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_008703 | 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 0.03 mol L⁻¹ and initially B is absent. At equilibrium, 61% of A has dissociated at constant volume. Find K_c. | {
"A": "0.11449",
"B": "1.01145",
"C": "2.11449",
"D": "0.22898"
} | A | 0.11449 | Let α=0.61. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.03)(0.61)²/(1−0.61)=0.11449. | {
"A": "Correct. The worked calculation gives 0.11449.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.11449, not 1.01145.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.11449, not 2.11449.",
"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_007464 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 96 mL of 0.10 M HCl is mixed with 43 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-0.58126",
"B": "1.14187",
"C": "1.41874",
"D": "3.41874"
} | C | 1.41874 | Excess H⁺ moles=0.10×(96−43)/1000=0.005300 mol. Total volume=0.139 L, so [H⁺]=0.038129 M and pH=−log₁₀[H⁺]=1.41874. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.41874, not -0.58126.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.41874, not 1.14187.",
"C": "Correct. The worked calculation gives 1.41874.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006492 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 22 kg is attached to an ideal spring of force constant 887 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.31498 s",
"B": "0.31498 s",
"C": "-1.68502 s",
"D": "-2.68502 s"
} | B | 0.31498 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(22/887)=0.31498 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31498 s, not 1.31498 s.",
"B": "Correct. The worked calculation gives 0.31498 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31498 s, not -1.68502 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_004512 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 6 m is acted on by a constant torque of 15 N m about its central axis. Find its angular acceleration. | {
"A": "1.16667 rad s⁻²",
"B": "3.16667 rad s⁻²",
"C": "0.25 rad s⁻²",
"D": "0.16667 rad s⁻²"
} | D | 0.16667 rad s⁻² | For a solid disc, I=½MR²=½(5)(6)²=90 kg m². Using τ=Iα, α=15/90=0.16667 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.16667 rad s⁻², not 1.16667 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.16667 rad s⁻², not 3.16667 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_005229 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +3 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "4.05 N",
"B": "6.075 N",
"C": "8.1 N",
"D": "9.1 N"
} | C | 8.1 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(3×10⁻⁶)/(10×10⁻²)²=8.1 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.1 N, not 4.05 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.1 N, not 6.075 N.",
"C": "Correct. The worked calculation gives 8.1 N.",
"D": "Incorrect. Substituting the stated values in... | [
"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_002410 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, 3], [3, 8]]. | {
"A": "-0.75",
"B": "-2",
"C": "-1",
"D": "1"
} | C | -1 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(8)−(3)(3)=-1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1, not -0.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1, not -2.",
"C": "Correct. The worked calculation gives -1.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_004507 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 4 m is acted on by a constant torque of 16 N m about its central axis. Find its angular acceleration. | {
"A": "1.5 rad s⁻²",
"B": "1 rad s⁻²",
"C": "4 rad s⁻²",
"D": "0 rad s⁻²"
} | B | 1 rad s⁻² | For a solid disc, I=½MR²=½(2)(4)²=16 kg m². Using τ=Iα, α=16/16=1 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1 rad s⁻², not 1.5 rad s⁻².",
"B": "Correct. The worked calculation gives 1 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1 rad s⁻², not 4 rad s⁻².",
"D": "Incorrect. Substituting t... | [
"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_008302 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 10 A for 16516 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": "40.75516 g",
"B": "54.34021 g",
"C": "43.47217 g",
"D": "6.43402 g"
} | B | 54.34021 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×10×16516/(2×96500)=54.34021 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 54.34021 g, not 40.75516 g.",
"B": "Correct. The worked calculation gives 54.34021 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 54.34021 g, not 43.47217 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_006877 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 34 mol H₂ and 5 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "10 mol",
"B": "-10 mol",
"C": "12 mol",
"D": "7 mol"
} | A | 10 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 34 mol H₂O; O₂ can produce 10 mol H₂O. The limiting condition is O₂; product=10 mol. | {
"A": "Correct. The worked calculation gives 10 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not -10 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 12 mol.",
"D": "Incorrect. Substituting the stated values... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008617 | 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 0.48 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": "-0.98304 K",
"B": "0.98304 K",
"C": "1.47456 K",
"D": "-2.01696 K"
} | B | 0.98304 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.512×0.48=0.98304 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.98304 K, not -0.98304 K.",
"B": "Correct. The worked calculation gives 0.98304 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.98304 K, not 1.47456 K.",
"D": "Incorrect. Substituting th... | [
"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_003754 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 8 m s⁻¹. A constant net force does 21 N of work over 6 m in the direction of motion. Find its final kinetic energy. | {
"A": "39.2 J",
"B": "286.5 J",
"C": "573 J",
"D": "382 J"
} | D | 382 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(8)²+(21)(6)=382 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 382 J, not 39.2 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 382 J, not 286.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 382 J, not 573 J.",
"... | [
"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_000821 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio 4. What is the sum of its first 12 terms? | {
"A": "44739242",
"B": "44739238",
"C": "44739240",
"D": "-44739240"
} | C | 44739240 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(4^12−1)/(4−1)=44739240. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 44739240, not 44739242.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 44739240, not 44739238.",
"C": "Correct. The worked calculation gives 44739240.",
"D": "Incorrect. Substituting the stat... | [
"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_000483 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 7 and common difference 8. Find the sum of its first 10 terms. | {
"A": "-430",
"B": "430",
"C": "429",
"D": "431"
} | B | 430 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=7, d=8, n=10: Sₙ=10/2[2(7)+(10−1)(8)]=430. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 430, not -430.",
"B": "Correct. The worked calculation gives 430.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 430, not 429.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_007087 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 2 mol of gas at 321 K and 0.44 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "119.72862 L",
"B": "59.86431 L",
"C": "239.45725 L",
"D": "121.72862 L"
} | A | 119.72862 L | PV=nRT, so V=nRT/P=(2)(0.082057)(321)/(0.44)=119.72862 L. | {
"A": "Correct. The worked calculation gives 119.72862 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 119.72862 L, not 59.86431 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 119.72862 L, not 239.45725 L.",
"D": "Incorrect. Substit... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002584 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, 4], [8, -4]]. | {
"A": "-5.8",
"B": "-54.4",
"C": "-68",
"D": "-81.6"
} | C | -68 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(-4)−(4)(8)=-68. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -68, not -5.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -68, not -54.4.",
"C": "Correct. The worked calculation gives -68.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_007880 | 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 93 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "2.8125 mmol L⁻¹",
"B": "5.8125 mmol L⁻¹",
"C": "6.8125 mmol L⁻¹",
"D": "1.58125 mmol L⁻¹"
} | B | 5.8125 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=93/2^4=5.8125 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.8125 mmol L⁻¹, not 2.8125 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 5.8125 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.8125 mmol L⁻¹, not 6.8125 mmol L⁻¹.",
"D"... | [
"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_002049 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 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": "0.48966",
"B": "0.32644",
"C": "0.16322",
"D": "-0.32644"
} | B | 0.32644 | Favourable pairs = C(12,2)+C(7,2)+C(11,2)=142. Total pairs=C(30,2)=435. Therefore P=142/435=0.32644. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32644, not 0.48966.",
"B": "Correct. The worked calculation gives 0.32644.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32644, not 0.16322.",
"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_001803 | 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 58 distinct elements? | {
"A": "61712",
"B": "30855",
"C": "30856",
"D": "23142"
} | C | 30856 | Order does not matter, so the count is C(58,3)=58!/[3!(55)!]=30856. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 30856, not 61712.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30856, not 30855.",
"C": "Correct. The worked calculation gives 30856.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_007301 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 13 mol of gas at 604 K and 1.58 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "-407.79213 L",
"B": "407.79213 L",
"C": "405.79213 L",
"D": "305.8441 L"
} | B | 407.79213 L | PV=nRT, so V=nRT/P=(13)(0.082057)(604)/(1.58)=407.79213 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 407.79213 L, not -407.79213 L.",
"B": "Correct. The worked calculation gives 407.79213 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 407.79213 L, not 405.79213 L.",
"D": "Incorrect. Subst... | [
"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_009043 | 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 1 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.6736 V",
"B": "1.3472 V",
"C": "0.3368 V",
"D": "0.5052 V"
} | A | 0.6736 V | Apply the Nernst equation: E=0.91−(0.0591/1)(4)=0.6736 V. | {
"A": "Correct. The worked calculation gives 0.6736 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6736 V, not 1.3472 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.6736 V, not 0.3368 V.",
"D": "Incorrect. Substituting the stat... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007085 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 17 mol of gas at 385 K and 0.93 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "-577.48717 L",
"B": "288.74358 L",
"C": "461.98973 L",
"D": "577.48717 L"
} | D | 577.48717 L | PV=nRT, so V=nRT/P=(17)(0.082057)(385)/(0.93)=577.48717 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 577.48717 L, not -577.48717 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 577.48717 L, not 288.74358 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5... | [
"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_006027 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 27 cm in front of a thin convex lens of focal length 15 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "4.25",
"B": "1.125",
"C": "2.5",
"D": "1.25"
} | D | 1.25 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(27)(15)/(27−15)=33.75 cm. Thus |m|=v/u=33.75/27=1.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.25, not 4.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.25, not 1.125.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.25, not 2.5.",
"D": "Corr... | [
"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_005792 | 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 3.2 atm at 412 K. What is its pressure at 586 K? | {
"A": "7.55146 atm",
"B": "4.55146 atm",
"C": "3.41359 atm",
"D": "6.55146 atm"
} | B | 4.55146 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.2)(586)/(412)=4.55146 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.55146 atm, not 7.55146 atm.",
"B": "Correct. The worked calculation gives 4.55146 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.55146 atm, not 3.41359 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001547 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (0x² -8x +0) dx. | {
"A": "-19.2",
"B": "-12",
"C": "-0.6",
"D": "-16"
} | D | -16 | An antiderivative is (0/3)x³+(-8/2)x²+(0)x. Evaluating between 0 and 2 gives (0/3)(2)³+(-8/2)(2)²+(0)(2)=-16. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -16, not -19.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -16, not -12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -16, not -0.6.",
"D": "Correct... | [
"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_009344 | 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_36N_3X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "-2",
"B": "1",
"C": "4",
"D": "3"
} | B | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+3−36−3)/2=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not -2.",
"B": "Correct. The worked calculation gives 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 4.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009513 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_5H_3N_2X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "4",
"B": "-4",
"C": "1",
"D": "1.4"
} | A | 4 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×5+2+2−3−3)/2=4. | {
"A": "Correct. The worked calculation gives 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not -4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000261 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 -7x +3=0, let its roots be α and β. What is α²+β²? | {
"A": "4.5625",
"B": "1.5625",
"C": "3.125",
"D": "-1.5625"
} | B | 1.5625 | By Vieta's relations, α+β = 7/4 and αβ = 3/4. Then α²+β²=(α+β)²−2αβ = (7/4)²−2(3/4) = 1.5625. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.5625, not 4.5625.",
"B": "Correct. The worked calculation gives 1.5625.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.5625, not 3.125.",
"D": "Incorrect. Substituting the stated values i... | [
"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_002574 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -8], [8, -1]]. | {
"A": "47.2",
"B": "70.8",
"C": "59",
"D": "60"
} | C | 59 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(-1)−(-8)(8)=59. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 59, not 47.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 59, not 70.8.",
"C": "Correct. The worked calculation gives 59.",
"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_007528 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 43 mL of 0.10 M HCl is mixed with 75 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "14.43327",
"B": "12.43327",
"C": "24.86654",
"D": "18.6499"
} | B | 12.43327 | Excess OH⁻ moles=0.10×(75−43)/1000=0.003200 mol. Total volume=0.118 L, so [OH⁻]=0.027119 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.43327. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.43327, not 14.43327.",
"B": "Correct. The worked calculation gives 12.43327.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.43327, not 24.86654.",
"D": "Incorrect. Substituting the stat... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009403 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_3H_4N_3X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "-3",
"C": "1",
"D": "0"
} | A | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×3+2+3−4−1)/2=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.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005030 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +7 μC are separated by 12 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "8.75 N",
"B": "17.5 N",
"C": "15.5 N",
"D": "13.125 N"
} | B | 17.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(7×10⁻⁶)/(12×10⁻²)²=17.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 17.5 N, not 8.75 N.",
"B": "Correct. The worked calculation gives 17.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17.5 N, not 15.5 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_005405 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 42 μF capacitor is charged to a potential difference of 17 V. Calculate the energy stored, expressed in μJ. | {
"A": "4551.75 μJ",
"B": "-6069 μJ",
"C": "6069 μJ",
"D": "7282.8 μJ"
} | C | 6069 μJ | U=½CV². Since C=42 μF, U in μJ is ½×42×(17)²=6069 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6069 μJ, not 4551.75 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6069 μJ, not -6069 μJ.",
"C": "Correct. The worked calculation gives 6069 μJ.",
"D": "Incorrect. Substituting the state... | [
"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_000023 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -17x -9=0, let its roots be α and β. What is α²+β²? | {
"A": "-81.25",
"B": "40.625",
"C": "79.25",
"D": "81.25"
} | D | 81.25 | By Vieta's relations, α+β = 17/2 and αβ = -9/2. Then α²+β²=(α+β)²−2αβ = (17/2)²−2(-9/2) = 81.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 81.25, not -81.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 81.25, not 40.625.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 81.25, not 79.25.",
"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_000304 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +17x -9=0, let its roots be α and β. What is α²+β²? | {
"A": "13.16",
"B": "12.128",
"C": "-15.16",
"D": "15.16"
} | D | 15.16 | By Vieta's relations, α+β = -17/5 and αβ = -9/5. Then α²+β²=(α+β)²−2αβ = (-17/5)²−2(-9/5) = 15.16. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15.16, not 13.16.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15.16, not 12.128.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15.16, not -15.16.",
"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_001308 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ -5x² +5x+7. Evaluate f′(5). | {
"A": "165",
"B": "332",
"C": "330",
"D": "331"
} | C | 330 | Differentiate: f′(x)=3(5)x²+2(-5)x+(5). At x=5, f′(5)=3(5)(5)²+2(-5)(5)+(5)=330. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 330, not 165.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 330, not 332.",
"C": "Correct. The worked calculation gives 330.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_004498 | 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 58 N m about its central axis. Find its angular acceleration. | {
"A": "10.88889 rad s⁻²",
"B": "13.88889 rad s⁻²",
"C": "-12.88889 rad s⁻²",
"D": "12.88889 rad s⁻²"
} | D | 12.88889 rad s⁻² | For a solid disc, I=½MR²=½(9)(1)²=4.5 kg m². Using τ=Iα, α=58/4.5=12.88889 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.88889 rad s⁻², not 10.88889 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.88889 rad s⁻², not 13.88889 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governi... | [
"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_001955 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 27 distinct elements? | {
"A": "2220075",
"B": "222008.5",
"C": "1665056.25",
"D": "2220076"
} | A | 2220075 | Order does not matter, so the count is C(27,8)=27!/[8!(19)!]=2220075. | {
"A": "Correct. The worked calculation gives 2220075.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2220075, not 222008.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2220075, not 1665056.25.",
"D": "Incorrect. Substituting the state... | [
"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_001625 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (-4x² +0x +2) dx. | {
"A": "-9.66667",
"B": "-6.66667",
"C": "-10",
"D": "-5"
} | B | -6.66667 | An antiderivative is (-4/3)x³+(0/2)x²+(2)x. Evaluating between 0 and 2 gives (-4/3)(2)³+(0/2)(2)²+(2)(2)=-6.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -6.66667, not -9.66667.",
"B": "Correct. The worked calculation gives -6.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -6.66667, not -10.",
"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_006294 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 26 cm in front of a thin convex lens of focal length 18 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "2.25",
"B": "4.25",
"C": "1.6875",
"D": "3.25"
} | A | 2.25 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(26)(18)/(26−18)=58.5 cm. Thus |m|=v/u=58.5/26=2.25. | {
"A": "Correct. The worked calculation gives 2.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.25, not 4.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.25, not 1.6875.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_001626 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (-3x² -4x +2) dx. | {
"A": "-163",
"B": "-165",
"C": "-198",
"D": "-82.5"
} | B | -165 | An antiderivative is (-3/3)x³+(-4/2)x²+(2)x. Evaluating between 0 and 5 gives (-3/3)(5)³+(-4/2)(5)²+(2)(5)=-165. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -165, not -163.",
"B": "Correct. The worked calculation gives -165.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -165, not -198.",
"D": "Incorrect. Substituting the stated values into the g... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007258 | 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 353 K and 2.04 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "106.49309 L",
"B": "113.59263 L",
"C": "141.99079 L",
"D": "70.99539 L"
} | C | 141.99079 L | PV=nRT, so V=nRT/P=(10)(0.082057)(353)/(2.04)=141.99079 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 141.99079 L, not 106.49309 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 141.99079 L, not 113.59263 L.",
"C": "Correct. The worked calculation gives 141.99079 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003941 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 7 m s⁻¹. A constant net force does 11 N of work over 17 m in the direction of motion. Find its final kinetic energy. | {
"A": "405.5 J",
"B": "406.5 J",
"C": "408.5 J",
"D": "407.5 J"
} | D | 407.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(7)²+(11)(17)=407.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 407.5 J, not 405.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 407.5 J, not 406.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 407.5 J, not 408.5... | [
"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_003064 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-10-1i)/(7+7i). What is Re(z), the real part of z? | {
"A": "1.21429",
"B": "-1.17857",
"C": "-1.78571",
"D": "-0.78571"
} | D | -0.78571 | Multiply numerator and denominator by the conjugate (7-7i). Then Re(z)=(ac+bd)/(c²+d²)=((-10)(7)+(-1)(7))/(7²+(7)²)=-0.78571. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.78571, not 1.21429.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.78571, not -1.17857.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.78571, not -... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002001 | 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 62 distinct elements? | {
"A": "56730",
"B": "37820",
"C": "37819",
"D": "28365"
} | B | 37820 | Order does not matter, so the count is C(62,3)=62!/[3!(59)!]=37820. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 37820, not 56730.",
"B": "Correct. The worked calculation gives 37820.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 37820, not 37819.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_002453 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -4], [1, 1]]. | {
"A": "4.5",
"B": "9",
"C": "7",
"D": "6.75"
} | B | 9 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(1)−(-4)(1)=9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9, not 4.5.",
"B": "Correct. The worked calculation gives 9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9, not 7.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_000921 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 12 and common ratio -3. What is the sum of its first 5 terms? | {
"A": "732",
"B": "366",
"C": "1098",
"D": "549"
} | A | 732 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=12(-3^5−1)/(-3−1)=732. | {
"A": "Correct. The worked calculation gives 732.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 732, not 366.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 732, not 1098.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006844 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 12 mol H₂ and 18 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "13 mol",
"B": "9 mol",
"C": "6 mol",
"D": "12 mol"
} | D | 12 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 12 mol H₂O; O₂ can produce 36 mol H₂O. The limiting condition is H₂; product=12 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 13 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 9 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12 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_002051 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 11 red, 6 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.33597",
"B": "2.33597",
"C": "0.16798",
"D": "-2.66403"
} | A | 0.33597 | Favourable pairs = C(11,2)+C(6,2)+C(6,2)=85. Total pairs=C(23,2)=253. Therefore P=85/253=0.33597. | {
"A": "Correct. The worked calculation gives 0.33597.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33597, not 2.33597.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33597, not 0.16798.",
"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_003458 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 72 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "730.70498 m",
"B": "365.35249 m",
"C": "487.13665 m",
"D": "243.56833 m"
} | C | 487.13665 m | Range R=u²sin(2θ)/g. Substituting u=72, θ=55° and g=10 gives R=(72)²sin(110°)/10=487.13665 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 487.13665 m, not 730.70498 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 487.13665 m, not 365.35249 m.",
"C": "Correct. The worked calculation gives 487.13665 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_006374 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 5 kg is attached to an ideal spring of force constant 166 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "2.34711 s",
"B": "3.34711 s",
"C": "1.03471 s",
"D": "0.34711 s"
} | D | 0.34711 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(5/166)=0.34711 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34711 s, not 2.34711 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34711 s, not 3.34711 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34711 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_009569 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_6H_2N_3X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "10.5",
"B": "1.7",
"C": "5",
"D": "7"
} | D | 7 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+3−2−1)/2=7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 10.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 1.7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 5.",
"D": "Correct. The work... | [
"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_007252 | 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 314 K and 1.76 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "176.67658 L",
"B": "175.67658 L",
"C": "87.83829 L",
"D": "140.54126 L"
} | B | 175.67658 L | PV=nRT, so V=nRT/P=(12)(0.082057)(314)/(1.76)=175.67658 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 175.67658 L, not 176.67658 L.",
"B": "Correct. The worked calculation gives 175.67658 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 175.67658 L, not 87.83829 L.",
"D": "Incorrect. Substit... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008368 | 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 1.59 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": "3.81408 K",
"B": "1.08141 K",
"C": "1.62816 K",
"D": "0.81408 K"
} | D | 0.81408 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.512×1.59=0.81408 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.81408 K, not 3.81408 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.81408 K, not 1.08141 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.81408 K,... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003139 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-14-11i)/(10+12i). What is Re(z), the real part of z? | {
"A": "-2.11475",
"B": "-1.11475",
"C": "-0.11475",
"D": "-2.22951"
} | B | -1.11475 | Multiply numerator and denominator by the conjugate (10-12i). Then Re(z)=(ac+bd)/(c²+d²)=((-14)(10)+(-11)(12))/(10²+(12)²)=-1.11475. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.11475, not -2.11475.",
"B": "Correct. The worked calculation gives -1.11475.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.11475, not -0.11475.",
"D": "Incorrect. Substituting the stat... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002393 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, 2], [8, 2]]. | {
"A": "4",
"B": "-6",
"C": "-4",
"D": "-2"
} | C | -4 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(2)−(2)(8)=-4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4, not 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -4, not -6.",
"C": "Correct. The worked calculation gives -4.",
"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_001169 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=1x³ -2x² -9x+7. Evaluate f′(2). | {
"A": "-2.5",
"B": "-3.75",
"C": "-5",
"D": "-10"
} | C | -5 | Differentiate: f′(x)=3(1)x²+2(-2)x+(-9). At x=2, f′(2)=3(1)(2)²+2(-2)(2)+(-9)=-5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -5, not -2.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -5, not -3.75.",
"C": "Correct. The worked calculation gives -5.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_005156 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +2 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "34 N",
"B": "33 N",
"C": "-35 N",
"D": "35 N"
} | D | 35 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(2×10⁻⁶)/(6×10⁻²)²=35 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 35 N, not 34 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 35 N, not 33 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 35 N, not -35 N.",
"D": "Cor... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002370 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, 7], [4, -2]]. | {
"A": "-46",
"B": "-43",
"C": "-3.4",
"D": "-44"
} | D | -44 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(-2)−(7)(4)=-44. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -44, not -46.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -44, not -43.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -44, not -3.4.",
"D": "Correct. ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005685 | 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 3 atm at 200 K. What is its pressure at 538 K? | {
"A": "7.07 atm",
"B": "9.07 atm",
"C": "8.07 atm",
"D": "4.035 atm"
} | C | 8.07 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3)(538)/(200)=8.07 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.07 atm, not 7.07 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.07 atm, not 9.07 atm.",
"C": "Correct. The worked calculation gives 8.07 atm.",
"D": "Incorrect. Substituting the stat... | [
"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_007163 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 14 mol of gas at 210 K and 1.6 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "148.77974 L",
"B": "180.93568 L",
"C": "75.38987 L",
"D": "150.77974 L"
} | D | 150.77974 L | PV=nRT, so V=nRT/P=(14)(0.082057)(210)/(1.6)=150.77974 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 150.77974 L, not 148.77974 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 150.77974 L, not 180.93568 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15... | [
"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_009427 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_6H_3N_3X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "7.5",
"B": "6",
"C": "5",
"D": "2.5"
} | C | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+3−3−4)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 6.",
"C": "Correct. The worked calculation gives 5.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007148 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 15 mol of gas at 322 K and 0.75 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "53.84471 L",
"B": "528.44708 L",
"C": "526.44708 L",
"D": "792.67062 L"
} | B | 528.44708 L | PV=nRT, so V=nRT/P=(15)(0.082057)(322)/(0.75)=528.44708 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 528.44708 L, not 53.84471 L.",
"B": "Correct. The worked calculation gives 528.44708 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 528.44708 L, not 526.44708 L.",
"D": "Incorrect. Substit... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002260 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 9 blue and 8 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "3.30769",
"B": "0.30769",
"C": "0.61538",
"D": "-0.30769"
} | B | 0.30769 | Favourable pairs = C(9,2)+C(9,2)+C(8,2)=100. Total pairs=C(26,2)=325. Therefore P=100/325=0.30769. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not 3.30769.",
"B": "Correct. The worked calculation gives 0.30769.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not 0.61538.",
"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_009158 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.40 V, transfers 2 electrons, and has reaction quotient Q=10^1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.68522 V",
"B": "1.37045 V",
"C": "-1.37045 V",
"D": "2.7409 V"
} | B | 1.37045 V | Apply the Nernst equation: E=1.40−(0.0591/2)(1)=1.37045 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.37045 V, not 0.68522 V.",
"B": "Correct. The worked calculation gives 1.37045 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.37045 V, not -1.37045 V.",
"D": "Incorrect. Substituting th... | [
"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_002382 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, 6], [2, 0]]. | {
"A": "12",
"B": "-12",
"C": "-18",
"D": "-0.2"
} | B | -12 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(0)−(6)(2)=-12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -12, not 12.",
"B": "Correct. The worked calculation gives -12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -12, not -18.",
"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_001481 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (1x² -7x +2) dx. | {
"A": "-17.5",
"B": "-24.75",
"C": "-8.25",
"D": "-16.5"
} | D | -16.5 | An antiderivative is (1/3)x³+(-7/2)x²+(2)x. Evaluating between 0 and 3 gives (1/3)(3)³+(-7/2)(3)²+(2)(3)=-16.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -16.5, not -17.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -16.5, not -24.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -16.5, not -8.25.",
"D"... | [
"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_001616 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (3x² +7x +4) dx. | {
"A": "921.6",
"B": "576",
"C": "768",
"D": "614.4"
} | C | 768 | An antiderivative is (3/3)x³+(7/2)x²+(4)x. Evaluating between 0 and 8 gives (3/3)(8)³+(7/2)(8)²+(4)(8)=768. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 768, not 921.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 768, not 576.",
"C": "Correct. The worked calculation gives 768.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_000844 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio 4. What is the sum of its first 9 terms? | {
"A": "174760",
"B": "174762",
"C": "262143",
"D": "349524"
} | B | 174762 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(4^9−1)/(4−1)=174762. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 174762, not 174760.",
"B": "Correct. The worked calculation gives 174762.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 174762, not 262143.",
"D": "Incorrect. Substituting the stated values ... | [
"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_009605 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_5H_1N_2X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "2",
"B": "5",
"C": "1.5",
"D": "10"
} | B | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×5+2+2−1−3)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.",
"B": "Correct. The worked calculation gives 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 1.5.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009659 | 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_25X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "6",
"B": "3",
"C": "9",
"D": "4.5"
} | A | 6 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+0−25−1)/2=6. | {
"A": "Correct. The worked calculation gives 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"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_000896 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio 3. What is the sum of its first 11 terms? | {
"A": "620013",
"B": "310005.5",
"C": "465008.25",
"D": "620011"
} | D | 620011 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(3^11−1)/(3−1)=620011. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 620011, not 620013.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 620011, not 310005.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 620011, not 465008.2... | [
"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_006252 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 46 cm in front of a thin convex lens of focal length 10 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "2.27778",
"B": "-0.72222",
"C": "0.27778",
"D": "1.27778"
} | C | 0.27778 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(46)(10)/(46−10)=12.77778 cm. Thus |m|=v/u=12.77778/46=0.27778. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.27778, not 2.27778.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.27778, not -0.72222.",
"C": "Correct. The worked calculation gives 0.27778.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004249 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 28 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.37. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "86.12 N",
"B": "9.512 N",
"C": "87.12 N",
"D": "85.12 N"
} | D | 85.12 N | Net force=mg(sinθ−μcosθ)=28×10×(0.6−0.37×0.8)=85.12 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 85.12 N, not 86.12 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 85.12 N, not 9.512 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 85.12 N, not 87.12... | [
"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_002486 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, -8], [5, 7]]. | {
"A": "96",
"B": "48",
"C": "115.2",
"D": "72"
} | A | 96 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(7)−(-8)(5)=96. | {
"A": "Correct. The worked calculation gives 96.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 96, not 48.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 96, not 115.2.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_007745 | 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 98 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "49 mmol L⁻¹",
"B": "58.8 mmol L⁻¹",
"C": "24.5 mmol L⁻¹",
"D": "73.5 mmol L⁻¹"
} | A | 49 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=98/2^1=49 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 49 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 49 mmol L⁻¹, not 58.8 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 49 mmol L⁻¹, not 24.5 mmol L⁻¹.",
"D": "Incorrect. Su... | [
"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_009651 | 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_12N_2X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "7",
"B": "10",
"C": "5",
"D": "6"
} | A | 7 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×12+2+2−12−2)/2=7. | {
"A": "Correct. The worked calculation gives 7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 5.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002230 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 6 blue and 9 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.35294",
"B": "0.35294",
"C": "0.70588",
"D": "-0.64706"
} | B | 0.35294 | Favourable pairs = C(3,2)+C(6,2)+C(9,2)=54. Total pairs=C(18,2)=153. Therefore P=54/153=0.35294. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35294, not 1.35294.",
"B": "Correct. The worked calculation gives 0.35294.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35294, not 0.70588.",
"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_006125 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 20 cm in front of a thin convex lens of focal length 11 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.12222",
"B": "4.22222",
"C": "0.91667",
"D": "1.22222"
} | D | 1.22222 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(20)(11)/(20−11)=24.44444 cm. Thus |m|=v/u=24.44444/20=1.22222. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.22222, not 1.12222.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.22222, not 4.22222.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.22222, not 0.916... | [
"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_000155 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -17x -8=0, let its roots be α and β. What is α²+β²? | {
"A": "82.25",
"B": "80.25",
"C": "64.2",
"D": "-80.25"
} | B | 80.25 | By Vieta's relations, α+β = 17/2 and αβ = -8/2. Then α²+β²=(α+β)²−2αβ = (17/2)²−2(-8/2) = 80.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 80.25, not 82.25.",
"B": "Correct. The worked calculation gives 80.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 80.25, not 64.2.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_008168 | 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 15 A for 5552 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": "29.40041 g",
"B": "3.74004 g",
"C": "28.40041 g",
"D": "27.40041 g"
} | D | 27.40041 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×15×5552/(2×96500)=27.40041 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 27.40041 g, not 29.40041 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 27.40041 g, not 3.74004 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 27.4004... | [
"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_006245 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 70 cm in front of a thin convex lens of focal length 23 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.48936",
"B": "0.73404",
"C": "0.24468",
"D": "0.48936"
} | D | 0.48936 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(70)(23)/(70−23)=34.25532 cm. Thus |m|=v/u=34.25532/70=0.48936. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.48936, not -0.48936.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.48936, not 0.73404.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.48936, not 0.24... | [
"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_002757 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-5, 9, -1) and v=(-4, -5, 3), calculate u·v. | {
"A": "-28",
"B": "-56",
"C": "-33.6",
"D": "28"
} | A | -28 | The dot product is the sum of corresponding component products: (-5)(-4)+(9)(-5)+(-1)(3)=-28. | {
"A": "Correct. The worked calculation gives -28.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -28, not -56.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -28, not -33.6.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_005404 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 72 μF capacitor is charged to a potential difference of 20 V. Calculate the energy stored, expressed in μJ. | {
"A": "14401 μJ",
"B": "1441 μJ",
"C": "14400 μJ",
"D": "14399 μJ"
} | C | 14400 μJ | U=½CV². Since C=72 μF, U in μJ is ½×72×(20)²=14400 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14400 μJ, not 14401 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14400 μJ, not 1441 μJ.",
"C": "Correct. The worked calculation gives 14400 μJ.",
"D": "Incorrect. Substituting the state... | [
"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_003379 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 62 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "295.46748 m",
"B": "296.46748 m",
"C": "294.46748 m",
"D": "235.57399 m"
} | C | 294.46748 m | Range R=u²sin(2θ)/g. Substituting u=62, θ=25° and g=10 gives R=(62)²sin(50°)/10=294.46748 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 294.46748 m, not 295.46748 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 294.46748 m, not 296.46748 m.",
"C": "Correct. The worked calculation gives 294.46748 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_006677 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 33 mol H₂ and 8 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "32 mol",
"B": "12.8 mol",
"C": "16 mol",
"D": "-16 mol"
} | C | 16 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 33 mol H₂O; O₂ can produce 16 mol H₂O. The limiting condition is O₂; product=16 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 32 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 12.8 mol.",
"C": "Correct. The worked calculation gives 16 mol.",
"D": "Incorrect. Substituting the stated value... | [
"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_001543 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (-1x² +1x +3) dx. | {
"A": "4.5",
"B": "2.5",
"C": "6.5",
"D": "3.375"
} | A | 4.5 | An antiderivative is (-1/3)x³+(1/2)x²+(3)x. Evaluating between 0 and 3 gives (-1/3)(3)³+(1/2)(3)²+(3)(3)=4.5. | {
"A": "Correct. The worked calculation gives 4.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.5, not 2.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.5, not 6.5.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_009159 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.40 V, transfers 1 electrons, and has reaction quotient Q=10^0. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.14 V",
"B": "1.05 V",
"C": "0.4 V",
"D": "1.4 V"
} | D | 1.4 V | Apply the Nernst equation: E=1.40−(0.0591/1)(0)=1.4 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.4 V, not 1.14 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4 V, not 1.05 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.4 V, not 0.4 V.",
"D... | [
"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_002786 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(6, 5, 0) and v=(5, -2, 8), calculate u·v. | {
"A": "19",
"B": "15",
"C": "10",
"D": "20"
} | D | 20 | The dot product is the sum of corresponding component products: (6)(5)+(5)(-2)+(0)(8)=20. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20, not 19.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20, not 15.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20, not 10.",
"D": "Correct. The wor... | [
"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_004696 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 12 Ω and 13 Ω are connected in series; this combination is connected in parallel with a 19 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.22316 A",
"B": "3.33474 A",
"C": "0.22316 A",
"D": "4.22316 A"
} | A | 2.22316 A | Series branch resistance=12+13=25 Ω. Parallel equivalent R_eq=(25×19)/(25+19)=10.79545 Ω. Total current I=V/R_eq=24/10.79545=2.22316 A. | {
"A": "Correct. The worked calculation gives 2.22316 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.22316 A, not 3.33474 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.22316 A, not 0.22316 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000501 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 26 and common difference 10. Find the sum of its first 31 terms. | {
"A": "5456",
"B": "10912",
"C": "546.6",
"D": "5457"
} | A | 5456 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=26, d=10, n=31: Sₙ=31/2[2(26)+(31−1)(10)]=5456. | {
"A": "Correct. The worked calculation gives 5456.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5456, not 10912.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5456, not 546.6.",
"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_006609 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 25 kg is attached to an ideal spring of force constant 393 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.49557 s",
"B": "1.00887 s",
"C": "3.50443 s",
"D": "0.50443 s"
} | D | 0.50443 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(25/393)=0.50443 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.50443 s, not -2.49557 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.50443 s, not 1.00887 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.50443 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_003326 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-1-5i)/(3+6i). What is Re(z), the real part of z? | {
"A": "-2.73333",
"B": "-0.73333",
"C": "2.26667",
"D": "-0.55"
} | B | -0.73333 | Multiply numerator and denominator by the conjugate (3-6i). Then Re(z)=(ac+bd)/(c²+d²)=((-1)(3)+(-5)(6))/(3²+(6)²)=-0.73333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.73333, not -2.73333.",
"B": "Correct. The worked calculation gives -0.73333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.73333, not 2.26667.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003258 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-12-2i)/(2+9i). What is Re(z), the real part of z? | {
"A": "-0.24706",
"B": "2.50588",
"C": "-0.74118",
"D": "-0.49412"
} | D | -0.49412 | Multiply numerator and denominator by the conjugate (2-9i). Then Re(z)=(ac+bd)/(c²+d²)=((-12)(2)+(-2)(9))/(2²+(9)²)=-0.49412. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.49412, not -0.24706.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.49412, not 2.50588.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.49412, not -... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007869 | 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 79 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "-0.38281 mmol L⁻¹",
"B": "1.61719 mmol L⁻¹",
"C": "0.92578 mmol L⁻¹",
"D": "0.61719 mmol L⁻¹"
} | D | 0.61719 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=79/2^7=0.61719 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.61719 mmol L⁻¹, not -0.38281 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.61719 mmol L⁻¹, not 1.61719 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the govern... | [
"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_005497 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 80 μF capacitor is charged to a potential difference of 29 V. Calculate the energy stored, expressed in μJ. | {
"A": "67280 μJ",
"B": "50460 μJ",
"C": "40368 μJ",
"D": "33640 μJ"
} | D | 33640 μJ | U=½CV². Since C=80 μF, U in μJ is ½×80×(29)²=33640 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33640 μJ, not 67280 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33640 μJ, not 50460 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 33640 μJ, not ... | [
"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_000865 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio -2. What is the sum of its first 6 terms? | {
"A": "-3.2",
"B": "-33.6",
"C": "-84",
"D": "-42"
} | D | -42 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(-2^6−1)/(-2−1)=-42. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -42, not -3.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -42, not -33.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -42, not -84.",
"D": "Correct... | [
"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_009358 | 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_10N_1X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "14",
"B": "7",
"C": "5",
"D": "4"
} | B | 7 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×12+2+1−10−3)/2=7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 14.",
"B": "Correct. The worked calculation gives 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 5.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001720 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 6 elements can be selected from a set of 83 distinct elements? | {
"A": "452936577.6",
"B": "377447148",
"C": "283085361",
"D": "37744715.8"
} | B | 377447148 | Order does not matter, so the count is C(83,6)=83!/[6!(77)!]=377447148. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 377447148, not 452936577.6.",
"B": "Correct. The worked calculation gives 377447148.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 377447148, not 283085361.",
"D": "Incorrect. Substituting t... | [
"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_006086 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 75 cm in front of a thin convex lens of focal length 17 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.2931",
"B": "3.2931",
"C": "0.58621",
"D": "-2.7069"
} | A | 0.2931 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(75)(17)/(75−17)=21.98276 cm. Thus |m|=v/u=21.98276/75=0.2931. | {
"A": "Correct. The worked calculation gives 0.2931.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.2931, not 3.2931.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.2931, not 0.58621.",
"D": "Incorrect. Substituting the stated values... | [
"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_007265 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 13 mol of gas at 445 K and 0.59 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "804.57584 L",
"B": "81.45758 L",
"C": "803.57584 L",
"D": "1609.15168 L"
} | A | 804.57584 L | PV=nRT, so V=nRT/P=(13)(0.082057)(445)/(0.59)=804.57584 L. | {
"A": "Correct. The worked calculation gives 804.57584 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 804.57584 L, not 81.45758 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 804.57584 L, not 803.57584 L.",
"D": "Incorrect. Substit... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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