calculate u·v. | {
"A": "4.2",
"B": "32",
"C": "33",
"D": "31"
} | B | 32 | The dot product is the sum of corresponding component products: (4)(5)+(6)(4)+(-2)(6)=32. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 32, not 4.2.",
"B": "Correct. The worked calculation gives 32.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 32, not 33.",
"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_009756 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(Cl)_2]^+0, each Cl ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "1.2",
"B": "3",
"C": "-1",
"D": "2"
} | D | 2 | Let the formal oxidation state of Fe be x. Charge balance gives x+(2)(−1)=+0; hence x=0+2=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not -1.",
"D": "Correct. The worked... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005391 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 25 μF capacitor is charged to a potential difference of 7 V. Calculate the energy stored, expressed in μJ. | {
"A": "-612.5 μJ",
"B": "490 μJ",
"C": "614.5 μJ",
"D": "612.5 μJ"
} | D | 612.5 μJ | U=½CV². Since C=25 μF, U in μJ is ½×25×(7)²=612.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 612.5 μJ, not -612.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 612.5 μJ, not 490 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 612.5 μJ, not 6... | [
"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_006134 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 74 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": "-1.62963",
"B": "0.37037",
"C": "0.55556",
"D": "0.74074"
} | B | 0.37037 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(74)(20)/(74−20)=27.40741 cm. Thus |m|=v/u=27.40741/74=0.37037. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.37037, not -1.62963.",
"B": "Correct. The worked calculation gives 0.37037.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.37037, not 0.55556.",
"D": "Incorrect. Substituting the stated v... | [
"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_008199 | 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 12 A for 9576 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": "45.3694 g",
"B": "-37.80783 g",
"C": "4.78078 g",
"D": "37.80783 g"
} | D | 37.80783 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×12×9576/(2×96500)=37.80783 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 37.80783 g, not 45.3694 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 37.80783 g, not -37.80783 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 37.807... | [
"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_007090 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 16 mol of gas at 422 K and 1.8 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "31.78049 L",
"B": "307.80492 L",
"C": "615.60985 L",
"D": "305.80492 L"
} | B | 307.80492 L | PV=nRT, so V=nRT/P=(16)(0.082057)(422)/(1.8)=307.80492 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 307.80492 L, not 31.78049 L.",
"B": "Correct. The worked calculation gives 307.80492 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 307.80492 L, not 615.60985 L.",
"D": "Incorrect. Substit... | [
"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_003336 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(10+11i)/(2+9i). What is Re(z), the real part of z? | {
"A": "-0.6",
"B": "3.4",
"C": "1.4",
"D": "1.14"
} | C | 1.4 | Multiply numerator and denominator by the conjugate (2-9i). Then Re(z)=(ac+bd)/(c²+d²)=((10)(2)+(11)(9))/(2²+(9)²)=1.4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.4, not -0.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4, not 3.4.",
"C": "Correct. The worked calculation gives 1.4.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_003659 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 16 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "23.6 m",
"B": "19.2 m",
"C": "27.6 m",
"D": "25.6 m"
} | D | 25.6 m | Range R=u²sin(2θ)/g. Substituting u=16, θ=45° and g=10 gives R=(16)²sin(90°)/10=25.6 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 25.6 m, not 23.6 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 25.6 m, not 19.2 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 25.6 m, not 27.6 m.",
... | [
"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_006320 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 115 cm in front of a thin convex lens of focal length 29 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "3.33721",
"B": "-0.66279",
"C": "0.33721",
"D": "-2.66279"
} | C | 0.33721 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(115)(29)/(115−29)=38.77907 cm. Thus |m|=v/u=38.77907/115=0.33721. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33721, not 3.33721.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33721, not -0.66279.",
"C": "Correct. The worked calculation gives 0.33721.",
"D": "Incorrect. Substituting the stated v... | [
"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_003765 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 4 m s⁻¹. A constant net force does 19 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "298 J",
"B": "296 J",
"C": "297 J",
"D": "299 J"
} | C | 297 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(4)²+(19)(11)=297 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 297 J, not 298 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 297 J, not 296 J.",
"C": "Correct. The worked calculation gives 297 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_005200 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +7 μC are separated by 12 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "4.0625 N",
"B": "-30.625 N",
"C": "30.625 N",
"D": "15.3125 N"
} | C | 30.625 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(7×10⁻⁶)/(12×10⁻²)²=30.625 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 30.625 N, not 4.0625 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30.625 N, not -30.625 N.",
"C": "Correct. The worked calculation gives 30.625 N.",
"D": "Incorrect. Substituting the sta... | [
"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_003285 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-10-2i)/(7+8i). What is Re(z), the real part of z? | {
"A": "-2.76106",
"B": "0.92389",
"C": "-0.76106",
"D": "-3.76106"
} | C | -0.76106 | Multiply numerator and denominator by the conjugate (7-8i). Then Re(z)=(ac+bd)/(c²+d²)=((-10)(7)+(-2)(8))/(7²+(8)²)=-0.76106. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.76106, not -2.76106.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.76106, not 0.92389.",
"C": "Correct. The worked calculation gives -0.76106.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000484 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -19 and common difference 15. Find the sum of its first 22 terms. | {
"A": "305.7",
"B": "3049",
"C": "3656.4",
"D": "3047"
} | D | 3047 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-19, d=15, n=22: Sₙ=22/2[2(-19)+(22−1)(15)]=3047. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3047, not 305.7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3047, not 3049.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3047, not 3656.4.",
"D": "C... | [
"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_007647 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 84 mL of 0.10 M HCl is mixed with 99 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "11.91364",
"B": "-11.91364",
"C": "8.91364",
"D": "23.82728"
} | A | 11.91364 | Excess OH⁻ moles=0.10×(99−84)/1000=0.001500 mol. Total volume=0.183 L, so [OH⁻]=0.008197 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=11.91364. | {
"A": "Correct. The worked calculation gives 11.91364.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.91364, not -11.91364.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.91364, not 8.91364.",
"D": "Incorrect. Substituting the stat... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001017 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ -2x² -2x+7. Evaluate f′(5). | {
"A": "423.6",
"B": "351",
"C": "353",
"D": "354"
} | C | 353 | Differentiate: f′(x)=3(5)x²+2(-2)x+(-2). At x=5, f′(5)=3(5)(5)²+2(-2)(5)+(-2)=353. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 353, not 423.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 353, not 351.",
"C": "Correct. The worked calculation gives 353.",
"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_006935 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 26 mol H₂ and 12 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "3.4 mol",
"B": "24 mol",
"C": "12 mol",
"D": "26 mol"
} | B | 24 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 26 mol H₂O; O₂ can produce 24 mol H₂O. The limiting condition is O₂; product=24 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24 mol, not 3.4 mol.",
"B": "Correct. The worked calculation gives 24 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24 mol, not 12 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_005853 | 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 204 K. What is its pressure at 366 K? | {
"A": "-8.43235 atm",
"B": "8.43235 atm",
"C": "5.43235 atm",
"D": "1.84324 atm"
} | B | 8.43235 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.7)(366)/(204)=8.43235 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.43235 atm, not -8.43235 atm.",
"B": "Correct. The worked calculation gives 8.43235 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.43235 atm, not 5.43235 atm.",
"D": "Incorrect. Subst... | [
"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_009049 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.32 V, transfers 3 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.5618 V",
"B": "0.4382 V",
"C": "4.4382 V",
"D": "1.4382 V"
} | D | 1.4382 V | Apply the Nernst equation: E=1.32−(0.0591/3)(-6)=1.4382 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.4382 V, not -1.5618 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4382 V, not 0.4382 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.4382 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_007488 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 14 mL of 0.10 M HCl is mixed with 88 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "19.29095",
"B": "12.86063",
"C": "9.64547",
"D": "6.43032"
} | B | 12.86063 | Excess OH⁻ moles=0.10×(88−14)/1000=0.007400 mol. Total volume=0.102 L, so [OH⁻]=0.072549 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.86063. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.86063, not 19.29095.",
"B": "Correct. The worked calculation gives 12.86063.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.86063, not 9.64547.",
"D": "Incorrect. Substituting the state... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001360 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (-4x² +7x +7) dx. | {
"A": "-88.33333",
"B": "-45.16667",
"C": "-44.16667",
"D": "-53"
} | C | -44.16667 | An antiderivative is (-4/3)x³+(7/2)x²+(7)x. Evaluating between 0 and 5 gives (-4/3)(5)³+(7/2)(5)²+(7)(5)=-44.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -44.16667, not -88.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -44.16667, not -45.16667.",
"C": "Correct. The worked calculation gives -44.16667.",
"D": "Incorrect. Substituting the... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007211 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 18 mol of gas at 339 K and 2.52 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "149.02137 L",
"B": "198.69516 L",
"C": "20.86952 L",
"D": "199.69516 L"
} | B | 198.69516 L | PV=nRT, so V=nRT/P=(18)(0.082057)(339)/(2.52)=198.69516 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 198.69516 L, not 149.02137 L.",
"B": "Correct. The worked calculation gives 198.69516 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 198.69516 L, not 20.86952 L.",
"D": "Incorrect. Substit... | [
"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_008375 | 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 0.21 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": "1.252 K",
"B": "-1.748 K",
"C": "0.189 K",
"D": "0.252 K"
} | D | 0.252 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.6×0.21=0.252 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.252 K, not 1.252 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.252 K, not -1.748 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.252 K, not 0.18... | [
"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_007341 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 42 mL of 0.10 M HCl is mixed with 73 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "6.21533",
"B": "12.43066",
"C": "14.43066",
"D": "13.43066"
} | B | 12.43066 | Excess OH⁻ moles=0.10×(73−42)/1000=0.003100 mol. Total volume=0.115 L, so [OH⁻]=0.026957 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.43066. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.43066, not 6.21533.",
"B": "Correct. The worked calculation gives 12.43066.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.43066, not 14.43066.",
"D": "Incorrect. Substituting the state... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000836 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio 3. What is the sum of its first 5 terms? | {
"A": "244",
"B": "-242",
"C": "242",
"D": "241"
} | C | 242 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(3^5−1)/(3−1)=242. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 242, not 244.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 242, not -242.",
"C": "Correct. The worked calculation gives 242.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001998 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 12 elements can be selected from a set of 42 distinct elements? | {
"A": "11058116887",
"B": "11058116886",
"C": "16587175332",
"D": "11058116888"
} | D | 11058116888 | Order does not matter, so the count is C(42,12)=42!/[12!(30)!]=11058116888. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11058116888, not 11058116887.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11058116888, not 11058116886.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11... | [
"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_003245 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(13+1i)/(1+7i). What is Re(z), the real part of z? | {
"A": "0.4",
"B": "0.8",
"C": "1.04",
"D": "-2.6"
} | A | 0.4 | Multiply numerator and denominator by the conjugate (1-7i). Then Re(z)=(ac+bd)/(c²+d²)=((13)(1)+(1)(7))/(1²+(7)²)=0.4. | {
"A": "Correct. The worked calculation gives 0.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.4, not 0.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.4, not 1.04.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_000406 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -18 and common difference 8. Find the sum of its first 13 terms. | {
"A": "195",
"B": "391",
"C": "390",
"D": "392"
} | C | 390 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-18, d=8, n=13: Sₙ=13/2[2(-18)+(13−1)(8)]=390. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 390, not 195.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 390, not 391.",
"C": "Correct. The worked calculation gives 390.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_000452 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 0 and common difference 8. Find the sum of its first 26 terms. | {
"A": "2602",
"B": "2080",
"C": "2600",
"D": "-2600"
} | C | 2600 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=0, d=8, n=26: Sₙ=26/2[2(0)+(26−1)(8)]=2600. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2600, not 2602.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2600, not 2080.",
"C": "Correct. The worked calculation gives 2600.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_006541 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 5 kg is attached to an ideal spring of force constant 390 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.22646 s",
"B": "0.22646 s",
"C": "1.02265 s",
"D": "-1.77354 s"
} | B | 0.22646 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(5/390)=0.22646 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.22646 s, not -0.22646 s.",
"B": "Correct. The worked calculation gives 0.22646 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.22646 s, not 1.02265 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002587 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, -8], [6, 2]]. | {
"A": "90",
"B": "60",
"C": "61",
"D": "59"
} | B | 60 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(2)−(-8)(6)=60. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 60, not 90.",
"B": "Correct. The worked calculation gives 60.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 60, not 61.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_008387 | 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 2 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.04 K",
"B": "1.08 K",
"C": "2.08 K",
"D": "-2.08 K"
} | C | 2.08 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×2=2.08 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.08 K, not 1.04 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.08 K, not 1.08 K.",
"C": "Correct. The worked calculation gives 2.08 K.",
"D": "Incorrect. Substituting the stated values ... | [
"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_003036 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-14+2i)/(8+2i). What is Re(z), the real part of z? | {
"A": "-1.19118",
"B": "-1.58824",
"C": "-3.17647",
"D": "-2.38235"
} | B | -1.58824 | Multiply numerator and denominator by the conjugate (8-2i). Then Re(z)=(ac+bd)/(c²+d²)=((-14)(8)+(2)(2))/(8²+(2)²)=-1.58824. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.58824, not -1.19118.",
"B": "Correct. The worked calculation gives -1.58824.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.58824, not -3.17647.",
"D": "Incorrect. Substituting the stat... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000343 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 13 and common difference 8. Find the sum of its first 33 terms. | {
"A": "4653",
"B": "2326.5",
"C": "466.3",
"D": "3489.75"
} | A | 4653 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=13, d=8, n=33: Sₙ=33/2[2(13)+(33−1)(8)]=4653. | {
"A": "Correct. The worked calculation gives 4653.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4653, not 2326.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4653, not 466.3.",
"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_009646 | 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_30N_1X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "1.3",
"B": "3",
"C": "4.5",
"D": "5"
} | B | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×17+2+1−30−1)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.5.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007669 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 54 mL of 0.10 M HCl is mixed with 45 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "0.04139",
"B": "4.04139",
"C": "2.04139",
"D": "3.04139"
} | C | 2.04139 | Excess H⁺ moles=0.10×(54−45)/1000=0.000900 mol. Total volume=0.099 L, so [H⁺]=0.009091 M and pH=−log₁₀[H⁺]=2.04139. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.04139, not 0.04139.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.04139, not 4.04139.",
"C": "Correct. The worked calculation gives 2.04139.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004746 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 15 Ω and 13 Ω are connected in series; this combination is connected in parallel with a 3 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "6.64286 A",
"B": "8.85714 A",
"C": "4.42857 A",
"D": "1.42857 A"
} | C | 4.42857 A | Series branch resistance=15+13=28 Ω. Parallel equivalent R_eq=(28×3)/(28+3)=2.70968 Ω. Total current I=V/R_eq=12/2.70968=4.42857 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.42857 A, not 6.64286 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.42857 A, not 8.85714 A.",
"C": "Correct. The worked calculation gives 4.42857 A.",
"D": "Incorrect. Substituting the... | [
"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_004396 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 6 kg and radius 1 m is acted on by a constant torque of 32 N m about its central axis. Find its angular acceleration. | {
"A": "10.66667 rad s⁻²",
"B": "9.66667 rad s⁻²",
"C": "21.33333 rad s⁻²",
"D": "8 rad s⁻²"
} | A | 10.66667 rad s⁻² | For a solid disc, I=½MR²=½(6)(1)²=3 kg m². Using τ=Iα, α=32/3=10.66667 rad s⁻². | {
"A": "Correct. The worked calculation gives 10.66667 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.66667 rad s⁻², not 9.66667 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10.66667 rad s⁻², not 21.33333 rad s⁻².",
... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007195 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 11 mol of gas at 496 K and 2.73 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "81.99688 L",
"B": "163.99377 L",
"C": "-163.99377 L",
"D": "161.99377 L"
} | B | 163.99377 L | PV=nRT, so V=nRT/P=(11)(0.082057)(496)/(2.73)=163.99377 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 163.99377 L, not 81.99688 L.",
"B": "Correct. The worked calculation gives 163.99377 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 163.99377 L, not -163.99377 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_003131 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(0-2i)/(10+4i). What is Re(z), the real part of z? | {
"A": "0.9931",
"B": "0.06897",
"C": "-0.06897",
"D": "1.93103"
} | C | -0.06897 | Multiply numerator and denominator by the conjugate (10-4i). Then Re(z)=(ac+bd)/(c²+d²)=((0)(10)+(-2)(4))/(10²+(4)²)=-0.06897. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.06897, not 0.9931.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.06897, not 0.06897.",
"C": "Correct. The worked calculation gives -0.06897.",
"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_007152 | 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 220 K and 0.65 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "249.95825 L",
"B": "83.31942 L",
"C": "167.63883 L",
"D": "166.63883 L"
} | D | 166.63883 L | PV=nRT, so V=nRT/P=(6)(0.082057)(220)/(0.65)=166.63883 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 166.63883 L, not 249.95825 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 166.63883 L, not 83.31942 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 166... | [
"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_004680 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 12 Ω and 9 Ω are connected in series; this combination is connected in parallel with a 14 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.14286 A",
"B": "1.60714 A",
"C": "1.21429 A",
"D": "-2.14286 A"
} | A | 2.14286 A | Series branch resistance=12+9=21 Ω. Parallel equivalent R_eq=(21×14)/(21+14)=8.4 Ω. Total current I=V/R_eq=18/8.4=2.14286 A. | {
"A": "Correct. The worked calculation gives 2.14286 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.14286 A, not 1.60714 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.14286 A, not 1.21429 A.",
"D": "Incorrect. Substituting the... | [
"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_006473 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 3 kg is attached to an ideal spring of force constant 384 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.17678 s",
"B": "-0.17678 s",
"C": "-1.82322 s",
"D": "-0.82322 s"
} | A | 0.17678 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(3/384)=0.17678 s. | {
"A": "Correct. The worked calculation gives 0.17678 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.17678 s, not -0.17678 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.17678 s, not -1.82322 s.",
"D": "Incorrect. Substituting t... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009917 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(CN)_3]^+1, each CN ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "5",
"B": "1.4",
"C": "4",
"D": "6"
} | C | 4 | Let the formal oxidation state of Pt be x. Charge balance gives x+(3)(−1)=+1; hence x=1+3=+4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.4.",
"C": "Correct. The worked calculation gives 4.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_003205 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(11-15i)/(12+12i). What is Re(z), the real part of z? | {
"A": "-2.16667",
"B": "0.83333",
"C": "-0.16667",
"D": "0.16667"
} | C | -0.16667 | Multiply numerator and denominator by the conjugate (12-12i). Then Re(z)=(ac+bd)/(c²+d²)=((11)(12)+(-15)(12))/(12²+(12)²)=-0.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.16667, not -2.16667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.16667, not 0.83333.",
"C": "Correct. The worked calculation gives -0.16667.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001043 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-3x³ -4x² +4x+7. Evaluate f′(-3). | {
"A": "-53",
"B": "-26.5",
"C": "-55",
"D": "-39.75"
} | A | -53 | Differentiate: f′(x)=3(-3)x²+2(-4)x+(4). At x=-3, f′(-3)=3(-3)(-3)²+2(-4)(-3)+(4)=-53. | {
"A": "Correct. The worked calculation gives -53.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -53, not -26.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -53, not -55.",
"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_003089 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-9-13i)/(1+11i). What is Re(z), the real part of z? | {
"A": "-2.2459",
"B": "-1.2459",
"C": "1.2459",
"D": "1.7541"
} | B | -1.2459 | Multiply numerator and denominator by the conjugate (1-11i). Then Re(z)=(ac+bd)/(c²+d²)=((-9)(1)+(-13)(11))/(1²+(11)²)=-1.2459. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.2459, not -2.2459.",
"B": "Correct. The worked calculation gives -1.2459.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.2459, not 1.2459.",
"D": "Incorrect. Substituting the stated val... | [
"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_001713 | 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 15 distinct elements? | {
"A": "103",
"B": "105",
"C": "104",
"D": "107"
} | B | 105 | Order does not matter, so the count is C(15,2)=15!/[2!(13)!]=105. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 105, not 103.",
"B": "Correct. The worked calculation gives 105.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 105, not 104.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_004442 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 9 kg and radius 1 m is acted on by a constant torque of 22 N m about its central axis. Find its angular acceleration. | {
"A": "4.88889 rad s⁻²",
"B": "6.88889 rad s⁻²",
"C": "1.48889 rad s⁻²",
"D": "7.88889 rad s⁻²"
} | A | 4.88889 rad s⁻² | For a solid disc, I=½MR²=½(9)(1)²=4.5 kg m². Using τ=Iα, α=22/4.5=4.88889 rad s⁻². | {
"A": "Correct. The worked calculation gives 4.88889 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.88889 rad s⁻², not 6.88889 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.88889 rad s⁻², not 1.48889 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_005056 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +5 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "50 N",
"B": "37.5 N",
"C": "52 N",
"D": "49 N"
} | A | 50 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(5×10⁻⁶)/(6×10⁻²)²=50 N. | {
"A": "Correct. The worked calculation gives 50 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 50 N, not 37.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 50 N, not 52 N.",
"D": "Incorrect. Substituting the stated values into the... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006480 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 1 kg is attached to an ideal spring of force constant 457 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.00936 s",
"B": "2.09356 s",
"C": "-2.90644 s",
"D": "0.09356 s"
} | D | 0.09356 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(1/457)=0.09356 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.09356 s, not 1.00936 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.09356 s, not 2.09356 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.09356 s,... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004815 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 3 Ω are connected in series; this combination is connected in parallel with a 18 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.54167 A",
"B": "5.3125 A",
"C": "3.54167 A",
"D": "4.54167 A"
} | C | 3.54167 A | Series branch resistance=13+3=16 Ω. Parallel equivalent R_eq=(16×18)/(16+18)=8.47059 Ω. Total current I=V/R_eq=30/8.47059=3.54167 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.54167 A, not 1.54167 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.54167 A, not 5.3125 A.",
"C": "Correct. The worked calculation gives 3.54167 A.",
"D": "Incorrect. Substituting the ... | [
"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_003655 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 98 m s⁻¹ at 15° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "720.3 m",
"B": "576.24 m",
"C": "480.2 m",
"D": "478.2 m"
} | C | 480.2 m | Range R=u²sin(2θ)/g. Substituting u=98, θ=15° and g=10 gives R=(98)²sin(30°)/10=480.2 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 480.2 m, not 720.3 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 480.2 m, not 576.24 m.",
"C": "Correct. The worked calculation gives 480.2 m.",
"D": "Incorrect. Substituting the stated v... | [
"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_002422 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, 2], [2, 2]]. | {
"A": "7.5",
"B": "20",
"C": "13",
"D": "10"
} | D | 10 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(2)−(2)(2)=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 7.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 20.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 13.",
"D": "Correct. The wo... | [
"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_002616 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, -2], [4, 5]]. | {
"A": "55",
"B": "51",
"C": "63.6",
"D": "53"
} | D | 53 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(5)−(-2)(4)=53. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 53, not 55.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 53, not 51.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 53, not 63.6.",
"D": "Correct. The w... | [
"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_005758 | 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 2.3 atm at 354 K. What is its pressure at 454 K? | {
"A": "-0.05028 atm",
"B": "2.94972 atm",
"C": "4.42458 atm",
"D": "5.94972 atm"
} | B | 2.94972 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.3)(454)/(354)=2.94972 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.94972 atm, not -0.05028 atm.",
"B": "Correct. The worked calculation gives 2.94972 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.94972 atm, not 4.42458 atm.",
"D": "Incorrect. Subst... | [
"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_005848 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.6 atm at 448 K. What is its pressure at 488 K? | {
"A": "0.65357 atm",
"B": "-0.65357 atm",
"C": "1.30714 atm",
"D": "-0.34643 atm"
} | A | 0.65357 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.6)(488)/(448)=0.65357 atm. | {
"A": "Correct. The worked calculation gives 0.65357 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.65357 atm, not -0.65357 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.65357 atm, not 1.30714 atm.",
"D": "Incorrect. Subst... | [
"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_000172 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 +8x -6=0, let its roots be α and β. What is α²+β²? | {
"A": "2.02041",
"B": "6.02041",
"C": "4.02041",
"D": "3.02041"
} | D | 3.02041 | By Vieta's relations, α+β = -8/7 and αβ = -6/7. Then α²+β²=(α+β)²−2αβ = (-8/7)²−2(-6/7) = 3.02041. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.02041, not 2.02041.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.02041, not 6.02041.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.02041, not 4.020... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006032 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 40 cm in front of a thin convex lens of focal length 9 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.02903",
"B": "0.29032",
"C": "0.43548",
"D": "3.29032"
} | B | 0.29032 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(40)(9)/(40−9)=11.6129 cm. Thus |m|=v/u=11.6129/40=0.29032. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29032, not 1.02903.",
"B": "Correct. The worked calculation gives 0.29032.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29032, not 0.43548.",
"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_002862 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-2, -3, -6) and v=(8, -3, 7), calculate u·v. | {
"A": "-47",
"B": "49",
"C": "-49",
"D": "-51"
} | C | -49 | The dot product is the sum of corresponding component products: (-2)(8)+(-3)(-3)+(-6)(7)=-49. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -49, not -47.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -49, not 49.",
"C": "Correct. The worked calculation gives -49.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009175 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.51 V, transfers 1 electrons, and has reaction quotient Q=10^2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.3918 V",
"B": "0.1959 V",
"C": "0.5877 V",
"D": "-0.6082 V"
} | A | 0.3918 V | Apply the Nernst equation: E=0.51−(0.0591/1)(2)=0.3918 V. | {
"A": "Correct. The worked calculation gives 0.3918 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3918 V, not 0.1959 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3918 V, not 0.5877 V.",
"D": "Incorrect. Substituting the stat... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006660 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 2 kg is attached to an ideal spring of force constant 896 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "3.09449 s",
"B": "0.09449 s",
"C": "-2.90551 s",
"D": "1.09449 s"
} | B | 0.09449 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(2/896)=0.09449 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.09449 s, not 3.09449 s.",
"B": "Correct. The worked calculation gives 0.09449 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.09449 s, not -2.90551 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009284 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.79 V, transfers 3 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.51863 V",
"B": "0.34575 V",
"C": "0.6915 V",
"D": "2.6915 V"
} | C | 0.6915 V | Apply the Nernst equation: E=0.79−(0.0591/3)(5)=0.6915 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6915 V, not 0.51863 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6915 V, not 0.34575 V.",
"C": "Correct. The worked calculation gives 0.6915 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_003516 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 108 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "893.51424 m",
"B": "-893.51424 m",
"C": "1340.27136 m",
"D": "90.35142 m"
} | A | 893.51424 m | Range R=u²sin(2θ)/g. Substituting u=108, θ=25° and g=10 gives R=(108)²sin(50°)/10=893.51424 m. | {
"A": "Correct. The worked calculation gives 893.51424 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 893.51424 m, not -893.51424 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 893.51424 m, not 1340.27136 m.",
"D": "Incorrect. Subs... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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