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_005348 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 9 μF capacitor is charged to a potential difference of 4 V. Calculate the energy stored, expressed in μJ. | {
"A": "8.2 μJ",
"B": "86.4 μJ",
"C": "72 μJ",
"D": "36 μJ"
} | C | 72 μJ | U=½CV². Since C=9 μF, U in μJ is ½×9×(4)²=72 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 72 μJ, not 8.2 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 72 μJ, not 86.4 μJ.",
"C": "Correct. The worked calculation gives 72 μJ.",
"D": "Incorrect. Substituting the stated values in... | [
"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_003835 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 3 m s⁻¹. A constant net force does 24 N of work over 10 m in the direction of motion. Find its final kinetic energy. | {
"A": "203.625 J",
"B": "135.75 J",
"C": "407.25 J",
"D": "271.5 J"
} | D | 271.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(3)²+(24)(10)=271.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 271.5 J, not 203.625 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 271.5 J, not 135.75 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 271.5 J, not 40... | [
"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_007642 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 57 mL of 0.10 M HCl is mixed with 84 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "18.42322",
"B": "-12.28214",
"C": "9.28214",
"D": "12.28214"
} | D | 12.28214 | Excess OH⁻ moles=0.10×(84−57)/1000=0.002700 mol. Total volume=0.141 L, so [OH⁻]=0.019149 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.28214. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.28214, not 18.42322.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.28214, not -12.28214.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.28214, not... | [
"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_008743 | 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 0.12 mol L⁻¹ and initially B is absent. At equilibrium, 66% of A has dissociated at constant volume. Find K_c. | {
"A": "0.46122",
"B": "0.61496",
"C": "0.30748",
"D": "2.61496"
} | B | 0.61496 | Let α=0.66. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.12)(0.66)²/(1−0.66)=0.61496. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.61496, not 0.46122.",
"B": "Correct. The worked calculation gives 0.61496.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.61496, not 0.30748.",
"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_009400 | 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_7N_3X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "-3",
"C": "-2",
"D": "0"
} | D | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×3+2+3−7−4)/2=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"D": "Correct. The worked ... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001964 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 86 distinct elements? | {
"A": "3540894603246",
"B": "3540894603244",
"C": "2832715682596.7998",
"D": "1770447301623"
} | A | 3540894603246 | Order does not matter, so the count is C(86,10)=86!/[10!(76)!]=3540894603246. | {
"A": "Correct. The worked calculation gives 3540894603246.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3540894603246, not 3540894603244.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3540894603246, not 2832715682596.7998.",
"D": "In... | [
"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_006572 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 3 kg is attached to an ideal spring of force constant 1180 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.20169 s",
"B": "-0.89916 s",
"C": "0.10084 s",
"D": "1.01008 s"
} | C | 0.10084 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(3/1180)=0.10084 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.10084 s, not 0.20169 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.10084 s, not -0.89916 s.",
"C": "Correct. The worked calculation gives 0.10084 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_000347 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 20 and common difference 4. Find the sum of its first 34 terms. | {
"A": "2926",
"B": "2925",
"C": "2924",
"D": "4386"
} | C | 2924 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=20, d=4, n=34: Sₙ=34/2[2(20)+(34−1)(4)]=2924. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2924, not 2926.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2924, not 2925.",
"C": "Correct. The worked calculation gives 2924.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006344 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 13 kg is attached to an ideal spring of force constant 734 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.26617 s",
"B": "0.26617 s",
"C": "-1.73383 s",
"D": "0.13308 s"
} | B | 0.26617 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(13/734)=0.26617 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.26617 s, not -0.26617 s.",
"B": "Correct. The worked calculation gives 0.26617 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.26617 s, not -1.73383 s.",
"D": "Incorrect. Substituting t... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004488 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 1 m is acted on by a constant torque of 62 N m about its central axis. Find its angular acceleration. | {
"A": "62 rad s⁻²",
"B": "46.5 rad s⁻²",
"C": "7.2 rad s⁻²",
"D": "-62 rad s⁻²"
} | A | 62 rad s⁻² | For a solid disc, I=½MR²=½(2)(1)²=1 kg m². Using τ=Iα, α=62/1=62 rad s⁻². | {
"A": "Correct. The worked calculation gives 62 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 62 rad s⁻², not 46.5 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 62 rad s⁻², not 7.2 rad s⁻².",
"D": "Incorrect. Substitu... | [
"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_000738 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio 5. What is the sum of its first 10 terms? | {
"A": "2441406",
"B": "3662109",
"C": "488282.2",
"D": "4882812"
} | D | 4882812 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(5^10−1)/(5−1)=4882812. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4882812, not 2441406.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4882812, not 3662109.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4882812, not 48828... | [
"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_004631 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 12 kg and radius 2 m is acted on by a constant torque of 57 N m about its central axis. Find its angular acceleration. | {
"A": "2.375 rad s⁻²",
"B": "1.375 rad s⁻²",
"C": "-0.625 rad s⁻²",
"D": "4.75 rad s⁻²"
} | A | 2.375 rad s⁻² | For a solid disc, I=½MR²=½(12)(2)²=24 kg m². Using τ=Iα, α=57/24=2.375 rad s⁻². | {
"A": "Correct. The worked calculation gives 2.375 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.375 rad s⁻², not 1.375 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.375 rad s⁻², not -0.625 rad s⁻².",
"D": "Incorr... | [
"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_008864 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.51 mol L⁻¹ and initially B is absent. At equilibrium, 26% of A has dissociated at constant volume. Find K_c. | {
"A": "1.05518",
"B": "0.55176",
"C": "0.82764",
"D": "1.10352"
} | B | 0.55176 | Let α=0.26. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.51)(0.26)²/(1−0.26)=0.55176. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.55176, not 1.05518.",
"B": "Correct. The worked calculation gives 0.55176.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.55176, not 0.82764.",
"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_008252 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 13 A for 14439 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": "30.87926 g",
"B": "74.11022 g",
"C": "61.75852 g",
"D": "59.75852 g"
} | C | 61.75852 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×14439/(2×96500)=61.75852 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 61.75852 g, not 30.87926 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 61.75852 g, not 74.11022 g.",
"C": "Correct. The worked calculation gives 61.75852 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_000813 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio -3. What is the sum of its first 12 terms? | {
"A": "-597870",
"B": "-797160",
"C": "-797158",
"D": "-797161"
} | B | -797160 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(-3^12−1)/(-3−1)=-797160. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -797160, not -597870.",
"B": "Correct. The worked calculation gives -797160.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -797160, not -797158.",
"D": "Incorrect. Substituting the stated va... | [
"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_002405 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 4], [2, 0]]. | {
"A": "-5",
"B": "0.2",
"C": "-8",
"D": "8"
} | C | -8 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(0)−(4)(2)=-8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -8, not -5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -8, not 0.2.",
"C": "Correct. The worked calculation gives -8.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005249 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +3 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "37.96875 N",
"B": "30.375 N",
"C": "18.98438 N",
"D": "56.95312 N"
} | A | 37.96875 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(3×10⁻⁶)/(8×10⁻²)²=37.96875 N. | {
"A": "Correct. The worked calculation gives 37.96875 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 37.96875 N, not 30.375 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 37.96875 N, not 18.98438 N.",
"D": "Incorrect. Substituting ... | [
"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_001157 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=0x³ +10x² +4x+7. Evaluate f′(-1). | {
"A": "-8",
"B": "-0.6",
"C": "-18",
"D": "-16"
} | D | -16 | Differentiate: f′(x)=3(0)x²+2(10)x+(4). At x=-1, f′(-1)=3(0)(-1)²+2(10)(-1)+(4)=-16. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -16, not -8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -16, not -0.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -16, not -18.",
"D": "Correct. T... | [
"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_005477 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 22 μF capacitor is charged to a potential difference of 30 V. Calculate the energy stored, expressed in μJ. | {
"A": "9900 μJ",
"B": "11880 μJ",
"C": "991 μJ",
"D": "9899 μJ"
} | A | 9900 μJ | U=½CV². Since C=22 μF, U in μJ is ½×22×(30)²=9900 μJ. | {
"A": "Correct. The worked calculation gives 9900 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9900 μJ, not 11880 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9900 μJ, not 991 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006352 | 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 1041 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.29075 s",
"B": "1.29075 s",
"C": "2.29075 s",
"D": "3.29075 s"
} | A | 0.29075 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(22/1041)=0.29075 s. | {
"A": "Correct. The worked calculation gives 0.29075 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29075 s, not 1.29075 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29075 s, not 2.29075 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007110 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 6 mol of gas at 513 K and 2.57 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "98.27683 L",
"B": "78.62146 L",
"C": "97.27683 L",
"D": "99.27683 L"
} | A | 98.27683 L | PV=nRT, so V=nRT/P=(6)(0.082057)(513)/(2.57)=98.27683 L. | {
"A": "Correct. The worked calculation gives 98.27683 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 98.27683 L, not 78.62146 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 98.27683 L, not 97.27683 L.",
"D": "Incorrect. Substitutin... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005547 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 62 μF capacitor is charged to a potential difference of 36 V. Calculate the energy stored, expressed in μJ. | {
"A": "20088 μJ",
"B": "40176 μJ",
"C": "40175 μJ",
"D": "60264 μJ"
} | B | 40176 μJ | U=½CV². Since C=62 μF, U in μJ is ½×62×(36)²=40176 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 40176 μJ, not 20088 μJ.",
"B": "Correct. The worked calculation gives 40176 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 40176 μJ, not 40175 μJ.",
"D": "Incorrect. Substituting the stat... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009342 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_9H_7X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "7.5",
"B": "3.75",
"C": "5",
"D": "4"
} | C | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×9+2+0−7−3)/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 3.75.",
"C": "Correct. The worked calculation gives 5.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000381 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 17 and common difference 3. Find the sum of its first 15 terms. | {
"A": "570",
"B": "684",
"C": "855",
"D": "456"
} | A | 570 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=17, d=3, n=15: Sₙ=15/2[2(17)+(15−1)(3)]=570. | {
"A": "Correct. The worked calculation gives 570.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 570, not 684.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 570, not 855.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003087 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-3-5i)/(3+2i). What is Re(z), the real part of z? | {
"A": "-0.73077",
"B": "-1.46154",
"C": "1.46154",
"D": "0.85385"
} | B | -1.46154 | Multiply numerator and denominator by the conjugate (3-2i). Then Re(z)=(ac+bd)/(c²+d²)=((-3)(3)+(-5)(2))/(3²+(2)²)=-1.46154. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.46154, not -0.73077.",
"B": "Correct. The worked calculation gives -1.46154.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.46154, not 1.46154.",
"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_005140 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +7 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "348 N",
"B": "349 N",
"C": "350 N",
"D": "420 N"
} | C | 350 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(7×10⁻⁶)/(3×10⁻²)²=350 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 350 N, not 348 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 350 N, not 349 N.",
"C": "Correct. The worked calculation gives 350 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005441 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 55 μF capacitor is charged to a potential difference of 38 V. Calculate the energy stored, expressed in μJ. | {
"A": "39710 μJ",
"B": "-39710 μJ",
"C": "59565 μJ",
"D": "39711 μJ"
} | A | 39710 μJ | U=½CV². Since C=55 μF, U in μJ is ½×55×(38)²=39710 μJ. | {
"A": "Correct. The worked calculation gives 39710 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39710 μJ, not -39710 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39710 μJ, not 59565 μJ.",
"D": "Incorrect. Substituting the sta... | [
"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_005577 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 38 μF capacitor is charged to a potential difference of 11 V. Calculate the energy stored, expressed in μJ. | {
"A": "2299 μJ",
"B": "230.9 μJ",
"C": "2758.8 μJ",
"D": "1839.2 μJ"
} | A | 2299 μJ | U=½CV². Since C=38 μF, U in μJ is ½×38×(11)²=2299 μJ. | {
"A": "Correct. The worked calculation gives 2299 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2299 μJ, not 230.9 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2299 μJ, not 2758.8 μJ.",
"D": "Incorrect. Substituting the stated... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003644 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 51 m s⁻¹ at 35° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "244.41405 m",
"B": "293.29686 m",
"C": "245.41405 m",
"D": "246.41405 m"
} | A | 244.41405 m | Range R=u²sin(2θ)/g. Substituting u=51, θ=35° and g=10 gives R=(51)²sin(70°)/10=244.41405 m. | {
"A": "Correct. The worked calculation gives 244.41405 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 244.41405 m, not 293.29686 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 244.41405 m, not 245.41405 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_004792 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 12 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 10 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "6.98462 A",
"B": "2.98462 A",
"C": "7.47692 A",
"D": "4.98462 A"
} | D | 4.98462 A | Series branch resistance=12+14=26 Ω. Parallel equivalent R_eq=(26×10)/(26+10)=7.22222 Ω. Total current I=V/R_eq=36/7.22222=4.98462 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.98462 A, not 6.98462 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.98462 A, not 2.98462 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.98462 A,... | [
"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_002571 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, 8], [3, -1]]. | {
"A": "25",
"B": "-24",
"C": "-37.5",
"D": "-25"
} | D | -25 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(-1)−(8)(3)=-25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -25, not 25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -25, not -24.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -25, not -37.5.",
"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_009421 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_17H_14N_2X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "2.1",
"B": "-11",
"C": "11",
"D": "12"
} | C | 11 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×17+2+2−14−2)/2=11. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11, not 2.1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11, not -11.",
"C": "Correct. The worked calculation gives 11.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"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_006690 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 5 mol H₂ and 16 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "3 mol",
"B": "3.75 mol",
"C": "5 mol",
"D": "8 mol"
} | C | 5 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 5 mol H₂O; O₂ can produce 32 mol H₂O. The limiting condition is H₂; product=5 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5 mol, not 3 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5 mol, not 3.75 mol.",
"C": "Correct. The worked calculation gives 5 mol.",
"D": "Incorrect. Substituting the stated values in... | [
"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_000051 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 -13x -12=0, let its roots be α and β. What is α²+β²? | {
"A": "2.65625",
"B": "18.5625",
"C": "19.875",
"D": "16.5625"
} | D | 16.5625 | By Vieta's relations, α+β = 13/4 and αβ = -12/4. Then α²+β²=(α+β)²−2αβ = (13/4)²−2(-12/4) = 16.5625. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16.5625, not 2.65625.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16.5625, not 18.5625.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16.5625, not 19.87... | [
"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_000979 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio 4. What is the sum of its first 7 terms? | {
"A": "21842",
"B": "21843",
"C": "21844",
"D": "21845"
} | C | 21844 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(4^7−1)/(4−1)=21844. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21844, not 21842.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21844, not 21843.",
"C": "Correct. The worked calculation gives 21844.",
"D": "Incorrect. Substituting the stated values into ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001393 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (2x² -2x -3) dx. | {
"A": "32.5",
"B": "86.66667",
"C": "52",
"D": "43.33333"
} | D | 43.33333 | An antiderivative is (2/3)x³+(-2/2)x²+(-3)x. Evaluating between 0 and 5 gives (2/3)(5)³+(-2/2)(5)²+(-3)(5)=43.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 43.33333, not 32.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 43.33333, not 86.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 43.33333, not 52."... | [
"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_006985 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 11 mol H₂ and 20 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "11 mol",
"B": "22 mol",
"C": "14 mol",
"D": "10 mol"
} | A | 11 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 11 mol H₂O; O₂ can produce 40 mol H₂O. The limiting condition is H₂; product=11 mol. | {
"A": "Correct. The worked calculation gives 11 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11 mol, not 22 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11 mol, not 14 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_007815 | 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 80 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "2.25 mmol L⁻¹",
"B": "-1.25 mmol L⁻¹",
"C": "3.25 mmol L⁻¹",
"D": "1.25 mmol L⁻¹"
} | D | 1.25 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=80/2^6=1.25 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.25 mmol L⁻¹, not 2.25 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.25 mmol L⁻¹, not -1.25 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004585 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 11 kg and radius 6 m is acted on by a constant torque of 57 N m about its central axis. Find its angular acceleration. | {
"A": "1.02879 rad s⁻²",
"B": "0.28788 rad s⁻²",
"C": "-0.28788 rad s⁻²",
"D": "0.43182 rad s⁻²"
} | B | 0.28788 rad s⁻² | For a solid disc, I=½MR²=½(11)(6)²=198 kg m². Using τ=Iα, α=57/198=0.28788 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.28788 rad s⁻², not 1.02879 rad s⁻².",
"B": "Correct. The worked calculation gives 0.28788 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.28788 rad s⁻², not -0.28788 rad s⁻².",
"D... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008030 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 7 A for 7840 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": "18.05637 g",
"B": "-18.05637 g",
"C": "16.05637 g",
"D": "17.05637 g"
} | A | 18.05637 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×7×7840/(2×96500)=18.05637 g. | {
"A": "Correct. The worked calculation gives 18.05637 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18.05637 g, not -18.05637 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18.05637 g, not 16.05637 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003977 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 3 kg block initially moves at 0 m s⁻¹. A constant net force does 29 N of work over 3 m in the direction of motion. Find its final kinetic energy. | {
"A": "89 J",
"B": "87 J",
"C": "86 J",
"D": "43.5 J"
} | B | 87 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(3)(0)²+(29)(3)=87 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 87 J, not 89 J.",
"B": "Correct. The worked calculation gives 87 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 87 J, not 86 J.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_000341 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 28 and common difference 9. Find the sum of its first 31 terms. | {
"A": "-5053",
"B": "5053",
"C": "5054",
"D": "3789.75"
} | B | 5053 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=28, d=9, n=31: Sₙ=31/2[2(28)+(31−1)(9)]=5053. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5053, not -5053.",
"B": "Correct. The worked calculation gives 5053.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5053, not 5054.",
"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_004397 | 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 10 N m about its central axis. Find its angular acceleration. | {
"A": "0.11111 rad s⁻²",
"B": "2.11111 rad s⁻²",
"C": "0.05556 rad s⁻²",
"D": "3.11111 rad s⁻²"
} | A | 0.11111 rad s⁻² | For a solid disc, I=½MR²=½(5)(6)²=90 kg m². Using τ=Iα, α=10/90=0.11111 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.11111 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.11111 rad s⁻², not 2.11111 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.11111 rad s⁻², not 0.05556 rad s⁻².",
"D"... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004524 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 4 kg and radius 5 m is acted on by a constant torque of 21 N m about its central axis. Find its angular acceleration. | {
"A": "1.42 rad s⁻²",
"B": "0.42 rad s⁻²",
"C": "-0.58 rad s⁻²",
"D": "0.21 rad s⁻²"
} | B | 0.42 rad s⁻² | For a solid disc, I=½MR²=½(4)(5)²=50 kg m². Using τ=Iα, α=21/50=0.42 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.42 rad s⁻², not 1.42 rad s⁻².",
"B": "Correct. The worked calculation gives 0.42 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.42 rad s⁻², not -0.58 rad s⁻².",
"D": "Incorrect. ... | [
"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_009529 | 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_20N_1X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "5",
"B": "8",
"C": "9",
"D": "1.8"
} | B | 8 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+1−20−3)/2=8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 5.",
"B": "Correct. The worked calculation gives 8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, 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_003207 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-2-12i)/(3+2i). What is Re(z), the real part of z? | {
"A": "-0.30769",
"B": "-1.73077",
"C": "-3.46154",
"D": "-2.30769"
} | D | -2.30769 | Multiply numerator and denominator by the conjugate (3-2i). Then Re(z)=(ac+bd)/(c²+d²)=((-2)(3)+(-12)(2))/(3²+(2)²)=-2.30769. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2.30769, not -0.30769.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2.30769, not -1.73077.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2.30769, 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_009662 | 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_13H_14N_1X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "10",
"B": "7",
"C": "10.5",
"D": "14"
} | B | 7 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×13+2+1−14−1)/2=7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 10.",
"B": "Correct. The worked calculation gives 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 10.5.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002758 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(9, -3, 8) and v=(5, 8, -7), calculate u·v. | {
"A": "-37",
"B": "-52.5",
"C": "-33",
"D": "-35"
} | D | -35 | The dot product is the sum of corresponding component products: (9)(5)+(-3)(8)+(8)(-7)=-35. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -35, not -37.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -35, not -52.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -35, not -33.",
"D": "Correct.... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004673 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 10 Ω are connected in series; this combination is connected in parallel with a 20 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.26118 A",
"B": "3.91765 A",
"C": "2.61176 A",
"D": "5.61176 A"
} | C | 2.61176 A | Series branch resistance=7+10=17 Ω. Parallel equivalent R_eq=(17×20)/(17+20)=9.18919 Ω. Total current I=V/R_eq=24/9.18919=2.61176 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.61176 A, not 1.26118 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.61176 A, not 3.91765 A.",
"C": "Correct. The worked calculation gives 2.61176 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_000159 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 +9x +7=0, let its roots be α and β. What is α²+β²? | {
"A": "0.08333",
"B": "-0.0625",
"C": "-0.08333",
"D": "-3.08333"
} | C | -0.08333 | By Vieta's relations, α+β = -9/6 and αβ = 7/6. Then α²+β²=(α+β)²−2αβ = (-9/6)²−2(7/6) = -0.08333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.08333, not 0.08333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.08333, not -0.0625.",
"C": "Correct. The worked calculation gives -0.08333.",
"D": "Incorrect. Substituting the stated... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008172 | 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 4 A for 8324 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": "21.9098 g",
"B": "11.9549 g",
"C": "10.9549 g",
"D": "8.9549 g"
} | C | 10.9549 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×8324/(2×96500)=10.9549 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.9549 g, not 21.9098 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.9549 g, not 11.9549 g.",
"C": "Correct. The worked calculation gives 10.9549 g.",
"D": "Incorrect. Substituting the... | [
"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_000687 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio -2. What is the sum of its first 12 terms? | {
"A": "-1365",
"B": "-682.5",
"C": "-1367",
"D": "-2047.5"
} | A | -1365 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(-2^12−1)/(-2−1)=-1365. | {
"A": "Correct. The worked calculation gives -1365.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1365, not -682.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1365, not -1367.",
"D": "Incorrect. Substituting the stated values into... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001620 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (6x² -5x -3) dx. | {
"A": "540.5",
"B": "541.5",
"C": "542.5",
"D": "-542.5"
} | C | 542.5 | An antiderivative is (6/3)x³+(-5/2)x²+(-3)x. Evaluating between 0 and 7 gives (6/3)(7)³+(-5/2)(7)²+(-3)(7)=542.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 542.5, not 540.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 542.5, not 541.5.",
"C": "Correct. The worked calculation gives 542.5.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_005013 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +7 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "38.88889 N",
"B": "39.88889 N",
"C": "40.88889 N",
"D": "29.16667 N"
} | A | 38.88889 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(7×10⁻⁶)/(9×10⁻²)²=38.88889 N. | {
"A": "Correct. The worked calculation gives 38.88889 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 38.88889 N, not 39.88889 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 38.88889 N, not 40.88889 N.",
"D": "Incorrect. Substitutin... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005671 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 71 μF capacitor is charged to a potential difference of 3 V. Calculate the energy stored, expressed in μJ. | {
"A": "479.25 μJ",
"B": "319.5 μJ",
"C": "317.5 μJ",
"D": "-319.5 μJ"
} | B | 319.5 μJ | U=½CV². Since C=71 μF, U in μJ is ½×71×(3)²=319.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 319.5 μJ, not 479.25 μJ.",
"B": "Correct. The worked calculation gives 319.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 319.5 μJ, not 317.5 μJ.",
"D": "Incorrect. Substituting the sta... | [
"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_001640 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (5x² -7x +0) dx. | {
"A": "-2.83333",
"B": "1.83333",
"C": "-1.83333",
"D": "0.16667"
} | C | -1.83333 | An antiderivative is (5/3)x³+(-7/2)x²+(0)x. Evaluating between 0 and 1 gives (5/3)(1)³+(-7/2)(1)²+(0)(1)=-1.83333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.83333, not -2.83333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.83333, not 1.83333.",
"C": "Correct. The worked calculation gives -1.83333.",
"D": "Incorrect. Substituting the state... | [
"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_001845 | 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 13 distinct elements? | {
"A": "1287",
"B": "1285",
"C": "129.7",
"D": "1288"
} | A | 1287 | Order does not matter, so the count is C(13,8)=13!/[8!(5)!]=1287. | {
"A": "Correct. The worked calculation gives 1287.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1287, not 1285.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1287, not 129.7.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_008959 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.37 mol L⁻¹ and initially B is absent. At equilibrium, 55% of A has dissociated at constant volume. Find K_c. | {
"A": "6.68378",
"B": "3.68378",
"C": "1.36838",
"D": "1.84189"
} | B | 3.68378 | Let α=0.55. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.37)(0.55)²/(1−0.55)=3.68378. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.68378, not 6.68378.",
"B": "Correct. The worked calculation gives 3.68378.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.68378, not 1.36838.",
"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_004393 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 4 m is acted on by a constant torque of 62 N m about its central axis. Find its angular acceleration. | {
"A": "1.55 rad s⁻²",
"B": "-0.45 rad s⁻²",
"C": "1.1625 rad s⁻²",
"D": "-1.55 rad s⁻²"
} | A | 1.55 rad s⁻² | For a solid disc, I=½MR²=½(5)(4)²=40 kg m². Using τ=Iα, α=62/40=1.55 rad s⁻². | {
"A": "Correct. The worked calculation gives 1.55 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.55 rad s⁻², not -0.45 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.55 rad s⁻², not 1.1625 rad s⁻².",
"D": "Incorrect... | [
"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_005035 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +4 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "14.4 N",
"B": "6.2 N",
"C": "4.2 N",
"D": "7.2 N"
} | D | 7.2 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(4×10⁻⁶)/(10×10⁻²)²=7.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.2 N, not 14.4 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.2 N, not 6.2 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.2 N, not 4.2 N.",
"D"... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001319 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=0x³ -2x² -1x+7. Evaluate f′(1). | {
"A": "-3",
"B": "-3.75",
"C": "-5",
"D": "5"
} | C | -5 | Differentiate: f′(x)=3(0)x²+2(-2)x+(-1). At x=1, f′(1)=3(0)(1)²+2(-2)(1)+(-1)=-5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -5, not -3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -5, not -3.75.",
"C": "Correct. The worked calculation gives -5.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_002309 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 12 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": "0.32043",
"B": "-0.67957",
"C": "0.64086",
"D": "1.03204"
} | A | 0.32043 | Favourable pairs = C(8,2)+C(12,2)+C(11,2)=149. Total pairs=C(31,2)=465. Therefore P=149/465=0.32043. | {
"A": "Correct. The worked calculation gives 0.32043.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32043, not -0.67957.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32043, not 0.64086.",
"D": "Incorrect. Substituting the stated v... | [
"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_009046 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.34 V, transfers 2 electrons, and has reaction quotient Q=10^-4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.5418 V",
"B": "2.1873 V",
"C": "-1.5418 V",
"D": "1.4582 V"
} | D | 1.4582 V | Apply the Nernst equation: E=1.34−(0.0591/2)(-4)=1.4582 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.4582 V, not -0.5418 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4582 V, not 2.1873 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.4582 V, not... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005785 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.7 atm at 444 K. What is its pressure at 612 K? | {
"A": "7.44324 atm",
"B": "-3.72162 atm",
"C": "3.72162 atm",
"D": "5.72162 atm"
} | C | 3.72162 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.7)(612)/(444)=3.72162 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.72162 atm, not 7.44324 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.72162 atm, not -3.72162 atm.",
"C": "Correct. The worked calculation gives 3.72162 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007740 | 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 23 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "0.13477 mmol L⁻¹",
"B": "1.17969 mmol L⁻¹",
"C": "0.35938 mmol L⁻¹",
"D": "0.17969 mmol L⁻¹"
} | D | 0.17969 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=23/2^7=0.17969 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.17969 mmol L⁻¹, not 0.13477 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.17969 mmol L⁻¹, not 1.17969 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governi... | [
"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_008322 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 8 A for 5568 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": "21.9835 g",
"B": "12.65567 g",
"C": "14.65567 g",
"D": "16.65567 g"
} | C | 14.65567 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×8×5568/(2×96500)=14.65567 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14.65567 g, not 21.9835 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14.65567 g, not 12.65567 g.",
"C": "Correct. The worked calculation gives 14.65567 g.",
"D": "Incorrect. Substituting... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003151 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(1+5i)/(4+1i). What is Re(z), the real part of z? | {
"A": "3.52941",
"B": "0.79412",
"C": "1.52941",
"D": "0.52941"
} | D | 0.52941 | Multiply numerator and denominator by the conjugate (4-1i). Then Re(z)=(ac+bd)/(c²+d²)=((1)(4)+(5)(1))/(4²+(1)²)=0.52941. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.52941, not 3.52941.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.52941, not 0.79412.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.52941, not 1.529... | [
"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_002719 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(8, 6, 5) and v=(-2, 4, -6), calculate u·v. | {
"A": "-22",
"B": "-21",
"C": "-44",
"D": "22"
} | A | -22 | The dot product is the sum of corresponding component products: (8)(-2)+(6)(4)+(5)(-6)=-22. | {
"A": "Correct. The worked calculation gives -22.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -22, not -21.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -22, not -44.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_009320 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.65 V, transfers 2 electrons, and has reaction quotient Q=10^2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.5909 V",
"B": "1.1818 V",
"C": "3.5909 V",
"D": "-1.4091 V"
} | A | 0.5909 V | Apply the Nernst equation: E=0.65−(0.0591/2)(2)=0.5909 V. | {
"A": "Correct. The worked calculation gives 0.5909 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.5909 V, not 1.1818 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5909 V, not 3.5909 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_007207 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 19 mol of gas at 187 K and 2.98 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "-97.83507 L",
"B": "96.83507 L",
"C": "117.40209 L",
"D": "97.83507 L"
} | D | 97.83507 L | PV=nRT, so V=nRT/P=(19)(0.082057)(187)/(2.98)=97.83507 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 97.83507 L, not -97.83507 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 97.83507 L, not 96.83507 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 97.83... | [
"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_008720 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.2 mol L⁻¹ and initially B is absent. At equilibrium, 51% of A has dissociated at constant volume. Find K_c. | {
"A": "2.54792",
"B": "3.82188",
"C": "-0.45208",
"D": "1.25479"
} | A | 2.54792 | Let α=0.51. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.2)(0.51)²/(1−0.51)=2.54792. | {
"A": "Correct. The worked calculation gives 2.54792.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.54792, not 3.82188.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.54792, not -0.45208.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004921 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 3 Ω are connected in series; this combination is connected in parallel with a 11 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.5035 A",
"B": "5.03497 A",
"C": "7.55245 A",
"D": "8.03497 A"
} | B | 5.03497 A | Series branch resistance=10+3=13 Ω. Parallel equivalent R_eq=(13×11)/(13+11)=5.95833 Ω. Total current I=V/R_eq=30/5.95833=5.03497 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.03497 A, not 1.5035 A.",
"B": "Correct. The worked calculation gives 5.03497 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.03497 A, not 7.55245 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_007735 | 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 29 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "2.625 mmol L⁻¹",
"B": "2.71875 mmol L⁻¹",
"C": "1.3625 mmol L⁻¹",
"D": "3.625 mmol L⁻¹"
} | D | 3.625 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=29/2^3=3.625 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.625 mmol L⁻¹, not 2.625 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.625 mmol L⁻¹, not 2.71875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing rel... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002295 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 10 blue and 7 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.671",
"B": "-0.329",
"C": "0.24675",
"D": "0.329"
} | D | 0.329 | Favourable pairs = C(5,2)+C(10,2)+C(7,2)=76. Total pairs=C(22,2)=231. Therefore P=76/231=0.329. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.329, not -0.671.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.329, not -0.329.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.329, not 0.24675.",
... | [
"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_004424 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 1 m is acted on by a constant torque of 76 N m about its central axis. Find its angular acceleration. | {
"A": "30.4 rad s⁻²",
"B": "28.4 rad s⁻²",
"C": "36.48 rad s⁻²",
"D": "-30.4 rad s⁻²"
} | A | 30.4 rad s⁻² | For a solid disc, I=½MR²=½(5)(1)²=2.5 kg m². Using τ=Iα, α=76/2.5=30.4 rad s⁻². | {
"A": "Correct. The worked calculation gives 30.4 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30.4 rad s⁻², not 28.4 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30.4 rad s⁻², not 36.48 rad s⁻².",
"D": "Incorrect. ... | [
"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_003889 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 13 kg block initially moves at 3 m s⁻¹. A constant net force does 20 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "279.5 J",
"B": "278.5 J",
"C": "417.75 J",
"D": "208.875 J"
} | B | 278.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(13)(3)²+(20)(11)=278.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 278.5 J, not 279.5 J.",
"B": "Correct. The worked calculation gives 278.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 278.5 J, not 417.75 J.",
"D": "Incorrect. Substituting the stated v... | [
"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_007717 | 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 18 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "7 mmol L⁻¹",
"B": "6 mmol L⁻¹",
"C": "1.9 mmol L⁻¹",
"D": "9 mmol L⁻¹"
} | D | 9 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=18/2^1=9 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9 mmol L⁻¹, not 7 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9 mmol L⁻¹, not 6 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9 mmol... | [
"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_003524 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 26 m s⁻¹ at 30° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "60.54332 m",
"B": "59.54332 m",
"C": "58.54332 m",
"D": "6.85433 m"
} | C | 58.54332 m | Range R=u²sin(2θ)/g. Substituting u=26, θ=30° and g=10 gives R=(26)²sin(60°)/10=58.54332 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 58.54332 m, not 60.54332 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 58.54332 m, not 59.54332 m.",
"C": "Correct. The worked calculation gives 58.54332 m.",
"D": "Incorrect. Substitutin... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000553 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -6 and common difference 13. Find the sum of its first 26 terms. | {
"A": "4069",
"B": "4068",
"C": "-4069",
"D": "3255.2"
} | A | 4069 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-6, d=13, n=26: Sₙ=26/2[2(-6)+(26−1)(13)]=4069. | {
"A": "Correct. The worked calculation gives 4069.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4069, not 4068.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4069, not -4069.",
"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_007802 | 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 23 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "4.75 mmol L⁻¹",
"B": "4.3125 mmol L⁻¹",
"C": "8.625 mmol L⁻¹",
"D": "5.75 mmol L⁻¹"
} | D | 5.75 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=23/2^2=5.75 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.75 mmol L⁻¹, not 4.75 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.75 mmol L⁻¹, not 4.3125 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relatio... | [
"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_005252 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +1 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "11.02041 N",
"B": "7.5102 N",
"C": "5.5102 N",
"D": "4.13265 N"
} | C | 5.5102 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(1×10⁻⁶)/(7×10⁻²)²=5.5102 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.5102 N, not 11.02041 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.5102 N, not 7.5102 N.",
"C": "Correct. The worked calculation gives 5.5102 N.",
"D": "Incorrect. Substituting the st... | [
"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_001369 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (-4x² +7x +7) dx. | {
"A": "-237.83333",
"B": "-235.83333",
"C": "-236.83333",
"D": "-22.68333"
} | C | -236.83333 | An antiderivative is (-4/3)x³+(7/2)x²+(7)x. Evaluating between 0 and 7 gives (-4/3)(7)³+(7/2)(7)²+(7)(7)=-236.83333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -236.83333, not -237.83333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -236.83333, not -235.83333.",
"C": "Correct. The worked calculation gives -236.83333.",
"D": "Incorrect. Substitutin... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006339 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 8 kg is attached to an ideal spring of force constant 948 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.81627 s",
"B": "-1.81627 s",
"C": "0.18373 s",
"D": "1.01837 s"
} | C | 0.18373 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(8/948)=0.18373 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.18373 s, not -2.81627 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.18373 s, not -1.81627 s.",
"C": "Correct. The worked calculation gives 0.18373 s.",
"D": "Incorrect. Substituting t... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008068 | 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 26245 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": "129.52519 g",
"B": "131.52519 g",
"C": "103.62016 g",
"D": "64.7626 g"
} | A | 129.52519 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×15×26245/(2×96500)=129.52519 g. | {
"A": "Correct. The worked calculation gives 129.52519 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 129.52519 g, not 131.52519 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 129.52519 g, not 103.62016 g.",
"D": "Incorrect. Substi... | [
"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_002360 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -6], [6, -1]]. | {
"A": "32",
"B": "31",
"C": "4.1",
"D": "15.5"
} | B | 31 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(-1)−(-6)(6)=31. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 31, not 32.",
"B": "Correct. The worked calculation gives 31.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 31, not 4.1.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006033 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 61 cm in front of a thin convex lens of focal length 13 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.54167",
"B": "0.13542",
"C": "0.27083",
"D": "-0.27083"
} | C | 0.27083 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(61)(13)/(61−13)=16.52083 cm. Thus |m|=v/u=16.52083/61=0.27083. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.27083, not 0.54167.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.27083, not 0.13542.",
"C": "Correct. The worked calculation gives 0.27083.",
"D": "Incorrect. Substituting the stated va... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008367 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.21 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.63 K",
"B": "1.26 K",
"C": "1.63 K",
"D": "2.63 K"
} | A | 0.63 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×1.0×0.21=0.63 K. | {
"A": "Correct. The worked calculation gives 0.63 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.63 K, not 1.26 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.63 K, not 1.63 K.",
"D": "Incorrect. Substituting the stated values ... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000970 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio -3. What is the sum of its first 5 terms? | {
"A": "244",
"B": "366",
"C": "122",
"D": "243"
} | A | 244 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(-3^5−1)/(-3−1)=244. | {
"A": "Correct. The worked calculation gives 244.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 244, not 366.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 244, not 122.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_001968 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 12 elements can be selected from a set of 51 distinct elements? | {
"A": "158753389899",
"B": "119065042425",
"C": "15875338991",
"D": "158753389900"
} | D | 158753389900 | Order does not matter, so the count is C(51,12)=51!/[12!(39)!]=158753389900. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 158753389900, not 158753389899.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 158753389900, not 119065042425.",
"C": "Incorrect. Substituting the stated values into the governing relation give... | [
"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_007172 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 6 mol of gas at 417 K and 0.33 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "466.60594 L",
"B": "622.14125 L",
"C": "620.14125 L",
"D": "624.14125 L"
} | B | 622.14125 L | PV=nRT, so V=nRT/P=(6)(0.082057)(417)/(0.33)=622.14125 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 622.14125 L, not 466.60594 L.",
"B": "Correct. The worked calculation gives 622.14125 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 622.14125 L, not 620.14125 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_002304 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 6 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.33793",
"B": "0.67586",
"C": "1.33793",
"D": "-0.33793"
} | A | 0.33793 | Favourable pairs = C(12,2)+C(6,2)+C(12,2)=147. Total pairs=C(30,2)=435. Therefore P=147/435=0.33793. | {
"A": "Correct. The worked calculation gives 0.33793.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33793, not 0.67586.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33793, not 1.33793.",
"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_007585 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 57 mL of 0.10 M HCl is mixed with 11 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "3.16975",
"B": "0.58488",
"C": "1.16975",
"D": "0.87731"
} | C | 1.16975 | Excess H⁺ moles=0.10×(57−11)/1000=0.004600 mol. Total volume=0.068 L, so [H⁺]=0.067647 M and pH=−log₁₀[H⁺]=1.16975. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.16975, not 3.16975.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.16975, not 0.58488.",
"C": "Correct. The worked calculation gives 1.16975.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005583 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 35 μF capacitor is charged to a potential difference of 38 V. Calculate the energy stored, expressed in μJ. | {
"A": "50540 μJ",
"B": "25272 μJ",
"C": "25270 μJ",
"D": "-25270 μJ"
} | C | 25270 μJ | U=½CV². Since C=35 μF, U in μJ is ½×35×(38)²=25270 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 25270 μJ, not 50540 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 25270 μJ, not 25272 μJ.",
"C": "Correct. The worked calculation gives 25270 μJ.",
"D": "Incorrect. Substituting the stat... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003887 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block initially moves at 8 m s⁻¹. A constant net force does 11 N of work over 4 m in the direction of motion. Find its final kinetic energy. | {
"A": "-524 J",
"B": "524 J",
"C": "393 J",
"D": "526 J"
} | B | 524 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(15)(8)²+(11)(4)=524 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 524 J, not -524 J.",
"B": "Correct. The worked calculation gives 524 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 524 J, not 393 J.",
"D": "Incorrect. Substituting the stated values into... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006444 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 21 kg is attached to an ideal spring of force constant 976 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.70663 s",
"B": "0.58674 s",
"C": "0.29337 s",
"D": "3.29337 s"
} | C | 0.29337 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(21/976)=0.29337 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29337 s, not -2.70663 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29337 s, not 0.58674 s.",
"C": "Correct. The worked calculation gives 0.29337 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_008985 | 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 0.05 mol L⁻¹ and initially B is absent. At equilibrium, 16% of A has dissociated at constant volume. Find K_c. | {
"A": "0.0061",
"B": "-0.9939",
"C": "3.0061",
"D": "-0.0061"
} | A | 0.0061 | Let α=0.16. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.05)(0.16)²/(1−0.16)=0.0061. | {
"A": "Correct. The worked calculation gives 0.0061.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.0061, not -0.9939.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.0061, not 3.0061.",
"D": "Incorrect. Substituting the stated values... | [
"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_006559 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 1 kg is attached to an ideal spring of force constant 309 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "3.11378 s",
"B": "0.17066 s",
"C": "-2.88622 s",
"D": "0.11378 s"
} | D | 0.11378 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(1/309)=0.11378 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.11378 s, not 3.11378 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.11378 s, not 0.17066 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.11378 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_002886 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, 1, -2) and v=(5, 8, 6), calculate u·v. | {
"A": "4",
"B": "1",
"C": "0",
"D": "3"
} | B | 1 | The dot product is the sum of corresponding component products: (1)(5)+(1)(8)+(-2)(6)=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 4.",
"B": "Correct. The worked calculation gives 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_009584 | 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_10H_16N_1X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "2",
"B": "4.5",
"C": "1.5",
"D": "3"
} | D | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×10+2+1−16−1)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.5.",
"D": "Correct. The worke... | [
"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_004345 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 11 kg and radius 5 m is acted on by a constant torque of 73 N m about its central axis. Find its angular acceleration. | {
"A": "1.53091 rad s⁻²",
"B": "0.53091 rad s⁻²",
"C": "0.39818 rad s⁻²",
"D": "0.79636 rad s⁻²"
} | B | 0.53091 rad s⁻² | For a solid disc, I=½MR²=½(11)(5)²=137.5 kg m². Using τ=Iα, α=73/137.5=0.53091 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.53091 rad s⁻², not 1.53091 rad s⁻².",
"B": "Correct. The worked calculation gives 0.53091 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.53091 rad s⁻², not 0.39818 rad s⁻².",
"D"... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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