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_008134 | 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 10556 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "13.89235 g",
"B": "20.83853 g",
"C": "15.89235 g",
"D": "14.89235 g"
} | A | 13.89235 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×10556/(2×96500)=13.89235 g. | {
"A": "Correct. The worked calculation gives 13.89235 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13.89235 g, not 20.83853 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13.89235 g, not 15.89235 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_003716 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block initially moves at 5 m s⁻¹. A constant net force does 22 N of work over 15 m in the direction of motion. Find its final kinetic energy. | {
"A": "51.5 J",
"B": "507 J",
"C": "404 J",
"D": "505 J"
} | D | 505 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(14)(5)²+(22)(15)=505 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 505 J, not 51.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 505 J, not 507 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 505 J, not 404 J.",
"D"... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005262 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +8 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "35.55556 N",
"B": "53.33333 N",
"C": "37.55556 N",
"D": "34.55556 N"
} | A | 35.55556 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(8×10⁻⁶)/(9×10⁻²)²=35.55556 N. | {
"A": "Correct. The worked calculation gives 35.55556 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 35.55556 N, not 53.33333 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 35.55556 N, not 37.55556 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_003389 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 75 m s⁻¹ at 75° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "279.25 m",
"B": "210.9375 m",
"C": "29.125 m",
"D": "281.25 m"
} | D | 281.25 m | Range R=u²sin(2θ)/g. Substituting u=75, θ=75° and g=10 gives R=(75)²sin(150°)/10=281.25 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 281.25 m, not 279.25 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 281.25 m, not 210.9375 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 281.25 m, no... | [
"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_002054 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 7 red, 4 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-2.68571",
"B": "0.62857",
"C": "0.31429",
"D": "-1.68571"
} | C | 0.31429 | Favourable pairs = C(7,2)+C(4,2)+C(4,2)=33. Total pairs=C(15,2)=105. Therefore P=33/105=0.31429. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31429, not -2.68571.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31429, not 0.62857.",
"C": "Correct. The worked calculation gives 0.31429.",
"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_005261 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +9 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "632 N",
"B": "630 N",
"C": "945 N",
"D": "628 N"
} | B | 630 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(9×10⁻⁶)/(3×10⁻²)²=630 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 630 N, not 632 N.",
"B": "Correct. The worked calculation gives 630 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 630 N, not 945 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_000632 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -4 and common difference 6. Find the sum of its first 10 terms. | {
"A": "232",
"B": "230",
"C": "172.5",
"D": "345"
} | B | 230 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-4, d=6, n=10: Sₙ=10/2[2(-4)+(10−1)(6)]=230. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 230, not 232.",
"B": "Correct. The worked calculation gives 230.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 230, not 172.5.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_006488 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 4 kg is attached to an ideal spring of force constant 640 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "2.15811 s",
"B": "-0.84189 s",
"C": "1.01581 s",
"D": "0.15811 s"
} | D | 0.15811 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(4/640)=0.15811 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.15811 s, not 2.15811 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.15811 s, not -0.84189 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.15811 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_006721 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 28 mol H₂ and 7 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "-14 mol",
"B": "11 mol",
"C": "16 mol",
"D": "14 mol"
} | D | 14 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 28 mol H₂O; O₂ can produce 14 mol H₂O. The limiting condition is O₂; product=14 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14 mol, not -14 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14 mol, not 11 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14 mol, not 16 mol.",... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004875 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 11 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 4 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.14 A",
"B": "8.4 A",
"C": "-11.4 A",
"D": "11.4 A"
} | D | 11.4 A | Series branch resistance=11+4=15 Ω. Parallel equivalent R_eq=(15×4)/(15+4)=3.15789 Ω. Total current I=V/R_eq=36/3.15789=11.4 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.4 A, not 2.14 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.4 A, not 8.4 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.4 A, not -11.4 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_003156 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-15+7i)/(10+1i). What is Re(z), the real part of z? | {
"A": "-2.41584",
"B": "-0.41584",
"C": "-1.41584",
"D": "-3.41584"
} | C | -1.41584 | Multiply numerator and denominator by the conjugate (10-1i). Then Re(z)=(ac+bd)/(c²+d²)=((-15)(10)+(7)(1))/(10²+(1)²)=-1.41584. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.41584, not -2.41584.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.41584, not -0.41584.",
"C": "Correct. The worked calculation gives -1.41584.",
"D": "Incorrect. Substituting the stat... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005080 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +2 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "-22.5 N",
"B": "45 N",
"C": "21.5 N",
"D": "22.5 N"
} | D | 22.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(2×10⁻⁶)/(4×10⁻²)²=22.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22.5 N, not -22.5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22.5 N, not 45 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22.5 N, not 21.5 N.",
... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009417 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_5H_7X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "0.75",
"B": "1",
"C": "3",
"D": "1.5"
} | B | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×5+2+0−7−3)/2=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.75.",
"B": "Correct. The worked calculation gives 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 3.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"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_006540 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 7 kg is attached to an ideal spring of force constant 696 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "3.20057 s",
"B": "0.30086 s",
"C": "0.20057 s",
"D": "-0.79943 s"
} | C | 0.20057 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(7/696)=0.20057 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.20057 s, not 3.20057 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.20057 s, not 0.30086 s.",
"C": "Correct. The worked calculation gives 0.20057 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_002920 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(3, 5, -3) and v=(8, 9, -7), calculate u·v. | {
"A": "67.5",
"B": "90",
"C": "108",
"D": "88"
} | B | 90 | The dot product is the sum of corresponding component products: (3)(8)+(5)(9)+(-3)(-7)=90. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 90, not 67.5.",
"B": "Correct. The worked calculation gives 90.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 90, not 108.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008043 | 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 9092 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": "19.44416 g",
"B": "36.88832 g",
"C": "40.88832 g",
"D": "38.88832 g"
} | D | 38.88832 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×9092/(2×96500)=38.88832 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 38.88832 g, not 19.44416 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 38.88832 g, not 36.88832 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 38.888... | [
"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_004917 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 4 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "13.33333 A",
"B": "7.75 A",
"C": "11.33333 A",
"D": "10.33333 A"
} | D | 10.33333 A | Series branch resistance=13+14=27 Ω. Parallel equivalent R_eq=(27×4)/(27+4)=3.48387 Ω. Total current I=V/R_eq=36/3.48387=10.33333 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.33333 A, not 13.33333 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.33333 A, not 7.75 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10.33333 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_000905 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio -3. What is the sum of its first 12 terms? | {
"A": "-265720",
"B": "-26571",
"C": "-132860",
"D": "-265719"
} | A | -265720 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(-3^12−1)/(-3−1)=-265720. | {
"A": "Correct. The worked calculation gives -265720.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -265720, not -26571.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -265720, not -132860.",
"D": "Incorrect. Substituting the stated val... | [
"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_008897 | 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 1.18 mol L⁻¹ and initially B is absent. At equilibrium, 15% of A has dissociated at constant volume. Find K_c. | {
"A": "0.18741",
"B": "1.12494",
"C": "2.12494",
"D": "0.12494"
} | D | 0.12494 | Let α=0.15. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.18)(0.15)²/(1−0.15)=0.12494. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.12494, not 0.18741.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.12494, not 1.12494.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.12494, not 2.124... | [
"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_002326 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 7 red, 4 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": "1.31373",
"B": "-0.68627",
"C": "1.03137",
"D": "0.31373"
} | D | 0.31373 | Favourable pairs = C(7,2)+C(4,2)+C(7,2)=48. Total pairs=C(18,2)=153. Therefore P=48/153=0.31373. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31373, not 1.31373.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31373, not -0.68627.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31373, not 1.03... | [
"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_005830 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.7 atm at 431 K. What is its pressure at 521 K? | {
"A": "-2.15383 atm",
"B": "-0.84617 atm",
"C": "0.84617 atm",
"D": "1.08462 atm"
} | C | 0.84617 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.7)(521)/(431)=0.84617 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.84617 atm, not -2.15383 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.84617 atm, not -0.84617 atm.",
"C": "Correct. The worked calculation gives 0.84617 atm.",
"D": "Incorrect. Subs... | [
"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_002392 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, 6], [7, -7]]. | {
"A": "-98",
"B": "-99",
"C": "98",
"D": "-96"
} | A | -98 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(-7)−(6)(7)=-98. | {
"A": "Correct. The worked calculation gives -98.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -98, not -99.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -98, not 98.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002994 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-3, 1, 5) and v=(3, 4, 9), calculate u·v. | {
"A": "20",
"B": "40",
"C": "60",
"D": "30"
} | B | 40 | The dot product is the sum of corresponding component products: (-3)(3)+(1)(4)+(5)(9)=40. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 40, not 20.",
"B": "Correct. The worked calculation gives 40.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 40, not 60.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_008155 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 2 A for 29217 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": "17.22569 g",
"B": "9.61285 g",
"C": "2.92257 g",
"D": "19.22569 g"
} | D | 19.22569 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×2×29217/(2×96500)=19.22569 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19.22569 g, not 17.22569 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19.22569 g, not 9.61285 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19.2256... | [
"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_000932 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio -3. What is the sum of its first 7 terms? | {
"A": "1092",
"B": "1094",
"C": "1095",
"D": "547"
} | B | 1094 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(-3^7−1)/(-3−1)=1094. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1094, not 1092.",
"B": "Correct. The worked calculation gives 1094.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1094, not 1095.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_000912 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio 2. What is the sum of its first 10 terms? | {
"A": "6547.2",
"B": "9820.8",
"C": "8184",
"D": "12276"
} | C | 8184 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(2^10−1)/(2−1)=8184. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8184, not 6547.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8184, not 9820.8.",
"C": "Correct. The worked calculation gives 8184.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_009798 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(CN)_4]^-1, each CN ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "3",
"B": "4",
"C": "0",
"D": "1"
} | A | 3 | Let the formal oxidation state of Cr be x. Charge balance gives x+(4)(−1)=-1; hence x=-1+4=+3. | {
"A": "Correct. The worked calculation gives 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 0.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002434 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, 3], [2, 8]]. | {
"A": "1",
"B": "2",
"C": "1.5",
"D": "3"
} | B | 2 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(8)−(3)(2)=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.5.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004072 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.21. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "12.96 N",
"B": "2.728 N",
"C": "20.736 N",
"D": "17.28 N"
} | D | 17.28 N | Net force=mg(sinθ−μcosθ)=4×10×(0.6−0.21×0.8)=17.28 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 17.28 N, not 12.96 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17.28 N, not 2.728 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17.28 N, not 20.73... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001413 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (2x² +0x +3) dx. | {
"A": "2.75",
"B": "1.83333",
"C": "3.66667",
"D": "1.66667"
} | C | 3.66667 | An antiderivative is (2/3)x³+(0/2)x²+(3)x. Evaluating between 0 and 1 gives (2/3)(1)³+(0/2)(1)²+(3)(1)=3.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.66667, not 2.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.66667, not 1.83333.",
"C": "Correct. The worked calculation gives 3.66667.",
"D": "Incorrect. Substituting the stated value... | [
"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_008289 | 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 14827 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": "-39.02651 g",
"B": "41.02651 g",
"C": "39.02651 g",
"D": "40.02651 g"
} | C | 39.02651 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×8×14827/(2×96500)=39.02651 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 39.02651 g, not -39.02651 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39.02651 g, not 41.02651 g.",
"C": "Correct. The worked calculation gives 39.02651 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_007563 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 92 mL of 0.10 M HCl is mixed with 26 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-0.74766",
"B": "4.25234",
"C": "1.25234",
"D": "0.62617"
} | C | 1.25234 | Excess H⁺ moles=0.10×(92−26)/1000=0.006600 mol. Total volume=0.118 L, so [H⁺]=0.055932 M and pH=−log₁₀[H⁺]=1.25234. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.25234, not -0.74766.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.25234, not 4.25234.",
"C": "Correct. The worked calculation gives 1.25234.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005841 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.4 atm at 221 K. What is its pressure at 749 K? | {
"A": "7.45611 atm",
"B": "22.36833 atm",
"C": "14.91222 atm",
"D": "11.18416 atm"
} | C | 14.91222 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.4)(749)/(221)=14.91222 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14.91222 atm, not 7.45611 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14.91222 atm, not 22.36833 atm.",
"C": "Correct. The worked calculation gives 14.91222 atm.",
"D": "Incorrect. Su... | [
"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_001020 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=1x³ +6x² +2x+7. Evaluate f′(-2). | {
"A": "-10",
"B": "-12",
"C": "0",
"D": "-5"
} | A | -10 | Differentiate: f′(x)=3(1)x²+2(6)x+(2). At x=-2, f′(-2)=3(1)(-2)²+2(6)(-2)+(2)=-10. | {
"A": "Correct. The worked calculation gives -10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -10, not -12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -10, not 0.",
"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_005635 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 5 μF capacitor is charged to a potential difference of 29 V. Calculate the energy stored, expressed in μJ. | {
"A": "2104.5 μJ",
"B": "4205 μJ",
"C": "2102.5 μJ",
"D": "2101.5 μJ"
} | C | 2102.5 μJ | U=½CV². Since C=5 μF, U in μJ is ½×5×(29)²=2102.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2102.5 μJ, not 2104.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2102.5 μJ, not 4205 μJ.",
"C": "Correct. The worked calculation gives 2102.5 μJ.",
"D": "Incorrect. Substituting the s... | [
"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_000314 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 +11x -10=0, let its roots be α and β. What is α²+β²? | {
"A": "40.25",
"B": "-40.25",
"C": "80.5",
"D": "39.25"
} | A | 40.25 | By Vieta's relations, α+β = -11/2 and αβ = -10/2. Then α²+β²=(α+β)²−2αβ = (-11/2)²−2(-10/2) = 40.25. | {
"A": "Correct. The worked calculation gives 40.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 40.25, not -40.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 40.25, not 80.5.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_009681 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(CN)_5]^+2, each CN ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "5.25",
"B": "4",
"C": "7",
"D": "1.7"
} | C | 7 | Let the formal oxidation state of Cr be x. Charge balance gives x+(5)(−1)=+2; hence x=2+5=+7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 5.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 4.",
"C": "Correct. The worked calculation gives 7.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009447 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_12H_23N_1X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "0",
"C": "-3",
"D": "2"
} | B | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×12+2+1−23−4)/2=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 3.",
"B": "Correct. The worked calculation gives 0.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008250 | 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 8291 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": "30.68851 g",
"B": "39.91802 g",
"C": "5.0918 g",
"D": "40.91802 g"
} | D | 40.91802 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×15×8291/(2×96500)=40.91802 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 40.91802 g, not 30.68851 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 40.91802 g, not 39.91802 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 40.918... | [
"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_005164 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +5 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "-87.5 N",
"B": "87.5 N",
"C": "175 N",
"D": "89.5 N"
} | B | 87.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(5×10⁻⁶)/(6×10⁻²)²=87.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 87.5 N, not -87.5 N.",
"B": "Correct. The worked calculation gives 87.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 87.5 N, not 175 N.",
"D": "Incorrect. Substituting the stated values ... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006774 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 2 mol H₂ and 2 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "3 mol",
"B": "2 mol",
"C": "5 mol",
"D": "-1 mol"
} | B | 2 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 2 mol H₂O; O₂ can produce 4 mol H₂O. The limiting condition is H₂; product=2 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 3 mol.",
"B": "Correct. The worked calculation gives 2 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 5 mol.",
"D": "Incorrect. Substituting the stated values into ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006448 | 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 551 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.14758 s",
"B": "-0.14758 s",
"C": "0.14758 s",
"D": "0.22136 s"
} | C | 0.14758 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(3/551)=0.14758 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.14758 s, not 1.14758 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.14758 s, not -0.14758 s.",
"C": "Correct. The worked calculation gives 0.14758 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_003373 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 100 m s⁻¹ at 18° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "705.3423 m",
"B": "585.78525 m",
"C": "881.67788 m",
"D": "587.78525 m"
} | D | 587.78525 m | Range R=u²sin(2θ)/g. Substituting u=100, θ=18° and g=10 gives R=(100)²sin(36°)/10=587.78525 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 587.78525 m, not 705.3423 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 587.78525 m, not 585.78525 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 587... | [
"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_006207 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 55 cm in front of a thin convex lens of focal length 21 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.61765",
"B": "0.46324",
"C": "1.23529",
"D": "2.61765"
} | A | 0.61765 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(55)(21)/(55−21)=33.97059 cm. Thus |m|=v/u=33.97059/55=0.61765. | {
"A": "Correct. The worked calculation gives 0.61765.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.61765, not 0.46324.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.61765, not 1.23529.",
"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_007966 | 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 70 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "6.5625 mmol L⁻¹",
"B": "4.375 mmol L⁻¹",
"C": "8.75 mmol L⁻¹",
"D": "3.28125 mmol L⁻¹"
} | B | 4.375 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=70/2^4=4.375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.375 mmol L⁻¹, not 6.5625 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 4.375 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.375 mmol L⁻¹, not 8.75 mmol L⁻¹.",
"D": "In... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009056 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.62 V, transfers 3 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.5215 V",
"B": "1.05215 V",
"C": "3.5215 V",
"D": "-0.5215 V"
} | A | 0.5215 V | Apply the Nernst equation: E=0.62−(0.0591/3)(5)=0.5215 V. | {
"A": "Correct. The worked calculation gives 0.5215 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.5215 V, not 1.05215 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5215 V, not 3.5215 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003508 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 45 m s⁻¹ at 65° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "154.124 m",
"B": "155.124 m",
"C": "-155.124 m",
"D": "186.1488 m"
} | B | 155.124 m | Range R=u²sin(2θ)/g. Substituting u=45, θ=65° and g=10 gives R=(45)²sin(130°)/10=155.124 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 155.124 m, not 154.124 m.",
"B": "Correct. The worked calculation gives 155.124 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 155.124 m, not -155.124 m.",
"D": "Incorrect. Substituting th... | [
"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_004195 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 38 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.44. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "95.24 N",
"B": "92.24 N",
"C": "141.36 N",
"D": "94.24 N"
} | D | 94.24 N | Net force=mg(sinθ−μcosθ)=38×10×(0.6−0.44×0.8)=94.24 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 94.24 N, not 95.24 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 94.24 N, not 92.24 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 94.24 N, not 141.3... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009120 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.80 V, transfers 1 electrons, and has reaction quotient Q=10^0. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.8 V",
"B": "-0.8 V",
"C": "-1.2 V",
"D": "1.2 V"
} | A | 0.8 V | Apply the Nernst equation: E=0.80−(0.0591/1)(0)=0.8 V. | {
"A": "Correct. The worked calculation gives 0.8 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8 V, not -0.8 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8 V, not -1.2 V.",
"D": "Incorrect. Substituting the stated values int... | [
"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_001097 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ +6x² +6x+7. Evaluate f′(2). | {
"A": "-78",
"B": "78",
"C": "8.8",
"D": "77"
} | B | 78 | Differentiate: f′(x)=3(4)x²+2(6)x+(6). At x=2, f′(2)=3(4)(2)²+2(6)(2)+(6)=78. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 78, not -78.",
"B": "Correct. The worked calculation gives 78.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 78, not 8.8.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"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_007864 | 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 52 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "9.75 mmol L⁻¹",
"B": "13 mmol L⁻¹",
"C": "14 mmol L⁻¹",
"D": "15 mmol L⁻¹"
} | B | 13 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=52/2^2=13 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13 mmol L⁻¹, not 9.75 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 13 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13 mmol L⁻¹, not 14 mmol L⁻¹.",
"D": "Incorrect. Subs... | [
"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_007831 | 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 36 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "0.5625 mmol L⁻¹",
"B": "-0.71875 mmol L⁻¹",
"C": "0.21094 mmol L⁻¹",
"D": "0.28125 mmol L⁻¹"
} | D | 0.28125 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=36/2^7=0.28125 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.28125 mmol L⁻¹, not 0.5625 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.28125 mmol L⁻¹, not -0.71875 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_005733 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.2 atm at 228 K. What is its pressure at 695 K? | {
"A": "5.48684 atm",
"B": "1.82895 atm",
"C": "3.65789 atm",
"D": "4.65789 atm"
} | C | 3.65789 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.2)(695)/(228)=3.65789 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.65789 atm, not 5.48684 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.65789 atm, not 1.82895 atm.",
"C": "Correct. The worked calculation gives 3.65789 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008996 | 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 mol L⁻¹ and initially B is absent. At equilibrium, 29% of A has dissociated at constant volume. Find K_c. | {
"A": "1.04738",
"B": "0.4738",
"C": "-0.4738",
"D": "-0.5262"
} | B | 0.4738 | Let α=0.29. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1)(0.29)²/(1−0.29)=0.4738. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.4738, not 1.04738.",
"B": "Correct. The worked calculation gives 0.4738.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.4738, not -0.4738.",
"D": "Incorrect. Substituting the stated value... | [
"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_003129 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-6+9i)/(12+6i). What is Re(z), the real part of z? | {
"A": "-0.1",
"B": "-0.15",
"C": "2.9",
"D": "-3.1"
} | A | -0.1 | Multiply numerator and denominator by the conjugate (12-6i). Then Re(z)=(ac+bd)/(c²+d²)=((-6)(12)+(9)(6))/(12²+(6)²)=-0.1. | {
"A": "Correct. The worked calculation gives -0.1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.1, not -0.15.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.1, not 2.9.",
"D": "Incorrect. Substituting the stated values into the g... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005673 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.7 atm at 420 K. What is its pressure at 736 K? | {
"A": "1.48952 atm",
"B": "2.97905 atm",
"C": "-2.97905 atm",
"D": "2.23429 atm"
} | B | 2.97905 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.7)(736)/(420)=2.97905 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.97905 atm, not 1.48952 atm.",
"B": "Correct. The worked calculation gives 2.97905 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.97905 atm, not -2.97905 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_007266 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 9 mol of gas at 387 K and 2.79 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "76.82918 L",
"B": "102.4389 L",
"C": "204.8778 L",
"D": "104.4389 L"
} | B | 102.4389 L | PV=nRT, so V=nRT/P=(9)(0.082057)(387)/(2.79)=102.4389 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 102.4389 L, not 76.82918 L.",
"B": "Correct. The worked calculation gives 102.4389 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 102.4389 L, not 204.8778 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_002133 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 4 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.59341",
"B": "-0.7033",
"C": "0.22253",
"D": "0.2967"
} | D | 0.2967 | Favourable pairs = C(6,2)+C(4,2)+C(4,2)=27. Total pairs=C(14,2)=91. Therefore P=27/91=0.2967. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.2967, not 0.59341.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.2967, not -0.7033.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.2967, not 0.22253.... | [
"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_004197 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 47 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.43. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "118.32 N",
"B": "60.16 N",
"C": "120.32 N",
"D": "13.032 N"
} | C | 120.32 N | Net force=mg(sinθ−μcosθ)=47×10×(0.6−0.43×0.8)=120.32 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 120.32 N, not 118.32 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 120.32 N, not 60.16 N.",
"C": "Correct. The worked calculation gives 120.32 N.",
"D": "Incorrect. Substituting the state... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003705 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block initially moves at 10 m s⁻¹. A constant net force does 15 N of work over 16 m in the direction of motion. Find its final kinetic energy. | {
"A": "705 J",
"B": "-940 J",
"C": "470 J",
"D": "940 J"
} | D | 940 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(14)(10)²+(15)(16)=940 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 940 J, not 705 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 940 J, not -940 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 940 J, not 470 J.",
"D"... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001335 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ -3x² +1x+7. Evaluate f′(4). | {
"A": "-262",
"B": "-131.5",
"C": "-263",
"D": "-526"
} | C | -263 | Differentiate: f′(x)=3(-5)x²+2(-3)x+(1). At x=4, f′(4)=3(-5)(4)²+2(-3)(4)+(1)=-263. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -263, not -262.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -263, not -131.5.",
"C": "Correct. The worked calculation gives -263.",
"D": "Incorrect. Substituting the stated values into the... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003894 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 3 m s⁻¹. A constant net force does 16 N of work over 16 m in the direction of motion. Find its final kinetic energy. | {
"A": "372 J",
"B": "310 J",
"C": "465 J",
"D": "232.5 J"
} | B | 310 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(3)²+(16)(16)=310 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 310 J, not 372 J.",
"B": "Correct. The worked calculation gives 310 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 310 J, not 465 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_007260 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 12 mol of gas at 451 K and 2.15 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "154.91598 L",
"B": "103.27732 L",
"C": "21.65546 L",
"D": "206.55464 L"
} | D | 206.55464 L | PV=nRT, so V=nRT/P=(12)(0.082057)(451)/(2.15)=206.55464 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 206.55464 L, not 154.91598 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 206.55464 L, not 103.27732 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20... | [
"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_008909 | 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 0.68 mol L⁻¹ and initially B is absent. At equilibrium, 12% of A has dissociated at constant volume. Find K_c. | {
"A": "0.03338",
"B": "3.04451",
"C": "0.04451",
"D": "2.04451"
} | C | 0.04451 | Let α=0.12. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.68)(0.12)²/(1−0.12)=0.04451. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.04451, not 0.03338.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.04451, not 3.04451.",
"C": "Correct. The worked calculation gives 0.04451.",
"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_000793 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 3. What is the sum of its first 11 terms? | {
"A": "1771460",
"B": "885729",
"C": "885730",
"D": "885728"
} | C | 885730 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(3^11−1)/(3−1)=885730. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 885730, not 1771460.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 885730, not 885729.",
"C": "Correct. The worked calculation gives 885730.",
"D": "Incorrect. Substituting the stated values... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002297 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 5 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.29167",
"B": "0.29167",
"C": "0.58333",
"D": "2.29167"
} | B | 0.29167 | Favourable pairs = C(5,2)+C(5,2)+C(6,2)=35. Total pairs=C(16,2)=120. Therefore P=35/120=0.29167. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29167, not 1.29167.",
"B": "Correct. The worked calculation gives 0.29167.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29167, not 0.58333.",
"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_000075 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 +12x +8=0, let its roots be α and β. What is α²+β²? | {
"A": "0.33333",
"B": "1.33333",
"C": "1.13333",
"D": "2"
} | B | 1.33333 | By Vieta's relations, α+β = -12/6 and αβ = 8/6. Then α²+β²=(α+β)²−2αβ = (-12/6)²−2(8/6) = 1.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.33333, not 0.33333.",
"B": "Correct. The worked calculation gives 1.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.33333, not 1.13333.",
"D": "Incorrect. Substituting the stated va... | [
"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_002287 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 11 red, 12 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": "0.48966",
"B": "-1.67356",
"C": "0.32644",
"D": "-0.32644"
} | C | 0.32644 | Favourable pairs = C(11,2)+C(12,2)+C(7,2)=142. Total pairs=C(30,2)=435. Therefore P=142/435=0.32644. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32644, not 0.48966.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32644, not -1.67356.",
"C": "Correct. The worked calculation gives 0.32644.",
"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_004324 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 49 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.29. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "360.64 N",
"B": "180.32 N",
"C": "182.32 N",
"D": "144.256 N"
} | B | 180.32 N | Net force=mg(sinθ−μcosθ)=49×10×(0.6−0.29×0.8)=180.32 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 180.32 N, not 360.64 N.",
"B": "Correct. The worked calculation gives 180.32 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 180.32 N, not 182.32 N.",
"D": "Incorrect. Substituting the stat... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005918 | 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 2.1 atm at 238 K. What is its pressure at 509 K? | {
"A": "-4.49118 atm",
"B": "2.49118 atm",
"C": "4.49118 atm",
"D": "1.44912 atm"
} | C | 4.49118 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.1)(509)/(238)=4.49118 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.49118 atm, not -4.49118 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.49118 atm, not 2.49118 atm.",
"C": "Correct. The worked calculation gives 4.49118 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_001567 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (-1x² +2x +2) dx. | {
"A": "-6.66667",
"B": "-7.66667",
"C": "-9.66667",
"D": "-5"
} | A | -6.66667 | An antiderivative is (-1/3)x³+(2/2)x²+(2)x. Evaluating between 0 and 5 gives (-1/3)(5)³+(2/2)(5)²+(2)(5)=-6.66667. | {
"A": "Correct. The worked calculation gives -6.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -6.66667, not -7.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -6.66667, not -9.66667.",
"D": "Incorrect. Substituting the stat... | [
"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_009251 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.49 V, transfers 3 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.4112 V",
"B": "-1.4112 V",
"C": "4.4112 V",
"D": "0.4112 V"
} | A | 1.4112 V | Apply the Nernst equation: E=1.49−(0.0591/3)(4)=1.4112 V. | {
"A": "Correct. The worked calculation gives 1.4112 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4112 V, not -1.4112 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.4112 V, not 4.4112 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007350 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 77 mL of 0.10 M HCl is mixed with 10 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.11134",
"B": "1.11344",
"C": "-0.88656",
"D": "4.11344"
} | B | 1.11344 | Excess H⁺ moles=0.10×(77−10)/1000=0.006700 mol. Total volume=0.087 L, so [H⁺]=0.077011 M and pH=−log₁₀[H⁺]=1.11344. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.11344, not 1.11134.",
"B": "Correct. The worked calculation gives 1.11344.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.11344, not -0.88656.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009941 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(CN)_6]^+0, each CN ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "8",
"B": "1.6",
"C": "7",
"D": "6"
} | D | 6 | Let the formal oxidation state of Cr be x. Charge balance gives x+(6)(−1)=+0; hence x=0+6=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 1.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 7.",
"D": "Correct. The worked ... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005960 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.2 atm at 373 K. What is its pressure at 745 K? | {
"A": "12.78284 atm",
"B": "8.39142 atm",
"C": "4.39142 atm",
"D": "6.39142 atm"
} | D | 6.39142 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.2)(745)/(373)=6.39142 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.39142 atm, not 12.78284 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.39142 atm, not 8.39142 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6... | [
"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_006006 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 53 cm in front of a thin convex lens of focal length 18 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "3.51429",
"B": "0.77143",
"C": "2.51429",
"D": "0.51429"
} | D | 0.51429 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(53)(18)/(53−18)=27.25714 cm. Thus |m|=v/u=27.25714/53=0.51429. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.51429, not 3.51429.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.51429, not 0.77143.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.51429, not 2.514... | [
"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_002674 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(6, 0, 6) and v=(-7, -6, -2), calculate u·v. | {
"A": "-56",
"B": "-54",
"C": "-108",
"D": "-27"
} | B | -54 | The dot product is the sum of corresponding component products: (6)(-7)+(0)(-6)+(6)(-2)=-54. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -54, not -56.",
"B": "Correct. The worked calculation gives -54.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -54, not -108.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_009332 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.24 V, transfers 3 electrons, and has reaction quotient Q=10^0. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.24 V",
"B": "1.86 V",
"C": "1.24 V",
"D": "3.24 V"
} | C | 1.24 V | Apply the Nernst equation: E=1.24−(0.0591/3)(0)=1.24 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.24 V, not -1.24 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.24 V, not 1.86 V.",
"C": "Correct. The worked calculation gives 1.24 V.",
"D": "Incorrect. Substituting the stated values... | [
"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_004820 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 11 Ω and 3 Ω are connected in series; this combination is connected in parallel with a 3 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "9.10714 A",
"B": "12.14286 A",
"C": "-12.14286 A",
"D": "11.14286 A"
} | B | 12.14286 A | Series branch resistance=11+3=14 Ω. Parallel equivalent R_eq=(14×3)/(14+3)=2.47059 Ω. Total current I=V/R_eq=30/2.47059=12.14286 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.14286 A, not 9.10714 A.",
"B": "Correct. The worked calculation gives 12.14286 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.14286 A, not -12.14286 A.",
"D": "Incorrect. Substitutin... | [
"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_007041 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 20 mol of gas at 609 K and 0.49 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "2040.70257 L",
"B": "2041.70257 L",
"C": "2039.70257 L",
"D": "1529.77693 L"
} | C | 2039.70257 L | PV=nRT, so V=nRT/P=(20)(0.082057)(609)/(0.49)=2039.70257 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2039.70257 L, not 2040.70257 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2039.70257 L, not 2041.70257 L.",
"C": "Correct. The worked calculation gives 2039.70257 L.",
"D": "Incorrect. S... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008499 | 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 0.37 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.555 K",
"B": "0.74 K",
"C": "1.48 K",
"D": "3.74 K"
} | B | 0.74 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×0.37=0.74 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.74 K, not 0.555 K.",
"B": "Correct. The worked calculation gives 0.74 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.74 K, not 1.48 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_003305 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(5+6i)/(7+7i). What is Re(z), the real part of z? | {
"A": "0.58929",
"B": "0.78571",
"C": "1.57143",
"D": "-0.21429"
} | B | 0.78571 | Multiply numerator and denominator by the conjugate (7-7i). Then Re(z)=(ac+bd)/(c²+d²)=((5)(7)+(6)(7))/(7²+(7)²)=0.78571. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.78571, not 0.58929.",
"B": "Correct. The worked calculation gives 0.78571.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.78571, not 1.57143.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005307 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +8 μC are separated by 5 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "21.16 N",
"B": "201.6 N",
"C": "302.4 N",
"D": "161.28 N"
} | B | 201.6 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(8×10⁻⁶)/(5×10⁻²)²=201.6 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 201.6 N, not 21.16 N.",
"B": "Correct. The worked calculation gives 201.6 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 201.6 N, not 302.4 N.",
"D": "Incorrect. Substituting the stated va... | [
"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_009095 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.16 V, transfers 3 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "4.1994 V",
"B": "1.1994 V",
"C": "1.7991 V",
"D": "-0.8006 V"
} | B | 1.1994 V | Apply the Nernst equation: E=1.16−(0.0591/3)(-2)=1.1994 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.1994 V, not 4.1994 V.",
"B": "Correct. The worked calculation gives 1.1994 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1994 V, not 1.7991 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_002103 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 10 blue and 9 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-1.68966",
"B": "-0.31034",
"C": "0.31034",
"D": "-0.68966"
} | C | 0.31034 | Favourable pairs = C(10,2)+C(10,2)+C(9,2)=126. Total pairs=C(29,2)=406. Therefore P=126/406=0.31034. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31034, not -1.68966.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31034, not -0.31034.",
"C": "Correct. The worked calculation gives 0.31034.",
"D": "Incorrect. Substituting the stated ... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004539 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 9 kg and radius 1 m is acted on by a constant torque of 40 N m about its central axis. Find its angular acceleration. | {
"A": "-8.88889 rad s⁻²",
"B": "5.88889 rad s⁻²",
"C": "8.88889 rad s⁻²",
"D": "9.88889 rad s⁻²"
} | C | 8.88889 rad s⁻² | For a solid disc, I=½MR²=½(9)(1)²=4.5 kg m². Using τ=Iα, α=40/4.5=8.88889 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.88889 rad s⁻², not -8.88889 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.88889 rad s⁻², not 5.88889 rad s⁻².",
"C": "Correct. The worked calculation gives 8.88889 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_006673 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 22 mol H₂ and 12 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "3.2 mol",
"B": "22 mol",
"C": "21 mol",
"D": "20 mol"
} | B | 22 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 22 mol H₂O; O₂ can produce 24 mol H₂O. The limiting condition is H₂; product=22 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22 mol, not 3.2 mol.",
"B": "Correct. The worked calculation gives 22 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22 mol, not 21 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_004511 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 13 kg and radius 3 m is acted on by a constant torque of 81 N m about its central axis. Find its angular acceleration. | {
"A": "1.38462 rad s⁻²",
"B": "-1.38462 rad s⁻²",
"C": "2.07692 rad s⁻²",
"D": "2.76923 rad s⁻²"
} | A | 1.38462 rad s⁻² | For a solid disc, I=½MR²=½(13)(3)²=58.5 kg m². Using τ=Iα, α=81/58.5=1.38462 rad s⁻². | {
"A": "Correct. The worked calculation gives 1.38462 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.38462 rad s⁻², not -1.38462 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.38462 rad s⁻², not 2.07692 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_008189 | 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 6130 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": "9.06746 g",
"B": "10.06746 g",
"C": "4.03373 g",
"D": "8.06746 g"
} | D | 8.06746 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×6130/(2×96500)=8.06746 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.06746 g, not 9.06746 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.06746 g, not 10.06746 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.06746 g... | [
"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_009269 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.47 V, transfers 3 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.01385 V",
"B": "2.7036 V",
"C": "1.3518 V",
"D": "-0.6482 V"
} | C | 1.3518 V | Apply the Nernst equation: E=1.47−(0.0591/3)(6)=1.3518 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.3518 V, not 1.01385 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.3518 V, not 2.7036 V.",
"C": "Correct. The worked calculation gives 1.3518 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009081 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.19 V, transfers 2 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "4.33775 V",
"B": "1.33775 V",
"C": "1.00331 V",
"D": "-1.66225 V"
} | B | 1.33775 V | Apply the Nernst equation: E=1.19−(0.0591/2)(-5)=1.33775 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.33775 V, not 4.33775 V.",
"B": "Correct. The worked calculation gives 1.33775 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.33775 V, not 1.00331 V.",
"D": "Incorrect. Substituting the... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000125 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 -13x +4=0, let its roots be α and β. What is α²+β²? | {
"A": "193.2",
"B": "160",
"C": "322",
"D": "161"
} | D | 161 | By Vieta's relations, α+β = 13/1 and αβ = 4/1. Then α²+β²=(α+β)²−2αβ = (13/1)²−2(4/1) = 161. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 161, not 193.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 161, not 160.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 161, not 322.",
"D": "Correct.... | [
"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_004880 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 20 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.84545 A",
"B": "1.26818 A",
"C": "-0.15455 A",
"D": "-2.15455 A"
} | A | 0.84545 A | Series branch resistance=4+7=11 Ω. Parallel equivalent R_eq=(11×20)/(11+20)=7.09677 Ω. Total current I=V/R_eq=6/7.09677=0.84545 A. | {
"A": "Correct. The worked calculation gives 0.84545 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.84545 A, not 1.26818 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.84545 A, not -0.15455 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008476 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.62 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.65888 K",
"B": "1.16589 K",
"C": "4.65888 K",
"D": "-1.34112 K"
} | A | 1.65888 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×1.62=1.65888 K. | {
"A": "Correct. The worked calculation gives 1.65888 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.65888 K, not 1.16589 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.65888 K, not 4.65888 K.",
"D": "Incorrect. Substituting the... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005620 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 2 μF capacitor is charged to a potential difference of 40 V. Calculate the energy stored, expressed in μJ. | {
"A": "2400 μJ",
"B": "1599 μJ",
"C": "1600 μJ",
"D": "1601 μJ"
} | C | 1600 μJ | U=½CV². Since C=2 μF, U in μJ is ½×2×(40)²=1600 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1600 μJ, not 2400 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1600 μJ, not 1599 μJ.",
"C": "Correct. The worked calculation gives 1600 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_001693 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 11 elements can be selected from a set of 53 distinct elements? | {
"A": "7622375307",
"B": "114335629590",
"C": "57167814795",
"D": "76223753060"
} | D | 76223753060 | Order does not matter, so the count is C(53,11)=53!/[11!(42)!]=76223753060. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 76223753060, not 7622375307.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 76223753060, not 114335629590.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 76... | [
"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_006076 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 82 cm in front of a thin convex lens of focal length 25 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.65789",
"B": "0.4386",
"C": "0.32895",
"D": "3.4386"
} | B | 0.4386 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(82)(25)/(82−25)=35.96491 cm. Thus |m|=v/u=35.96491/82=0.4386. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.4386, not 0.65789.",
"B": "Correct. The worked calculation gives 0.4386.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.4386, not 0.32895.",
"D": "Incorrect. Substituting the stated value... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003721 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block initially moves at 8 m s⁻¹. A constant net force does 9 N of work over 6 m in the direction of motion. Find its final kinetic energy. | {
"A": "502 J",
"B": "1004 J",
"C": "501 J",
"D": "503 J"
} | A | 502 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(14)(8)²+(9)(6)=502 J. | {
"A": "Correct. The worked calculation gives 502 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 502 J, not 1004 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 502 J, not 501 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_004798 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 2 Ω are connected in series; this combination is connected in parallel with a 5 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.16 A",
"B": "1.6 A",
"C": "-0.4 A",
"D": "4.6 A"
} | B | 1.6 A | Series branch resistance=13+2=15 Ω. Parallel equivalent R_eq=(15×5)/(15+5)=3.75 Ω. Total current I=V/R_eq=6/3.75=1.6 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.6 A, not 1.16 A.",
"B": "Correct. The worked calculation gives 1.6 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.6 A, not -0.4 A.",
"D": "Incorrect. Substituting the stated values int... | [
"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_000801 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio 4. What is the sum of its first 9 terms? | {
"A": "393214.5",
"B": "78643.9",
"C": "-786429",
"D": "786429"
} | D | 786429 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(4^9−1)/(4−1)=786429. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 786429, not 393214.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 786429, not 78643.9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 786429, not -786429... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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