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_007633 | 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 61 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "11.40157",
"B": "14.40157",
"C": "-11.40157",
"D": "13.40157"
} | A | 11.40157 | Excess OH⁻ moles=0.10×(61−58)/1000=0.000300 mol. Total volume=0.119 L, so [OH⁻]=0.002521 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=11.40157. | {
"A": "Correct. The worked calculation gives 11.40157.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.40157, not 14.40157.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.40157, not -11.40157.",
"D": "Incorrect. Substituting the sta... | [
"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_004709 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 14 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 4 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.65909 A",
"B": "3.65909 A",
"C": "1.65909 A",
"D": "3.98864 A"
} | A | 2.65909 A | Series branch resistance=14+8=22 Ω. Parallel equivalent R_eq=(22×4)/(22+4)=3.38462 Ω. Total current I=V/R_eq=9/3.38462=2.65909 A. | {
"A": "Correct. The worked calculation gives 2.65909 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.65909 A, not 3.65909 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.65909 A, not 1.65909 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_006712 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 1 mol H₂ and 31 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "0.5 mol",
"B": "2 mol",
"C": "1 mol",
"D": "1.5 mol"
} | C | 1 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 1 mol H₂O; O₂ can produce 62 mol H₂O. The limiting condition is H₂; product=1 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1 mol, not 0.5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1 mol, not 2 mol.",
"C": "Correct. The worked calculation gives 1 mol.",
"D": "Incorrect. Substituting the stated values int... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007719 | 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 20 minutes? | {
"A": "43.5 mmol L⁻¹",
"B": "34.8 mmol L⁻¹",
"C": "87 mmol L⁻¹",
"D": "65.25 mmol L⁻¹"
} | A | 43.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=87/2^1=43.5 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 43.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 43.5 mmol L⁻¹, not 34.8 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 43.5 mmol L⁻¹, not 87 mmol L⁻¹.",
"D": "Incorrect... | [
"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_009511 | 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_8H_4X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "10",
"B": "2",
"C": "7",
"D": "5"
} | D | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×8+2+0−4−4)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.",
"D": "Correct. The worked c... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006714 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 39 mol H₂ and 21 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "40 mol",
"B": "19.5 mol",
"C": "38 mol",
"D": "39 mol"
} | D | 39 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 39 mol H₂O; O₂ can produce 42 mol H₂O. The limiting condition is H₂; product=39 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 39 mol, not 40 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39 mol, not 19.5 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39 mol, not 38 mol."... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009533 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_10H_9N_1X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "-5",
"B": "8",
"C": "4",
"D": "5"
} | D | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×10+2+1−9−4)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not -5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 4.",
"D": "Correct. The worked c... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006818 | 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 28 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "10 mol",
"B": "15 mol",
"C": "11 mol",
"D": "7 mol"
} | A | 10 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 10 mol H₂O; O₂ can produce 56 mol H₂O. The limiting condition is H₂; product=10 mol. | {
"A": "Correct. The worked calculation gives 10 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 15 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 11 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_000566 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -5 and common difference 14. Find the sum of its first 17 terms. | {
"A": "-1819",
"B": "1364.25",
"C": "1819",
"D": "182.9"
} | C | 1819 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-5, d=14, n=17: Sₙ=17/2[2(-5)+(17−1)(14)]=1819. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1819, not -1819.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1819, not 1364.25.",
"C": "Correct. The worked calculation gives 1819.",
"D": "Incorrect. Substituting the stated values into t... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002824 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(6, 4, 3) and v=(-3, -3, 9), calculate u·v. | {
"A": "-4.5",
"B": "-1.5",
"C": "-3",
"D": "0"
} | C | -3 | The dot product is the sum of corresponding component products: (6)(-3)+(4)(-3)+(3)(9)=-3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -3, not -4.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -3, not -1.5.",
"C": "Correct. The worked calculation gives -3.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_004835 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 12 Ω and 9 Ω are connected in series; this combination is connected in parallel with a 10 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "5.65714 A",
"B": "-2.65714 A",
"C": "2.65714 A",
"D": "1.32857 A"
} | C | 2.65714 A | Series branch resistance=12+9=21 Ω. Parallel equivalent R_eq=(21×10)/(21+10)=6.77419 Ω. Total current I=V/R_eq=18/6.77419=2.65714 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.65714 A, not 5.65714 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.65714 A, not -2.65714 A.",
"C": "Correct. The worked calculation gives 2.65714 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007369 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 35 mL of 0.10 M HCl is mixed with 98 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "6.33774",
"B": "12.67549",
"C": "13.67549",
"D": "14.67549"
} | B | 12.67549 | Excess OH⁻ moles=0.10×(98−35)/1000=0.006300 mol. Total volume=0.133 L, so [OH⁻]=0.047368 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.67549. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.67549, not 6.33774.",
"B": "Correct. The worked calculation gives 12.67549.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.67549, not 13.67549.",
"D": "Incorrect. Substituting the state... | [
"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_007396 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 91 mL of 0.10 M HCl is mixed with 54 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.59317",
"B": "-1.40683",
"C": "-1.59317",
"D": "0.79658"
} | A | 1.59317 | Excess H⁺ moles=0.10×(91−54)/1000=0.003700 mol. Total volume=0.145 L, so [H⁺]=0.025517 M and pH=−log₁₀[H⁺]=1.59317. | {
"A": "Correct. The worked calculation gives 1.59317.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.59317, not -1.40683.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.59317, not -1.59317.",
"D": "Incorrect. Substituting the stated ... | [
"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_005386 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 3 μF capacitor is charged to a potential difference of 33 V. Calculate the energy stored, expressed in μJ. | {
"A": "2450.25 μJ",
"B": "1632.5 μJ",
"C": "1633.5 μJ",
"D": "1225.125 μJ"
} | C | 1633.5 μJ | U=½CV². Since C=3 μF, U in μJ is ½×3×(33)²=1633.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1633.5 μJ, not 2450.25 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1633.5 μJ, not 1632.5 μJ.",
"C": "Correct. The worked calculation gives 1633.5 μJ.",
"D": "Incorrect. Substituting th... | [
"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_001056 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=7x³ -5x² -1x+7. Evaluate f′(3). | {
"A": "237",
"B": "158",
"C": "157",
"D": "156"
} | B | 158 | Differentiate: f′(x)=3(7)x²+2(-5)x+(-1). At x=3, f′(3)=3(7)(3)²+2(-5)(3)+(-1)=158. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 158, not 237.",
"B": "Correct. The worked calculation gives 158.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 158, not 157.",
"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_005143 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +9 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "111.90625 N",
"B": "114.90625 N",
"C": "113.90625 N",
"D": "227.8125 N"
} | C | 113.90625 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(9×10⁻⁶)/(8×10⁻²)²=113.90625 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 113.90625 N, not 111.90625 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 113.90625 N, not 114.90625 N.",
"C": "Correct. The worked calculation gives 113.90625 N.",
"D": "Incorrect. Substi... | [
"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_004034 | 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 0.38. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "11.952 N",
"B": "109.52 N",
"C": "111.52 N",
"D": "54.76 N"
} | B | 109.52 N | Net force=mg(sinθ−μcosθ)=37×10×(0.6−0.38×0.8)=109.52 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 109.52 N, not 11.952 N.",
"B": "Correct. The worked calculation gives 109.52 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 109.52 N, not 111.52 N.",
"D": "Incorrect. Substituting the stat... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003802 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 0 m s⁻¹. A constant net force does 21 N of work over 20 m in the direction of motion. Find its final kinetic energy. | {
"A": "-420 J",
"B": "420 J",
"C": "315 J",
"D": "504 J"
} | B | 420 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(0)²+(21)(20)=420 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 420 J, not -420 J.",
"B": "Correct. The worked calculation gives 420 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 420 J, not 315 J.",
"D": "Incorrect. Substituting the stated values into... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003055 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(7+5i)/(7+5i). What is Re(z), the real part of z? | {
"A": "1",
"B": "0",
"C": "1.5",
"D": "4"
} | A | 1 | Multiply numerator and denominator by the conjugate (7-5i). Then Re(z)=(ac+bd)/(c²+d²)=((7)(7)+(5)(5))/(7²+(5)²)=1. | {
"A": "Correct. The worked calculation gives 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.5.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_001296 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ +6x² -5x+7. Evaluate f′(0). | {
"A": "0.5",
"B": "-5",
"C": "-7",
"D": "-6"
} | B | -5 | Differentiate: f′(x)=3(4)x²+2(6)x+(-5). At x=0, f′(0)=3(4)(0)²+2(6)(0)+(-5)=-5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -5, not 0.5.",
"B": "Correct. The worked calculation gives -5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -5, not -7.",
"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_008843 | 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 0.92 mol L⁻¹ and initially B is absent. At equilibrium, 15% of A has dissociated at constant volume. Find K_c. | {
"A": "0.09741",
"B": "0.07306",
"C": "0.14612",
"D": "0.19482"
} | A | 0.09741 | Let α=0.15. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.92)(0.15)²/(1−0.15)=0.09741. | {
"A": "Correct. The worked calculation gives 0.09741.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.09741, not 0.07306.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.09741, not 0.14612.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000587 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -12 and common difference 3. Find the sum of its first 17 terms. | {
"A": "206",
"B": "203",
"C": "204",
"D": "163.2"
} | C | 204 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-12, d=3, n=17: Sₙ=17/2[2(-12)+(17−1)(3)]=204. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 204, not 206.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 204, not 203.",
"C": "Correct. The worked calculation gives 204.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001690 | 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 30 distinct elements? | {
"A": "7153575",
"B": "14307152",
"C": "14307150",
"D": "1430716"
} | C | 14307150 | Order does not matter, so the count is C(30,9)=30!/[9!(21)!]=14307150. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14307150, not 7153575.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14307150, not 14307152.",
"C": "Correct. The worked calculation gives 14307150.",
"D": "Incorrect. Substituting the state... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006139 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 88 cm in front of a thin convex lens of focal length 26 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.83871",
"B": "0.31452",
"C": "0.41935",
"D": "2.41935"
} | C | 0.41935 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(88)(26)/(88−26)=36.90323 cm. Thus |m|=v/u=36.90323/88=0.41935. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.41935, not 0.83871.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.41935, not 0.31452.",
"C": "Correct. The worked calculation gives 0.41935.",
"D": "Incorrect. Substituting the stated va... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000526 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 14 and common difference 14. Find the sum of its first 14 terms. | {
"A": "2205",
"B": "-1470",
"C": "1470",
"D": "1469"
} | C | 1470 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=14, d=14, n=14: Sₙ=14/2[2(14)+(14−1)(14)]=1470. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1470, not 2205.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1470, not -1470.",
"C": "Correct. The worked calculation gives 1470.",
"D": "Incorrect. Substituting the stated values into the ... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006274 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 86 cm in front of a thin convex lens of focal length 27 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.91525",
"B": "3.45763",
"C": "1.04576",
"D": "0.45763"
} | D | 0.45763 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(86)(27)/(86−27)=39.35593 cm. Thus |m|=v/u=39.35593/86=0.45763. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.45763, not 0.91525.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.45763, not 3.45763.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.45763, not 1.045... | [
"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_003495 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 20 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "40 m",
"B": "30 m",
"C": "42 m",
"D": "41 m"
} | A | 40 m | Range R=u²sin(2θ)/g. Substituting u=20, θ=45° and g=10 gives R=(20)²sin(90°)/10=40 m. | {
"A": "Correct. The worked calculation gives 40 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 40 m, not 30 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 40 m, not 42 m.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_008567 | 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 0.74 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.074 K",
"B": "0.74 K",
"C": "0.37 K",
"D": "1.74 K"
} | B | 0.74 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×1.0×0.74=0.74 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.74 K, not 1.074 K.",
"B": "Correct. The worked calculation gives 0.74 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.74 K, not 0.37 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007819 | 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 21 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "-1.6875 mmol L⁻¹",
"B": "1.96875 mmol L⁻¹",
"C": "1.3125 mmol L⁻¹",
"D": "0.3125 mmol L⁻¹"
} | C | 1.3125 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=21/2^4=1.3125 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.3125 mmol L⁻¹, not -1.6875 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.3125 mmol L⁻¹, not 1.96875 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 1.3125 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_005585 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 23 μF capacitor is charged to a potential difference of 3 V. Calculate the energy stored, expressed in μJ. | {
"A": "103.5 μJ",
"B": "82.8 μJ",
"C": "101.5 μJ",
"D": "77.625 μJ"
} | A | 103.5 μJ | U=½CV². Since C=23 μF, U in μJ is ½×23×(3)²=103.5 μJ. | {
"A": "Correct. The worked calculation gives 103.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 103.5 μJ, not 82.8 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 103.5 μJ, not 101.5 μJ.",
"D": "Incorrect. Substituting the state... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002928 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(0, -1, 2) and v=(-2, 6, -3), calculate u·v. | {
"A": "12",
"B": "-11",
"C": "-9",
"D": "-12"
} | D | -12 | The dot product is the sum of corresponding component products: (0)(-2)+(-1)(6)+(2)(-3)=-12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -12, not 12.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -12, not -11.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -12, not -9.",
"D": "Correct. The... | [
"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_009163 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.41 V, transfers 1 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.10182 V",
"B": "2.9382 V",
"C": "1.4691 V",
"D": "0.4691 V"
} | C | 1.4691 V | Apply the Nernst equation: E=1.41−(0.0591/1)(-1)=1.4691 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.4691 V, not 1.10182 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4691 V, not 2.9382 V.",
"C": "Correct. The worked calculation gives 1.4691 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_003072 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(10+11i)/(10+1i). What is Re(z), the real part of z? | {
"A": "1.09901",
"B": "0.09901",
"C": "-1.09901",
"D": "1.1099"
} | A | 1.09901 | Multiply numerator and denominator by the conjugate (10-1i). Then Re(z)=(ac+bd)/(c²+d²)=((10)(10)+(11)(1))/(10²+(1)²)=1.09901. | {
"A": "Correct. The worked calculation gives 1.09901.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.09901, not 0.09901.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.09901, not -1.09901.",
"D": "Incorrect. Substituting the stated v... | [
"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_002590 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, 4], [5, -7]]. | {
"A": "55",
"B": "-27.5",
"C": "-55",
"D": "-56"
} | C | -55 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(-7)−(4)(5)=-55. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -55, not 55.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -55, not -27.5.",
"C": "Correct. The worked calculation gives -55.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_009853 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(Cl)_2]^+0, each Cl ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "2",
"B": "4",
"C": "-2",
"D": "3"
} | A | 2 | Let the formal oxidation state of Mn be x. Charge balance gives x+(2)(−1)=+0; hence x=0+2=+2. | {
"A": "Correct. The worked calculation gives 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"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_003414 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 33 m s⁻¹ at 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "108.24556 m",
"B": "53.62278 m",
"C": "107.24556 m",
"D": "85.79645 m"
} | C | 107.24556 m | Range R=u²sin(2θ)/g. Substituting u=33, θ=40° and g=10 gives R=(33)²sin(80°)/10=107.24556 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 107.24556 m, not 108.24556 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 107.24556 m, not 53.62278 m.",
"C": "Correct. The worked calculation gives 107.24556 m.",
"D": "Incorrect. Substit... | [
"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_004446 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 15 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": "3.368 rad s⁻²",
"B": "0.368 rad s⁻²",
"C": "-1.632 rad s⁻²",
"D": "-2.632 rad s⁻²"
} | B | 0.368 rad s⁻² | For a solid disc, I=½MR²=½(15)(5)²=187.5 kg m². Using τ=Iα, α=69/187.5=0.368 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.368 rad s⁻², not 3.368 rad s⁻².",
"B": "Correct. The worked calculation gives 0.368 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.368 rad s⁻², not -1.632 rad s⁻².",
"D": "Incorr... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002140 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 12 blue and 8 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.16138",
"B": "-0.67725",
"C": "0.32275",
"D": "-0.32275"
} | C | 0.32275 | Favourable pairs = C(8,2)+C(12,2)+C(8,2)=122. Total pairs=C(28,2)=378. Therefore P=122/378=0.32275. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32275, not 0.16138.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32275, not -0.67725.",
"C": "Correct. The worked calculation gives 0.32275.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006640 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 13 kg is attached to an ideal spring of force constant 272 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.56276 s",
"B": "2.43724 s",
"C": "1.43724 s",
"D": "0.43724 s"
} | D | 0.43724 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(13/272)=0.43724 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.43724 s, not -0.56276 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.43724 s, not 2.43724 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.43724 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009923 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(CN)_3]^-3, each CN ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "0",
"B": "1",
"C": "-3",
"D": "3"
} | A | 0 | Let the formal oxidation state of Fe be x. Charge balance gives x+(3)(−1)=-3; hence x=-3+3=+0. | {
"A": "Correct. The worked calculation gives 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"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_007968 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 62 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "46.5 mmol L⁻¹",
"B": "15.5 mmol L⁻¹",
"C": "31 mmol L⁻¹",
"D": "24.8 mmol L⁻¹"
} | C | 31 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=62/2^1=31 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 31 mmol L⁻¹, not 46.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 31 mmol L⁻¹, not 15.5 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 31 mmol L⁻¹.",
"D": "Incorrect. Su... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009622 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_12H_12X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "6",
"B": "8",
"C": "4.5",
"D": "4"
} | A | 6 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×12+2+0−12−2)/2=6. | {
"A": "Correct. The worked calculation gives 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.5.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001326 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-1x³ +6x² -8x+7. Evaluate f′(5). | {
"A": "-23",
"B": "-27.6",
"C": "-46",
"D": "-11.5"
} | A | -23 | Differentiate: f′(x)=3(-1)x²+2(6)x+(-8). At x=5, f′(5)=3(-1)(5)²+2(6)(5)+(-8)=-23. | {
"A": "Correct. The worked calculation gives -23.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -23, not -27.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -23, not -46.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_003315 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(0-9i)/(1+5i). What is Re(z), the real part of z? | {
"A": "0.26923",
"B": "1.26923",
"C": "1.73077",
"D": "-1.73077"
} | D | -1.73077 | Multiply numerator and denominator by the conjugate (1-5i). Then Re(z)=(ac+bd)/(c²+d²)=((0)(1)+(-9)(5))/(1²+(5)²)=-1.73077. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.73077, not 0.26923.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.73077, not 1.26923.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.73077, not 1.... | [
"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_005089 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +2 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "12.6 N",
"B": "6.3 N",
"C": "9.45 N",
"D": "11.6 N"
} | A | 12.6 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(2×10⁻⁶)/(10×10⁻²)²=12.6 N. | {
"A": "Correct. The worked calculation gives 12.6 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.6 N, not 6.3 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.6 N, not 9.45 N.",
"D": "Incorrect. Substituting the stated values i... | [
"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_007970 | 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 76 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "-19 mmol L⁻¹",
"B": "17 mmol L⁻¹",
"C": "18 mmol L⁻¹",
"D": "19 mmol L⁻¹"
} | D | 19 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=76/2^2=19 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19 mmol L⁻¹, not -19 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19 mmol L⁻¹, not 17 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 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_007178 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 2 mol of gas at 452 K and 1.96 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "39.8467 L",
"B": "45.41604 L",
"C": "37.8467 L",
"D": "56.77005 L"
} | C | 37.8467 L | PV=nRT, so V=nRT/P=(2)(0.082057)(452)/(1.96)=37.8467 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 37.8467 L, not 39.8467 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 37.8467 L, not 45.41604 L.",
"C": "Correct. The worked calculation gives 37.8467 L.",
"D": "Incorrect. Substituting th... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007063 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 15 mol of gas at 598 K and 2.5 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "296.42052 L",
"B": "235.53641 L",
"C": "220.81539 L",
"D": "294.42052 L"
} | D | 294.42052 L | PV=nRT, so V=nRT/P=(15)(0.082057)(598)/(2.5)=294.42052 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 294.42052 L, not 296.42052 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 294.42052 L, not 235.53641 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003786 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 2 m s⁻¹. A constant net force does 19 N of work over 5 m in the direction of motion. Find its final kinetic energy. | {
"A": "103 J",
"B": "77.25 J",
"C": "-103 J",
"D": "123.6 J"
} | A | 103 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(2)²+(19)(5)=103 J. | {
"A": "Correct. The worked calculation gives 103 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 103 J, not 77.25 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 103 J, not -103 J.",
"D": "Incorrect. Substituting the stated values in... | [
"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_009304 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.81 V, transfers 1 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.4855 V",
"B": "0.5145 V",
"C": "-0.5145 V",
"D": "0.77175 V"
} | B | 0.5145 V | Apply the Nernst equation: E=0.81−(0.0591/1)(5)=0.5145 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5145 V, not -0.4855 V.",
"B": "Correct. The worked calculation gives 0.5145 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5145 V, not -0.5145 V.",
"D": "Incorrect. Substituting the st... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000375 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 24 and common difference 5. Find the sum of its first 33 terms. | {
"A": "3432",
"B": "3433",
"C": "3430",
"D": "3431"
} | A | 3432 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=24, d=5, n=33: Sₙ=33/2[2(24)+(33−1)(5)]=3432. | {
"A": "Correct. The worked calculation gives 3432.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3432, not 3433.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3432, not 3430.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008005 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 5 A for 5898 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": "6.70267 g",
"B": "8.70267 g",
"C": "19.40534 g",
"D": "9.70267 g"
} | D | 9.70267 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×5×5898/(2×96500)=9.70267 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.70267 g, not 6.70267 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.70267 g, not 8.70267 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.70267 g,... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002778 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-6, -3, -7) and v=(1, 3, 8), calculate u·v. | {
"A": "-70",
"B": "-35.5",
"C": "-71",
"D": "-73"
} | C | -71 | The dot product is the sum of corresponding component products: (-6)(1)+(-3)(3)+(-7)(8)=-71. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -71, not -70.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -71, not -35.5.",
"C": "Correct. The worked calculation gives -71.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007091 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 3 mol of gas at 592 K and 0.27 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "269.87636 L",
"B": "54.97527 L",
"C": "539.75271 L",
"D": "538.75271 L"
} | C | 539.75271 L | PV=nRT, so V=nRT/P=(3)(0.082057)(592)/(0.27)=539.75271 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 539.75271 L, not 269.87636 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 539.75271 L, not 54.97527 L.",
"C": "Correct. The worked calculation gives 539.75271 L.",
"D": "Incorrect. Substit... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000655 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -15 and common difference 6. Find the sum of its first 11 terms. | {
"A": "132",
"B": "166",
"C": "165",
"D": "167"
} | C | 165 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-15, d=6, n=11: Sₙ=11/2[2(-15)+(11−1)(6)]=165. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 165, not 132.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 165, not 166.",
"C": "Correct. The worked calculation gives 165.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009309 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.65 V, transfers 1 electrons, and has reaction quotient Q=10^0. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.65 V",
"B": "0.65 V",
"C": "0.325 V",
"D": "0.975 V"
} | B | 0.65 V | Apply the Nernst equation: E=0.65−(0.0591/1)(0)=0.65 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.65 V, not 1.65 V.",
"B": "Correct. The worked calculation gives 0.65 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.65 V, not 0.325 V.",
"D": "Incorrect. Substituting the stated values... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005266 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +9 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "49.625 N",
"B": "50.625 N",
"C": "48.625 N",
"D": "-50.625 N"
} | B | 50.625 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(9×10⁻⁶)/(4×10⁻²)²=50.625 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 50.625 N, not 49.625 N.",
"B": "Correct. The worked calculation gives 50.625 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 50.625 N, not 48.625 N.",
"D": "Incorrect. Substituting the stat... | [
"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_007246 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 7 mol of gas at 255 K and 1.98 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "72.97563 L",
"B": "73.97563 L",
"C": "55.48172 L",
"D": "-73.97563 L"
} | B | 73.97563 L | PV=nRT, so V=nRT/P=(7)(0.082057)(255)/(1.98)=73.97563 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 73.97563 L, not 72.97563 L.",
"B": "Correct. The worked calculation gives 73.97563 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 73.97563 L, not 55.48172 L.",
"D": "Incorrect. Substitutin... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008514 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "2.512 K",
"B": "1.024 K",
"C": "3.512 K",
"D": "0.512 K"
} | D | 0.512 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.512×1=0.512 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.512 K, not 2.512 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.512 K, not 1.024 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.512 K, not 3.512... | [
"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_000158 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 -9x -11=0, let its roots be α and β. What is α²+β²? | {
"A": "16.33333",
"B": "24.5",
"C": "15.33333",
"D": "19.6"
} | A | 16.33333 | By Vieta's relations, α+β = 9/3 and αβ = -11/3. Then α²+β²=(α+β)²−2αβ = (9/3)²−2(-11/3) = 16.33333. | {
"A": "Correct. The worked calculation gives 16.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16.33333, not 24.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16.33333, not 15.33333.",
"D": "Incorrect. Substituting the stated v... | [
"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_004571 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 2 m is acted on by a constant torque of 7 N m about its central axis. Find its angular acceleration. | {
"A": "2.7 rad s⁻²",
"B": "-0.3 rad s⁻²",
"C": "0.7 rad s⁻²",
"D": "-2.3 rad s⁻²"
} | C | 0.7 rad s⁻² | For a solid disc, I=½MR²=½(5)(2)²=10 kg m². Using τ=Iα, α=7/10=0.7 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7 rad s⁻², not 2.7 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7 rad s⁻², not -0.3 rad s⁻².",
"C": "Correct. The worked calculation gives 0.7 rad s⁻².",
"D": "Incorrect. Subst... | [
"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_000976 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio 5. What is the sum of its first 8 terms? | {
"A": "39063.4",
"B": "468748.8",
"C": "390623",
"D": "390624"
} | D | 390624 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(5^8−1)/(5−1)=390624. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 390624, not 39063.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 390624, not 468748.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 390624, not 390623.... | [
"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_001891 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 12 elements can be selected from a set of 18 distinct elements? | {
"A": "18564",
"B": "18566",
"C": "27846",
"D": "9282"
} | A | 18564 | Order does not matter, so the count is C(18,12)=18!/[12!(6)!]=18564. | {
"A": "Correct. The worked calculation gives 18564.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18564, not 18566.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18564, not 27846.",
"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_006451 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 6 kg is attached to an ideal spring of force constant 963 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.15787 s",
"B": "1.15787 s",
"C": "-1.84213 s",
"D": "0.07893 s"
} | A | 0.15787 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(6/963)=0.15787 s. | {
"A": "Correct. The worked calculation gives 0.15787 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.15787 s, not 1.15787 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.15787 s, not -1.84213 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_003584 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 29 m s⁻¹ at 50° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "80.82233 m",
"B": "84.82233 m",
"C": "82.82233 m",
"D": "124.2335 m"
} | C | 82.82233 m | Range R=u²sin(2θ)/g. Substituting u=29, θ=50° and g=10 gives R=(29)²sin(100°)/10=82.82233 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 82.82233 m, not 80.82233 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 82.82233 m, not 84.82233 m.",
"C": "Correct. The worked calculation gives 82.82233 m.",
"D": "Incorrect. Substitutin... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005471 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 43 μF capacitor is charged to a potential difference of 19 V. Calculate the energy stored, expressed in μJ. | {
"A": "7760.5 μJ",
"B": "7763.5 μJ",
"C": "7761.5 μJ",
"D": "15523 μJ"
} | C | 7761.5 μJ | U=½CV². Since C=43 μF, U in μJ is ½×43×(19)²=7761.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7761.5 μJ, not 7760.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7761.5 μJ, not 7763.5 μJ.",
"C": "Correct. The worked calculation gives 7761.5 μJ.",
"D": "Incorrect. Substituting the... | [
"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_004888 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 10 Ω are connected in series; this combination is connected in parallel with a 8 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.53289 A",
"B": "-0.93421 A",
"C": "3.06579 A",
"D": "1.06579 A"
} | D | 1.06579 A | Series branch resistance=9+10=19 Ω. Parallel equivalent R_eq=(19×8)/(19+8)=5.62963 Ω. Total current I=V/R_eq=6/5.62963=1.06579 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.06579 A, not 0.53289 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.06579 A, not -0.93421 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.06579 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_002020 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 7 red, 12 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": "0.35145",
"B": "0.26359",
"C": "0.17572",
"D": "3.35145"
} | A | 0.35145 | Favourable pairs = C(7,2)+C(12,2)+C(5,2)=97. Total pairs=C(24,2)=276. Therefore P=97/276=0.35145. | {
"A": "Correct. The worked calculation gives 0.35145.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35145, not 0.26359.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35145, not 0.17572.",
"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_008794 | 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 1.53 mol L⁻¹ and initially B is absent. At equilibrium, 45% of A has dissociated at constant volume. Find K_c. | {
"A": "2.25327",
"B": "1.25327",
"C": "1.68995",
"D": "3.25327"
} | A | 2.25327 | Let α=0.45. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.53)(0.45)²/(1−0.45)=2.25327. | {
"A": "Correct. The worked calculation gives 2.25327.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.25327, not 1.25327.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.25327, not 1.68995.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000047 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 +6x -12=0, let its roots be α and β. What is α²+β²? | {
"A": "7.25",
"B": "9.25",
"C": "8.25",
"D": "5.25"
} | C | 8.25 | By Vieta's relations, α+β = -6/4 and αβ = -12/4. Then α²+β²=(α+β)²−2αβ = (-6/4)²−2(-12/4) = 8.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.25, not 7.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.25, not 9.25.",
"C": "Correct. The worked calculation gives 8.25.",
"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_001113 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ -9x² +9x+7. Evaluate f′(-2). | {
"A": "139.5",
"B": "74.4",
"C": "93",
"D": "111.6"
} | C | 93 | Differentiate: f′(x)=3(4)x²+2(-9)x+(9). At x=-2, f′(-2)=3(4)(-2)²+2(-9)(-2)+(9)=93. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 93, not 139.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 93, not 74.4.",
"C": "Correct. The worked calculation gives 93.",
"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_009876 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(OH)_3]^+0, each OH ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "6",
"B": "3",
"C": "1.3",
"D": "4"
} | B | 3 | Let the formal oxidation state of Pd be x. Charge balance gives x+(3)(−1)=+0; hence x=0+3=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"D": "Incorrect. Substituting the stated values into the governing 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_008578 | 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 0.53 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.5512 K",
"B": "0.4134 K",
"C": "3.5512 K",
"D": "0.5512 K"
} | D | 0.5512 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×0.53=0.5512 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5512 K, not -0.5512 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.5512 K, not 0.4134 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5512 K, not... | [
"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_003227 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(12-13i)/(9+5i). What is Re(z), the real part of z? | {
"A": "0.40566",
"B": "0.81132",
"C": "0.60849",
"D": "-1.59434"
} | A | 0.40566 | Multiply numerator and denominator by the conjugate (9-5i). Then Re(z)=(ac+bd)/(c²+d²)=((12)(9)+(-13)(5))/(9²+(5)²)=0.40566. | {
"A": "Correct. The worked calculation gives 0.40566.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.40566, not 0.81132.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.40566, not 0.60849.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003548 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 57 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "152.65307 m",
"B": "305.30613 m",
"C": "457.9592 m",
"D": "304.30613 m"
} | B | 305.30613 m | Range R=u²sin(2θ)/g. Substituting u=57, θ=55° and g=10 gives R=(57)²sin(110°)/10=305.30613 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 305.30613 m, not 152.65307 m.",
"B": "Correct. The worked calculation gives 305.30613 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 305.30613 m, not 457.9592 m.",
"D": "Incorrect. Substit... | [
"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_007257 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 6 mol of gas at 526 K and 1.18 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "109.73385 L",
"B": "263.36125 L",
"C": "-219.46771 L",
"D": "219.46771 L"
} | D | 219.46771 L | PV=nRT, so V=nRT/P=(6)(0.082057)(526)/(1.18)=219.46771 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 219.46771 L, not 109.73385 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 219.46771 L, not 263.36125 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005956 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.6 atm at 225 K. What is its pressure at 742 K? | {
"A": "2.27644 atm",
"B": "6.27644 atm",
"C": "10.55289 atm",
"D": "5.27644 atm"
} | D | 5.27644 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.6)(742)/(225)=5.27644 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.27644 atm, not 2.27644 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.27644 atm, not 6.27644 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.... | [
"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_002629 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, 5], [5, 4]]. | {
"A": "-8.5",
"B": "-34",
"C": "-17",
"D": "-25.5"
} | C | -17 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(4)−(5)(5)=-17. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -17, not -8.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -17, not -34.",
"C": "Correct. The worked calculation gives -17.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_008413 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.44 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.576 K",
"B": "5.76 K",
"C": "-5.76 K",
"D": "7.76 K"
} | B | 5.76 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×1.0×1.44=5.76 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.76 K, not 1.576 K.",
"B": "Correct. The worked calculation gives 5.76 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.76 K, not -5.76 K.",
"D": "Incorrect. Substituting the stated value... | [
"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_001479 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (1x² -7x +2) dx. | {
"A": "37.33333",
"B": "-37.33333",
"C": "-29.86667",
"D": "-74.66667"
} | B | -37.33333 | An antiderivative is (1/3)x³+(-7/2)x²+(2)x. Evaluating between 0 and 8 gives (1/3)(8)³+(-7/2)(8)²+(2)(8)=-37.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -37.33333, not 37.33333.",
"B": "Correct. The worked calculation gives -37.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -37.33333, not -29.86667.",
"D": "Incorrect. Substituting the ... | [
"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_004949 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 10 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.33333 A",
"B": "4.66667 A",
"C": "6.66667 A",
"D": "3.5 A"
} | B | 4.66667 A | Series branch resistance=10+8=18 Ω. Parallel equivalent R_eq=(18×10)/(18+10)=6.42857 Ω. Total current I=V/R_eq=30/6.42857=4.66667 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.66667 A, not 2.33333 A.",
"B": "Correct. The worked calculation gives 4.66667 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.66667 A, not 6.66667 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_002539 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, 2], [6, 2]]. | {
"A": "-2",
"B": "2",
"C": "-5",
"D": "1"
} | A | -2 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(2)−(2)(6)=-2. | {
"A": "Correct. The worked calculation gives -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2, not -5.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000404 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 13 and common difference 12. Find the sum of its first 9 terms. | {
"A": "548",
"B": "-549",
"C": "549",
"D": "551"
} | C | 549 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=13, d=12, n=9: Sₙ=9/2[2(13)+(9−1)(12)]=549. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 549, not 548.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 549, not -549.",
"C": "Correct. The worked calculation gives 549.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000972 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 5. What is the sum of its first 8 terms? | {
"A": "97657",
"B": "976560",
"C": "976561",
"D": "488280"
} | B | 976560 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(5^8−1)/(5−1)=976560. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 976560, not 97657.",
"B": "Correct. The worked calculation gives 976560.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 976560, not 976561.",
"D": "Incorrect. Substituting the stated values i... | [
"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_002055 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 3 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.4",
"B": "-1.6",
"C": "-2.6",
"D": "-0.4"
} | A | 0.4 | Favourable pairs = C(6,2)+C(3,2)+C(12,2)=84. Total pairs=C(21,2)=210. Therefore P=84/210=0.4. | {
"A": "Correct. The worked calculation gives 0.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.4, not -1.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.4, not -2.6.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_008855 | 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 0.91 mol L⁻¹ and initially B is absent. At equilibrium, 44% of A has dissociated at constant volume. Find K_c. | {
"A": "1.2584",
"B": "2.2584",
"C": "1.8876",
"D": "-0.7416"
} | A | 1.2584 | Let α=0.44. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.91)(0.44)²/(1−0.44)=1.2584. | {
"A": "Correct. The worked calculation gives 1.2584.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.2584, not 2.2584.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2584, not 1.8876.",
"D": "Incorrect. Substituting the stated values ... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001898 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 2 elements can be selected from a set of 36 distinct elements? | {
"A": "945",
"B": "315",
"C": "630",
"D": "628"
} | C | 630 | Order does not matter, so the count is C(36,2)=36!/[2!(34)!]=630. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 630, not 945.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 630, not 315.",
"C": "Correct. The worked calculation gives 630.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_008849 | 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 0.63 mol L⁻¹ and initially B is absent. At equilibrium, 72% of A has dissociated at constant volume. Find K_c. | {
"A": "7.6656",
"B": "3.6656",
"C": "6.9984",
"D": "4.6656"
} | D | 4.6656 | Let α=0.72. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.63)(0.72)²/(1−0.72)=4.6656. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.6656, not 7.6656.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.6656, not 3.6656.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.6656, not 6.9984.",
... | [
"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_003037 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(13+2i)/(2+12i). What is Re(z), the real part of z? | {
"A": "0.33784",
"B": "-0.66216",
"C": "0.16892",
"D": "0.25338"
} | A | 0.33784 | Multiply numerator and denominator by the conjugate (2-12i). Then Re(z)=(ac+bd)/(c²+d²)=((13)(2)+(2)(12))/(2²+(12)²)=0.33784. | {
"A": "Correct. The worked calculation gives 0.33784.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33784, not -0.66216.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33784, not 0.16892.",
"D": "Incorrect. Substituting the stated v... | [
"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_002784 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-5, -2, -6) and v=(-7, -2, -1), calculate u·v. | {
"A": "54",
"B": "47",
"C": "5.5",
"D": "45"
} | D | 45 | The dot product is the sum of corresponding component products: (-5)(-7)+(-2)(-2)+(-6)(-1)=45. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45, not 54.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 45, not 47.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 45, not 5.5.",
"D": "Correct. The wo... | [
"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_008397 | 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 0.7 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-2.58 K",
"B": "0.42 K",
"C": "3.42 K",
"D": "0.315 K"
} | B | 0.42 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.6×0.7=0.42 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.42 K, not -2.58 K.",
"B": "Correct. The worked calculation gives 0.42 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.42 K, not 3.42 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009870 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(CN)_2]^-1, each CN ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "2",
"B": "1",
"C": "1.1",
"D": "-1"
} | B | 1 | Let the formal oxidation state of Co 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 2.",
"B": "Correct. The worked calculation gives 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.1.",
"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_006437 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 7 kg is attached to an ideal spring of force constant 1012 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.83366 s",
"B": "1.16634 s",
"C": "0.16634 s",
"D": "1.01663 s"
} | C | 0.16634 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(7/1012)=0.16634 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.16634 s, not -1.83366 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.16634 s, not 1.16634 s.",
"C": "Correct. The worked calculation gives 0.16634 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_000085 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 -13x -11=0, let its roots be α and β. What is α²+β²? | {
"A": "8.37",
"B": "14.16",
"C": "12.16",
"D": "11.16"
} | D | 11.16 | By Vieta's relations, α+β = 13/5 and αβ = -11/5. Then α²+β²=(α+β)²−2αβ = (13/5)²−2(-11/5) = 11.16. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.16, not 8.37.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.16, not 14.16.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.16, not 12.16.",
"D": ... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004872 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 15 Ω are connected in series; this combination is connected in parallel with a 13 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.16599 A",
"B": "1.16599 A",
"C": "-1.16599 A",
"D": "3.16599 A"
} | B | 1.16599 A | Series branch resistance=4+15=19 Ω. Parallel equivalent R_eq=(19×13)/(19+13)=7.71875 Ω. Total current I=V/R_eq=9/7.71875=1.16599 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.16599 A, not 0.16599 A.",
"B": "Correct. The worked calculation gives 1.16599 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.16599 A, not -1.16599 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006474 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 22 kg is attached to an ideal spring of force constant 419 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.54172 s",
"B": "-0.45828 s",
"C": "0.45828 s",
"D": "0.34371 s"
} | C | 0.45828 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(22/419)=0.45828 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.45828 s, not -1.54172 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.45828 s, not -0.45828 s.",
"C": "Correct. The worked calculation gives 0.45828 s.",
"D": "Incorrect. Substituting t... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006494 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 20 kg is attached to an ideal spring of force constant 1151 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.26364 s",
"B": "1.26364 s",
"C": "0.13182 s",
"D": "0.39546 s"
} | A | 0.26364 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(20/1151)=0.26364 s. | {
"A": "Correct. The worked calculation gives 0.26364 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.26364 s, not 1.26364 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.26364 s, not 0.13182 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_004816 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 16 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.25 A",
"B": "1.125 A",
"C": "1.225 A",
"D": "-2.25 A"
} | A | 2.25 A | Series branch resistance=4+4=8 Ω. Parallel equivalent R_eq=(8×16)/(8+16)=5.33333 Ω. Total current I=V/R_eq=12/5.33333=2.25 A. | {
"A": "Correct. The worked calculation gives 2.25 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.25 A, not 1.125 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.25 A, not 1.225 A.",
"D": "Incorrect. Substituting the stated value... | [
"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_006782 | 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 8 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "2.6 mol",
"B": "16 mol",
"C": "17 mol",
"D": "-16 mol"
} | B | 16 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 19 mol H₂O; O₂ can produce 16 mol H₂O. The limiting condition is O₂; product=16 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 2.6 mol.",
"B": "Correct. The worked calculation gives 16 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 17 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_009528 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_3H_0N_1X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "6",
"C": "1.3",
"D": "5"
} | A | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×3+2+1−0−3)/2=3. | {
"A": "Correct. The worked calculation gives 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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