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_004421 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 1 m is acted on by a constant torque of 71 N m about its central axis. Find its angular acceleration. | {
"A": "18.28571 rad s⁻²",
"B": "21.28571 rad s⁻²",
"C": "20.28571 rad s⁻²",
"D": "30.42857 rad s⁻²"
} | C | 20.28571 rad s⁻² | For a solid disc, I=½MR²=½(7)(1)²=3.5 kg m². Using τ=Iα, α=71/3.5=20.28571 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20.28571 rad s⁻², not 18.28571 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20.28571 rad s⁻², not 21.28571 rad s⁻².",
"C": "Correct. The worked calculation gives 20.28571 rad s⁻².",
... | [
"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_006742 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 2 mol H₂ and 13 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "-2 mol",
"B": "4 mol",
"C": "2 mol",
"D": "-1 mol"
} | C | 2 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 2 mol H₂O; O₂ can produce 26 mol H₂O. The limiting condition is H₂; product=2 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not -2 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 4 mol.",
"C": "Correct. The worked calculation gives 2 mol.",
"D": "Incorrect. Substituting the stated values into... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005141 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +5 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "302 N",
"B": "300 N",
"C": "450 N",
"D": "150 N"
} | B | 300 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(5×10⁻⁶)/(3×10⁻²)²=300 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 300 N, not 302 N.",
"B": "Correct. The worked calculation gives 300 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 300 N, not 450 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003086 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(10+5i)/(3+8i). What is Re(z), the real part of z? | {
"A": "-1.0411",
"B": "-0.9589",
"C": "0.9589",
"D": "1.09589"
} | C | 0.9589 | Multiply numerator and denominator by the conjugate (3-8i). Then Re(z)=(ac+bd)/(c²+d²)=((10)(3)+(5)(8))/(3²+(8)²)=0.9589. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9589, not -1.0411.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9589, not -0.9589.",
"C": "Correct. The worked calculation gives 0.9589.",
"D": "Incorrect. Substituting the stated value... | [
"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_004242 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 38 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.18. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "346.56 N",
"B": "173.28 N",
"C": "174.28 N",
"D": "172.28 N"
} | B | 173.28 N | Net force=mg(sinθ−μcosθ)=38×10×(0.6−0.18×0.8)=173.28 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 173.28 N, not 346.56 N.",
"B": "Correct. The worked calculation gives 173.28 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 173.28 N, not 174.28 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_001364 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (-2x² +4x -1) dx. | {
"A": "-6",
"B": "0.7",
"C": "-3",
"D": "-1.5"
} | C | -3 | An antiderivative is (-2/3)x³+(4/2)x²+(-1)x. Evaluating between 0 and 3 gives (-2/3)(3)³+(4/2)(3)²+(-1)(3)=-3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -3, not -6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -3, not 0.7.",
"C": "Correct. The worked calculation gives -3.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"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_002201 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 8 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": "0.31077",
"B": "1.03108",
"C": "-1.68923",
"D": "1.31077"
} | A | 0.31077 | Favourable pairs = C(8,2)+C(8,2)+C(10,2)=101. Total pairs=C(26,2)=325. Therefore P=101/325=0.31077. | {
"A": "Correct. The worked calculation gives 0.31077.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31077, not 1.03108.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31077, not -1.68923.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009698 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(CN)_3]^-3, each CN ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "0",
"B": "-2",
"C": "1",
"D": "2"
} | A | 0 | Let the formal oxidation state of Cu be x. Charge balance gives x+(3)(−1)=-3; hence x=-3+3=+0. | {
"A": "Correct. The worked calculation gives 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"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_002147 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 11 red, 3 blue and 5 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.60234",
"B": "0.39766",
"C": "-2.60234",
"D": "-1.60234"
} | B | 0.39766 | Favourable pairs = C(11,2)+C(3,2)+C(5,2)=68. Total pairs=C(19,2)=171. Therefore P=68/171=0.39766. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.39766, not -0.60234.",
"B": "Correct. The worked calculation gives 0.39766.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.39766, not -2.60234.",
"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_005636 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 66 μF capacitor is charged to a potential difference of 27 V. Calculate the energy stored, expressed in μJ. | {
"A": "18042.75 μJ",
"B": "24058 μJ",
"C": "24057 μJ",
"D": "-24057 μJ"
} | C | 24057 μJ | U=½CV². Since C=66 μF, U in μJ is ½×66×(27)²=24057 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24057 μJ, not 18042.75 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24057 μJ, not 24058 μJ.",
"C": "Correct. The worked calculation gives 24057 μJ.",
"D": "Incorrect. Substituting the s... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001836 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 22 distinct elements? | {
"A": "19750.5",
"B": "39501",
"C": "21067.2",
"D": "26334"
} | D | 26334 | Order does not matter, so the count is C(22,5)=22!/[5!(17)!]=26334. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26334, not 19750.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26334, not 39501.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26334, not 21067.2.",
... | [
"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_008565 | 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 0.67 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.804 K",
"B": "0.603 K",
"C": "0.804 K",
"D": "-1.196 K"
} | C | 0.804 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.6×0.67=0.804 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.804 K, not 1.804 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.804 K, not 0.603 K.",
"C": "Correct. The worked calculation gives 0.804 K.",
"D": "Incorrect. Substituting the stated va... | [
"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_003854 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 1 m s⁻¹. A constant net force does 27 N of work over 16 m in the direction of motion. Find its final kinetic energy. | {
"A": "438 J",
"B": "-438 J",
"C": "44.8 J",
"D": "328.5 J"
} | A | 438 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(1)²+(27)(16)=438 J. | {
"A": "Correct. The worked calculation gives 438 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 438 J, not -438 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 438 J, not 44.8 J.",
"D": "Incorrect. Substituting the stated values int... | [
"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_008297 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 10 A for 9322 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": "15.33541 g",
"B": "4.06708 g",
"C": "31.67083 g",
"D": "30.67083 g"
} | D | 30.67083 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×10×9322/(2×96500)=30.67083 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 30.67083 g, not 15.33541 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30.67083 g, not 4.06708 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30.6708... | [
"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_005166 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +9 μC are separated by 12 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "40.375 N",
"B": "41.375 N",
"C": "39.375 N",
"D": "37.375 N"
} | C | 39.375 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(9×10⁻⁶)/(12×10⁻²)²=39.375 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 39.375 N, not 40.375 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39.375 N, not 41.375 N.",
"C": "Correct. The worked calculation gives 39.375 N.",
"D": "Incorrect. Substituting the stat... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007521 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 97 mL of 0.10 M HCl is mixed with 55 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "0.7793",
"B": "1.55859",
"C": "1.16895",
"D": "2.33789"
} | B | 1.55859 | Excess H⁺ moles=0.10×(97−55)/1000=0.004200 mol. Total volume=0.152 L, so [H⁺]=0.027632 M and pH=−log₁₀[H⁺]=1.55859. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.55859, not 0.7793.",
"B": "Correct. The worked calculation gives 1.55859.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.55859, not 1.16895.",
"D": "Incorrect. Substituting the stated val... | [
"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_008266 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 9 A for 8918 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": "28.40745 g",
"B": "27.40745 g",
"C": "26.40745 g",
"D": "3.64074 g"
} | C | 26.40745 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×9×8918/(2×96500)=26.40745 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26.40745 g, not 28.40745 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26.40745 g, not 27.40745 g.",
"C": "Correct. The worked calculation gives 26.40745 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_009125 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.90 V, transfers 1 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.3955 V",
"B": "0.6045 V",
"C": "1.209 V",
"D": "-0.3955 V"
} | B | 0.6045 V | Apply the Nernst equation: E=0.90−(0.0591/1)(5)=0.6045 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6045 V, not -1.3955 V.",
"B": "Correct. The worked calculation gives 0.6045 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.6045 V, not 1.209 V.",
"D": "Incorrect. Substituting the stat... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005179 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +4 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "1.44444 N",
"B": "6.44444 N",
"C": "-4.44444 N",
"D": "4.44444 N"
} | D | 4.44444 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(4×10⁻⁶)/(9×10⁻²)²=4.44444 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.44444 N, not 1.44444 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.44444 N, not 6.44444 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.44444 N,... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000597 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 24 and common difference 6. Find the sum of its first 32 terms. | {
"A": "2808",
"B": "3742",
"C": "3745",
"D": "3744"
} | D | 3744 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=24, d=6, n=32: Sₙ=32/2[2(24)+(32−1)(6)]=3744. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3744, not 2808.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3744, not 3742.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3744, not 3745.",
"D": "Corr... | [
"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_001524 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (5x² +6x -1) dx. | {
"A": "-711.66667",
"B": "711.66667",
"C": "569.33333",
"D": "1067.5"
} | B | 711.66667 | An antiderivative is (5/3)x³+(6/2)x²+(-1)x. Evaluating between 0 and 7 gives (5/3)(7)³+(6/2)(7)²+(-1)(7)=711.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 711.66667, not -711.66667.",
"B": "Correct. The worked calculation gives 711.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 711.66667, not 569.33333.",
"D": "Incorrect. Substituting th... | [
"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_001052 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-2x³ -8x² -10x+7. Evaluate f′(1). | {
"A": "-2.2",
"B": "32",
"C": "-48",
"D": "-32"
} | D | -32 | Differentiate: f′(x)=3(-2)x²+2(-8)x+(-10). At x=1, f′(1)=3(-2)(1)²+2(-8)(1)+(-10)=-32. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -32, not -2.2.",
"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 -48.",
"D": "Correct. T... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000711 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio 4. What is the sum of its first 10 terms? | {
"A": "1048575",
"B": "1398100",
"C": "699050",
"D": "559240"
} | C | 699050 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(4^10−1)/(4−1)=699050. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 699050, not 1048575.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 699050, not 1398100.",
"C": "Correct. The worked calculation gives 699050.",
"D": "Incorrect. Substituting the stated value... | [
"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_001377 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (4x² -4x +0) dx. | {
"A": "217",
"B": "216",
"C": "162",
"D": "432"
} | B | 216 | An antiderivative is (4/3)x³+(-4/2)x²+(0)x. Evaluating between 0 and 6 gives (4/3)(6)³+(-4/2)(6)²+(0)(6)=216. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 216, not 217.",
"B": "Correct. The worked calculation gives 216.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 216, not 162.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_008647 | 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 1.34 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-2.196 K",
"B": "0.804 K",
"C": "1.608 K",
"D": "0.402 K"
} | B | 0.804 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.6×1.34=0.804 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.804 K, not -2.196 K.",
"B": "Correct. The worked calculation gives 0.804 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.804 K, not 1.608 K.",
"D": "Incorrect. Substituting the stated v... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003795 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 1 m s⁻¹. A constant net force does 19 N of work over 5 m in the direction of motion. Find its final kinetic energy. | {
"A": "75 J",
"B": "100 J",
"C": "50 J",
"D": "150 J"
} | B | 100 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(1)²+(19)(5)=100 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 100 J, not 75 J.",
"B": "Correct. The worked calculation gives 100 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 100 J, not 50 J.",
"D": "Incorrect. Substituting the stated values into th... | [
"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_008058 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 9 A for 7324 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": "17.34991 g",
"B": "3.16874 g",
"C": "21.68739 g",
"D": "43.37478 g"
} | C | 21.68739 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×9×7324/(2×96500)=21.68739 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21.68739 g, not 17.34991 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21.68739 g, not 3.16874 g.",
"C": "Correct. The worked calculation gives 21.68739 g.",
"D": "Incorrect. Substituting... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009039 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.18 V, transfers 2 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.50405 V",
"B": "1.0027 V",
"C": "0.0027 V",
"D": "-0.9973 V"
} | B | 1.0027 V | Apply the Nernst equation: E=1.18−(0.0591/2)(6)=1.0027 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0027 V, not 1.50405 V.",
"B": "Correct. The worked calculation gives 1.0027 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0027 V, not 0.0027 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_007990 | 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 41 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "1.28125 mmol L⁻¹",
"B": "3.28125 mmol L⁻¹",
"C": "-0.71875 mmol L⁻¹",
"D": "-1.71875 mmol L⁻¹"
} | A | 1.28125 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=41/2^5=1.28125 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 1.28125 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.28125 mmol L⁻¹, not 3.28125 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.28125 mmol L⁻¹, not -0.71875 mmol L⁻¹.",... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009366 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_9H_17N_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "1.5",
"B": "2",
"C": "-1",
"D": "4"
} | B | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×9+2+1−17−0)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.5.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not -1.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004262 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.34. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "22.14 N",
"B": "29.52 N",
"C": "14.76 N",
"D": "30.52 N"
} | B | 29.52 N | Net force=mg(sinθ−μcosθ)=9×10×(0.6−0.34×0.8)=29.52 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 29.52 N, not 22.14 N.",
"B": "Correct. The worked calculation gives 29.52 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29.52 N, not 14.76 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000638 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 3 and common difference 13. Find the sum of its first 20 terms. | {
"A": "2530",
"B": "3036",
"C": "2528",
"D": "2532"
} | A | 2530 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=3, d=13, n=20: Sₙ=20/2[2(3)+(20−1)(13)]=2530. | {
"A": "Correct. The worked calculation gives 2530.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2530, not 3036.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2530, not 2528.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008028 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 8 A for 17297 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": "36.42228 g",
"B": "45.52785 g",
"C": "54.63343 g",
"D": "22.76393 g"
} | B | 45.52785 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×8×17297/(2×96500)=45.52785 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45.52785 g, not 36.42228 g.",
"B": "Correct. The worked calculation gives 45.52785 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 45.52785 g, not 54.63343 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_003438 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 73 m s⁻¹ at 15° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "27.645 m",
"B": "266.45 m",
"C": "399.675 m",
"D": "199.8375 m"
} | B | 266.45 m | Range R=u²sin(2θ)/g. Substituting u=73, θ=15° and g=10 gives R=(73)²sin(30°)/10=266.45 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 266.45 m, not 27.645 m.",
"B": "Correct. The worked calculation gives 266.45 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 266.45 m, not 399.675 m.",
"D": "Incorrect. Substituting the sta... | [
"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_009997 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(Cl)_4]^-2, each Cl ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "0",
"B": "-2",
"C": "-1",
"D": "2"
} | D | 2 | Let the formal oxidation state of Mn be x. Charge balance gives x+(4)(−1)=-2; hence x=-2+4=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not -1.",
"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_004840 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 9 Ω are connected in series; this combination is connected in parallel with a 3 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "5.66667 A",
"B": "9.33333 A",
"C": "-4.66667 A",
"D": "4.66667 A"
} | D | 4.66667 A | Series branch resistance=9+9=18 Ω. Parallel equivalent R_eq=(18×3)/(18+3)=2.57143 Ω. Total current I=V/R_eq=12/2.57143=4.66667 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.66667 A, not 5.66667 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.66667 A, not 9.33333 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.66667 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_006316 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 27 cm in front of a thin convex lens of focal length 7 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.35",
"B": "-2.65",
"C": "0.525",
"D": "0.2625"
} | A | 0.35 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(27)(7)/(27−7)=9.45 cm. Thus |m|=v/u=9.45/27=0.35. | {
"A": "Correct. The worked calculation gives 0.35.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35, not -2.65.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35, not 0.525.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_002305 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 6 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": "0.32",
"B": "-0.68",
"C": "0.48",
"D": "0.24"
} | A | 0.32 | Favourable pairs = C(9,2)+C(6,2)+C(10,2)=96. Total pairs=C(25,2)=300. Therefore P=96/300=0.32. | {
"A": "Correct. The worked calculation gives 0.32.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32, not -0.68.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32, not 0.48.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_003206 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-6+2i)/(10+3i). What is Re(z), the real part of z? | {
"A": "0.95046",
"B": "0.50459",
"C": "-3.49541",
"D": "-0.49541"
} | D | -0.49541 | Multiply numerator and denominator by the conjugate (10-3i). Then Re(z)=(ac+bd)/(c²+d²)=((-6)(10)+(2)(3))/(10²+(3)²)=-0.49541. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.49541, not 0.95046.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.49541, not 0.50459.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.49541, not -3... | [
"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_006798 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 15 mol H₂ and 30 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "17 mol",
"B": "22.5 mol",
"C": "7.5 mol",
"D": "15 mol"
} | D | 15 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 15 mol H₂O; O₂ can produce 60 mol H₂O. The limiting condition is H₂; product=15 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15 mol, not 17 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15 mol, not 22.5 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15 mol, not 7.5 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_006758 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 2 mol H₂ and 31 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "3 mol",
"B": "4 mol",
"C": "1.5 mol",
"D": "2 mol"
} | D | 2 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 2 mol H₂O; O₂ can produce 62 mol H₂O. The limiting condition is H₂; product=2 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 3 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 4 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 1.5 mol.",
"D... | [
"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_006651 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 5 kg is attached to an ideal spring of force constant 495 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.0201 s",
"B": "-0.79899 s",
"C": "-0.20101 s",
"D": "0.20101 s"
} | D | 0.20101 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(5/495)=0.20101 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.20101 s, not 1.0201 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.20101 s, not -0.79899 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.20101 s,... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002428 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -8], [4, 7]]. | {
"A": "67",
"B": "69",
"C": "80.4",
"D": "53.6"
} | A | 67 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(7)−(-8)(4)=67. | {
"A": "Correct. The worked calculation gives 67.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 67, not 69.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 67, not 80.4.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009541 | 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_11H_17N_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "6",
"B": "8",
"C": "4",
"D": "5"
} | C | 4 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+1−17−0)/2=4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 8.",
"C": "Correct. The worked calculation gives 4.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008816 | 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 1.88 mol L⁻¹ and initially B is absent. At equilibrium, 44% of A has dissociated at constant volume. Find K_c. | {
"A": "1.94983",
"B": "4.59977",
"C": "2.59977",
"D": "1.29989"
} | C | 2.59977 | Let α=0.44. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.88)(0.44)²/(1−0.44)=2.59977. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.59977, not 1.94983.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.59977, not 4.59977.",
"C": "Correct. The worked calculation gives 2.59977.",
"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_000372 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 0 and common difference 13. Find the sum of its first 32 terms. | {
"A": "6450",
"B": "6447",
"C": "4836",
"D": "6448"
} | D | 6448 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=0, d=13, n=32: Sₙ=32/2[2(0)+(32−1)(13)]=6448. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6448, not 6450.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6448, not 6447.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6448, not 4836.",
"D": "Corr... | [
"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_004933 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 15 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 6 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.41379 A",
"B": "3.41379 A",
"C": "1.24138 A",
"D": "1.81034 A"
} | A | 2.41379 A | Series branch resistance=15+14=29 Ω. Parallel equivalent R_eq=(29×6)/(29+6)=4.97143 Ω. Total current I=V/R_eq=12/4.97143=2.41379 A. | {
"A": "Correct. The worked calculation gives 2.41379 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.41379 A, not 3.41379 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.41379 A, not 1.24138 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_004423 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 6 m is acted on by a constant torque of 92 N m about its central axis. Find its angular acceleration. | {
"A": "1.91667 rad s⁻²",
"B": "5.55556 rad s⁻²",
"C": "-0.44444 rad s⁻²",
"D": "2.55556 rad s⁻²"
} | D | 2.55556 rad s⁻² | For a solid disc, I=½MR²=½(2)(6)²=36 kg m². Using τ=Iα, α=92/36=2.55556 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.55556 rad s⁻², not 1.91667 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.55556 rad s⁻², not 5.55556 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing r... | [
"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_006727 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 27 mol H₂ and 4 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "9 mol",
"B": "4 mol",
"C": "12 mol",
"D": "8 mol"
} | D | 8 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 27 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 9 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8 mol, not 4 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8 mol, not 12 mol.",
"D"... | [
"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_006189 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 127 cm in front of a thin convex lens of focal length 26 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.02574",
"B": "1.25743",
"C": "0.25743",
"D": "-0.25743"
} | C | 0.25743 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(127)(26)/(127−26)=32.69307 cm. Thus |m|=v/u=32.69307/127=0.25743. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25743, not 1.02574.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25743, not 1.25743.",
"C": "Correct. The worked calculation gives 0.25743.",
"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_000456 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -13 and common difference 15. Find the sum of its first 19 terms. | {
"A": "2316",
"B": "2318",
"C": "1738.5",
"D": "2320"
} | B | 2318 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-13, d=15, n=19: Sₙ=19/2[2(-13)+(19−1)(15)]=2318. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2318, not 2316.",
"B": "Correct. The worked calculation gives 2318.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2318, not 1738.5.",
"D": "Incorrect. Substituting the stated values into the... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000567 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -7 and common difference 5. Find the sum of its first 30 terms. | {
"A": "-1965",
"B": "1966",
"C": "2947.5",
"D": "1965"
} | D | 1965 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-7, d=5, n=30: Sₙ=30/2[2(-7)+(30−1)(5)]=1965. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1965, not -1965.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1965, not 1966.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1965, not 2947.5.",
"D": "C... | [
"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_002115 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 5 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "3.29524",
"B": "0.44286",
"C": "-1.70476",
"D": "0.29524"
} | D | 0.29524 | Favourable pairs = C(6,2)+C(5,2)+C(4,2)=31. Total pairs=C(15,2)=105. Therefore P=31/105=0.29524. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29524, not 3.29524.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29524, not 0.44286.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29524, not -1.70... | [
"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_000758 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio -3. What is the sum of its first 6 terms? | {
"A": "-364",
"B": "-182",
"C": "182",
"D": "-180"
} | B | -182 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(-3^6−1)/(-3−1)=-182. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -182, not -364.",
"B": "Correct. The worked calculation gives -182.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -182, not 182.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_008695 | 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, 44% of A has dissociated at constant volume. Find K_c. | {
"A": "1.68709",
"B": "3.68709",
"C": "-1.31291",
"D": "1.26531"
} | A | 1.68709 | Let α=0.44. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.22)(0.44)²/(1−0.44)=1.68709. | {
"A": "Correct. The worked calculation gives 1.68709.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.68709, not 3.68709.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.68709, not -1.31291.",
"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_008060 | 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 3 A for 22163 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": "26.2511 g",
"B": "-21.87591 g",
"C": "22.87591 g",
"D": "21.87591 g"
} | D | 21.87591 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×3×22163/(2×96500)=21.87591 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21.87591 g, not 26.2511 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21.87591 g, not -21.87591 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21.875... | [
"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_006612 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 10 kg is attached to an ideal spring of force constant 1054 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.19481 s",
"B": "0.38962 s",
"C": "0.0974 s",
"D": "-0.19481 s"
} | A | 0.19481 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(10/1054)=0.19481 s. | {
"A": "Correct. The worked calculation gives 0.19481 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.19481 s, not 0.38962 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.19481 s, not 0.0974 s.",
"D": "Incorrect. Substituting the ... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005593 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 23 μF capacitor is charged to a potential difference of 14 V. Calculate the energy stored, expressed in μJ. | {
"A": "1127 μJ",
"B": "2255 μJ",
"C": "2254 μJ",
"D": "2253 μJ"
} | C | 2254 μJ | U=½CV². Since C=23 μF, U in μJ is ½×23×(14)²=2254 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2254 μJ, not 1127 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2254 μJ, not 2255 μJ.",
"C": "Correct. The worked calculation gives 2254 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006273 | 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 15 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-2.68085",
"B": "0.6383",
"C": "-0.31915",
"D": "0.31915"
} | D | 0.31915 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(62)(15)/(62−15)=19.78723 cm. Thus |m|=v/u=19.78723/62=0.31915. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31915, not -2.68085.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31915, not 0.6383.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31915, not -0.31... | [
"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_008641 | 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 1.23 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": "3.69 K",
"B": "2.69 K",
"C": "1.69 K",
"D": "4.69 K"
} | A | 3.69 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×1.0×1.23=3.69 K. | {
"A": "Correct. The worked calculation gives 3.69 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.69 K, not 2.69 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.69 K, not 1.69 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_002080 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 7 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": "0.38961",
"B": "0.19481",
"C": "0.29221",
"D": "2.38961"
} | A | 0.38961 | Favourable pairs = C(12,2)+C(7,2)+C(3,2)=90. Total pairs=C(22,2)=231. Therefore P=90/231=0.38961. | {
"A": "Correct. The worked calculation gives 0.38961.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.38961, not 0.19481.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.38961, not 0.29221.",
"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_004300 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.18. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "22.8 N",
"B": "68.4 N",
"C": "45.6 N",
"D": "91.2 N"
} | C | 45.6 N | Net force=mg(sinθ−μcosθ)=10×10×(0.6−0.18×0.8)=45.6 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45.6 N, not 22.8 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 45.6 N, not 68.4 N.",
"C": "Correct. The worked calculation gives 45.6 N.",
"D": "Incorrect. Substituting the stated values ... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005356 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 44 μF capacitor is charged to a potential difference of 16 V. Calculate the energy stored, expressed in μJ. | {
"A": "5632 μJ",
"B": "5634 μJ",
"C": "-5632 μJ",
"D": "6758.4 μJ"
} | A | 5632 μJ | U=½CV². Since C=44 μF, U in μJ is ½×44×(16)²=5632 μJ. | {
"A": "Correct. The worked calculation gives 5632 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5632 μJ, not 5634 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5632 μJ, not -5632 μJ.",
"D": "Incorrect. Substituting the stated v... | [
"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_003367 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 48 m s⁻¹ at 18° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "135.42572 m",
"B": "137.42572 m",
"C": "134.42572 m",
"D": "162.51087 m"
} | A | 135.42572 m | Range R=u²sin(2θ)/g. Substituting u=48, θ=18° and g=10 gives R=(48)²sin(36°)/10=135.42572 m. | {
"A": "Correct. The worked calculation gives 135.42572 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 135.42572 m, not 137.42572 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 135.42572 m, not 134.42572 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_008442 | 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 1.77 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-2.124 K",
"B": "5.124 K",
"C": "1.124 K",
"D": "2.124 K"
} | D | 2.124 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.6×1.77=2.124 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.124 K, not -2.124 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.124 K, not 5.124 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.124 K, not 1.12... | [
"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_004413 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 3 kg and radius 4 m is acted on by a constant torque of 11 N m about its central axis. Find its angular acceleration. | {
"A": "0.91667 rad s⁻²",
"B": "-0.54167 rad s⁻²",
"C": "0.45833 rad s⁻²",
"D": "-0.45833 rad s⁻²"
} | C | 0.45833 rad s⁻² | For a solid disc, I=½MR²=½(3)(4)²=24 kg m². Using τ=Iα, α=11/24=0.45833 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.45833 rad s⁻², not 0.91667 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.45833 rad s⁻², not -0.54167 rad s⁻².",
"C": "Correct. The worked calculation gives 0.45833 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_005382 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 48 μF capacitor is charged to a potential difference of 14 V. Calculate the energy stored, expressed in μJ. | {
"A": "3763.2 μJ",
"B": "2352 μJ",
"C": "3528 μJ",
"D": "4704 μJ"
} | D | 4704 μJ | U=½CV². Since C=48 μF, U in μJ is ½×48×(14)²=4704 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4704 μJ, not 3763.2 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4704 μJ, not 2352 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4704 μJ, not 352... | [
"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_006687 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 40 mol H₂ and 6 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "12 mol",
"B": "2.2 mol",
"C": "14 mol",
"D": "6 mol"
} | A | 12 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 40 mol H₂O; O₂ can produce 12 mol H₂O. The limiting condition is O₂; product=12 mol. | {
"A": "Correct. The worked calculation gives 12 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 2.2 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 14 mol.",
"D": "Incorrect. Substituting the stated values... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003664 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 50 m s⁻¹ at 30° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "217.50635 m",
"B": "218.50635 m",
"C": "216.50635 m",
"D": "324.75953 m"
} | C | 216.50635 m | Range R=u²sin(2θ)/g. Substituting u=50, θ=30° and g=10 gives R=(50)²sin(60°)/10=216.50635 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 216.50635 m, not 217.50635 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 216.50635 m, not 218.50635 m.",
"C": "Correct. The worked calculation gives 216.50635 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_009326 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.81 V, transfers 1 electrons, and has reaction quotient Q=10^-4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.9536 V",
"B": "0.7848 V",
"C": "1.10464 V",
"D": "1.0464 V"
} | D | 1.0464 V | Apply the Nernst equation: E=0.81−(0.0591/1)(-4)=1.0464 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0464 V, not -1.9536 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0464 V, not 0.7848 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0464 V, not... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003788 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 6 m s⁻¹. A constant net force does 6 N of work over 7 m in the direction of motion. Find its final kinetic energy. | {
"A": "252 J",
"B": "84 J",
"C": "168 J",
"D": "166 J"
} | C | 168 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(6)²+(6)(7)=168 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 168 J, not 252 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 168 J, not 84 J.",
"C": "Correct. The worked calculation gives 168 J.",
"D": "Incorrect. Substituting the stated values into t... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002313 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 9 blue and 9 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.63448",
"B": "1.03172",
"C": "0.31724",
"D": "-0.31724"
} | C | 0.31724 | Favourable pairs = C(12,2)+C(9,2)+C(9,2)=138. Total pairs=C(30,2)=435. Therefore P=138/435=0.31724. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31724, not 0.63448.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31724, not 1.03172.",
"C": "Correct. The worked calculation gives 0.31724.",
"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_002601 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, -4], [6, -3]]. | {
"A": "0",
"B": "1.3",
"C": "3",
"D": "6"
} | C | 3 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(-3)−(-4)(6)=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"C": "Correct. The worked calculation gives 3.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004075 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 23 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.15. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "110.4 N",
"B": "55.2 N",
"C": "111.4 N",
"D": "220.8 N"
} | A | 110.4 N | Net force=mg(sinθ−μcosθ)=23×10×(0.6−0.15×0.8)=110.4 N. | {
"A": "Correct. The worked calculation gives 110.4 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 110.4 N, not 55.2 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 110.4 N, not 111.4 N.",
"D": "Incorrect. Substituting the stated val... | [
"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_000875 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio -3. What is the sum of its first 6 terms? | {
"A": "-2002",
"B": "-2402.4",
"C": "-2000",
"D": "-1601.6"
} | A | -2002 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(-3^6−1)/(-3−1)=-2002. | {
"A": "Correct. The worked calculation gives -2002.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2002, not -2402.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2002, not -2000.",
"D": "Incorrect. Substituting the stated values int... | [
"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_009902 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(OH)_5]^-1, each OH ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "4",
"B": "6",
"C": "-4",
"D": "2"
} | A | 4 | Let the formal oxidation state of Co be x. Charge balance gives x+(5)(−1)=-1; hence x=-1+5=+4. | {
"A": "Correct. The worked calculation gives 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not -4.",
"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_001352 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (4x² +1x -4) dx. | {
"A": "681.66667",
"B": "512",
"C": "682.66667",
"D": "683.66667"
} | C | 682.66667 | An antiderivative is (4/3)x³+(1/2)x²+(-4)x. Evaluating between 0 and 8 gives (4/3)(8)³+(1/2)(8)²+(-4)(8)=682.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 682.66667, not 681.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 682.66667, not 512.",
"C": "Correct. The worked calculation gives 682.66667.",
"D": "Incorrect. Substituting the state... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006806 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 7 mol H₂ and 33 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "-7 mol",
"B": "7 mol",
"C": "5 mol",
"D": "9 mol"
} | B | 7 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 7 mol H₂O; O₂ can produce 66 mol H₂O. The limiting condition is H₂; product=7 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7 mol, not -7 mol.",
"B": "Correct. The worked calculation gives 7 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7 mol, not 5 mol.",
"D": "Incorrect. Substituting the stated values into... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007680 | 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 93 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "1.14531 mmol L⁻¹",
"B": "1.45312 mmol L⁻¹",
"C": "2.45312 mmol L⁻¹",
"D": "-0.54688 mmol L⁻¹"
} | B | 1.45312 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=93/2^6=1.45312 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.45312 mmol L⁻¹, not 1.14531 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 1.45312 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.45312 mmol L⁻¹, not 2.45312 mmol L⁻¹.",
... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005095 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +2 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "-7.43802 N",
"B": "5.57851 N",
"C": "6.43802 N",
"D": "7.43802 N"
} | D | 7.43802 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(2×10⁻⁶)/(11×10⁻²)²=7.43802 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.43802 N, not -7.43802 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.43802 N, not 5.57851 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.43802 N... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000144 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 +14x -8=0, let its roots be α and β. What is α²+β²? | {
"A": "212",
"B": "318",
"C": "213",
"D": "211"
} | A | 212 | By Vieta's relations, α+β = -14/1 and αβ = -8/1. Then α²+β²=(α+β)²−2αβ = (-14/1)²−2(-8/1) = 212. | {
"A": "Correct. The worked calculation gives 212.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 212, not 318.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 212, not 213.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_000519 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -19 and common difference 7. Find the sum of its first 10 terms. | {
"A": "123",
"B": "62.5",
"C": "125",
"D": "187.5"
} | C | 125 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-19, d=7, n=10: Sₙ=10/2[2(-19)+(10−1)(7)]=125. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 125, not 123.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 125, not 62.5.",
"C": "Correct. The worked calculation gives 125.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009780 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(Cl)_4]^+0, each Cl ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "4",
"B": "7",
"C": "6",
"D": "3"
} | A | 4 | Let the formal oxidation state of Cr be x. Charge balance gives x+(4)(−1)=+0; hence x=0+4=+4. | {
"A": "Correct. The worked calculation gives 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 6.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005287 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +2 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "68.5 N",
"B": "67.5 N",
"C": "50.625 N",
"D": "66.5 N"
} | B | 67.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(2×10⁻⁶)/(4×10⁻²)²=67.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 67.5 N, not 68.5 N.",
"B": "Correct. The worked calculation gives 67.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 67.5 N, not 50.625 N.",
"D": "Incorrect. Substituting the stated value... | [
"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_001344 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (-1x² -7x +5) dx. | {
"A": "-352.66667",
"B": "-354.66667",
"C": "-356.66667",
"D": "-532"
} | B | -354.66667 | An antiderivative is (-1/3)x³+(-7/2)x²+(5)x. Evaluating between 0 and 8 gives (-1/3)(8)³+(-7/2)(8)²+(5)(8)=-354.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -354.66667, not -352.66667.",
"B": "Correct. The worked calculation gives -354.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -354.66667, not -356.66667.",
"D": "Incorrect. Substitutin... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008566 | 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 1.69 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "5.6364 K",
"B": "1.9773 K",
"C": "1.3182 K",
"D": "2.6364 K"
} | D | 2.6364 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.52×1.69=2.6364 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.6364 K, not 5.6364 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.6364 K, not 1.9773 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.6364 K, not ... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002706 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(3, -7, 7) and v=(-7, 5, 0), calculate u·v. | {
"A": "-56",
"B": "-58",
"C": "-57",
"D": "-42"
} | A | -56 | The dot product is the sum of corresponding component products: (3)(-7)+(-7)(5)+(7)(0)=-56. | {
"A": "Correct. The worked calculation gives -56.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -56, not -58.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -56, not -57.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001880 | 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 74 distinct elements? | {
"A": "21944067106416",
"B": "21944067106414",
"C": "21944067106417",
"D": "21944067106418"
} | A | 21944067106416 | Order does not matter, so the count is C(74,12)=74!/[12!(62)!]=21944067106416. | {
"A": "Correct. The worked calculation gives 21944067106416.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21944067106416, not 21944067106414.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21944067106416, not 21944067106417.",
"D": "In... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009445 | 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_24. Treat X as the total number of monovalent halogen atoms. | {
"A": "2.25",
"B": "1.5",
"C": "3",
"D": "6"
} | C | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×14+2+0−24−0)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.5.",
"C": "Correct. The worked calculation gives 3.",
"D": "Incorrect. Substituting the stated values into the 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_000323 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 +1x -8=0, let its roots be α and β. What is α²+β²? | {
"A": "6.09375",
"B": "2.0625",
"C": "4.0625",
"D": "-4.0625"
} | C | 4.0625 | By Vieta's relations, α+β = -1/4 and αβ = -8/4. Then α²+β²=(α+β)²−2αβ = (-1/4)²−2(-8/4) = 4.0625. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.0625, not 6.09375.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.0625, not 2.0625.",
"C": "Correct. The worked calculation gives 4.0625.",
"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_005476 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 9 μF capacitor is charged to a potential difference of 13 V. Calculate the energy stored, expressed in μJ. | {
"A": "1521 μJ",
"B": "759.5 μJ",
"C": "760.5 μJ",
"D": "1140.75 μJ"
} | C | 760.5 μJ | U=½CV². Since C=9 μF, U in μJ is ½×9×(13)²=760.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 760.5 μJ, not 1521 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 760.5 μJ, not 759.5 μJ.",
"C": "Correct. The worked calculation gives 760.5 μJ.",
"D": "Incorrect. Substituting the state... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009590 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_10H_6N_3X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "13.5",
"B": "9",
"C": "6",
"D": "11"
} | B | 9 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×10+2+3−6−1)/2=9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9, not 13.5.",
"B": "Correct. The worked calculation gives 9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9, not 6.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006957 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 26 mol H₂ and 8 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "15 mol",
"B": "14 mol",
"C": "16 mol",
"D": "19.2 mol"
} | C | 16 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 26 mol H₂O; O₂ can produce 16 mol H₂O. The limiting condition is O₂; product=16 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 15 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 14 mol.",
"C": "Correct. The worked calculation gives 16 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_009657 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_8H_14. Treat X as the total number of monovalent halogen atoms. | {
"A": "1.2",
"B": "2",
"C": "1",
"D": "4"
} | B | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×8+2+0−14−0)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.2.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"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_000185 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 +6x +2=0, let its roots be α and β. What is α²+β²? | {
"A": "-0.16327",
"B": "0.16327",
"C": "0.08163",
"D": "3.16327"
} | B | 0.16327 | By Vieta's relations, α+β = -6/7 and αβ = 2/7. Then α²+β²=(α+β)²−2αβ = (-6/7)²−2(2/7) = 0.16327. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.16327, not -0.16327.",
"B": "Correct. The worked calculation gives 0.16327.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.16327, not 0.08163.",
"D": "Incorrect. Substituting the stated v... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009883 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(OH)_2]^+0, each OH ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "-2",
"B": "3",
"C": "4",
"D": "2"
} | D | 2 | Let the formal oxidation state of Fe be x. Charge balance gives x+(2)(−1)=+0; hence x=0+2=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 4.",
"D": "Correct. The worked c... | [
"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_003670 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 91 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "622.52757 m",
"B": "779.15946 m",
"C": "78.81595 m",
"D": "778.15946 m"
} | D | 778.15946 m | Range R=u²sin(2θ)/g. Substituting u=91, θ=55° and g=10 gives R=(91)²sin(110°)/10=778.15946 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 778.15946 m, not 622.52757 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 778.15946 m, not 779.15946 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 77... | [
"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_002170 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 5 blue and 7 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.30833",
"B": "-0.69167",
"C": "-2.69167",
"D": "0.4625"
} | A | 0.30833 | Favourable pairs = C(4,2)+C(5,2)+C(7,2)=37. Total pairs=C(16,2)=120. Therefore P=37/120=0.30833. | {
"A": "Correct. The worked calculation gives 0.30833.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30833, not -0.69167.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30833, not -2.69167.",
"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_002903 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-3, -5, -7) and v=(1, 3, 5), calculate u·v. | {
"A": "53",
"B": "-4.3",
"C": "-26.5",
"D": "-53"
} | D | -53 | The dot product is the sum of corresponding component products: (-3)(1)+(-5)(3)+(-7)(5)=-53. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -53, not 53.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -53, not -4.3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -53, not -26.5.",
"D": "Correct.... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009194 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.42 V, transfers 1 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.33095 V",
"B": "4.7746 V",
"C": "-0.2254 V",
"D": "1.7746 V"
} | D | 1.7746 V | Apply the Nernst equation: E=1.42−(0.0591/1)(-6)=1.7746 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.7746 V, not 1.33095 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.7746 V, not 4.7746 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.7746 V, not... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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