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_005174 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +3 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "28.55102 N",
"B": "26.55102 N",
"C": "27.55102 N",
"D": "22.04082 N"
} | C | 27.55102 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(3×10⁻⁶)/(7×10⁻²)²=27.55102 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 27.55102 N, not 28.55102 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 27.55102 N, not 26.55102 N.",
"C": "Correct. The worked calculation gives 27.55102 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_007959 | 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 47 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "3.9375 mmol L⁻¹",
"B": "5.875 mmol L⁻¹",
"C": "1.9375 mmol L⁻¹",
"D": "2.9375 mmol L⁻¹"
} | D | 2.9375 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=47/2^4=2.9375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.9375 mmol L⁻¹, not 3.9375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.9375 mmol L⁻¹, not 5.875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing re... | [
"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_008318 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 12 A for 20337 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": "78.29427 g",
"B": "80.29427 g",
"C": "96.35312 g",
"D": "9.02943 g"
} | B | 80.29427 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×12×20337/(2×96500)=80.29427 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 80.29427 g, not 78.29427 g.",
"B": "Correct. The worked calculation gives 80.29427 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 80.29427 g, not 96.35312 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_004267 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 37 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.42. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "97.68 N",
"B": "117.216 N",
"C": "78.144 N",
"D": "99.68 N"
} | A | 97.68 N | Net force=mg(sinθ−μcosθ)=37×10×(0.6−0.42×0.8)=97.68 N. | {
"A": "Correct. The worked calculation gives 97.68 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 97.68 N, not 117.216 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 97.68 N, not 78.144 N.",
"D": "Incorrect. Substituting the stated... | [
"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_002579 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, -2], [3, 4]]. | {
"A": "31",
"B": "4",
"C": "28",
"D": "30"
} | D | 30 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(4)−(-2)(3)=30. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 30, not 31.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30, not 28.",
"D": "Correct. The work... | [
"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_007962 | 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 87 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "-0.32031 mmol L⁻¹",
"B": "2.67969 mmol L⁻¹",
"C": "0.67969 mmol L⁻¹",
"D": "-2.32031 mmol L⁻¹"
} | C | 0.67969 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=87/2^7=0.67969 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.67969 mmol L⁻¹, not -0.32031 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.67969 mmol L⁻¹, not 2.67969 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.67969 mmol L⁻¹.",... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006425 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 15 kg is attached to an ideal spring of force constant 920 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.38307 s",
"B": "0.51075 s",
"C": "0.25538 s",
"D": "-1.74462 s"
} | C | 0.25538 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(15/920)=0.25538 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25538 s, not 0.38307 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25538 s, not 0.51075 s.",
"C": "Correct. The worked calculation gives 0.25538 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_008129 | 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 20812 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "27.38989 g",
"B": "54.77977 g",
"C": "32.86786 g",
"D": "28.38989 g"
} | A | 27.38989 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×20812/(2×96500)=27.38989 g. | {
"A": "Correct. The worked calculation gives 27.38989 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 27.38989 g, not 54.77977 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 27.38989 g, not 32.86786 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_008020 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 9 A for 19958 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": "59.09843 g",
"B": "-59.09843 g",
"C": "29.54922 g",
"D": "47.27874 g"
} | A | 59.09843 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×9×19958/(2×96500)=59.09843 g. | {
"A": "Correct. The worked calculation gives 59.09843 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 59.09843 g, not -59.09843 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 59.09843 g, not 29.54922 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_002261 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 3 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": "1.03077",
"B": "2.30769",
"C": "-0.69231",
"D": "0.30769"
} | D | 0.30769 | Favourable pairs = C(6,2)+C(3,2)+C(4,2)=24. Total pairs=C(13,2)=78. Therefore P=24/78=0.30769. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not 1.03077.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not 2.30769.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not -0.69... | [
"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_004784 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 2 Ω and 15 Ω are connected in series; this combination is connected in parallel with a 18 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "5.14706 A",
"B": "3.43137 A",
"C": "1.34314 A",
"D": "-3.43137 A"
} | B | 3.43137 A | Series branch resistance=2+15=17 Ω. Parallel equivalent R_eq=(17×18)/(17+18)=8.74286 Ω. Total current I=V/R_eq=30/8.74286=3.43137 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.43137 A, not 5.14706 A.",
"B": "Correct. The worked calculation gives 3.43137 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.43137 A, not 1.34314 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001293 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ -9x² -10x+7. Evaluate f′(1). | {
"A": "-16",
"B": "-18",
"C": "-32",
"D": "-8"
} | A | -16 | Differentiate: f′(x)=3(4)x²+2(-9)x+(-10). At x=1, f′(1)=3(4)(1)²+2(-9)(1)+(-10)=-16. | {
"A": "Correct. The worked calculation gives -16.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -16, not -18.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -16, not -32.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006598 | 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 878 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.17536 s",
"B": "2.11691 s",
"C": "0.11691 s",
"D": "3.11691 s"
} | C | 0.11691 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(3/878)=0.11691 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.11691 s, not 0.17536 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.11691 s, not 2.11691 s.",
"C": "Correct. The worked calculation gives 0.11691 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_004018 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 31 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.11. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "157.72 N",
"B": "158.72 N",
"C": "190.464 N",
"D": "119.04 N"
} | B | 158.72 N | Net force=mg(sinθ−μcosθ)=31×10×(0.6−0.11×0.8)=158.72 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 158.72 N, not 157.72 N.",
"B": "Correct. The worked calculation gives 158.72 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 158.72 N, not 190.464 N.",
"D": "Incorrect. Substituting the sta... | [
"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_005506 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 69 μF capacitor is charged to a potential difference of 3 V. Calculate the energy stored, expressed in μJ. | {
"A": "310.5 μJ",
"B": "311.5 μJ",
"C": "621 μJ",
"D": "308.5 μJ"
} | A | 310.5 μJ | U=½CV². Since C=69 μF, U in μJ is ½×69×(3)²=310.5 μJ. | {
"A": "Correct. The worked calculation gives 310.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 310.5 μJ, not 311.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 310.5 μJ, not 621 μJ.",
"D": "Incorrect. Substituting the stated... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004164 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 41 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.28. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "154.16 N",
"B": "-154.16 N",
"C": "156.16 N",
"D": "184.992 N"
} | A | 154.16 N | Net force=mg(sinθ−μcosθ)=41×10×(0.6−0.28×0.8)=154.16 N. | {
"A": "Correct. The worked calculation gives 154.16 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 154.16 N, not -154.16 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 154.16 N, not 156.16 N.",
"D": "Incorrect. Substituting the sta... | [
"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_001744 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 16 distinct elements? | {
"A": "8007",
"B": "8008",
"C": "9609.6",
"D": "801.8"
} | B | 8008 | Order does not matter, so the count is C(16,10)=16!/[10!(6)!]=8008. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8008, not 8007.",
"B": "Correct. The worked calculation gives 8008.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8008, not 9609.6.",
"D": "Incorrect. Substituting the stated values into the... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007339 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 58 mL of 0.10 M HCl is mixed with 57 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "3.0607",
"B": "4.0607",
"C": "-3.0607",
"D": "6.0607"
} | A | 3.0607 | Excess H⁺ moles=0.10×(58−57)/1000=0.000100 mol. Total volume=0.115 L, so [H⁺]=0.000870 M and pH=−log₁₀[H⁺]=3.0607. | {
"A": "Correct. The worked calculation gives 3.0607.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.0607, not 4.0607.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.0607, not -3.0607.",
"D": "Incorrect. Substituting the stated values... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006763 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 13 mol H₂ and 17 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "9.75 mol",
"B": "13 mol",
"C": "-13 mol",
"D": "14 mol"
} | B | 13 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 13 mol H₂O; O₂ can produce 34 mol H₂O. The limiting condition is H₂; product=13 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13 mol, not 9.75 mol.",
"B": "Correct. The worked calculation gives 13 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13 mol, not -13 mol.",
"D": "Incorrect. Substituting the stated valu... | [
"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_001922 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 9 elements can be selected from a set of 50 distinct elements? | {
"A": "3758150550",
"B": "2505433700",
"C": "2505433701",
"D": "1252716850"
} | B | 2505433700 | Order does not matter, so the count is C(50,9)=50!/[9!(41)!]=2505433700. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2505433700, not 3758150550.",
"B": "Correct. The worked calculation gives 2505433700.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2505433700, not 2505433701.",
"D": "Incorrect. Substitutin... | [
"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_003474 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 62 m s⁻¹ at 15° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "96.1 m",
"B": "384.4 m",
"C": "192.2 m",
"D": "-192.2 m"
} | C | 192.2 m | Range R=u²sin(2θ)/g. Substituting u=62, θ=15° and g=10 gives R=(62)²sin(30°)/10=192.2 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 192.2 m, not 96.1 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 192.2 m, not 384.4 m.",
"C": "Correct. The worked calculation gives 192.2 m.",
"D": "Incorrect. Substituting the stated val... | [
"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_001735 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 3 elements can be selected from a set of 45 distinct elements? | {
"A": "14190",
"B": "14189",
"C": "14188",
"D": "14191"
} | A | 14190 | Order does not matter, so the count is C(45,3)=45!/[3!(42)!]=14190. | {
"A": "Correct. The worked calculation gives 14190.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14190, not 14189.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14190, not 14188.",
"D": "Incorrect. Substituting the stated values into ... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006949 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 19 mol H₂ and 32 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "-19 mol",
"B": "15.2 mol",
"C": "22.8 mol",
"D": "19 mol"
} | D | 19 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 19 mol H₂O; O₂ can produce 64 mol H₂O. The limiting condition is H₂; product=19 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19 mol, not -19 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19 mol, not 15.2 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19 mol, not 22.8 mo... | [
"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_008796 | 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 0.17 mol L⁻¹ and initially B is absent. At equilibrium, 70% of A has dissociated at constant volume. Find K_c. | {
"A": "1.11067",
"B": "1.11107",
"C": "0.833",
"D": "-1.11067"
} | A | 1.11067 | Let α=0.7. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.17)(0.7)²/(1−0.7)=1.11067. | {
"A": "Correct. The worked calculation gives 1.11067.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.11067, not 1.11107.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.11067, not 0.833.",
"D": "Incorrect. Substituting the stated valu... | [
"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_005968 | 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 2.9 atm at 440 K. What is its pressure at 656 K? | {
"A": "6.32364 atm",
"B": "1.43236 atm",
"C": "4.32364 atm",
"D": "2.32364 atm"
} | C | 4.32364 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.9)(656)/(440)=4.32364 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.32364 atm, not 6.32364 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.32364 atm, not 1.43236 atm.",
"C": "Correct. The worked calculation gives 4.32364 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_001432 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (2x² -8x +7) dx. | {
"A": "3.66667",
"B": "0.66667",
"C": "-3.66667",
"D": "1.36667"
} | A | 3.66667 | An antiderivative is (2/3)x³+(-8/2)x²+(7)x. Evaluating between 0 and 1 gives (2/3)(1)³+(-8/2)(1)²+(7)(1)=3.66667. | {
"A": "Correct. The worked calculation gives 3.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.66667, not 0.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.66667, not -3.66667.",
"D": "Incorrect. Substituting the stated v... | [
"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_003689 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 12 m s⁻¹. A constant net force does 14 N of work over 6 m in the direction of motion. Find its final kinetic energy. | {
"A": "876 J",
"B": "700.8 J",
"C": "1051.2 J",
"D": "1752 J"
} | A | 876 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(12)²+(14)(6)=876 J. | {
"A": "Correct. The worked calculation gives 876 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 876 J, not 700.8 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 876 J, not 1051.2 J.",
"D": "Incorrect. Substituting the stated values ... | [
"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_001012 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-2x³ -9x² -2x+7. Evaluate f′(-2). | {
"A": "10",
"B": "7",
"C": "7.5",
"D": "9"
} | A | 10 | Differentiate: f′(x)=3(-2)x²+2(-9)x+(-2). At x=-2, f′(-2)=3(-2)(-2)²+2(-9)(-2)+(-2)=10. | {
"A": "Correct. The worked calculation gives 10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 7.5.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_002902 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-4, 4, -5) and v=(-1, -1, -4), calculate u·v. | {
"A": "19",
"B": "30",
"C": "20",
"D": "21"
} | C | 20 | The dot product is the sum of corresponding component products: (-4)(-1)+(4)(-1)+(-5)(-4)=20. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20, not 19.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20, not 30.",
"C": "Correct. The worked calculation gives 20.",
"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_005046 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +5 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "352 N",
"B": "350 N",
"C": "525 N",
"D": "175 N"
} | B | 350 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(5×10⁻⁶)/(3×10⁻²)²=350 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 350 N, not 352 N.",
"B": "Correct. The worked calculation gives 350 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 350 N, not 525 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_003699 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block initially moves at 4 m s⁻¹. A constant net force does 6 N of work over 9 m in the direction of motion. Find its final kinetic energy. | {
"A": "112.8 J",
"B": "94 J",
"C": "141 J",
"D": "96 J"
} | B | 94 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(5)(4)²+(6)(9)=94 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 94 J, not 112.8 J.",
"B": "Correct. The worked calculation gives 94 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 94 J, not 141 J.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_003288 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(9-8i)/(12+10i). What is Re(z), the real part of z? | {
"A": "0.22951",
"B": "-0.11475",
"C": "-0.88525",
"D": "0.11475"
} | D | 0.11475 | Multiply numerator and denominator by the conjugate (12-10i). Then Re(z)=(ac+bd)/(c²+d²)=((9)(12)+(-8)(10))/(12²+(10)²)=0.11475. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.11475, not 0.22951.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.11475, not -0.11475.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.11475, not -0.8... | [
"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_007547 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 38 mL of 0.10 M HCl is mixed with 38 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "3.5",
"B": "6",
"C": "7",
"D": "1.7"
} | C | 7 | Equal moles of strong acid and base are present. They neutralize completely, so at 25°C pH=7.00. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 3.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 6.",
"C": "Correct. The worked calculation gives 7.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_006841 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 15 mol H₂ and 24 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "15 mol",
"B": "14 mol",
"C": "13 mol",
"D": "7.5 mol"
} | A | 15 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 15 mol H₂O; O₂ can produce 48 mol H₂O. The limiting condition is H₂; product=15 mol. | {
"A": "Correct. The worked calculation gives 15 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15 mol, not 14 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15 mol, not 13 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_009025 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.58 V, transfers 2 electrons, and has reaction quotient Q=10^1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.41284 V",
"B": "-0.44955 V",
"C": "0.55045 V",
"D": "3.55045 V"
} | C | 0.55045 V | Apply the Nernst equation: E=0.58−(0.0591/2)(1)=0.55045 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.55045 V, not 0.41284 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.55045 V, not -0.44955 V.",
"C": "Correct. The worked calculation gives 0.55045 V.",
"D": "Incorrect. Substituting th... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009431 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_13H_7N_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "12",
"B": "15",
"C": "11",
"D": "-12"
} | A | 12 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×13+2+3−7−0)/2=12. | {
"A": "Correct. The worked calculation gives 12.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12, not 15.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12, not 11.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005741 | 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 5 atm at 220 K. What is its pressure at 338 K? | {
"A": "-7.68182 atm",
"B": "7.68182 atm",
"C": "4.68182 atm",
"D": "8.68182 atm"
} | B | 7.68182 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(5)(338)/(220)=7.68182 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.68182 atm, not -7.68182 atm.",
"B": "Correct. The worked calculation gives 7.68182 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.68182 atm, not 4.68182 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_009052 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.18 V, transfers 2 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.0618 V",
"B": "1.10618 V",
"C": "0.0618 V",
"D": "2.1236 V"
} | A | 1.0618 V | Apply the Nernst equation: E=1.18−(0.0591/2)(4)=1.0618 V. | {
"A": "Correct. The worked calculation gives 1.0618 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0618 V, not 1.10618 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0618 V, not 0.0618 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_004434 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 3 kg and radius 5 m is acted on by a constant torque of 69 N m about its central axis. Find its angular acceleration. | {
"A": "-0.16 rad s⁻²",
"B": "2.84 rad s⁻²",
"C": "1.84 rad s⁻²",
"D": "3.84 rad s⁻²"
} | C | 1.84 rad s⁻² | For a solid disc, I=½MR²=½(3)(5)²=37.5 kg m². Using τ=Iα, α=69/37.5=1.84 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.84 rad s⁻², not -0.16 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.84 rad s⁻², not 2.84 rad s⁻².",
"C": "Correct. The worked calculation gives 1.84 rad s⁻².",
"D": "Incorrect. ... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000206 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 -3x -8=0, let its roots be α and β. What is α²+β²? | {
"A": "3.16667",
"B": "9.5",
"C": "4.33333",
"D": "6.33333"
} | D | 6.33333 | By Vieta's relations, α+β = 3/3 and αβ = -8/3. Then α²+β²=(α+β)²−2αβ = (3/3)²−2(-8/3) = 6.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.33333, not 3.16667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.33333, not 9.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.33333, not 4.33333."... | [
"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_001155 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ -5x² +1x+7. Evaluate f′(-2). | {
"A": "97.2",
"B": "60.75",
"C": "82",
"D": "81"
} | D | 81 | Differentiate: f′(x)=3(5)x²+2(-5)x+(1). At x=-2, f′(-2)=3(5)(-2)²+2(-5)(-2)+(1)=81. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 81, not 97.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 81, not 60.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 81, not 82.",
"D": "Correct. Th... | [
"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_003719 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block initially moves at 11 m s⁻¹. A constant net force does 9 N of work over 9 m in the direction of motion. Find its final kinetic energy. | {
"A": "303 J",
"B": "151.5 J",
"C": "242.4 J",
"D": "202 J"
} | D | 202 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(2)(11)²+(9)(9)=202 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 202 J, not 303 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 202 J, not 151.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 202 J, not 242.4 J.",
... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005995 | 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 atm at 268 K. What is its pressure at 447 K? | {
"A": "-6.67164 atm",
"B": "9.67164 atm",
"C": "10.00746 atm",
"D": "6.67164 atm"
} | D | 6.67164 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4)(447)/(268)=6.67164 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.67164 atm, not -6.67164 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.67164 atm, not 9.67164 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_006163 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 101 cm in front of a thin convex lens of focal length 28 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.38356",
"B": "-0.61644",
"C": "0.57534",
"D": "3.38356"
} | A | 0.38356 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(101)(28)/(101−28)=38.73973 cm. Thus |m|=v/u=38.73973/101=0.38356. | {
"A": "Correct. The worked calculation gives 0.38356.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.38356, not -0.61644.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.38356, not 0.57534.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000180 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 +18x -2=0, let its roots be α and β. What is α²+β²? | {
"A": "85",
"B": "83",
"C": "81",
"D": "-83"
} | B | 83 | By Vieta's relations, α+β = -18/2 and αβ = -2/2. Then α²+β²=(α+β)²−2αβ = (-18/2)²−2(-2/2) = 83. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 83, not 85.",
"B": "Correct. The worked calculation gives 83.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 83, not 81.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_003877 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block initially moves at 11 m s⁻¹. A constant net force does 28 N of work over 6 m in the direction of motion. Find its final kinetic energy. | {
"A": "796.5 J",
"B": "398.25 J",
"C": "532 J",
"D": "531 J"
} | D | 531 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(6)(11)²+(28)(6)=531 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 531 J, not 796.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 531 J, not 398.25 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 531 J, not 532 J.",
... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004650 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 3 kg and radius 5 m is acted on by a constant torque of 65 N m about its central axis. Find its angular acceleration. | {
"A": "0.73333 rad s⁻²",
"B": "1.73333 rad s⁻²",
"C": "3.73333 rad s⁻²",
"D": "4.73333 rad s⁻²"
} | B | 1.73333 rad s⁻² | For a solid disc, I=½MR²=½(3)(5)²=37.5 kg m². Using τ=Iα, α=65/37.5=1.73333 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.73333 rad s⁻², not 0.73333 rad s⁻².",
"B": "Correct. The worked calculation gives 1.73333 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.73333 rad s⁻², not 3.73333 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_009112 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.79 V, transfers 2 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.12135 V",
"B": "-1.12135 V",
"C": "3.87865 V",
"D": "0.87865 V"
} | D | 0.87865 V | Apply the Nernst equation: E=0.79−(0.0591/2)(-3)=0.87865 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.87865 V, not -0.12135 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.87865 V, not -1.12135 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.87865 ... | [
"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_009489 | 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_14H_5X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "24",
"B": "12",
"C": "6",
"D": "18"
} | B | 12 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×14+2+0−5−1)/2=12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12, not 24.",
"B": "Correct. The worked calculation gives 12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12, not 6.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005161 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +9 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "7.61224 N",
"B": "99.18367 N",
"C": "66.12245 N",
"D": "49.59184 N"
} | C | 66.12245 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(9×10⁻⁶)/(7×10⁻²)²=66.12245 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 66.12245 N, not 7.61224 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 66.12245 N, not 99.18367 N.",
"C": "Correct. The worked calculation gives 66.12245 N.",
"D": "Incorrect. Substituting... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000312 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 -16x +8=0, let its roots be α and β. What is α²+β²? | {
"A": "6.04",
"B": "5.04",
"C": "1.704",
"D": "7.04"
} | D | 7.04 | By Vieta's relations, α+β = 16/5 and αβ = 8/5. Then α²+β²=(α+β)²−2αβ = (16/5)²−2(8/5) = 7.04. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.04, not 6.04.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.04, not 5.04.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.04, not 1.704.",
"D": "Cor... | [
"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_009951 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(Cl)_4]^+1, each Cl ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "8",
"B": "5",
"C": "10",
"D": "3.75"
} | B | 5 | Let the formal oxidation state of Cr be x. Charge balance gives x+(4)(−1)=+1; hence x=1+4=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 8.",
"B": "Correct. The worked calculation gives 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 10.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_004807 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 14 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 19 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.1203 A",
"B": "5.1203 A",
"C": "1.1203 A",
"D": "4.2406 A"
} | A | 2.1203 A | Series branch resistance=14+14=28 Ω. Parallel equivalent R_eq=(28×19)/(28+19)=11.31915 Ω. Total current I=V/R_eq=24/11.31915=2.1203 A. | {
"A": "Correct. The worked calculation gives 2.1203 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.1203 A, not 5.1203 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.1203 A, not 1.1203 A.",
"D": "Incorrect. Substituting the stat... | [
"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_001405 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (-1x² +3x +0) dx. | {
"A": "4",
"B": "-2.66667",
"C": "2.66667",
"D": "3.66667"
} | C | 2.66667 | An antiderivative is (-1/3)x³+(3/2)x²+(0)x. Evaluating between 0 and 4 gives (-1/3)(4)³+(3/2)(4)²+(0)(4)=2.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.66667, not 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.66667, not -2.66667.",
"C": "Correct. The worked calculation gives 2.66667.",
"D": "Incorrect. Substituting the stated values ... | [
"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_002176 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 12 blue and 10 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.31452",
"B": "1.03145",
"C": "0.31452",
"D": "0.62903"
} | C | 0.31452 | Favourable pairs = C(10,2)+C(12,2)+C(10,2)=156. Total pairs=C(32,2)=496. Therefore P=156/496=0.31452. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31452, not 1.31452.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31452, not 1.03145.",
"C": "Correct. The worked calculation gives 0.31452.",
"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_000293 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -5x +3=0, let its roots be α and β. What is α²+β²? | {
"A": "4.25",
"B": "3.25",
"C": "6.25",
"D": "2.25"
} | B | 3.25 | By Vieta's relations, α+β = 5/2 and αβ = 3/2. Then α²+β²=(α+β)²−2αβ = (5/2)²−2(3/2) = 3.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.25, not 4.25.",
"B": "Correct. The worked calculation gives 3.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.25, not 6.25.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_002728 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(6, 9, 6) and v=(-6, 6, -2), calculate u·v. | {
"A": "4",
"B": "9",
"C": "6",
"D": "-6"
} | C | 6 | The dot product is the sum of corresponding component products: (6)(-6)+(9)(6)+(6)(-2)=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"C": "Correct. The worked calculation gives 6.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008113 | 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 11 A for 7727 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": "20.974 g",
"B": "33.5584 g",
"C": "27.96533 g",
"D": "3.79653 g"
} | C | 27.96533 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×7727/(2×96500)=27.96533 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 27.96533 g, not 20.974 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 27.96533 g, not 33.5584 g.",
"C": "Correct. The worked calculation gives 27.96533 g.",
"D": "Incorrect. Substituting t... | [
"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_006864 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 48 mol H₂ and 15 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "24 mol",
"B": "45 mol",
"C": "30 mol",
"D": "22.5 mol"
} | C | 30 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 48 mol H₂O; O₂ can produce 30 mol H₂O. The limiting condition is O₂; product=30 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 30 mol, not 24 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30 mol, not 45 mol.",
"C": "Correct. The worked calculation gives 30 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_006827 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 15 mol H₂ and 2 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "3 mol",
"B": "4 mol",
"C": "7 mol",
"D": "2 mol"
} | B | 4 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 15 mol H₂O; O₂ can produce 4 mol H₂O. The limiting condition is O₂; product=4 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4 mol, not 3 mol.",
"B": "Correct. The worked calculation gives 4 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4 mol, not 7 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_006577 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 1 kg is attached to an ideal spring of force constant 798 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.0708 s",
"B": "1.00708 s",
"C": "3.0708 s",
"D": "0.0354 s"
} | A | 0.0708 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(1/798)=0.0708 s. | {
"A": "Correct. The worked calculation gives 0.0708 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.0708 s, not 1.00708 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.0708 s, not 3.0708 s.",
"D": "Incorrect. Substituting the sta... | [
"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_006816 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 10 mol H₂ and 5 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "7.5 mol",
"B": "20 mol",
"C": "10 mol",
"D": "15 mol"
} | C | 10 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 10 mol H₂O; O₂ can produce 10 mol H₂O. The limiting condition is neither; stoichiometric; product=10 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 7.5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 20 mol.",
"C": "Correct. The worked calculation gives 10 mol.",
"D": "Incorrect. Substituting the stated values... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001034 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ +2x² +0x+7. Evaluate f′(1). | {
"A": "0.2",
"B": "-8",
"C": "-6",
"D": "-4"
} | B | -8 | Differentiate: f′(x)=3(-4)x²+2(2)x+(0). At x=1, f′(1)=3(-4)(1)²+2(2)(1)+(0)=-8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -8, not 0.2.",
"B": "Correct. The worked calculation gives -8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -8, not -6.",
"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_001312 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=3x³ -9x² +11x+7. Evaluate f′(-2). | {
"A": "66.4",
"B": "62.25",
"C": "9.3",
"D": "83"
} | D | 83 | Differentiate: f′(x)=3(3)x²+2(-9)x+(11). At x=-2, f′(-2)=3(3)(-2)²+2(-9)(-2)+(11)=83. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 83, not 66.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 83, not 62.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 83, not 9.3.",
"D": "Correct. T... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004130 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.18. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "50.16 N",
"B": "51.16 N",
"C": "52.16 N",
"D": "60.192 N"
} | A | 50.16 N | Net force=mg(sinθ−μcosθ)=11×10×(0.6−0.18×0.8)=50.16 N. | {
"A": "Correct. The worked calculation gives 50.16 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 50.16 N, not 51.16 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 50.16 N, not 52.16 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001809 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 34 distinct elements? | {
"A": "13112815",
"B": "131128140",
"C": "98346105",
"D": "-131128140"
} | B | 131128140 | Order does not matter, so the count is C(34,10)=34!/[10!(24)!]=131128140. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 131128140, not 13112815.",
"B": "Correct. The worked calculation gives 131128140.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 131128140, not 98346105.",
"D": "Incorrect. Substituting the s... | [
"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_003068 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(7-5i)/(3+8i). What is Re(z), the real part of z? | {
"A": "0.26027",
"B": "-0.26027",
"C": "0.97397",
"D": "0.73973"
} | B | -0.26027 | Multiply numerator and denominator by the conjugate (3-8i). Then Re(z)=(ac+bd)/(c²+d²)=((7)(3)+(-5)(8))/(3²+(8)²)=-0.26027. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.26027, not 0.26027.",
"B": "Correct. The worked calculation gives -0.26027.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.26027, not 0.97397.",
"D": "Incorrect. Substituting the stated... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004250 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.39. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "29.8 N",
"B": "26.8 N",
"C": "14.4 N",
"D": "28.8 N"
} | D | 28.8 N | Net force=mg(sinθ−μcosθ)=10×10×(0.6−0.39×0.8)=28.8 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28.8 N, not 29.8 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28.8 N, not 26.8 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28.8 N, not 14.4 N.",
... | [
"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_008234 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 10 A for 21832 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": "143.66135 g",
"B": "71.83067 g",
"C": "70.83067 g",
"D": "-71.83067 g"
} | B | 71.83067 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×10×21832/(2×96500)=71.83067 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 71.83067 g, not 143.66135 g.",
"B": "Correct. The worked calculation gives 71.83067 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 71.83067 g, not 70.83067 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_002676 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(6, -5, 7) and v=(6, 5, 1), calculate u·v. | {
"A": "19",
"B": "13.5",
"C": "36",
"D": "18"
} | D | 18 | The dot product is the sum of corresponding component products: (6)(6)+(-5)(5)+(7)(1)=18. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18, not 19.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18, not 13.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18, not 36.",
"D": "Correct. The w... | [
"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_004336 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 28 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.35. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "88.6 N",
"B": "89.6 N",
"C": "90.6 N",
"D": "67.2 N"
} | B | 89.6 N | Net force=mg(sinθ−μcosθ)=28×10×(0.6−0.35×0.8)=89.6 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 89.6 N, not 88.6 N.",
"B": "Correct. The worked calculation gives 89.6 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 89.6 N, not 90.6 N.",
"D": "Incorrect. Substituting the stated values ... | [
"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_005103 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +8 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "78.75 N",
"B": "59.0625 N",
"C": "94.5 N",
"D": "8.875 N"
} | A | 78.75 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(8×10⁻⁶)/(8×10⁻²)²=78.75 N. | {
"A": "Correct. The worked calculation gives 78.75 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 78.75 N, not 59.0625 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 78.75 N, not 94.5 N.",
"D": "Incorrect. Substituting the stated v... | [
"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_008340 | 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 0.89 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "4.602 K",
"B": "1.2015 K",
"C": "1.602 K",
"D": "-1.398 K"
} | C | 1.602 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.6×0.89=1.602 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.602 K, not 4.602 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.602 K, not 1.2015 K.",
"C": "Correct. The worked calculation gives 1.602 K.",
"D": "Incorrect. Substituting the stated v... | [
"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_002417 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, -4], [7, -6]]. | {
"A": "22",
"B": "33",
"C": "-22",
"D": "23"
} | A | 22 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(-6)−(-4)(7)=22. | {
"A": "Correct. The worked calculation gives 22.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22, not 33.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22, not -22.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004023 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 42 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.26. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "329.28 N",
"B": "164.64 N",
"C": "131.712 N",
"D": "163.64 N"
} | B | 164.64 N | Net force=mg(sinθ−μcosθ)=42×10×(0.6−0.26×0.8)=164.64 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 164.64 N, not 329.28 N.",
"B": "Correct. The worked calculation gives 164.64 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 164.64 N, not 131.712 N.",
"D": "Incorrect. Substituting the sta... | [
"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_009850 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(CN)_6]^-3, each CN ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "2.25",
"B": "3",
"C": "4",
"D": "4.5"
} | B | 3 | Let the formal oxidation state of Mn be x. Charge balance gives x+(6)(−1)=-3; hence x=-3+6=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.",
"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_001726 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 12 distinct elements? | {
"A": "742.5",
"B": "495",
"C": "497",
"D": "493"
} | B | 495 | Order does not matter, so the count is C(12,8)=12!/[8!(4)!]=495. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 495, not 742.5.",
"B": "Correct. The worked calculation gives 495.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 495, not 497.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002179 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 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": "-0.66667",
"B": "0.33333",
"C": "0.25",
"D": "-1.66667"
} | B | 0.33333 | Favourable pairs = C(10,2)+C(5,2)+C(6,2)=70. Total pairs=C(21,2)=210. Therefore P=70/210=0.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not -0.66667.",
"B": "Correct. The worked calculation gives 0.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not 0.25.",
"D": "Incorrect. Substituting the stated valu... | [
"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_002401 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, 0], [1, 0]]. | {
"A": "-2",
"B": "3",
"C": "-3",
"D": "0"
} | D | 0 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(0)−(0)(1)=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"D": "Correct. The worked ... | [
"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_006561 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 16 kg is attached to an ideal spring of force constant 1032 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "3.24903 s",
"B": "0.24903 s",
"C": "-0.75097 s",
"D": "0.37354 s"
} | B | 0.24903 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(16/1032)=0.24903 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.24903 s, not 3.24903 s.",
"B": "Correct. The worked calculation gives 0.24903 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.24903 s, not -0.75097 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_008063 | 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 5833 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": "7.67659 g",
"B": "10.67659 g",
"C": "5.75744 g",
"D": "15.35318 g"
} | A | 7.67659 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×5833/(2×96500)=7.67659 g. | {
"A": "Correct. The worked calculation gives 7.67659 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.67659 g, not 10.67659 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.67659 g, not 5.75744 g.",
"D": "Incorrect. Substituting th... | [
"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_004037 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 19 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.36. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "-59.28 N",
"B": "29.64 N",
"C": "47.424 N",
"D": "59.28 N"
} | D | 59.28 N | Net force=mg(sinθ−μcosθ)=19×10×(0.6−0.36×0.8)=59.28 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 59.28 N, not -59.28 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 59.28 N, not 29.64 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 59.28 N, not 47.4... | [
"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_004744 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 20 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.28462 A",
"B": "1.52308 A",
"C": "4.52308 A",
"D": "-0.47692 A"
} | B | 1.52308 A | Series branch resistance=9+4=13 Ω. Parallel equivalent R_eq=(13×20)/(13+20)=7.87879 Ω. Total current I=V/R_eq=12/7.87879=1.52308 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.52308 A, not 2.28462 A.",
"B": "Correct. The worked calculation gives 1.52308 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.52308 A, not 4.52308 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009837 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(OH)_2]^-1, each OH ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "0.5",
"B": "0",
"C": "1",
"D": "3"
} | C | 1 | Let the formal oxidation state of Cu be x. Charge balance gives x+(2)(−1)=-1; hence x=-1+2=+1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.",
"C": "Correct. The worked calculation gives 1.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001627 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (-4x² -6x +2) dx. | {
"A": "-62.66667",
"B": "-125.33333",
"C": "-11.53333",
"D": "125.33333"
} | B | -125.33333 | An antiderivative is (-4/3)x³+(-6/2)x²+(2)x. Evaluating between 0 and 4 gives (-4/3)(4)³+(-6/2)(4)²+(2)(4)=-125.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -125.33333, not -62.66667.",
"B": "Correct. The worked calculation gives -125.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -125.33333, not -11.53333.",
"D": "Incorrect. Substituting ... | [
"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_008859 | 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 1.76 mol L⁻¹ and initially B is absent. At equilibrium, 66% of A has dissociated at constant volume. Find K_c. | {
"A": "13.52922",
"B": "7.01948",
"C": "9.01948",
"D": "12.01948"
} | C | 9.01948 | Let α=0.66. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.76)(0.66)²/(1−0.66)=9.01948. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.01948, not 13.52922.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.01948, not 7.01948.",
"C": "Correct. The worked calculation gives 9.01948.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004051 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 18 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.31. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "50.688 N",
"B": "63.36 N",
"C": "61.36 N",
"D": "7.336 N"
} | B | 63.36 N | Net force=mg(sinθ−μcosθ)=18×10×(0.6−0.31×0.8)=63.36 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 63.36 N, not 50.688 N.",
"B": "Correct. The worked calculation gives 63.36 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 63.36 N, not 61.36 N.",
"D": "Incorrect. Substituting the stated v... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005876 | 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 2.6 atm at 360 K. What is its pressure at 792 K? | {
"A": "2.86 atm",
"B": "5.72 atm",
"C": "-5.72 atm",
"D": "8.58 atm"
} | B | 5.72 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.6)(792)/(360)=5.72 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.72 atm, not 2.86 atm.",
"B": "Correct. The worked calculation gives 5.72 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.72 atm, not -5.72 atm.",
"D": "Incorrect. Substituting the sta... | [
"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_004170 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 35 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.26. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "138.2 N",
"B": "137.2 N",
"C": "102.9 N",
"D": "-137.2 N"
} | B | 137.2 N | Net force=mg(sinθ−μcosθ)=35×10×(0.6−0.26×0.8)=137.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 137.2 N, not 138.2 N.",
"B": "Correct. The worked calculation gives 137.2 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 137.2 N, not 102.9 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009928 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(CN)_5]^+0, each CN ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "1.5",
"B": "7",
"C": "3.75",
"D": "5"
} | D | 5 | Let the formal oxidation state of Pt be x. Charge balance gives x+(5)(−1)=+0; hence x=0+5=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.75.",
"D": "Correct. The work... | [
"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_008265 | 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 5159 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": "1.39478 g",
"B": "5.09217 g",
"C": "3.39478 g",
"D": "2.39478 g"
} | C | 3.39478 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×2×5159/(2×96500)=3.39478 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.39478 g, not 1.39478 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.39478 g, not 5.09217 g.",
"C": "Correct. The worked calculation gives 3.39478 g.",
"D": "Incorrect. Substituting the... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003348 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 74 m s⁻¹ at 30° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "473.23551 m",
"B": "474.23551 m",
"C": "948.47102 m",
"D": "569.08261 m"
} | B | 474.23551 m | Range R=u²sin(2θ)/g. Substituting u=74, θ=30° and g=10 gives R=(74)²sin(60°)/10=474.23551 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 474.23551 m, not 473.23551 m.",
"B": "Correct. The worked calculation gives 474.23551 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 474.23551 m, not 948.47102 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003653 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 112 m s⁻¹ at 15° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "625.2 m",
"B": "627.2 m",
"C": "470.4 m",
"D": "940.8 m"
} | B | 627.2 m | Range R=u²sin(2θ)/g. Substituting u=112, θ=15° and g=10 gives R=(112)²sin(30°)/10=627.2 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 627.2 m, not 625.2 m.",
"B": "Correct. The worked calculation gives 627.2 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 627.2 m, not 470.4 m.",
"D": "Incorrect. Substituting the stated va... | [
"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_002327 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 8 blue and 5 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.17333",
"B": "0.52",
"C": "0.34667",
"D": "-0.65333"
} | C | 0.34667 | Favourable pairs = C(12,2)+C(8,2)+C(5,2)=104. Total pairs=C(25,2)=300. Therefore P=104/300=0.34667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34667, not 0.17333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34667, not 0.52.",
"C": "Correct. The worked calculation gives 0.34667.",
"D": "Incorrect. Substituting the stated value... | [
"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_004238 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 9 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": "23.04 N",
"B": "17.28 N",
"C": "24.04 N",
"D": "3.304 N"
} | A | 23.04 N | Net force=mg(sinθ−μcosθ)=9×10×(0.6−0.43×0.8)=23.04 N. | {
"A": "Correct. The worked calculation gives 23.04 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23.04 N, not 17.28 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23.04 N, not 24.04 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004771 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 14 Ω and 13 Ω are connected in series; this combination is connected in parallel with a 15 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.7 A",
"B": "0.93333 A",
"C": "1.4 A",
"D": "1.86667 A"
} | B | 0.93333 A | Series branch resistance=14+13=27 Ω. Parallel equivalent R_eq=(27×15)/(27+15)=9.64286 Ω. Total current I=V/R_eq=9/9.64286=0.93333 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.93333 A, not 0.7 A.",
"B": "Correct. The worked calculation gives 0.93333 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.93333 A, not 1.4 A.",
"D": "Incorrect. Substituting the stated ... | [
"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_000965 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio -2. What is the sum of its first 6 terms? | {
"A": "-230",
"B": "-233",
"C": "231",
"D": "-231"
} | D | -231 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(-2^6−1)/(-2−1)=-231. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -231, not -230.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -231, not -233.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -231, not 231.",
"D": "Corre... | [
"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_005133 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +8 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "31.75 N",
"B": "40.5 N",
"C": "50.625 N",
"D": "33.75 N"
} | D | 33.75 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(8×10⁻⁶)/(8×10⁻²)²=33.75 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33.75 N, not 31.75 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33.75 N, not 40.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 33.75 N, not 50.625... | [
"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_004898 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 2 Ω are connected in series; this combination is connected in parallel with a 20 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.86667 A",
"B": "1.38667 A",
"C": "5.86667 A",
"D": "3.86667 A"
} | D | 3.86667 A | Series branch resistance=7+2=9 Ω. Parallel equivalent R_eq=(9×20)/(9+20)=6.2069 Ω. Total current I=V/R_eq=24/6.2069=3.86667 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.86667 A, not 1.86667 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.86667 A, not 1.38667 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.86667 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_009216 | 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 2 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.70865 V",
"B": "-2.29135 V",
"C": "-0.70865 V",
"D": "1.4173 V"
} | A | 0.70865 V | Apply the Nernst equation: E=0.62−(0.0591/2)(-3)=0.70865 V. | {
"A": "Correct. The worked calculation gives 0.70865 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.70865 V, not -2.29135 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.70865 V, not -0.70865 V.",
"D": "Incorrect. Substituting t... | [
"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 |
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