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_001877 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 3 elements can be selected from a set of 30 distinct elements? | {
"A": "-4060",
"B": "3045",
"C": "4062",
"D": "4060"
} | D | 4060 | Order does not matter, so the count is C(30,3)=30!/[3!(27)!]=4060. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4060, not -4060.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4060, not 3045.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4060, not 4062.",
"D": "Cor... | [
"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_003767 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 5 m s⁻¹. A constant net force does 24 N of work over 8 m in the direction of motion. Find its final kinetic energy. | {
"A": "327.5 J",
"B": "331.5 J",
"C": "395.4 J",
"D": "329.5 J"
} | D | 329.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(5)²+(24)(8)=329.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 329.5 J, not 327.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 329.5 J, not 331.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 329.5 J, not 395.4... | [
"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_004923 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 2 Ω and 14 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": "1.5 A",
"B": "2.25 A",
"C": "0.5 A",
"D": "1.125 A"
} | A | 1.5 A | Series branch resistance=2+14=16 Ω. Parallel equivalent R_eq=(16×16)/(16+16)=8 Ω. Total current I=V/R_eq=12/8=1.5 A. | {
"A": "Correct. The worked calculation gives 1.5 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.5 A, not 2.25 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.5 A, not 0.5 A.",
"D": "Incorrect. Substituting the stated values into... | [
"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_007348 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 61 mL of 0.10 M HCl is mixed with 79 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.10914",
"B": "13.10914",
"C": "18.16372",
"D": "11.10914"
} | A | 12.10914 | Excess OH⁻ moles=0.10×(79−61)/1000=0.001800 mol. Total volume=0.140 L, so [OH⁻]=0.012857 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.10914. | {
"A": "Correct. The worked calculation gives 12.10914.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.10914, not 13.10914.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.10914, not 18.16372.",
"D": "Incorrect. Substituting the stat... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001546 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (2x² -5x -2) dx. | {
"A": "-3.83333",
"B": "-0.83333",
"C": "-4.83333",
"D": "-6.83333"
} | A | -3.83333 | An antiderivative is (2/3)x³+(-5/2)x²+(-2)x. Evaluating between 0 and 1 gives (2/3)(1)³+(-5/2)(1)²+(-2)(1)=-3.83333. | {
"A": "Correct. The worked calculation gives -3.83333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -3.83333, not -0.83333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -3.83333, not -4.83333.",
"D": "Incorrect. Substituting the stat... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008384 | 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 0.51 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.0608 K",
"B": "1.5912 K",
"C": "1.10608 K",
"D": "0.5304 K"
} | A | 1.0608 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.52×0.51=1.0608 K. | {
"A": "Correct. The worked calculation gives 1.0608 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0608 K, not 1.5912 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0608 K, not 1.10608 K.",
"D": "Incorrect. Substituting the sta... | [
"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_009373 | 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_15H_1N_2X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "32",
"B": "24",
"C": "2.6",
"D": "16"
} | D | 16 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×15+2+2−1−1)/2=16. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16, not 32.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16, not 24.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16, not 2.6.",
"D": "Correct. The wo... | [
"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_007019 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 1 mol of gas at 500 K and 0.18 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "227.93611 L",
"B": "229.93611 L",
"C": "23.79361 L",
"D": "225.93611 L"
} | A | 227.93611 L | PV=nRT, so V=nRT/P=(1)(0.082057)(500)/(0.18)=227.93611 L. | {
"A": "Correct. The worked calculation gives 227.93611 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 227.93611 L, not 229.93611 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 227.93611 L, not 23.79361 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_005906 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.4 atm at 323 K. What is its pressure at 667 K? | {
"A": "7.02105 atm",
"B": "1.70211 atm",
"C": "-7.02105 atm",
"D": "9.02105 atm"
} | A | 7.02105 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.4)(667)/(323)=7.02105 atm. | {
"A": "Correct. The worked calculation gives 7.02105 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.02105 atm, not 1.70211 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.02105 atm, not -7.02105 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007048 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 18 mol of gas at 596 K and 1.33 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "661.88534 L",
"B": "529.50827 L",
"C": "-661.88534 L",
"D": "330.94267 L"
} | A | 661.88534 L | PV=nRT, so V=nRT/P=(18)(0.082057)(596)/(1.33)=661.88534 L. | {
"A": "Correct. The worked calculation gives 661.88534 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 661.88534 L, not 529.50827 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 661.88534 L, not -661.88534 L.",
"D": "Incorrect. Subst... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002187 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 3 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.26667",
"B": "-2.73333",
"C": "0.4",
"D": "-0.73333"
} | A | 0.26667 | Favourable pairs = C(4,2)+C(3,2)+C(3,2)=12. Total pairs=C(10,2)=45. Therefore P=12/45=0.26667. | {
"A": "Correct. The worked calculation gives 0.26667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.26667, not -2.73333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.26667, not 0.4.",
"D": "Incorrect. Substituting the stated value... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007776 | 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 60 minutes? | {
"A": "11.875 mmol L⁻¹",
"B": "2.0875 mmol L⁻¹",
"C": "7.875 mmol L⁻¹",
"D": "10.875 mmol L⁻¹"
} | D | 10.875 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=87/2^3=10.875 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.875 mmol L⁻¹, not 11.875 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.875 mmol L⁻¹, not 2.0875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing r... | [
"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_004430 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 3 m is acted on by a constant torque of 31 N m about its central axis. Find its angular acceleration. | {
"A": "3.44444 rad s⁻²",
"B": "2.58333 rad s⁻²",
"C": "-3.44444 rad s⁻²",
"D": "4.44444 rad s⁻²"
} | A | 3.44444 rad s⁻² | For a solid disc, I=½MR²=½(2)(3)²=9 kg m². Using τ=Iα, α=31/9=3.44444 rad s⁻². | {
"A": "Correct. The worked calculation gives 3.44444 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.44444 rad s⁻², not 2.58333 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.44444 rad s⁻², not -3.44444 rad s⁻².",
"D... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001734 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 60 distinct elements? | {
"A": "75394027566",
"B": "60315222052.8",
"C": "75394027568",
"D": "-75394027566"
} | A | 75394027566 | Order does not matter, so the count is C(60,10)=60!/[10!(50)!]=75394027566. | {
"A": "Correct. The worked calculation gives 75394027566.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 75394027566, not 60315222052.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 75394027566, not 75394027568.",
"D": "Incorrect. Subs... | [
"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_002366 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, -3], [4, 1]]. | {
"A": "14",
"B": "16",
"C": "13",
"D": "28"
} | A | 14 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(1)−(-3)(4)=14. | {
"A": "Correct. The worked calculation gives 14.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14, not 16.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14, not 13.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_002337 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 8 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "2.3834",
"B": "0.7668",
"C": "1.3834",
"D": "0.3834"
} | D | 0.3834 | Favourable pairs = C(12,2)+C(8,2)+C(3,2)=97. Total pairs=C(23,2)=253. Therefore P=97/253=0.3834. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3834, not 2.3834.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3834, not 0.7668.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3834, not 1.3834.",
... | [
"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_006849 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 17 mol H₂ and 6 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "10 mol",
"B": "13 mol",
"C": "15 mol",
"D": "12 mol"
} | D | 12 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 17 mol H₂O; O₂ can produce 12 mol H₂O. The limiting condition is O₂; product=12 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 10 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 13 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 15 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_005048 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +4 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "27 N",
"B": "33.75 N",
"C": "16.875 N",
"D": "67.5 N"
} | B | 33.75 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(4×10⁻⁶)/(8×10⁻²)²=33.75 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33.75 N, not 27 N.",
"B": "Correct. The worked calculation gives 33.75 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 33.75 N, not 16.875 N.",
"D": "Incorrect. Substituting the stated valu... | [
"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_009579 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_18H_8N_3X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "16",
"B": "12",
"C": "15",
"D": "2.5"
} | C | 15 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+3−8−3)/2=15. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15, not 16.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15, not 12.",
"C": "Correct. The worked calculation gives 15.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006067 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 26 cm in front of a thin convex lens of focal length 14 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.75",
"B": "4.16667",
"C": "1.16667",
"D": "2.33333"
} | C | 1.16667 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(26)(14)/(26−14)=30.33333 cm. Thus |m|=v/u=30.33333/26=1.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.16667, not 1.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.16667, not 4.16667.",
"C": "Correct. The worked calculation gives 1.16667.",
"D": "Incorrect. Substituting the stated value... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005055 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +3 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "911.25 N",
"B": "608.5 N",
"C": "607.5 N",
"D": "303.75 N"
} | C | 607.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(3×10⁻⁶)/(2×10⁻²)²=607.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 607.5 N, not 911.25 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 607.5 N, not 608.5 N.",
"C": "Correct. The worked calculation gives 607.5 N.",
"D": "Incorrect. Substituting the stated v... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004330 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 18 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.30. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "97.2 N",
"B": "64.8 N",
"C": "66.8 N",
"D": "7.48 N"
} | B | 64.8 N | Net force=mg(sinθ−μcosθ)=18×10×(0.6−0.30×0.8)=64.8 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 64.8 N, not 97.2 N.",
"B": "Correct. The worked calculation gives 64.8 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 64.8 N, not 66.8 N.",
"D": "Incorrect. Substituting the stated values ... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003876 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 13 kg block initially moves at 4 m s⁻¹. A constant net force does 24 N of work over 14 m in the direction of motion. Find its final kinetic energy. | {
"A": "352 J",
"B": "441 J",
"C": "442 J",
"D": "440 J"
} | D | 440 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(13)(4)²+(24)(14)=440 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 440 J, not 352 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 440 J, not 441 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 440 J, not 442 J.",
"D":... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009248 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.29 V, transfers 2 electrons, and has reaction quotient Q=10^3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.20135 V",
"B": "0.90101 V",
"C": "-1.20135 V",
"D": "-1.79865 V"
} | A | 1.20135 V | Apply the Nernst equation: E=1.29−(0.0591/2)(3)=1.20135 V. | {
"A": "Correct. The worked calculation gives 1.20135 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.20135 V, not 0.90101 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.20135 V, not -1.20135 V.",
"D": "Incorrect. Substituting th... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009548 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_14H_10N_2X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "9",
"B": "12",
"C": "18",
"D": "11"
} | A | 9 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×14+2+2−10−4)/2=9. | {
"A": "Correct. The worked calculation gives 9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9, not 12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9, not 18.",
"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_005789 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.5 atm at 299 K. What is its pressure at 402 K? | {
"A": "6.05017 atm",
"B": "7.05017 atm",
"C": "4.05017 atm",
"D": "3.05017 atm"
} | A | 6.05017 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.5)(402)/(299)=6.05017 atm. | {
"A": "Correct. The worked calculation gives 6.05017 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.05017 atm, not 7.05017 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.05017 atm, not 4.05017 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001805 | 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 83 distinct elements? | {
"A": "77480840752848",
"B": "145276576411590",
"C": "96851050941060",
"D": "9685105094107"
} | C | 96851050941060 | Order does not matter, so the count is C(83,12)=83!/[12!(71)!]=96851050941060. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 96851050941060, not 77480840752848.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 96851050941060, not 145276576411590.",
"C": "Correct. The worked calculation gives 96851050941060.",
"D": "I... | [
"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_000213 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -8x +11=0, let its roots be α and β. What is α²+β²? | {
"A": "5",
"B": "-5",
"C": "2.5",
"D": "7.5"
} | A | 5 | By Vieta's relations, α+β = 8/2 and αβ = 11/2. Then α²+β²=(α+β)²−2αβ = (8/2)²−2(11/2) = 5. | {
"A": "Correct. The worked calculation gives 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not -5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.5.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"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_009830 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(Cl)_2]^+2, each Cl ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "1.4",
"B": "2",
"C": "6",
"D": "4"
} | D | 4 | Let the formal oxidation state of Pd be x. Charge balance gives x+(2)(−1)=+2; hence x=2+2=+4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 6.",
"D": "Correct. The worked ... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001036 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-1x³ +4x² -7x+7. Evaluate f′(-2). | {
"A": "-36",
"B": "-35",
"C": "-26.25",
"D": "-34"
} | B | -35 | Differentiate: f′(x)=3(-1)x²+2(4)x+(-7). At x=-2, f′(-2)=3(-1)(-2)²+2(4)(-2)+(-7)=-35. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -35, not -36.",
"B": "Correct. The worked calculation gives -35.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -35, not -26.25.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_001206 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-1x³ +10x² +4x+7. Evaluate f′(1). | {
"A": "19",
"B": "31.5",
"C": "21",
"D": "3.1"
} | C | 21 | Differentiate: f′(x)=3(-1)x²+2(10)x+(4). At x=1, f′(1)=3(-1)(1)²+2(10)(1)+(4)=21. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21, not 19.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21, not 31.5.",
"C": "Correct. The worked calculation gives 21.",
"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_000470 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -15 and common difference 2. Find the sum of its first 28 terms. | {
"A": "338",
"B": "336",
"C": "334",
"D": "168"
} | B | 336 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-15, d=2, n=28: Sₙ=28/2[2(-15)+(28−1)(2)]=336. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 336, not 338.",
"B": "Correct. The worked calculation gives 336.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 336, not 334.",
"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_007814 | 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 12 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "-0.75 mmol L⁻¹",
"B": "-2.25 mmol L⁻¹",
"C": "0.375 mmol L⁻¹",
"D": "0.75 mmol L⁻¹"
} | D | 0.75 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=12/2^4=0.75 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.75 mmol L⁻¹, not -0.75 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.75 mmol L⁻¹, not -2.25 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relatio... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004258 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 19 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.44. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "-47.12 N",
"B": "45.12 N",
"C": "35.34 N",
"D": "47.12 N"
} | D | 47.12 N | Net force=mg(sinθ−μcosθ)=19×10×(0.6−0.44×0.8)=47.12 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 47.12 N, not -47.12 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 47.12 N, not 45.12 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 47.12 N, not 35.3... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003109 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(9+15i)/(1+12i). What is Re(z), the real part of z? | {
"A": "1.13034",
"B": "4.30345",
"C": "1.30345",
"D": "2.6069"
} | C | 1.30345 | Multiply numerator and denominator by the conjugate (1-12i). Then Re(z)=(ac+bd)/(c²+d²)=((9)(1)+(15)(12))/(1²+(12)²)=1.30345. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.30345, not 1.13034.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.30345, not 4.30345.",
"C": "Correct. The worked calculation gives 1.30345.",
"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_008880 | 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 0.96 mol L⁻¹ and initially B is absent. At equilibrium, 61% of A has dissociated at constant volume. Find K_c. | {
"A": "1.66375",
"B": "5.66375",
"C": "3.66375",
"D": "7.32751"
} | C | 3.66375 | Let α=0.61. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.96)(0.61)²/(1−0.61)=3.66375. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.66375, not 1.66375.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.66375, not 5.66375.",
"C": "Correct. The worked calculation gives 3.66375.",
"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_004153 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 48 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.22. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "101.76 N",
"B": "203.52 N",
"C": "305.28 N",
"D": "162.816 N"
} | B | 203.52 N | Net force=mg(sinθ−μcosθ)=48×10×(0.6−0.22×0.8)=203.52 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 203.52 N, not 101.76 N.",
"B": "Correct. The worked calculation gives 203.52 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 203.52 N, not 305.28 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_001005 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ +2x² -1x+7. Evaluate f′(-1). | {
"A": "-15",
"B": "-13.6",
"C": "-17",
"D": "-18"
} | C | -17 | Differentiate: f′(x)=3(-4)x²+2(2)x+(-1). At x=-1, f′(-1)=3(-4)(-1)²+2(2)(-1)+(-1)=-17. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -17, not -15.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -17, not -13.6.",
"C": "Correct. The worked calculation gives -17.",
"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_008719 | 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 0.2 mol L⁻¹ and initially B is absent. At equilibrium, 35% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.84923",
"B": "1.01508",
"C": "0.15077",
"D": "0.07538"
} | C | 0.15077 | Let α=0.35. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.2)(0.35)²/(1−0.35)=0.15077. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.15077, not -0.84923.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.15077, not 1.01508.",
"C": "Correct. The worked calculation gives 0.15077.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005122 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +4 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "1620 N",
"B": "82 N",
"C": "648 N",
"D": "810 N"
} | D | 810 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(4×10⁻⁶)/(2×10⁻²)²=810 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 810 N, not 1620 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 810 N, not 82 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 810 N, not 648 N.",
"D":... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005586 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 40 μF capacitor is charged to a potential difference of 38 V. Calculate the energy stored, expressed in μJ. | {
"A": "14440 μJ",
"B": "28878 μJ",
"C": "28880 μJ",
"D": "43320 μJ"
} | C | 28880 μJ | U=½CV². Since C=40 μF, U in μJ is ½×40×(38)²=28880 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28880 μJ, not 14440 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28880 μJ, not 28878 μJ.",
"C": "Correct. The worked calculation gives 28880 μJ.",
"D": "Incorrect. Substituting the stat... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008871 | 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 1.22 mol L⁻¹ and initially B is absent. At equilibrium, 19% of A has dissociated at constant volume. Find K_c. | {
"A": "3.21749",
"B": "1.02175",
"C": "0.21749",
"D": "0.16312"
} | C | 0.21749 | Let α=0.19. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.22)(0.19)²/(1−0.19)=0.21749. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.21749, not 3.21749.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.21749, not 1.02175.",
"C": "Correct. The worked calculation gives 0.21749.",
"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_008771 | 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 0.75 mol L⁻¹ and initially B is absent. At equilibrium, 46% of A has dissociated at constant volume. Find K_c. | {
"A": "0.58778",
"B": "2.17556",
"C": "1.17556",
"D": "1.76333"
} | C | 1.17556 | Let α=0.46. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.75)(0.46)²/(1−0.46)=1.17556. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.17556, not 0.58778.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.17556, not 2.17556.",
"C": "Correct. The worked calculation gives 1.17556.",
"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_002210 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 3 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.31818",
"B": "1.03182",
"C": "0.47727",
"D": "0.23864"
} | A | 0.31818 | Favourable pairs = C(3,2)+C(3,2)+C(6,2)=21. Total pairs=C(12,2)=66. Therefore P=21/66=0.31818. | {
"A": "Correct. The worked calculation gives 0.31818.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31818, not 1.03182.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31818, not 0.47727.",
"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_002016 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 7 blue and 10 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-1.68667",
"B": "0.62667",
"C": "-0.31333",
"D": "0.31333"
} | D | 0.31333 | Favourable pairs = C(8,2)+C(7,2)+C(10,2)=94. Total pairs=C(25,2)=300. Therefore P=94/300=0.31333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31333, not -1.68667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31333, not 0.62667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31333, not -0.3... | [
"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_000971 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio -2. What is the sum of its first 11 terms? | {
"A": "7513",
"B": "7511",
"C": "5634.75",
"D": "7515"
} | A | 7513 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(-2^11−1)/(-2−1)=7513. | {
"A": "Correct. The worked calculation gives 7513.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7513, not 7511.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7513, not 5634.75.",
"D": "Incorrect. Substituting the stated values into th... | [
"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_005991 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.4 atm at 262 K. What is its pressure at 749 K? | {
"A": "2.14351 atm",
"B": "1.14351 atm",
"C": "-1.14351 atm",
"D": "1.71527 atm"
} | B | 1.14351 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.4)(749)/(262)=1.14351 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.14351 atm, not 2.14351 atm.",
"B": "Correct. The worked calculation gives 1.14351 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.14351 atm, not -1.14351 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004060 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 17 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.28. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "61.92 N",
"B": "-63.92 N",
"C": "65.92 N",
"D": "63.92 N"
} | D | 63.92 N | Net force=mg(sinθ−μcosθ)=17×10×(0.6−0.28×0.8)=63.92 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 63.92 N, not 61.92 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 63.92 N, not -63.92 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 63.92 N, not 65.9... | [
"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_005507 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 16 μF capacitor is charged to a potential difference of 40 V. Calculate the energy stored, expressed in μJ. | {
"A": "12801 μJ",
"B": "12800 μJ",
"C": "10240 μJ",
"D": "25600 μJ"
} | B | 12800 μJ | U=½CV². Since C=16 μF, U in μJ is ½×16×(40)²=12800 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12800 μJ, not 12801 μJ.",
"B": "Correct. The worked calculation gives 12800 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12800 μJ, not 10240 μJ.",
"D": "Incorrect. Substituting the stat... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005044 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +8 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "180 N",
"B": "90 N",
"C": "135 N",
"D": "179 N"
} | A | 180 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(8×10⁻⁶)/(2×10⁻²)²=180 N. | {
"A": "Correct. The worked calculation gives 180 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 180 N, not 90 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 180 N, not 135 N.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_009957 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(Cl)_2]^-2, each Cl ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "0",
"B": "1",
"C": "-1",
"D": "2"
} | A | 0 | Let the formal oxidation state of Fe be x. Charge balance gives x+(2)(−1)=-2; hence x=-2+2=+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 -1.",
"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_006062 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 87 cm in front of a thin convex lens of focal length 20 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.14925",
"B": "0.22388",
"C": "0.29851",
"D": "3.29851"
} | C | 0.29851 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(87)(20)/(87−20)=25.97015 cm. Thus |m|=v/u=25.97015/87=0.29851. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29851, not 0.14925.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29851, not 0.22388.",
"C": "Correct. The worked calculation gives 0.29851.",
"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_008112 | 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 1 A for 9608 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": "3.16118 g",
"B": "6.32236 g",
"C": "4.16118 g",
"D": "-3.16118 g"
} | A | 3.16118 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×1×9608/(2×96500)=3.16118 g. | {
"A": "Correct. The worked calculation gives 3.16118 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.16118 g, not 6.32236 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.16118 g, not 4.16118 g.",
"D": "Incorrect. Substituting the... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006124 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 39 cm in front of a thin convex lens of focal length 23 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.14375",
"B": "-0.5625",
"C": "1.4375",
"D": "3.4375"
} | C | 1.4375 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(39)(23)/(39−23)=56.0625 cm. Thus |m|=v/u=56.0625/39=1.4375. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.4375, not 1.14375.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4375, not -0.5625.",
"C": "Correct. The worked calculation gives 1.4375.",
"D": "Incorrect. Substituting the stated value... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006802 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 41 mol H₂ and 4 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "-8 mol",
"B": "8 mol",
"C": "12 mol",
"D": "16 mol"
} | B | 8 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 41 mol H₂O; O₂ can produce 8 mol H₂O. The limiting condition is O₂; product=8 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8 mol, not -8 mol.",
"B": "Correct. The worked calculation gives 8 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8 mol, not 12 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_001345 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (-1x² -2x +1) dx. | {
"A": "102",
"B": "-102",
"C": "-9.2",
"D": "-100"
} | B | -102 | An antiderivative is (-1/3)x³+(-2/2)x²+(1)x. Evaluating between 0 and 6 gives (-1/3)(6)³+(-2/2)(6)²+(1)(6)=-102. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -102, not 102.",
"B": "Correct. The worked calculation gives -102.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -102, not -9.2.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_000495 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -11 and common difference 10. Find the sum of its first 10 terms. | {
"A": "408",
"B": "35",
"C": "340",
"D": "170"
} | C | 340 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-11, d=10, n=10: Sₙ=10/2[2(-11)+(10−1)(10)]=340. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 340, not 408.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 340, not 35.",
"C": "Correct. The worked calculation gives 340.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_002204 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 5 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": "0.30994",
"B": "-0.69006",
"C": "-0.30994",
"D": "3.30994"
} | A | 0.30994 | Favourable pairs = C(6,2)+C(5,2)+C(8,2)=53. Total pairs=C(19,2)=171. Therefore P=53/171=0.30994. | {
"A": "Correct. The worked calculation gives 0.30994.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30994, not -0.69006.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30994, not -0.30994.",
"D": "Incorrect. Substituting the stated ... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007303 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 1 mol of gas at 650 K and 2.59 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "24.71215 L",
"B": "16.47476 L",
"C": "20.59346 L",
"D": "18.59346 L"
} | C | 20.59346 L | PV=nRT, so V=nRT/P=(1)(0.082057)(650)/(2.59)=20.59346 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20.59346 L, not 24.71215 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20.59346 L, not 16.47476 L.",
"C": "Correct. The worked calculation gives 20.59346 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_001016 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ -5x² -9x+7. Evaluate f′(-1). | {
"A": "-14",
"B": "-28",
"C": "-17",
"D": "-0.4"
} | A | -14 | Differentiate: f′(x)=3(-5)x²+2(-5)x+(-9). At x=-1, f′(-1)=3(-5)(-1)²+2(-5)(-1)+(-9)=-14. | {
"A": "Correct. The worked calculation gives -14.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -14, not -28.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -14, not -17.",
"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_002834 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(6, -5, 2) and v=(0, -6, 1), calculate u·v. | {
"A": "64",
"B": "-32",
"C": "16",
"D": "32"
} | D | 32 | The dot product is the sum of corresponding component products: (6)(0)+(-5)(-6)+(2)(1)=32. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 32, not 64.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 32, not -32.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 32, not 16.",
"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_007270 | 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 625 K and 2.18 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "105.86482 L",
"B": "15.11531 L",
"C": "141.1531 L",
"D": "112.92248 L"
} | C | 141.1531 L | PV=nRT, so V=nRT/P=(6)(0.082057)(625)/(2.18)=141.1531 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 141.1531 L, not 105.86482 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 141.1531 L, not 15.11531 L.",
"C": "Correct. The worked calculation gives 141.1531 L.",
"D": "Incorrect. Substituti... | [
"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_007262 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 10 mol of gas at 566 K and 2.57 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "144.57358 L",
"B": "180.71697 L",
"C": "216.86037 L",
"D": "19.0717 L"
} | B | 180.71697 L | PV=nRT, so V=nRT/P=(10)(0.082057)(566)/(2.57)=180.71697 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 180.71697 L, not 144.57358 L.",
"B": "Correct. The worked calculation gives 180.71697 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 180.71697 L, not 216.86037 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000778 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio 2. What is the sum of its first 6 terms? | {
"A": "378",
"B": "376",
"C": "567",
"D": "-378"
} | A | 378 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(2^6−1)/(2−1)=378. | {
"A": "Correct. The worked calculation gives 378.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 378, not 376.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 378, not 567.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004172 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 31 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.45. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "74.4 N",
"B": "75.4 N",
"C": "72.4 N",
"D": "73.4 N"
} | A | 74.4 N | Net force=mg(sinθ−μcosθ)=31×10×(0.6−0.45×0.8)=74.4 N. | {
"A": "Correct. The worked calculation gives 74.4 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 74.4 N, not 75.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 74.4 N, not 72.4 N.",
"D": "Incorrect. Substituting the stated values ... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003390 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 62 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "361.21784 m",
"B": "433.46141 m",
"C": "180.60892 m",
"D": "-361.21784 m"
} | A | 361.21784 m | Range R=u²sin(2θ)/g. Substituting u=62, θ=55° and g=10 gives R=(62)²sin(110°)/10=361.21784 m. | {
"A": "Correct. The worked calculation gives 361.21784 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 361.21784 m, not 433.46141 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 361.21784 m, not 180.60892 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006801 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 5 mol H₂ and 7 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "2.5 mol",
"B": "5 mol",
"C": "3 mol",
"D": "10 mol"
} | B | 5 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 5 mol H₂O; O₂ can produce 14 mol H₂O. The limiting condition is H₂; product=5 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5 mol, not 2.5 mol.",
"B": "Correct. The worked calculation gives 5 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5 mol, not 3 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_001199 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ +1x² -6x+7. Evaluate f′(-3). | {
"A": "-240",
"B": "-60",
"C": "-120",
"D": "-119"
} | C | -120 | Differentiate: f′(x)=3(-4)x²+2(1)x+(-6). At x=-3, f′(-3)=3(-4)(-3)²+2(1)(-3)+(-6)=-120. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -120, not -240.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -120, not -60.",
"C": "Correct. The worked calculation gives -120.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_008841 | 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 1.13 mol L⁻¹ and initially B is absent. At equilibrium, 56% of A has dissociated at constant volume. Find K_c. | {
"A": "-3.22153",
"B": "4.22153",
"C": "3.22153",
"D": "4.83229"
} | C | 3.22153 | Let α=0.56. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.13)(0.56)²/(1−0.56)=3.22153. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.22153, not -3.22153.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.22153, not 4.22153.",
"C": "Correct. The worked calculation gives 3.22153.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001565 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (-2x² +1x +4) dx. | {
"A": "-554.66667",
"B": "-277.33333",
"C": "277.33333",
"D": "-275.33333"
} | B | -277.33333 | An antiderivative is (-2/3)x³+(1/2)x²+(4)x. Evaluating between 0 and 8 gives (-2/3)(8)³+(1/2)(8)²+(4)(8)=-277.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -277.33333, not -554.66667.",
"B": "Correct. The worked calculation gives -277.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -277.33333, not 277.33333.",
"D": "Incorrect. Substituting... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002842 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-4, 5, 2) and v=(0, -4, 8), calculate u·v. | {
"A": "-4",
"B": "0.6",
"C": "4",
"D": "-3"
} | A | -4 | The dot product is the sum of corresponding component products: (-4)(0)+(5)(-4)+(2)(8)=-4. | {
"A": "Correct. The worked calculation gives -4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -4, not 0.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -4, not 4.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007741 | 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 46 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "23 mmol L⁻¹",
"B": "18.4 mmol L⁻¹",
"C": "34.5 mmol L⁻¹",
"D": "11.5 mmol L⁻¹"
} | A | 23 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=46/2^1=23 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 23 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23 mmol L⁻¹, not 18.4 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23 mmol L⁻¹, not 34.5 mmol L⁻¹.",
"D": "Incorrect. Su... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000052 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +10x -5=0, let its roots be α and β. What is α²+β²? | {
"A": "13.44444",
"B": "7.22222",
"C": "17.44444",
"D": "14.44444"
} | D | 14.44444 | By Vieta's relations, α+β = -10/3 and αβ = -5/3. Then α²+β²=(α+β)²−2αβ = (-10/3)²−2(-5/3) = 14.44444. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14.44444, not 13.44444.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14.44444, not 7.22222.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14.44444, not 1... | [
"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_000696 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio -3. What is the sum of its first 12 terms? | {
"A": "-1195741",
"B": "-1195740",
"C": "1195740",
"D": "-2391480"
} | B | -1195740 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(-3^12−1)/(-3−1)=-1195740. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1195740, not -1195741.",
"B": "Correct. The worked calculation gives -1195740.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1195740, not 1195740.",
"D": "Incorrect. Substituting the state... | [
"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_004620 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 11 kg and radius 6 m is acted on by a constant torque of 21 N m about its central axis. Find its angular acceleration. | {
"A": "0.07955 rad s⁻²",
"B": "0.10606 rad s⁻²",
"C": "-1.89394 rad s⁻²",
"D": "2.10606 rad s⁻²"
} | B | 0.10606 rad s⁻² | For a solid disc, I=½MR²=½(11)(6)²=198 kg m². Using τ=Iα, α=21/198=0.10606 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.10606 rad s⁻², not 0.07955 rad s⁻².",
"B": "Correct. The worked calculation gives 0.10606 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.10606 rad s⁻², not -1.89394 rad s⁻².",
"D... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004749 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 3 Ω and 11 Ω are connected in series; this combination is connected in parallel with a 9 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.19048 A",
"B": "8.7619 A",
"C": "4.38095 A",
"D": "3.28571 A"
} | C | 4.38095 A | Series branch resistance=3+11=14 Ω. Parallel equivalent R_eq=(14×9)/(14+9)=5.47826 Ω. Total current I=V/R_eq=24/5.47826=4.38095 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.38095 A, not 2.19048 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.38095 A, not 8.7619 A.",
"C": "Correct. The worked calculation gives 4.38095 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_009258 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.98 V, transfers 3 electrons, and has reaction quotient Q=10^2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-2.0594 V",
"B": "1.8812 V",
"C": "0.9406 V",
"D": "1.09406 V"
} | C | 0.9406 V | Apply the Nernst equation: E=0.98−(0.0591/3)(2)=0.9406 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9406 V, not -2.0594 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9406 V, not 1.8812 V.",
"C": "Correct. The worked calculation gives 0.9406 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_006929 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 42 mol H₂ and 2 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "1.4 mol",
"B": "4 mol",
"C": "2 mol",
"D": "6 mol"
} | B | 4 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 42 mol H₂O; O₂ can produce 4 mol H₂O. The limiting condition is O₂; product=4 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4 mol, not 1.4 mol.",
"B": "Correct. The worked calculation gives 4 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4 mol, not 2 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_006539 | 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 225 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.3266 s",
"B": "2.3266 s",
"C": "0.1633 s",
"D": "1.3266 s"
} | A | 0.3266 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(6/225)=0.3266 s. | {
"A": "Correct. The worked calculation gives 0.3266 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3266 s, not 2.3266 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3266 s, not 0.1633 s.",
"D": "Incorrect. Substituting the stat... | [
"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_006761 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 44 mol H₂ and 13 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "26 mol",
"B": "3.6 mol",
"C": "13 mol",
"D": "-26 mol"
} | A | 26 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 44 mol H₂O; O₂ can produce 26 mol H₂O. The limiting condition is O₂; product=26 mol. | {
"A": "Correct. The worked calculation gives 26 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 3.6 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 13 mol.",
"D": "Incorrect. Substituting the stated values... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002130 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 8 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.15942",
"B": "0.63768",
"C": "1.31884",
"D": "0.31884"
} | D | 0.31884 | Favourable pairs = C(10,2)+C(8,2)+C(6,2)=88. Total pairs=C(24,2)=276. Therefore P=88/276=0.31884. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31884, not 0.15942.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31884, not 0.63768.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31884, not 1.318... | [
"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_002163 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 8 blue and 7 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.31053",
"B": "3.31053",
"C": "0.31053",
"D": "0.62105"
} | C | 0.31053 | Favourable pairs = C(5,2)+C(8,2)+C(7,2)=59. Total pairs=C(20,2)=190. Therefore P=59/190=0.31053. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31053, not 1.31053.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31053, not 3.31053.",
"C": "Correct. The worked calculation gives 0.31053.",
"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_008016 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 12 A for 5867 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "17.37301 g",
"B": "23.16401 g",
"C": "25.16401 g",
"D": "21.16401 g"
} | B | 23.16401 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×12×5867/(2×96500)=23.16401 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 23.16401 g, not 17.37301 g.",
"B": "Correct. The worked calculation gives 23.16401 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23.16401 g, not 25.16401 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001227 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=1x³ -7x² +4x+7. Evaluate f′(1). | {
"A": "-14",
"B": "-5.25",
"C": "-7",
"D": "-9"
} | C | -7 | Differentiate: f′(x)=3(1)x²+2(-7)x+(4). At x=1, f′(1)=3(1)(1)²+2(-7)(1)+(4)=-7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -7, not -14.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -7, not -5.25.",
"C": "Correct. The worked calculation gives -7.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_008360 | 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 1.71 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "8.13 K",
"B": "5.13 K",
"C": "2.13 K",
"D": "10.26 K"
} | B | 5.13 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×1.0×1.71=5.13 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.13 K, not 8.13 K.",
"B": "Correct. The worked calculation gives 5.13 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.13 K, not 2.13 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_000131 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 +0x -12=0, let its roots be α and β. What is α²+β²? | {
"A": "6",
"B": "8",
"C": "5",
"D": "9"
} | A | 6 | By Vieta's relations, α+β = 0/4 and αβ = -12/4. Then α²+β²=(α+β)²−2αβ = (0/4)²−2(-12/4) = 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 5.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_000238 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 -1x -11=0, let its roots be α and β. What is α²+β²? | {
"A": "8.5625",
"B": "5.5625",
"C": "11.125",
"D": "6.5625"
} | B | 5.5625 | By Vieta's relations, α+β = 1/4 and αβ = -11/4. Then α²+β²=(α+β)²−2αβ = (1/4)²−2(-11/4) = 5.5625. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.5625, not 8.5625.",
"B": "Correct. The worked calculation gives 5.5625.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.5625, not 11.125.",
"D": "Incorrect. Substituting the stated values ... | [
"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_005190 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +3 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "10.04132 N",
"B": "22.08264 N",
"C": "21.08264 N",
"D": "20.08264 N"
} | D | 20.08264 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(3×10⁻⁶)/(11×10⁻²)²=20.08264 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20.08264 N, not 10.04132 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20.08264 N, not 22.08264 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20.082... | [
"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_003612 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 80 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "599.40328 m",
"B": "902.10492 m",
"C": "481.12262 m",
"D": "601.40328 m"
} | D | 601.40328 m | Range R=u²sin(2θ)/g. Substituting u=80, θ=55° and g=10 gives R=(80)²sin(110°)/10=601.40328 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 601.40328 m, not 599.40328 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 601.40328 m, not 902.10492 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 60... | [
"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_003146 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(9+13i)/(7+12i). What is Re(z), the real part of z? | {
"A": "4.13472",
"B": "1.13472",
"C": "3.13472",
"D": "1.70207"
} | B | 1.13472 | Multiply numerator and denominator by the conjugate (7-12i). Then Re(z)=(ac+bd)/(c²+d²)=((9)(7)+(13)(12))/(7²+(12)²)=1.13472. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.13472, not 4.13472.",
"B": "Correct. The worked calculation gives 1.13472.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.13472, not 3.13472.",
"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_003282 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(12+15i)/(4+12i). What is Re(z), the real part of z? | {
"A": "2.1375",
"B": "-0.575",
"C": "1.425",
"D": "1.1425"
} | C | 1.425 | Multiply numerator and denominator by the conjugate (4-12i). Then Re(z)=(ac+bd)/(c²+d²)=((12)(4)+(15)(12))/(4²+(12)²)=1.425. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.425, not 2.1375.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.425, not -0.575.",
"C": "Correct. The worked calculation gives 1.425.",
"D": "Incorrect. Substituting the stated values int... | [
"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_003898 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 2 m s⁻¹. A constant net force does 8 N of work over 5 m in the direction of motion. Find its final kinetic energy. | {
"A": "54 J",
"B": "6.4 J",
"C": "-54 J",
"D": "27 J"
} | A | 54 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(2)²+(8)(5)=54 J. | {
"A": "Correct. The worked calculation gives 54 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 54 J, not 6.4 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 54 J, not -54 J.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_006321 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 62 cm in front of a thin convex lens of focal length 24 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.06316",
"B": "1.63158",
"C": "-2.36842",
"D": "0.63158"
} | D | 0.63158 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(62)(24)/(62−24)=39.15789 cm. Thus |m|=v/u=39.15789/62=0.63158. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.63158, not 1.06316.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.63158, not 1.63158.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.63158, not -2.36... | [
"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_005109 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +7 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "32.23967 N",
"B": "31.23967 N",
"C": "30.23967 N",
"D": "24.99174 N"
} | B | 31.23967 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(7×10⁻⁶)/(11×10⁻²)²=31.23967 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 31.23967 N, not 32.23967 N.",
"B": "Correct. The worked calculation gives 31.23967 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 31.23967 N, not 30.23967 N.",
"D": "Incorrect. Substitutin... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009812 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(OH)_3]^-1, each OH ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "1",
"B": "1.5",
"C": "2",
"D": "3"
} | C | 2 | Let the formal oxidation state of Mn be x. Charge balance gives x+(3)(−1)=-1; hence x=-1+3=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.5.",
"C": "Correct. The worked calculation gives 2.",
"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_003127 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-2-4i)/(10+6i). What is Re(z), the real part of z? | {
"A": "0.96765",
"B": "0.32353",
"C": "-2.32353",
"D": "-0.32353"
} | D | -0.32353 | Multiply numerator and denominator by the conjugate (10-6i). Then Re(z)=(ac+bd)/(c²+d²)=((-2)(10)+(-4)(6))/(10²+(6)²)=-0.32353. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.32353, not 0.96765.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.32353, not 0.32353.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.32353, not -2... | [
"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_000215 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 -4x -10=0, let its roots be α and β. What is α²+β²? | {
"A": "-8.44444",
"B": "6.44444",
"C": "6.33333",
"D": "8.44444"
} | D | 8.44444 | By Vieta's relations, α+β = 4/3 and αβ = -10/3. Then α²+β²=(α+β)²−2αβ = (4/3)²−2(-10/3) = 8.44444. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.44444, not -8.44444.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.44444, not 6.44444.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.44444, not 6.33... | [
"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_004887 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 12 Ω and 5 Ω are connected in series; this combination is connected in parallel with a 3 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "-2.35294 A",
"B": "3.52941 A",
"C": "5.35294 A",
"D": "2.35294 A"
} | D | 2.35294 A | Series branch resistance=12+5=17 Ω. Parallel equivalent R_eq=(17×3)/(17+3)=2.55 Ω. Total current I=V/R_eq=6/2.55=2.35294 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.35294 A, not -2.35294 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.35294 A, not 3.52941 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.35294 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_005784 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2 atm at 320 K. What is its pressure at 454 K? | {
"A": "5.675 atm",
"B": "0.8375 atm",
"C": "1.8375 atm",
"D": "2.8375 atm"
} | D | 2.8375 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2)(454)/(320)=2.8375 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.8375 atm, not 5.675 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.8375 atm, not 0.8375 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.8375 ... | [
"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_003803 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 5 m s⁻¹. A constant net force does 20 N of work over 2 m in the direction of motion. Find its final kinetic energy. | {
"A": "114.375 J",
"B": "76.25 J",
"C": "152.5 J",
"D": "16.25 J"
} | C | 152.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(5)²+(20)(2)=152.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 152.5 J, not 114.375 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 152.5 J, not 76.25 J.",
"C": "Correct. The worked calculation gives 152.5 J.",
"D": "Incorrect. Substituting the stated ... | [
"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 |
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