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_002259 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 9 blue and 7 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-2.68831",
"B": "0.31169",
"C": "-0.68831",
"D": "0.23377"
} | B | 0.31169 | Favourable pairs = C(6,2)+C(9,2)+C(7,2)=72. Total pairs=C(22,2)=231. Therefore P=72/231=0.31169. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31169, not -2.68831.",
"B": "Correct. The worked calculation gives 0.31169.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31169, not -0.68831.",
"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_006311 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 38 cm in front of a thin convex lens of focal length 26 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "4.16667",
"B": "1.21667",
"C": "-2.16667",
"D": "2.16667"
} | D | 2.16667 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(38)(26)/(38−26)=82.33333 cm. Thus |m|=v/u=82.33333/38=2.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.16667, not 4.16667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.16667, not 1.21667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.16667, not -2.16... | [
"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_006711 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 5 mol H₂ and 26 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "5 mol",
"B": "1.5 mol",
"C": "4 mol",
"D": "3 mol"
} | A | 5 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 5 mol H₂O; O₂ can produce 52 mol H₂O. The limiting condition is H₂; product=5 mol. | {
"A": "Correct. The worked calculation gives 5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5 mol, not 1.5 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5 mol, not 4 mol.",
"D": "Incorrect. Substituting the stated values int... | [
"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_009725 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(OH)_3]^+2, each OH ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "3.75",
"B": "1.5",
"C": "7.5",
"D": "5"
} | D | 5 | Let the formal oxidation state of Fe be x. Charge balance gives x+(3)(−1)=+2; hence x=2+3=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 1.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.5.",
"D": "Correct. The wo... | [
"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_005277 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +8 μC are separated by 5 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "15.4 N",
"B": "142 N",
"C": "216 N",
"D": "144 N"
} | D | 144 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(8×10⁻⁶)/(5×10⁻²)²=144 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 144 N, not 15.4 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 144 N, not 142 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 144 N, not 216 N.",
"D"... | [
"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_006526 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 8 kg is attached to an ideal spring of force constant 145 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.53022 s",
"B": "1.46978 s",
"C": "2.46978 s",
"D": "0.46978 s"
} | D | 0.46978 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(8/145)=0.46978 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.46978 s, not -1.53022 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.46978 s, not 1.46978 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.46978 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_006156 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 34 cm in front of a thin convex lens of focal length 8 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-2.69231",
"B": "0.30769",
"C": "-1.69231",
"D": "0.23077"
} | B | 0.30769 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(34)(8)/(34−8)=10.46154 cm. Thus |m|=v/u=10.46154/34=0.30769. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not -2.69231.",
"B": "Correct. The worked calculation gives 0.30769.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not -1.69231.",
"D": "Incorrect. Substituting the stated ... | [
"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_009719 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(Cl)_3]^+0, each Cl ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "-3",
"B": "0",
"C": "6",
"D": "3"
} | D | 3 | Let the formal oxidation state of Cr be x. Charge balance gives x+(3)(−1)=+0; hence x=0+3=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not -3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 0.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"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_008402 | 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 0.66 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": "3.64 K",
"B": "4.64 K",
"C": "2.64 K",
"D": "5.64 K"
} | C | 2.64 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×1.0×0.66=2.64 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.64 K, not 3.64 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.64 K, not 4.64 K.",
"C": "Correct. The worked calculation gives 2.64 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_001522 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (-3x² -3x -1) dx. | {
"A": "-421.5",
"B": "-508.2",
"C": "-424.5",
"D": "-423.5"
} | D | -423.5 | An antiderivative is (-3/3)x³+(-3/2)x²+(-1)x. Evaluating between 0 and 7 gives (-3/3)(7)³+(-3/2)(7)²+(-1)(7)=-423.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -423.5, not -421.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -423.5, not -508.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -423.5, not -424.5.",
... | [
"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_006927 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 3 mol H₂ and 11 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "1.5 mol",
"B": "-3 mol",
"C": "6 mol",
"D": "3 mol"
} | D | 3 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 3 mol H₂O; O₂ can produce 22 mol H₂O. The limiting condition is H₂; product=3 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3 mol, not 1.5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3 mol, not -3 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3 mol, not 6 mol.",
"... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004625 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 3 m is acted on by a constant torque of 6 N m about its central axis. Find its angular acceleration. | {
"A": "1.19048 rad s⁻²",
"B": "0.14286 rad s⁻²",
"C": "0.28571 rad s⁻²",
"D": "0.19048 rad s⁻²"
} | D | 0.19048 rad s⁻² | For a solid disc, I=½MR²=½(7)(3)²=31.5 kg m². Using τ=Iα, α=6/31.5=0.19048 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.19048 rad s⁻², not 1.19048 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.19048 rad s⁻², not 0.14286 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing r... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007093 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 9 mol of gas at 517 K and 1.61 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "118.57491 L",
"B": "284.57979 L",
"C": "235.14983 L",
"D": "237.14983 L"
} | D | 237.14983 L | PV=nRT, so V=nRT/P=(9)(0.082057)(517)/(1.61)=237.14983 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 237.14983 L, not 118.57491 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 237.14983 L, not 284.57979 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23... | [
"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_008193 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 5 A for 15994 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": "27.31137 g",
"B": "26.31137 g",
"C": "31.57365 g",
"D": "28.31137 g"
} | B | 26.31137 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×5×15994/(2×96500)=26.31137 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26.31137 g, not 27.31137 g.",
"B": "Correct. The worked calculation gives 26.31137 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26.31137 g, not 31.57365 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_000397 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 2 and common difference 12. Find the sum of its first 33 terms. | {
"A": "6401",
"B": "6402",
"C": "6400",
"D": "-6402"
} | B | 6402 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=2, d=12, n=33: Sₙ=33/2[2(2)+(33−1)(12)]=6402. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6402, not 6401.",
"B": "Correct. The worked calculation gives 6402.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6402, not 6400.",
"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_009781 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(CN)_6]^-4, each CN ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "4",
"B": "-1",
"C": "1.5",
"D": "2"
} | D | 2 | Let the formal oxidation state of Ni be x. Charge balance gives x+(6)(−1)=-4; hence x=-4+6=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not -1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.5.",
"D": "Correct. The worked... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002737 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-3, 7, 6) and v=(7, 0, 4), calculate u·v. | {
"A": "3",
"B": "-3",
"C": "1.3",
"D": "0"
} | A | 3 | The dot product is the sum of corresponding component products: (-3)(7)+(7)(0)+(6)(4)=3. | {
"A": "Correct. The worked calculation gives 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not -3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"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_006221 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 78 cm in front of a thin convex lens of focal length 22 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-1.60714",
"B": "0.39286",
"C": "-0.39286",
"D": "1.03929"
} | B | 0.39286 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(78)(22)/(78−22)=30.64286 cm. Thus |m|=v/u=30.64286/78=0.39286. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.39286, not -1.60714.",
"B": "Correct. The worked calculation gives 0.39286.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.39286, not -0.39286.",
"D": "Incorrect. Substituting the stated ... | [
"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_005303 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +5 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "140.625 N",
"B": "70.3125 N",
"C": "138.625 N",
"D": "139.625 N"
} | A | 140.625 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(5×10⁻⁶)/(4×10⁻²)²=140.625 N. | {
"A": "Correct. The worked calculation gives 140.625 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 140.625 N, not 70.3125 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 140.625 N, not 138.625 N.",
"D": "Incorrect. Substituting 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_005449 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 49 μF capacitor is charged to a potential difference of 8 V. Calculate the energy stored, expressed in μJ. | {
"A": "3136 μJ",
"B": "1254.4 μJ",
"C": "1568 μJ",
"D": "1569 μJ"
} | C | 1568 μJ | U=½CV². Since C=49 μF, U in μJ is ½×49×(8)²=1568 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1568 μJ, not 3136 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1568 μJ, not 1254.4 μJ.",
"C": "Correct. The worked calculation gives 1568 μJ.",
"D": "Incorrect. Substituting the stated ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000795 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio 4. What is the sum of its first 5 terms? | {
"A": "1364",
"B": "1091.2",
"C": "1023",
"D": "1366"
} | A | 1364 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(4^5−1)/(4−1)=1364. | {
"A": "Correct. The worked calculation gives 1364.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1364, not 1091.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1364, not 1023.",
"D": "Incorrect. Substituting the stated values into the... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005974 | 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 1.1 atm at 249 K. What is its pressure at 750 K? | {
"A": "0.31325 atm",
"B": "1.31325 atm",
"C": "6.31325 atm",
"D": "3.31325 atm"
} | D | 3.31325 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.1)(750)/(249)=3.31325 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.31325 atm, not 0.31325 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.31325 atm, not 1.31325 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.... | [
"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_004372 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 2 m is acted on by a constant torque of 37 N m about its central axis. Find its angular acceleration. | {
"A": "4.7 rad s⁻²",
"B": "3.7 rad s⁻²",
"C": "6.7 rad s⁻²",
"D": "0.7 rad s⁻²"
} | B | 3.7 rad s⁻² | For a solid disc, I=½MR²=½(5)(2)²=10 kg m². Using τ=Iα, α=37/10=3.7 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.7 rad s⁻², not 4.7 rad s⁻².",
"B": "Correct. The worked calculation gives 3.7 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.7 rad s⁻², not 6.7 rad s⁻².",
"D": "Incorrect. Substi... | [
"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_007101 | 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 565 K and 2.69 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "101.41012 L",
"B": "124.09215 L",
"C": "102.41012 L",
"D": "103.41012 L"
} | D | 103.41012 L | PV=nRT, so V=nRT/P=(6)(0.082057)(565)/(2.69)=103.41012 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 103.41012 L, not 101.41012 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 103.41012 L, not 124.09215 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10... | [
"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_000176 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +0x -2=0, let its roots be α and β. What is α²+β²? | {
"A": "-0.8",
"B": "1.2",
"C": "0.8",
"D": "-2.2"
} | C | 0.8 | By Vieta's relations, α+β = 0/5 and αβ = -2/5. Then α²+β²=(α+β)²−2αβ = (0/5)²−2(-2/5) = 0.8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8, not -0.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8, not 1.2.",
"C": "Correct. The worked calculation gives 0.8.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_000835 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio 5. What is the sum of its first 6 terms? | {
"A": "35154",
"B": "52731",
"C": "35153",
"D": "26365.5"
} | A | 35154 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(5^6−1)/(5−1)=35154. | {
"A": "Correct. The worked calculation gives 35154.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 35154, not 52731.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 35154, not 35153.",
"D": "Incorrect. Substituting the stated values into ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008668 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.88 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "5.85024 K",
"B": "3.85024 K",
"C": "0.85024 K",
"D": "2.88768 K"
} | B | 3.85024 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.512×1.88=3.85024 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.85024 K, not 5.85024 K.",
"B": "Correct. The worked calculation gives 3.85024 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.85024 K, not 0.85024 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_002961 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-3, 3, 1) and v=(1, -3, 6), calculate u·v. | {
"A": "6",
"B": "-6",
"C": "-4.5",
"D": "-3"
} | B | -6 | The dot product is the sum of corresponding component products: (-3)(1)+(3)(-3)+(1)(6)=-6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -6, not 6.",
"B": "Correct. The worked calculation gives -6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -6, not -4.5.",
"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_009769 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(OH)_6]^+3, each OH ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "6",
"B": "4.5",
"C": "9",
"D": "7"
} | C | 9 | Let the formal oxidation state of Ni be x. Charge balance gives x+(6)(−1)=+3; hence x=3+6=+9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9, not 4.5.",
"C": "Correct. The worked calculation gives 9.",
"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_002534 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 4], [2, 3]]. | {
"A": "1",
"B": "0.75",
"C": "-2",
"D": "4"
} | A | 1 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(3)−(4)(2)=1. | {
"A": "Correct. The worked calculation gives 1.",
"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": "Incorrect. Substituting the stated values into the governing re... | [
"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_009212 | 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 2 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.29385 V",
"B": "0.3918 V",
"C": "1.03918 V",
"D": "3.3918 V"
} | B | 0.3918 V | Apply the Nernst equation: E=0.51−(0.0591/2)(4)=0.3918 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3918 V, not 0.29385 V.",
"B": "Correct. The worked calculation gives 0.3918 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3918 V, not 1.03918 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_006724 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 14 mol H₂ and 16 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "14 mol",
"B": "7 mol",
"C": "13 mol",
"D": "16 mol"
} | A | 14 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 14 mol H₂O; O₂ can produce 32 mol H₂O. The limiting condition is H₂; product=14 mol. | {
"A": "Correct. The worked calculation gives 14 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14 mol, not 7 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14 mol, not 13 mol.",
"D": "Incorrect. Substituting the stated values i... | [
"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_001067 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=0x³ +3x² +0x+7. Evaluate f′(3). | {
"A": "14.4",
"B": "21.6",
"C": "18",
"D": "36"
} | C | 18 | Differentiate: f′(x)=3(0)x²+2(3)x+(0). At x=3, f′(3)=3(0)(3)²+2(3)(3)+(0)=18. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18, not 14.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18, not 21.6.",
"C": "Correct. The worked calculation gives 18.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_005274 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +8 μC are separated by 12 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "20 N",
"B": "25 N",
"C": "-25 N",
"D": "26 N"
} | B | 25 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(8×10⁻⁶)/(12×10⁻²)²=25 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 25 N, not 20 N.",
"B": "Correct. The worked calculation gives 25 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 25 N, not -25 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_004074 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.18. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "82.08 N",
"B": "56.72 N",
"C": "65.664 N",
"D": "54.72 N"
} | D | 54.72 N | Net force=mg(sinθ−μcosθ)=12×10×(0.6−0.18×0.8)=54.72 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 54.72 N, not 82.08 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 54.72 N, not 56.72 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 54.72 N, not 65.66... | [
"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_002244 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 11 red, 12 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.38154",
"B": "2.38154",
"C": "1.03815",
"D": "0.76308"
} | A | 0.38154 | Favourable pairs = C(11,2)+C(12,2)+C(3,2)=124. Total pairs=C(26,2)=325. Therefore P=124/325=0.38154. | {
"A": "Correct. The worked calculation gives 0.38154.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.38154, not 2.38154.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.38154, not 1.03815.",
"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_000693 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio 2. What is the sum of its first 9 terms? | {
"A": "460.9",
"B": "-4599",
"C": "5518.8",
"D": "4599"
} | D | 4599 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(2^9−1)/(2−1)=4599. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4599, not 460.9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4599, not -4599.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4599, not 5518.8.",
"D": "... | [
"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_002433 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -4], [9, 7]]. | {
"A": "53.25",
"B": "71",
"C": "142",
"D": "69"
} | B | 71 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(7)−(-4)(9)=71. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 71, not 53.25.",
"B": "Correct. The worked calculation gives 71.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 71, not 142.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_005168 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +7 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "1.77778 N",
"B": "9.77778 N",
"C": "7.77778 N",
"D": "5.83333 N"
} | C | 7.77778 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(7×10⁻⁶)/(9×10⁻²)²=7.77778 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.77778 N, not 1.77778 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.77778 N, not 9.77778 N.",
"C": "Correct. The worked calculation gives 7.77778 N.",
"D": "Incorrect. Substituting 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_008915 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.24 mol L⁻¹ and initially B is absent. At equilibrium, 56% of A has dissociated at constant volume. Find K_c. | {
"A": "5.30269",
"B": "2.65135",
"C": "3.53513",
"D": "7.07025"
} | C | 3.53513 | Let α=0.56. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.24)(0.56)²/(1−0.56)=3.53513. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.53513, not 5.30269.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.53513, not 2.65135.",
"C": "Correct. The worked calculation gives 3.53513.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001687 | 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 17 distinct elements? | {
"A": "-136",
"B": "108.8",
"C": "136",
"D": "68"
} | C | 136 | Order does not matter, so the count is C(17,2)=17!/[2!(15)!]=136. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 136, not -136.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 136, not 108.8.",
"C": "Correct. The worked calculation gives 136.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_008736 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.9 mol L⁻¹ and initially B is absent. At equilibrium, 56% of A has dissociated at constant volume. Find K_c. | {
"A": "5.56582",
"B": "3.56582",
"C": "2.56582",
"D": "-0.43418"
} | C | 2.56582 | Let α=0.56. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.9)(0.56)²/(1−0.56)=2.56582. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.56582, not 5.56582.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.56582, not 3.56582.",
"C": "Correct. The worked calculation gives 2.56582.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007798 | 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 73 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "1.57031 mmol L⁻¹",
"B": "-0.57031 mmol L⁻¹",
"C": "0.57031 mmol L⁻¹",
"D": "0.42773 mmol L⁻¹"
} | C | 0.57031 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=73/2^7=0.57031 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.57031 mmol L⁻¹, not 1.57031 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.57031 mmol L⁻¹, not -0.57031 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.57031 mmol L⁻¹.",... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008021 | 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 8 A for 26959 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": "141.91888 g",
"B": "70.95944 g",
"C": "35.47972 g",
"D": "53.21958 g"
} | B | 70.95944 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×8×26959/(2×96500)=70.95944 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 70.95944 g, not 141.91888 g.",
"B": "Correct. The worked calculation gives 70.95944 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 70.95944 g, not 35.47972 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009566 | 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_18H_1N_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "18",
"B": "20",
"C": "19",
"D": "22"
} | B | 20 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+3−1−0)/2=20. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20, not 18.",
"B": "Correct. The worked calculation gives 20.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20, not 19.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_004788 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 13 Ω are connected in series; this combination is connected in parallel with a 11 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.77622 A",
"B": "-0.22378 A",
"C": "1.77622 A",
"D": "1.55245 A"
} | A | 0.77622 A | Series branch resistance=13+13=26 Ω. Parallel equivalent R_eq=(26×11)/(26+11)=7.72973 Ω. Total current I=V/R_eq=6/7.72973=0.77622 A. | {
"A": "Correct. The worked calculation gives 0.77622 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.77622 A, not -0.22378 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.77622 A, not 1.77622 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_007089 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 10 mol of gas at 394 K and 2.83 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "114.2419 L",
"B": "137.09028 L",
"C": "91.39352 L",
"D": "85.68143 L"
} | A | 114.2419 L | PV=nRT, so V=nRT/P=(10)(0.082057)(394)/(2.83)=114.2419 L. | {
"A": "Correct. The worked calculation gives 114.2419 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 114.2419 L, not 137.09028 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 114.2419 L, not 91.39352 L.",
"D": "Incorrect. Substituti... | [
"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_006948 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 8 mol H₂ and 30 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "6 mol",
"B": "8 mol",
"C": "12 mol",
"D": "-8 mol"
} | B | 8 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 8 mol H₂O; O₂ can produce 60 mol H₂O. The limiting condition is H₂; product=8 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8 mol, not 6 mol.",
"B": "Correct. The worked calculation gives 8 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8 mol, not 12 mol.",
"D": "Incorrect. Substituting the stated values into... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000582 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 3 and common difference 14. Find the sum of its first 24 terms. | {
"A": "3936",
"B": "3937",
"C": "3935",
"D": "1968"
} | A | 3936 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=3, d=14, n=24: Sₙ=24/2[2(3)+(24−1)(14)]=3936. | {
"A": "Correct. The worked calculation gives 3936.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3936, not 3937.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3936, not 3935.",
"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_007749 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 62 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "5.8125 mmol L⁻¹",
"B": "-7.75 mmol L⁻¹",
"C": "7.75 mmol L⁻¹",
"D": "9.75 mmol L⁻¹"
} | C | 7.75 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=62/2^3=7.75 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.75 mmol L⁻¹, not 5.8125 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.75 mmol L⁻¹, not -7.75 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 7.75 mmol L⁻¹.",
"D": "Inco... | [
"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_005546 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 12 μF capacitor is charged to a potential difference of 2 V. Calculate the energy stored, expressed in μJ. | {
"A": "26 μJ",
"B": "25 μJ",
"C": "-24 μJ",
"D": "24 μJ"
} | D | 24 μJ | U=½CV². Since C=12 μF, U in μJ is ½×12×(2)²=24 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24 μJ, not 26 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24 μJ, not 25 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24 μJ, not -24 μJ.",
"D"... | [
"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_000527 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -16 and common difference 5. Find the sum of its first 30 terms. | {
"A": "847.5",
"B": "1271.25",
"C": "1695",
"D": "1693"
} | C | 1695 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-16, d=5, n=30: Sₙ=30/2[2(-16)+(30−1)(5)]=1695. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1695, not 847.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1695, not 1271.25.",
"C": "Correct. The worked calculation gives 1695.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_002028 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 7 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": "1.32011",
"B": "-0.32011",
"C": "2.32011",
"D": "0.32011"
} | D | 0.32011 | Favourable pairs = C(10,2)+C(7,2)+C(11,2)=121. Total pairs=C(28,2)=378. Therefore P=121/378=0.32011. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32011, not 1.32011.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32011, not -0.32011.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32011, not 2.32... | [
"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_003564 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 111 m s⁻¹ at 20° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "633.58289 m",
"B": "395.98931 m",
"C": "791.97861 m",
"D": "792.97861 m"
} | C | 791.97861 m | Range R=u²sin(2θ)/g. Substituting u=111, θ=20° and g=10 gives R=(111)²sin(40°)/10=791.97861 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 791.97861 m, not 633.58289 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 791.97861 m, not 395.98931 m.",
"C": "Correct. The worked calculation gives 791.97861 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008084 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 13 A for 29674 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": "101.53736 g",
"B": "126.92169 g",
"C": "13.69217 g",
"D": "190.38254 g"
} | B | 126.92169 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×29674/(2×96500)=126.92169 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 126.92169 g, not 101.53736 g.",
"B": "Correct. The worked calculation gives 126.92169 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 126.92169 g, not 13.69217 g.",
"D": "Incorrect. Substit... | [
"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_006460 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 4 kg is attached to an ideal spring of force constant 642 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.15787 s",
"B": "-2.84213 s",
"C": "2.15787 s",
"D": "1.01579 s"
} | A | 0.15787 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(4/642)=0.15787 s. | {
"A": "Correct. The worked calculation gives 0.15787 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.15787 s, not -2.84213 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.15787 s, not 2.15787 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_002347 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, -2], [1, -8]]. | {
"A": "-16",
"B": "-10.5",
"C": "-14",
"D": "-12"
} | C | -14 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(-8)−(-2)(1)=-14. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -14, not -16.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -14, not -10.5.",
"C": "Correct. The worked calculation gives -14.",
"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_001549 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (6x² -7x +0) dx. | {
"A": "74",
"B": "8.2",
"C": "72",
"D": "54"
} | C | 72 | An antiderivative is (6/3)x³+(-7/2)x²+(0)x. Evaluating between 0 and 4 gives (6/3)(4)³+(-7/2)(4)²+(0)(4)=72. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 72, not 74.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 72, not 8.2.",
"C": "Correct. The worked calculation gives 72.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004554 | 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 81 N m about its central axis. Find its angular acceleration. | {
"A": "21.6 rad s⁻²",
"B": "18 rad s⁻²",
"C": "16 rad s⁻²",
"D": "17 rad s⁻²"
} | B | 18 rad s⁻² | For a solid disc, I=½MR²=½(9)(1)²=4.5 kg m². Using τ=Iα, α=81/4.5=18 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18 rad s⁻², not 21.6 rad s⁻².",
"B": "Correct. The worked calculation gives 18 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18 rad s⁻², not 16 rad s⁻².",
"D": "Incorrect. Substitut... | [
"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_007830 | 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 24 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "1.3 mmol L⁻¹",
"B": "1 mmol L⁻¹",
"C": "3 mmol L⁻¹",
"D": "2.25 mmol L⁻¹"
} | C | 3 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=24/2^3=3 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3 mmol L⁻¹, not 1.3 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3 mmol L⁻¹, not 1 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 3 mmol L⁻¹.",
"D": "Incorrect. Substitut... | [
"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_000211 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 +10x +5=0, let its roots be α and β. What is α²+β²? | {
"A": "3.75",
"B": "2.8125",
"C": "4.75",
"D": "0.75"
} | A | 3.75 | By Vieta's relations, α+β = -10/4 and αβ = 5/4. Then α²+β²=(α+β)²−2αβ = (-10/4)²−2(5/4) = 3.75. | {
"A": "Correct. The worked calculation gives 3.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.75, not 2.8125.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.75, not 4.75.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_000816 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 12 and common ratio 2. What is the sum of its first 10 terms? | {
"A": "-12276",
"B": "9207",
"C": "12276",
"D": "12277"
} | C | 12276 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=12(2^10−1)/(2−1)=12276. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12276, not -12276.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12276, not 9207.",
"C": "Correct. The worked calculation gives 12276.",
"D": "Incorrect. Substituting the stated values into ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008094 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 2 A for 24846 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": "13.07955 g",
"B": "14.34944 g",
"C": "16.34944 g",
"D": "17.34944 g"
} | C | 16.34944 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×2×24846/(2×96500)=16.34944 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16.34944 g, not 13.07955 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16.34944 g, not 14.34944 g.",
"C": "Correct. The worked calculation gives 16.34944 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_008774 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.18 mol L⁻¹ and initially B is absent. At equilibrium, 22% of A has dissociated at constant volume. Find K_c. | {
"A": "2.04468",
"B": "-1.95532",
"C": "0.04468",
"D": "0.06702"
} | C | 0.04468 | Let α=0.22. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.18)(0.22)²/(1−0.22)=0.04468. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.04468, not 2.04468.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.04468, not -1.95532.",
"C": "Correct. The worked calculation gives 0.04468.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007219 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 12 mol of gas at 408 K and 1.65 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "486.971 L",
"B": "244.4855 L",
"C": "245.4855 L",
"D": "243.4855 L"
} | D | 243.4855 L | PV=nRT, so V=nRT/P=(12)(0.082057)(408)/(1.65)=243.4855 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 243.4855 L, not 486.971 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 243.4855 L, not 244.4855 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 243.485... | [
"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_009233 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.91 V, transfers 2 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.07918 V",
"B": "-0.2082 V",
"C": "0.7918 V",
"D": "0.3959 V"
} | C | 0.7918 V | Apply the Nernst equation: E=0.91−(0.0591/2)(4)=0.7918 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7918 V, not 1.07918 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7918 V, not -0.2082 V.",
"C": "Correct. The worked calculation gives 0.7918 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_005139 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +3 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "162 N",
"B": "135 N",
"C": "67.5 N",
"D": "202.5 N"
} | B | 135 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(3×10⁻⁶)/(2×10⁻²)²=135 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 135 N, not 162 N.",
"B": "Correct. The worked calculation gives 135 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 135 N, not 67.5 N.",
"D": "Incorrect. Substituting the stated values into... | [
"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_001179 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=7x³ -5x² -9x+7. Evaluate f′(-4). | {
"A": "183.5",
"B": "37.7",
"C": "734",
"D": "367"
} | D | 367 | Differentiate: f′(x)=3(7)x²+2(-5)x+(-9). At x=-4, f′(-4)=3(7)(-4)²+2(-5)(-4)+(-9)=367. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 367, not 183.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 367, not 37.7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 367, not 734.",
"D": "Correct... | [
"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_006604 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 21 kg is attached to an ideal spring of force constant 1082 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.27863 s",
"B": "3.27863 s",
"C": "1.27863 s",
"D": "0.20897 s"
} | A | 0.27863 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(21/1082)=0.27863 s. | {
"A": "Correct. The worked calculation gives 0.27863 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.27863 s, not 3.27863 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.27863 s, not 1.27863 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002790 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-1, 9, -7) and v=(5, 8, 7), calculate u·v. | {
"A": "2.8",
"B": "13.5",
"C": "18",
"D": "9"
} | C | 18 | The dot product is the sum of corresponding component products: (-1)(5)+(9)(8)+(-7)(7)=18. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18, not 2.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18, not 13.5.",
"C": "Correct. The worked calculation gives 18.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_008323 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 5 A for 12796 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": "25.2605 g",
"B": "15.78781 g",
"C": "21.05041 g",
"D": "10.52521 g"
} | C | 21.05041 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×5×12796/(2×96500)=21.05041 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21.05041 g, not 25.2605 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21.05041 g, not 15.78781 g.",
"C": "Correct. The worked calculation gives 21.05041 g.",
"D": "Incorrect. Substituting... | [
"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_006208 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 33 cm in front of a thin convex lens of focal length 9 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.375",
"B": "1.375",
"C": "-0.625",
"D": "0.75"
} | A | 0.375 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(33)(9)/(33−9)=12.375 cm. Thus |m|=v/u=12.375/33=0.375. | {
"A": "Correct. The worked calculation gives 0.375.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.375, not 1.375.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.375, not -0.625.",
"D": "Incorrect. Substituting the stated values into... | [
"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_003966 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 9 m s⁻¹. A constant net force does 13 N of work over 2 m in the direction of motion. Find its final kinetic energy. | {
"A": "-512 J",
"B": "768 J",
"C": "1024 J",
"D": "512 J"
} | D | 512 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(9)²+(13)(2)=512 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 512 J, not -512 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 512 J, not 768 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 512 J, not 1024 J.",
"D... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000774 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio 5. What is the sum of its first 5 terms? | {
"A": "4686",
"B": "6247",
"C": "6249",
"D": "6248"
} | D | 6248 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(5^5−1)/(5−1)=6248. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6248, not 4686.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6248, not 6247.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6248, not 6249.",
"D": "Corr... | [
"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_009603 | 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_12H_21X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "2",
"B": "0",
"C": "1",
"D": "1.5"
} | C | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×12+2+0−21−3)/2=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.",
"C": "Correct. The worked calculation gives 1.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009807 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(OH)_4]^+0, each OH ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "7",
"B": "3",
"C": "-4",
"D": "4"
} | D | 4 | Let the formal oxidation state of Mn 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 7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 3.",
"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_005310 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +7 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "1.98438 N",
"B": "-9.84375 N",
"C": "6.84375 N",
"D": "9.84375 N"
} | D | 9.84375 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(7×10⁻⁶)/(8×10⁻²)²=9.84375 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.84375 N, not 1.98438 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.84375 N, not -9.84375 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.84375 N... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005298 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +4 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "14.4 N",
"B": "16.4 N",
"C": "21.6 N",
"D": "28.8 N"
} | A | 14.4 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(4×10⁻⁶)/(10×10⁻²)²=14.4 N. | {
"A": "Correct. The worked calculation gives 14.4 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14.4 N, not 16.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14.4 N, not 21.6 N.",
"D": "Incorrect. Substituting the stated values ... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001528 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (4x² +4x +0) dx. | {
"A": "1.33333",
"B": "3.33333",
"C": "2.33333",
"D": "6.66667"
} | B | 3.33333 | An antiderivative is (4/3)x³+(4/2)x²+(0)x. Evaluating between 0 and 1 gives (4/3)(1)³+(4/2)(1)²+(0)(1)=3.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.33333, not 1.33333.",
"B": "Correct. The worked calculation gives 3.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.33333, not 2.33333.",
"D": "Incorrect. Substituting the stated va... | [
"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_008568 | 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 0.6 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-1.6928 K",
"B": "-2.6928 K",
"C": "0.3072 K",
"D": "0.1536 K"
} | C | 0.3072 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.512×0.6=0.3072 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3072 K, not -1.6928 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3072 K, not -2.6928 K.",
"C": "Correct. The worked calculation gives 0.3072 K.",
"D": "Incorrect. Substituting the st... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004192 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 17 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.31. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "61.84 N",
"B": "60.84 N",
"C": "59.84 N",
"D": "119.68 N"
} | C | 59.84 N | Net force=mg(sinθ−μcosθ)=17×10×(0.6−0.31×0.8)=59.84 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 59.84 N, not 61.84 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 59.84 N, not 60.84 N.",
"C": "Correct. The worked calculation gives 59.84 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001683 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 3 elements can be selected from a set of 18 distinct elements? | {
"A": "-816",
"B": "1224",
"C": "816",
"D": "814"
} | C | 816 | Order does not matter, so the count is C(18,3)=18!/[3!(15)!]=816. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 816, not -816.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 816, not 1224.",
"C": "Correct. The worked calculation gives 816.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009549 | 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_12H_23N_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "-1",
"B": "3",
"C": "5",
"D": "2"
} | D | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×12+2+1−23−0)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not -1.",
"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 5.",
"D": "Correct. The worked c... | [
"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_004700 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 11 Ω are connected in series; this combination is connected in parallel with a 13 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.77733 A",
"B": "0.583 A",
"C": "1.55466 A",
"D": "1.16599 A"
} | A | 0.77733 A | Series branch resistance=8+11=19 Ω. Parallel equivalent R_eq=(19×13)/(19+13)=7.71875 Ω. Total current I=V/R_eq=6/7.71875=0.77733 A. | {
"A": "Correct. The worked calculation gives 0.77733 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.77733 A, not 0.583 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.77733 A, not 1.55466 A.",
"D": "Incorrect. Substituting the s... | [
"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_000349 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -13 and common difference 10. Find the sum of its first 22 terms. | {
"A": "203.4",
"B": "2024",
"C": "1518",
"D": "2022"
} | B | 2024 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-13, d=10, n=22: Sₙ=22/2[2(-13)+(22−1)(10)]=2024. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2024, not 203.4.",
"B": "Correct. The worked calculation gives 2024.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2024, not 1518.",
"D": "Incorrect. Substituting the stated values into the ... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005158 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +4 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "8.25 N",
"B": "5.625 N",
"C": "14.25 N",
"D": "11.25 N"
} | D | 11.25 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(4×10⁻⁶)/(8×10⁻²)²=11.25 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.25 N, not 8.25 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.25 N, not 5.625 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.25 N, not 14.25 ... | [
"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_007267 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 19 mol of gas at 596 K and 0.33 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "2815.79839 L",
"B": "2111.84879 L",
"C": "2252.63871 L",
"D": "282.57984 L"
} | A | 2815.79839 L | PV=nRT, so V=nRT/P=(19)(0.082057)(596)/(0.33)=2815.79839 L. | {
"A": "Correct. The worked calculation gives 2815.79839 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2815.79839 L, not 2111.84879 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2815.79839 L, not 2252.63871 L.",
"D": "Incorrect. S... | [
"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_001763 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 4 elements can be selected from a set of 83 distinct elements? | {
"A": "3675240",
"B": "1837620",
"C": "1378215",
"D": "183763"
} | B | 1837620 | Order does not matter, so the count is C(83,4)=83!/[4!(79)!]=1837620. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1837620, not 3675240.",
"B": "Correct. The worked calculation gives 1837620.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1837620, not 1378215.",
"D": "Incorrect. Substituting the stated va... | [
"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_007801 | 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 38 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "1.1875 mmol L⁻¹",
"B": "1.11875 mmol L⁻¹",
"C": "0.89062 mmol L⁻¹",
"D": "2.1875 mmol L⁻¹"
} | A | 1.1875 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=38/2^5=1.1875 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 1.1875 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1875 mmol L⁻¹, not 1.11875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1875 mmol L⁻¹, not 0.89062 mmol L⁻¹.",
"... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000033 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 -2x +11=0, let its roots be α and β. What is α²+β²? | {
"A": "-2.24",
"B": "-1.24",
"C": "-8.48",
"D": "-4.24"
} | D | -4.24 | By Vieta's relations, α+β = 2/5 and αβ = 11/5. Then α²+β²=(α+β)²−2αβ = (2/5)²−2(11/5) = -4.24. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4.24, not -2.24.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -4.24, not -1.24.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -4.24, not -8.48.",
"D":... | [
"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_007724 | 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 89 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "-1.60938 mmol L⁻¹",
"B": "0.39062 mmol L⁻¹",
"C": "1.39062 mmol L⁻¹",
"D": "-1.39062 mmol L⁻¹"
} | C | 1.39062 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=89/2^6=1.39062 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.39062 mmol L⁻¹, not -1.60938 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.39062 mmol L⁻¹, not 0.39062 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 1.39062 mmol L⁻¹.",... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002303 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 9 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.35263",
"B": "0.70526",
"C": "0.35263",
"D": "-1.64737"
} | C | 0.35263 | Favourable pairs = C(8,2)+C(9,2)+C(3,2)=67. Total pairs=C(20,2)=190. Therefore P=67/190=0.35263. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35263, not 1.35263.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35263, not 0.70526.",
"C": "Correct. The worked calculation gives 0.35263.",
"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_000198 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -5x +1=0, let its roots be α and β. What is α²+β²? | {
"A": "1.525",
"B": "6.25",
"C": "5.25",
"D": "3.9375"
} | C | 5.25 | By Vieta's relations, α+β = 5/2 and αβ = 1/2. Then α²+β²=(α+β)²−2αβ = (5/2)²−2(1/2) = 5.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.25, not 1.525.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.25, not 6.25.",
"C": "Correct. The worked calculation gives 5.25.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_006223 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 147 cm in front of a thin convex lens of focal length 30 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.38462",
"B": "0.25641",
"C": "0.12821",
"D": "1.25641"
} | B | 0.25641 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(147)(30)/(147−30)=37.69231 cm. Thus |m|=v/u=37.69231/147=0.25641. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25641, not 0.38462.",
"B": "Correct. The worked calculation gives 0.25641.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25641, not 0.12821.",
"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_003815 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 0 m s⁻¹. A constant net force does 23 N of work over 17 m in the direction of motion. Find its final kinetic energy. | {
"A": "391 J",
"B": "782 J",
"C": "586.5 J",
"D": "293.25 J"
} | A | 391 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(0)²+(23)(17)=391 J. | {
"A": "Correct. The worked calculation gives 391 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 391 J, not 782 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 391 J, not 586.5 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_009737 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(Cl)_6]^-1, each Cl ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "3",
"B": "7",
"C": "1.5",
"D": "5"
} | D | 5 | Let the formal oxidation state of Cu be x. Charge balance gives x+(6)(−1)=-1; hence x=-1+6=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 1.5.",
"D": "Correct. The worked ... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000476 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -8 and common difference 9. Find the sum of its first 13 terms. | {
"A": "299",
"B": "597",
"C": "897",
"D": "598"
} | D | 598 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-8, d=9, n=13: Sₙ=13/2[2(-8)+(13−1)(9)]=598. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 598, not 299.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 598, not 597.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 598, not 897.",
"D": "Correct. T... | [
"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_002569 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 0], [4, 2]]. | {
"A": "1.8",
"B": "8",
"C": "12",
"D": "-8"
} | B | 8 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(2)−(0)(4)=8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 1.8.",
"B": "Correct. The worked calculation gives 8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 12.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"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_000468 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 2 and common difference 13. Find the sum of its first 21 terms. | {
"A": "2217.6",
"B": "2772",
"C": "1386",
"D": "2079"
} | B | 2772 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=2, d=13, n=21: Sₙ=21/2[2(2)+(21−1)(13)]=2772. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2772, not 2217.6.",
"B": "Correct. The worked calculation gives 2772.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2772, not 1386.",
"D": "Incorrect. Substituting the stated values into the... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000721 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 3 and common ratio -2. What is the sum of its first 8 terms? | {
"A": "-253",
"B": "-382.5",
"C": "-255",
"D": "-191.25"
} | C | -255 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=3(-2^8−1)/(-2−1)=-255. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -255, not -253.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -255, not -382.5.",
"C": "Correct. The worked calculation gives -255.",
"D": "Incorrect. Substituting the stated values into the... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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