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_008078 | 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 14 A for 29762 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": "14.70902 g",
"B": "137.09025 g",
"C": "136.09025 g",
"D": "102.81769 g"
} | B | 137.09025 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×29762/(2×96500)=137.09025 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 137.09025 g, not 14.70902 g.",
"B": "Correct. The worked calculation gives 137.09025 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 137.09025 g, not 136.09025 g.",
"D": "Incorrect. Substit... | [
"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_003432 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 80 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "642 m",
"B": "960 m",
"C": "640 m",
"D": "639 m"
} | C | 640 m | Range R=u²sin(2θ)/g. Substituting u=80, θ=45° and g=10 gives R=(80)²sin(90°)/10=640 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 640 m, not 642 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 640 m, not 960 m.",
"C": "Correct. The worked calculation gives 640 m.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_001753 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 19 distinct elements? | {
"A": "75584",
"B": "75582",
"C": "151164",
"D": "-75582"
} | B | 75582 | Order does not matter, so the count is C(19,8)=19!/[8!(11)!]=75582. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 75582, not 75584.",
"B": "Correct. The worked calculation gives 75582.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 75582, not 151164.",
"D": "Incorrect. Substituting the stated values into... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008624 | 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 0.55 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-2.45 K",
"B": "-1.45 K",
"C": "0.55 K",
"D": "0.825 K"
} | C | 0.55 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×1.0×0.55=0.55 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.55 K, not -2.45 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.55 K, not -1.45 K.",
"C": "Correct. The worked calculation gives 0.55 K.",
"D": "Incorrect. Substituting the stated value... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005086 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +5 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "168.75 N",
"B": "135 N",
"C": "126.5625 N",
"D": "-168.75 N"
} | A | 168.75 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(5×10⁻⁶)/(4×10⁻²)²=168.75 N. | {
"A": "Correct. The worked calculation gives 168.75 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 168.75 N, not 135 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 168.75 N, not 126.5625 N.",
"D": "Incorrect. Substituting the state... | [
"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_002184 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 5 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": "-0.68627",
"B": "0.15686",
"C": "0.31373",
"D": "0.47059"
} | C | 0.31373 | Favourable pairs = C(8,2)+C(5,2)+C(5,2)=48. Total pairs=C(18,2)=153. Therefore P=48/153=0.31373. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31373, not -0.68627.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31373, not 0.15686.",
"C": "Correct. The worked calculation gives 0.31373.",
"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_006991 | 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 23 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "7 mol",
"B": "3.5 mol",
"C": "-7 mol",
"D": "4 mol"
} | A | 7 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 7 mol H₂O; O₂ can produce 46 mol H₂O. The limiting condition is H₂; product=7 mol. | {
"A": "Correct. The worked calculation gives 7 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7 mol, not 3.5 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7 mol, not -7 mol.",
"D": "Incorrect. Substituting the stated values in... | [
"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_009434 | 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_7H_2N_2X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "14",
"B": "10",
"C": "7",
"D": "6"
} | C | 7 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+2−2−2)/2=7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 14.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 10.",
"C": "Correct. The worked calculation gives 7.",
"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_004464 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 5 m is acted on by a constant torque of 41 N m about its central axis. Find its angular acceleration. | {
"A": "0.615 rad s⁻²",
"B": "3.41 rad s⁻²",
"C": "0.41 rad s⁻²",
"D": "-0.59 rad s⁻²"
} | C | 0.41 rad s⁻² | For a solid disc, I=½MR²=½(8)(5)²=100 kg m². Using τ=Iα, α=41/100=0.41 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.41 rad s⁻², not 0.615 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.41 rad s⁻², not 3.41 rad s⁻².",
"C": "Correct. The worked calculation gives 0.41 rad s⁻².",
"D": "Incorrect. ... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009156 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.20 V, transfers 2 electrons, and has reaction quotient Q=10^-4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "3.3182 V",
"B": "1.9773 V",
"C": "1.3182 V",
"D": "0.98865 V"
} | C | 1.3182 V | Apply the Nernst equation: E=1.20−(0.0591/2)(-4)=1.3182 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.3182 V, not 3.3182 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.3182 V, not 1.9773 V.",
"C": "Correct. The worked calculation gives 1.3182 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_001013 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ +6x² -3x+7. Evaluate f′(4). | {
"A": "228",
"B": "285",
"C": "213.75",
"D": "-285"
} | B | 285 | Differentiate: f′(x)=3(5)x²+2(6)x+(-3). At x=4, f′(4)=3(5)(4)²+2(6)(4)+(-3)=285. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 285, not 228.",
"B": "Correct. The worked calculation gives 285.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 285, not 213.75.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006108 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 35 cm in front of a thin convex lens of focal length 27 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "2.375",
"B": "3.375",
"C": "1.3375",
"D": "1.375"
} | B | 3.375 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(35)(27)/(35−27)=118.125 cm. Thus |m|=v/u=118.125/35=3.375. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.375, not 2.375.",
"B": "Correct. The worked calculation gives 3.375.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.375, not 1.3375.",
"D": "Incorrect. Substituting the stated values into... | [
"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_005820 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.6 atm at 314 K. What is its pressure at 574 K? | {
"A": "8.40892 atm",
"B": "-8.40892 atm",
"C": "12.61338 atm",
"D": "10.40892 atm"
} | A | 8.40892 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.6)(574)/(314)=8.40892 atm. | {
"A": "Correct. The worked calculation gives 8.40892 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.40892 atm, not -8.40892 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.40892 atm, not 12.61338 atm.",
"D": "Incorrect. Subs... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008278 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 13 A for 14374 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": "61.4805 g",
"B": "62.4805 g",
"C": "59.4805 g",
"D": "49.1844 g"
} | A | 61.4805 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×14374/(2×96500)=61.4805 g. | {
"A": "Correct. The worked calculation gives 61.4805 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 61.4805 g, not 62.4805 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 61.4805 g, not 59.4805 g.",
"D": "Incorrect. Substituting the... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001068 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ -8x² +12x+7. Evaluate f′(5). | {
"A": "305",
"B": "307",
"C": "31.7",
"D": "153.5"
} | B | 307 | Differentiate: f′(x)=3(5)x²+2(-8)x+(12). At x=5, f′(5)=3(5)(5)²+2(-8)(5)+(12)=307. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 307, not 305.",
"B": "Correct. The worked calculation gives 307.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 307, not 31.7.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_009926 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(CN)_5]^+1, each CN ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "6",
"B": "1.6",
"C": "4.5",
"D": "5"
} | A | 6 | Let the formal oxidation state of Co be x. Charge balance gives x+(5)(−1)=+1; hence x=1+5=+6. | {
"A": "Correct. The worked calculation gives 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 1.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.5.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_000785 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 3 and common ratio 3. What is the sum of its first 7 terms? | {
"A": "3279",
"B": "6558",
"C": "1639.5",
"D": "3934.8"
} | A | 3279 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=3(3^7−1)/(3−1)=3279. | {
"A": "Correct. The worked calculation gives 3279.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3279, not 6558.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3279, not 1639.5.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_003396 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 24 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "66.18624 m",
"B": "22.06208 m",
"C": "44.12416 m",
"D": "33.09312 m"
} | C | 44.12416 m | Range R=u²sin(2θ)/g. Substituting u=24, θ=25° and g=10 gives R=(24)²sin(50°)/10=44.12416 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 44.12416 m, not 66.18624 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 44.12416 m, not 22.06208 m.",
"C": "Correct. The worked calculation gives 44.12416 m.",
"D": "Incorrect. Substitutin... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002974 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, -4, -6) and v=(0, 8, 6), calculate u·v. | {
"A": "-81.6",
"B": "-102",
"C": "-34",
"D": "-68"
} | D | -68 | The dot product is the sum of corresponding component products: (1)(0)+(-4)(8)+(-6)(6)=-68. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -68, not -81.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -68, not -102.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -68, not -34.",
"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_008836 | 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 1.49 mol L⁻¹ and initially B is absent. At equilibrium, 26% of A has dissociated at constant volume. Find K_c. | {
"A": "1.05445",
"B": "2.54445",
"C": "-2.45555",
"D": "0.54445"
} | D | 0.54445 | Let α=0.26. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.49)(0.26)²/(1−0.26)=0.54445. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.54445, not 1.05445.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.54445, not 2.54445.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.54445, not -2.45... | [
"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_000190 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 -6x -1=0, let its roots be α and β. What is α²+β²? | {
"A": "2.02041",
"B": "1.02041",
"C": "0.02041",
"D": "3.02041"
} | B | 1.02041 | By Vieta's relations, α+β = 6/7 and αβ = -1/7. Then α²+β²=(α+β)²−2αβ = (6/7)²−2(-1/7) = 1.02041. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.02041, not 2.02041.",
"B": "Correct. The worked calculation gives 1.02041.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.02041, not 0.02041.",
"D": "Incorrect. Substituting the stated va... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004892 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 12 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.8 A",
"B": "1.35 A",
"C": "2.7 A",
"D": "3.6 A"
} | A | 1.8 A | Series branch resistance=8+7=15 Ω. Parallel equivalent R_eq=(15×12)/(15+12)=6.66667 Ω. Total current I=V/R_eq=12/6.66667=1.8 A. | {
"A": "Correct. The worked calculation gives 1.8 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.8 A, not 1.35 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.8 A, not 2.7 A.",
"D": "Incorrect. Substituting the stated values into... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005917 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.6 atm at 320 K. What is its pressure at 513 K? | {
"A": "7.16812 atm",
"B": "6.25219 atm",
"C": "4.16812 atm",
"D": "6.16812 atm"
} | C | 4.16812 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.6)(513)/(320)=4.16812 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.16812 atm, not 7.16812 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.16812 atm, not 6.25219 atm.",
"C": "Correct. The worked calculation gives 4.16812 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004804 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 6 Ω are connected in series; this combination is connected in parallel with a 6 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.2 A",
"B": "3.15 A",
"C": "5.2 A",
"D": "6.3 A"
} | A | 4.2 A | Series branch resistance=9+6=15 Ω. Parallel equivalent R_eq=(15×6)/(15+6)=4.28571 Ω. Total current I=V/R_eq=18/4.28571=4.2 A. | {
"A": "Correct. The worked calculation gives 4.2 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.2 A, not 3.15 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.2 A, not 5.2 A.",
"D": "Incorrect. Substituting the stated values into... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007901 | 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 95 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "47.5 mmol L⁻¹",
"B": "57 mmol L⁻¹",
"C": "23.75 mmol L⁻¹",
"D": "5.75 mmol L⁻¹"
} | A | 47.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=95/2^1=47.5 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 47.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 47.5 mmol L⁻¹, not 57 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 47.5 mmol L⁻¹, not 23.75 mmol L⁻¹.",
"D": "Incorrec... | [
"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_007047 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 7 mol of gas at 461 K and 2.78 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "96.25106 L",
"B": "190.50211 L",
"C": "95.25106 L",
"D": "114.30127 L"
} | C | 95.25106 L | PV=nRT, so V=nRT/P=(7)(0.082057)(461)/(2.78)=95.25106 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 95.25106 L, not 96.25106 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 95.25106 L, not 190.50211 L.",
"C": "Correct. The worked calculation gives 95.25106 L.",
"D": "Incorrect. Substituti... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005601 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 18 μF capacitor is charged to a potential difference of 28 V. Calculate the energy stored, expressed in μJ. | {
"A": "7054 μJ",
"B": "10584 μJ",
"C": "7056 μJ",
"D": "8467.2 μJ"
} | C | 7056 μJ | U=½CV². Since C=18 μF, U in μJ is ½×18×(28)²=7056 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7056 μJ, not 7054 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7056 μJ, not 10584 μJ.",
"C": "Correct. The worked calculation gives 7056 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_007304 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 19 mol of gas at 530 K and 0.8 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "516.44624 L",
"B": "1034.89249 L",
"C": "104.28925 L",
"D": "1032.89249 L"
} | D | 1032.89249 L | PV=nRT, so V=nRT/P=(19)(0.082057)(530)/(0.8)=1032.89249 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1032.89249 L, not 516.44624 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1032.89249 L, not 1034.89249 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005867 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2 atm at 223 K. What is its pressure at 416 K? | {
"A": "2.79821 atm",
"B": "2.73094 atm",
"C": "3.73094 atm",
"D": "5.59641 atm"
} | C | 3.73094 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2)(416)/(223)=3.73094 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.73094 atm, not 2.79821 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.73094 atm, not 2.73094 atm.",
"C": "Correct. The worked calculation gives 3.73094 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007070 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 11 mol of gas at 400 K and 0.76 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "950.13368 L",
"B": "712.60026 L",
"C": "475.06684 L",
"D": "477.06684 L"
} | C | 475.06684 L | PV=nRT, so V=nRT/P=(11)(0.082057)(400)/(0.76)=475.06684 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 475.06684 L, not 950.13368 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 475.06684 L, not 712.60026 L.",
"C": "Correct. The worked calculation gives 475.06684 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002033 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 8 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": "0.46154",
"B": "-2.69231",
"C": "0.30769",
"D": "0.23077"
} | C | 0.30769 | Favourable pairs = C(9,2)+C(8,2)+C(9,2)=100. Total pairs=C(26,2)=325. Therefore P=100/325=0.30769. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not 0.46154.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not -2.69231.",
"C": "Correct. The worked calculation gives 0.30769.",
"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_000856 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 12 and common ratio 4. What is the sum of its first 12 terms? | {
"A": "6710887",
"B": "50331645",
"C": "67108861",
"D": "67108860"
} | D | 67108860 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=12(4^12−1)/(4−1)=67108860. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 67108860, not 6710887.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 67108860, not 50331645.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 67108860, not 6... | [
"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_004200 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 33 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.23. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "136.28 N",
"B": "139.28 N",
"C": "137.28 N",
"D": "68.64 N"
} | C | 137.28 N | Net force=mg(sinθ−μcosθ)=33×10×(0.6−0.23×0.8)=137.28 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 137.28 N, not 136.28 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 137.28 N, not 139.28 N.",
"C": "Correct. The worked calculation gives 137.28 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_005113 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +7 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "1102.5 N",
"B": "-1102.5 N",
"C": "551.25 N",
"D": "1104.5 N"
} | A | 1102.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(7×10⁻⁶)/(2×10⁻²)²=1102.5 N. | {
"A": "Correct. The worked calculation gives 1102.5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1102.5 N, not -1102.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1102.5 N, not 551.25 N.",
"D": "Incorrect. Substituting the sta... | [
"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_006568 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 9 kg is attached to an ideal spring of force constant 681 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.77008 s",
"B": "-2.77008 s",
"C": "0.22992 s",
"D": "-0.22992 s"
} | C | 0.22992 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(9/681)=0.22992 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.22992 s, not -0.77008 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.22992 s, not -2.77008 s.",
"C": "Correct. The worked calculation gives 0.22992 s.",
"D": "Incorrect. Substituting t... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006630 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 21 kg is attached to an ideal spring of force constant 23 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.91107 s",
"B": "3.91107 s",
"C": "0.91107 s",
"D": "2.91107 s"
} | A | 1.91107 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(21/23)=1.91107 s. | {
"A": "Correct. The worked calculation gives 1.91107 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.91107 s, not 3.91107 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.91107 s, not 0.91107 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_001137 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=1x³ +3x² -8x+7. Evaluate f′(-4). | {
"A": "24",
"B": "2.6",
"C": "15",
"D": "16"
} | D | 16 | Differentiate: f′(x)=3(1)x²+2(3)x+(-8). At x=-4, f′(-4)=3(1)(-4)²+2(3)(-4)+(-8)=16. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16, not 24.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16, not 2.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16, not 15.",
"D": "Correct. The wo... | [
"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_005594 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 55 μF capacitor is charged to a potential difference of 24 V. Calculate the energy stored, expressed in μJ. | {
"A": "15840 μJ",
"B": "31680 μJ",
"C": "12672 μJ",
"D": "19008 μJ"
} | A | 15840 μJ | U=½CV². Since C=55 μF, U in μJ is ½×55×(24)²=15840 μJ. | {
"A": "Correct. The worked calculation gives 15840 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15840 μJ, not 31680 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15840 μJ, not 12672 μJ.",
"D": "Incorrect. Substituting the stat... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004307 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 42 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.17. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "192.88 N",
"B": "196.88 N",
"C": "292.32 N",
"D": "194.88 N"
} | D | 194.88 N | Net force=mg(sinθ−μcosθ)=42×10×(0.6−0.17×0.8)=194.88 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 194.88 N, not 192.88 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 194.88 N, not 196.88 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 194.88 N, not ... | [
"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_000390 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 16 and common difference 13. Find the sum of its first 21 terms. | {
"A": "3066",
"B": "1533",
"C": "6132",
"D": "4599"
} | A | 3066 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=16, d=13, n=21: Sₙ=21/2[2(16)+(21−1)(13)]=3066. | {
"A": "Correct. The worked calculation gives 3066.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3066, not 1533.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3066, not 6132.",
"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_009488 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_12H_21N_1X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "-1",
"C": "1.5",
"D": "1"
} | D | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×12+2+1−21−4)/2=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not -1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.5.",
"D": "Correct. The worked... | [
"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_003785 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block initially moves at 2 m s⁻¹. A constant net force does 30 N of work over 15 m in the direction of motion. Find its final kinetic energy. | {
"A": "455 J",
"B": "452 J",
"C": "363.2 J",
"D": "454 J"
} | D | 454 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(2)(2)²+(30)(15)=454 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 454 J, not 455 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 454 J, not 452 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 454 J, not 363.2 J.",
"D... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000331 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 -11x +4=0, let its roots be α and β. What is α²+β²? | {
"A": "1.32653",
"B": "-1.67347",
"C": "2.32653",
"D": "-1.32653"
} | A | 1.32653 | By Vieta's relations, α+β = 11/7 and αβ = 4/7. Then α²+β²=(α+β)²−2αβ = (11/7)²−2(4/7) = 1.32653. | {
"A": "Correct. The worked calculation gives 1.32653.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.32653, not -1.67347.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.32653, not 2.32653.",
"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_005323 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +9 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "202.5 N",
"B": "135 N",
"C": "162 N",
"D": "108 N"
} | B | 135 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(9×10⁻⁶)/(6×10⁻²)²=135 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 135 N, not 202.5 N.",
"B": "Correct. The worked calculation gives 135 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 135 N, not 162 N.",
"D": "Incorrect. Substituting the stated values int... | [
"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_003595 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 90 m s⁻¹ at 18° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "475.10605 m",
"B": "477.10605 m",
"C": "380.88484 m",
"D": "476.10605 m"
} | D | 476.10605 m | Range R=u²sin(2θ)/g. Substituting u=90, θ=18° and g=10 gives R=(90)²sin(36°)/10=476.10605 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 476.10605 m, not 475.10605 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 476.10605 m, not 477.10605 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 47... | [
"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_000991 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 3 and common ratio 5. What is the sum of its first 6 terms? | {
"A": "8788.5",
"B": "11718",
"C": "-11718",
"D": "11720"
} | B | 11718 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=3(5^6−1)/(5−1)=11718. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11718, not 8788.5.",
"B": "Correct. The worked calculation gives 11718.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11718, not -11718.",
"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_008345 | 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 1.74 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.48 K",
"B": "3.48 K",
"C": "1.48 K",
"D": "2.48 K"
} | B | 3.48 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×1.74=3.48 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.48 K, not 0.48 K.",
"B": "Correct. The worked calculation gives 3.48 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.48 K, not 1.48 K.",
"D": "Incorrect. Substituting the stated values ... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005170 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +2 μC are separated by 12 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "5 N",
"B": "1.5 N",
"C": "6 N",
"D": "8 N"
} | A | 5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(2×10⁻⁶)/(12×10⁻²)²=5 N. | {
"A": "Correct. The worked calculation gives 5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5 N, not 1.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5 N, not 6 N.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_009625 | 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_10N_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "5",
"B": "7.5",
"C": "2.5",
"D": "3.75"
} | A | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×8+2+2−10−0)/2=5. | {
"A": "Correct. The worked calculation gives 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.5.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004121 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 48 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.28. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "144.384 N",
"B": "181.48 N",
"C": "90.24 N",
"D": "180.48 N"
} | D | 180.48 N | Net force=mg(sinθ−μcosθ)=48×10×(0.6−0.28×0.8)=180.48 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 180.48 N, not 144.384 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 180.48 N, not 181.48 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 180.48 N, not... | [
"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_008217 | 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 14 A for 27795 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": "127.02982 g",
"B": "128.02982 g",
"C": "256.05964 g",
"D": "96.02236 g"
} | B | 128.02982 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×27795/(2×96500)=128.02982 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 128.02982 g, not 127.02982 g.",
"B": "Correct. The worked calculation gives 128.02982 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 128.02982 g, not 256.05964 g.",
"D": "Incorrect. Substi... | [
"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_003602 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 68 m s⁻¹ at 18° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "273.7919 m",
"B": "135.89595 m",
"C": "203.84393 m",
"D": "271.7919 m"
} | D | 271.7919 m | Range R=u²sin(2θ)/g. Substituting u=68, θ=18° and g=10 gives R=(68)²sin(36°)/10=271.7919 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 271.7919 m, not 273.7919 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 271.7919 m, not 135.89595 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 271.7... | [
"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_006105 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 97 cm in front of a thin convex lens of focal length 24 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "3.32877",
"B": "0.32877",
"C": "0.24658",
"D": "-1.67123"
} | B | 0.32877 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(97)(24)/(97−24)=31.89041 cm. Thus |m|=v/u=31.89041/97=0.32877. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32877, not 3.32877.",
"B": "Correct. The worked calculation gives 0.32877.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32877, not 0.24658.",
"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_008914 | 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 1.62 mol L⁻¹ and initially B is absent. At equilibrium, 21% of A has dissociated at constant volume. Find K_c. | {
"A": "0.36173",
"B": "0.18087",
"C": "-1.63827",
"D": "-0.63827"
} | A | 0.36173 | Let α=0.21. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.62)(0.21)²/(1−0.21)=0.36173. | {
"A": "Correct. The worked calculation gives 0.36173.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36173, not 0.18087.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.36173, not -1.63827.",
"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_009875 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(Cl)_5]^+1, each Cl ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "9",
"B": "6",
"C": "7",
"D": "8"
} | B | 6 | Let the formal oxidation state of Mn be x. Charge balance gives x+(5)(−1)=+1; hence x=1+5=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"B": "Correct. The worked calculation gives 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 7.",
"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_008963 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.85 mol L⁻¹ and initially B is absent. At equilibrium, 18% of A has dissociated at constant volume. Find K_c. | {
"A": "0.13434",
"B": "0.10076",
"C": "-1.86566",
"D": "-2.86566"
} | A | 0.13434 | Let α=0.18. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.85)(0.18)²/(1−0.18)=0.13434. | {
"A": "Correct. The worked calculation gives 0.13434.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.13434, not 0.10076.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.13434, not -1.86566.",
"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_006643 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 2 kg is attached to an ideal spring of force constant 502 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.12624 s",
"B": "0.06312 s",
"C": "0.25248 s",
"D": "0.12624 s"
} | D | 0.12624 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(2/502)=0.12624 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.12624 s, not -0.12624 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.12624 s, not 0.06312 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.12624 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_000720 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio 5. What is the sum of its first 5 terms? | {
"A": "2343",
"B": "3514.5",
"C": "4685",
"D": "4686"
} | D | 4686 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(5^5−1)/(5−1)=4686. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4686, not 2343.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4686, not 3514.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4686, not 4685.",
"D": "Co... | [
"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_004951 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 2 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "15 A",
"B": "10 A",
"C": "13 A",
"D": "9 A"
} | B | 10 A | Series branch resistance=4+14=18 Ω. Parallel equivalent R_eq=(18×2)/(18+2)=1.8 Ω. Total current I=V/R_eq=18/1.8=10 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10 A, not 15 A.",
"B": "Correct. The worked calculation gives 10 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10 A, not 13 A.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_007417 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 10 mL of 0.10 M HCl is mixed with 21 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.55003",
"B": "-12.55003",
"C": "15.55003",
"D": "10.55003"
} | A | 12.55003 | Excess OH⁻ moles=0.10×(21−10)/1000=0.001100 mol. Total volume=0.031 L, so [OH⁻]=0.035484 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.55003. | {
"A": "Correct. The worked calculation gives 12.55003.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.55003, not -12.55003.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.55003, not 15.55003.",
"D": "Incorrect. Substituting the sta... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003314 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(15+13i)/(6+1i). What is Re(z), the real part of z? | {
"A": "4.78378",
"B": "2.78378",
"C": "-2.78378",
"D": "1.78378"
} | B | 2.78378 | Multiply numerator and denominator by the conjugate (6-1i). Then Re(z)=(ac+bd)/(c²+d²)=((15)(6)+(13)(1))/(6²+(1)²)=2.78378. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.78378, not 4.78378.",
"B": "Correct. The worked calculation gives 2.78378.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.78378, not -2.78378.",
"D": "Incorrect. Substituting the stated v... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005675 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.8 atm at 341 K. What is its pressure at 713 K? | {
"A": "7.52727 atm",
"B": "5.01818 atm",
"C": "15.05455 atm",
"D": "10.03636 atm"
} | D | 10.03636 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.8)(713)/(341)=10.03636 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.03636 atm, not 7.52727 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.03636 atm, not 5.01818 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives ... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009446 | 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_10X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "2.25",
"C": "6",
"D": "1.3"
} | A | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×8+2+0−10−2)/2=3. | {
"A": "Correct. The worked calculation gives 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, 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_001994 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 18 distinct elements? | {
"A": "4376.8",
"B": "65637",
"C": "43758",
"D": "21879"
} | C | 43758 | Order does not matter, so the count is C(18,8)=18!/[8!(10)!]=43758. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 43758, not 4376.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 43758, not 65637.",
"C": "Correct. The worked calculation gives 43758.",
"D": "Incorrect. Substituting the stated values into... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006328 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 99 cm in front of a thin convex lens of focal length 30 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-2.56522",
"B": "0.32609",
"C": "-1.56522",
"D": "0.43478"
} | D | 0.43478 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(99)(30)/(99−30)=43.04348 cm. Thus |m|=v/u=43.04348/99=0.43478. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.43478, not -2.56522.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.43478, not 0.32609.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.43478, not -1.5... | [
"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_009164 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.23 V, transfers 1 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.3482 V",
"B": "4.3482 V",
"C": "-1.6518 V",
"D": "2.3482 V"
} | A | 1.3482 V | Apply the Nernst equation: E=1.23−(0.0591/1)(-2)=1.3482 V. | {
"A": "Correct. The worked calculation gives 1.3482 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.3482 V, not 4.3482 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.3482 V, not -1.6518 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_002226 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 4 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.72727",
"B": "2.27273",
"C": "-0.27273",
"D": "0.27273"
} | D | 0.27273 | Favourable pairs = C(3,2)+C(4,2)+C(4,2)=15. Total pairs=C(11,2)=55. Therefore P=15/55=0.27273. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.27273, not -0.72727.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.27273, not 2.27273.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.27273, not -0.2... | [
"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_001812 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 84 distinct elements? | {
"A": "-43595145594",
"B": "87190291188",
"C": "65392718391",
"D": "43595145594"
} | D | 43595145594 | Order does not matter, so the count is C(84,8)=84!/[8!(76)!]=43595145594. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 43595145594, not -43595145594.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 43595145594, not 87190291188.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4... | [
"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_000949 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio 5. What is the sum of its first 5 terms? | {
"A": "3748.8",
"B": "3123",
"C": "3124",
"D": "6248"
} | C | 3124 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(5^5−1)/(5−1)=3124. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3124, not 3748.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3124, not 3123.",
"C": "Correct. The worked calculation gives 3124.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_008483 | 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 0.48 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.3744 K",
"B": "1.4992 K",
"C": "0.9984 K",
"D": "0.4992 K"
} | D | 0.4992 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×0.48=0.4992 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.4992 K, not 0.3744 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.4992 K, not 1.4992 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.4992 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_002415 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, -4], [6, 4]]. | {
"A": "-40",
"B": "20",
"C": "80",
"D": "40"
} | D | 40 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(4)−(-4)(6)=40. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 40, not -40.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 40, not 20.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 40, not 80.",
"D": "Correct. The wo... | [
"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_000682 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio -2. What is the sum of its first 7 terms? | {
"A": "215",
"B": "44",
"C": "430",
"D": "432"
} | C | 430 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(-2^7−1)/(-2−1)=430. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 430, not 215.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 430, not 44.",
"C": "Correct. The worked calculation gives 430.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_009493 | 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_13N_1X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "6",
"B": "3",
"C": "1",
"D": "4.5"
} | B | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×9+2+1−13−2)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.",
"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_002485 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, 1], [5, 0]]. | {
"A": "-2",
"B": "-7",
"C": "-5",
"D": "-4"
} | C | -5 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(0)−(1)(5)=-5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -5, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -5, not -7.",
"C": "Correct. The worked calculation gives -5.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003599 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 77 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1185.8 m",
"B": "889.35 m",
"C": "444.675 m",
"D": "592.9 m"
} | D | 592.9 m | Range R=u²sin(2θ)/g. Substituting u=77, θ=45° and g=10 gives R=(77)²sin(90°)/10=592.9 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 592.9 m, not 1185.8 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 592.9 m, not 889.35 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 592.9 m, not 444... | [
"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_009257 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.93 V, transfers 3 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.0285 V",
"B": "-1.9715 V",
"C": "0.51425 V",
"D": "0.77137 V"
} | A | 1.0285 V | Apply the Nernst equation: E=0.93−(0.0591/3)(-5)=1.0285 V. | {
"A": "Correct. The worked calculation gives 1.0285 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0285 V, not -1.9715 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0285 V, not 0.51425 V.",
"D": "Incorrect. Substituting the st... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000310 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +8x +12=0, let its roots be α and β. What is α²+β²? | {
"A": "-2.24",
"B": "-5.24",
"C": "-1.68",
"D": "-4.24"
} | A | -2.24 | By Vieta's relations, α+β = -8/5 and αβ = 12/5. Then α²+β²=(α+β)²−2αβ = (-8/5)²−2(12/5) = -2.24. | {
"A": "Correct. The worked calculation gives -2.24.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2.24, not -5.24.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2.24, not -1.68.",
"D": "Incorrect. Substituting the stated values into ... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003792 | 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 23 N of work over 10 m in the direction of motion. Find its final kinetic energy. | {
"A": "-236 J",
"B": "236 J",
"C": "237 J",
"D": "188.8 J"
} | B | 236 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(1)²+(23)(10)=236 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 236 J, not -236 J.",
"B": "Correct. The worked calculation gives 236 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 236 J, not 237 J.",
"D": "Incorrect. Substituting the stated values into... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009091 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.80 V, transfers 1 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.0955 V",
"B": "-1.0955 V",
"C": "-1.9045 V",
"D": "1.0955 V"
} | D | 1.0955 V | Apply the Nernst equation: E=0.80−(0.0591/1)(-5)=1.0955 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0955 V, not 0.0955 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0955 V, not -1.0955 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0955 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_004162 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.44. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "2.96 N",
"B": "3.96 N",
"C": "4.96 N",
"D": "-4.96 N"
} | C | 4.96 N | Net force=mg(sinθ−μcosθ)=2×10×(0.6−0.44×0.8)=4.96 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.96 N, not 2.96 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.96 N, not 3.96 N.",
"C": "Correct. The worked calculation gives 4.96 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_005686 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.9 atm at 425 K. What is its pressure at 487 K? | {
"A": "5.61482 atm",
"B": "8.42224 atm",
"C": "2.80741 atm",
"D": "11.22965 atm"
} | A | 5.61482 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.9)(487)/(425)=5.61482 atm. | {
"A": "Correct. The worked calculation gives 5.61482 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.61482 atm, not 8.42224 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.61482 atm, not 2.80741 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004738 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 20 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.2 A",
"B": "0.6 A",
"C": "0.2 A",
"D": "4.2 A"
} | A | 1.2 A | Series branch resistance=8+4=12 Ω. Parallel equivalent R_eq=(12×20)/(12+20)=7.5 Ω. Total current I=V/R_eq=9/7.5=1.2 A. | {
"A": "Correct. The worked calculation gives 1.2 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.2 A, not 0.6 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2 A, not 0.2 A.",
"D": "Incorrect. Substituting the stated values into ... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000321 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 +14x +7=0, let its roots be α and β. What is α²+β²? | {
"A": "136.5",
"B": "182",
"C": "183",
"D": "91"
} | B | 182 | By Vieta's relations, α+β = -14/1 and αβ = 7/1. Then α²+β²=(α+β)²−2αβ = (-14/1)²−2(7/1) = 182. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 182, not 136.5.",
"B": "Correct. The worked calculation gives 182.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 182, not 183.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_001572 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (4x² +2x +0) dx. | {
"A": "1.23333",
"B": "-0.66667",
"C": "4.33333",
"D": "2.33333"
} | D | 2.33333 | An antiderivative is (4/3)x³+(2/2)x²+(0)x. Evaluating between 0 and 1 gives (4/3)(1)³+(2/2)(1)²+(0)(1)=2.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.33333, not 1.23333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.33333, not -0.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.33333, not 4.33... | [
"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_008257 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 4 A for 11591 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": "22.88172 g",
"B": "13.25448 g",
"C": "-15.25448 g",
"D": "15.25448 g"
} | D | 15.25448 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×11591/(2×96500)=15.25448 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15.25448 g, not 22.88172 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15.25448 g, not 13.25448 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15.254... | [
"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_001559 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (2x² +4x +4) dx. | {
"A": "49",
"B": "36",
"C": "57.6",
"D": "48"
} | D | 48 | An antiderivative is (2/3)x³+(4/2)x²+(4)x. Evaluating between 0 and 3 gives (2/3)(3)³+(4/2)(3)²+(4)(3)=48. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 48, not 49.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 48, not 36.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 48, not 57.6.",
"D": "Correct. The w... | [
"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_009442 | 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_16H_14N_1X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "7",
"B": "15",
"C": "10",
"D": "5"
} | C | 10 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×16+2+1−14−1)/2=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 15.",
"C": "Correct. The worked calculation gives 10.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008857 | 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 1.65 mol L⁻¹ and initially B is absent. At equilibrium, 73% of A has dissociated at constant volume. Find K_c. | {
"A": "13.02644",
"B": "19.53967",
"C": "26.05289",
"D": "12.02644"
} | A | 13.02644 | Let α=0.73. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.65)(0.73)²/(1−0.73)=13.02644. | {
"A": "Correct. The worked calculation gives 13.02644.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13.02644, not 19.53967.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13.02644, not 26.05289.",
"D": "Incorrect. Substituting the stat... | [
"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_008470 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.7 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.68 K",
"B": "0.68 K",
"C": "4.68 K",
"D": "1.168 K"
} | A | 1.68 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.6×0.7=1.68 K. | {
"A": "Correct. The worked calculation gives 1.68 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.68 K, not 0.68 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.68 K, not 4.68 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_007243 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 9 mol of gas at 289 K and 2.25 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "94.85789 L",
"B": "-94.85789 L",
"C": "95.85789 L",
"D": "92.85789 L"
} | A | 94.85789 L | PV=nRT, so V=nRT/P=(9)(0.082057)(289)/(2.25)=94.85789 L. | {
"A": "Correct. The worked calculation gives 94.85789 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 94.85789 L, not -94.85789 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 94.85789 L, not 95.85789 L.",
"D": "Incorrect. Substituti... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000969 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 3. What is the sum of its first 7 terms? | {
"A": "8744",
"B": "16395",
"C": "13116",
"D": "10930"
} | D | 10930 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(3^7−1)/(3−1)=10930. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10930, not 8744.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10930, not 16395.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10930, not 13116.",
"D": ... | [
"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_007765 | 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 97 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "0.75781 mmol L⁻¹",
"B": "3.75781 mmol L⁻¹",
"C": "0.56836 mmol L⁻¹",
"D": "-0.75781 mmol L⁻¹"
} | A | 0.75781 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=97/2^7=0.75781 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 0.75781 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.75781 mmol L⁻¹, not 3.75781 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.75781 mmol L⁻¹, not 0.56836 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_003926 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 8 m s⁻¹. A constant net force does 10 N of work over 3 m in the direction of motion. Find its final kinetic energy. | {
"A": "573 J",
"B": "384 J",
"C": "382 J",
"D": "-382 J"
} | C | 382 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(8)²+(10)(3)=382 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 382 J, not 573 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 382 J, not 384 J.",
"C": "Correct. The worked calculation gives 382 J.",
"D": "Incorrect. Substituting the stated values into ... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008605 | 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 1.86 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.9672 K",
"B": "1.9344 K",
"C": "1.09672 K",
"D": "0.7254 K"
} | A | 0.9672 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.52×1.86=0.9672 K. | {
"A": "Correct. The worked calculation gives 0.9672 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9672 K, not 1.9344 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9672 K, not 1.09672 K.",
"D": "Incorrect. Substituting the sta... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002123 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 8 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.31954",
"B": "2.31954",
"C": "0.63908",
"D": "-0.31954"
} | A | 0.31954 | Favourable pairs = C(10,2)+C(8,2)+C(12,2)=139. Total pairs=C(30,2)=435. Therefore P=139/435=0.31954. | {
"A": "Correct. The worked calculation gives 0.31954.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31954, not 2.31954.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31954, not 0.63908.",
"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_003049 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-9+9i)/(3+8i). What is Re(z), the real part of z? | {
"A": "0.46233",
"B": "0.30822",
"C": "0.61644",
"D": "2.61644"
} | C | 0.61644 | Multiply numerator and denominator by the conjugate (3-8i). Then Re(z)=(ac+bd)/(c²+d²)=((-9)(3)+(9)(8))/(3²+(8)²)=0.61644. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.61644, not 0.46233.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.61644, not 0.30822.",
"C": "Correct. The worked calculation gives 0.61644.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005570 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 44 μF capacitor is charged to a potential difference of 15 V. Calculate the energy stored, expressed in μJ. | {
"A": "4950 μJ",
"B": "4952 μJ",
"C": "5940 μJ",
"D": "-4950 μJ"
} | A | 4950 μJ | U=½CV². Since C=44 μF, U in μJ is ½×44×(15)²=4950 μJ. | {
"A": "Correct. The worked calculation gives 4950 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4950 μJ, not 4952 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4950 μJ, not 5940 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_003482 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 26 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "81.12 m",
"B": "7.76 m",
"C": "66.6 m",
"D": "67.6 m"
} | D | 67.6 m | Range R=u²sin(2θ)/g. Substituting u=26, θ=45° and g=10 gives R=(26)²sin(90°)/10=67.6 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 67.6 m, not 81.12 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 67.6 m, not 7.76 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 67.6 m, not 66.6 m.",... | [
"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_004199 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 25 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.29. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "73.6 N",
"B": "184 N",
"C": "-92 N",
"D": "92 N"
} | D | 92 N | Net force=mg(sinθ−μcosθ)=25×10×(0.6−0.29×0.8)=92 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 92 N, not 73.6 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 92 N, not 184 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 92 N, not -92 N.",
"D": "... | [
"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_000754 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio 5. What is the sum of its first 12 terms? | {
"A": "61035158",
"B": "91552734",
"C": "48828124.8",
"D": "61035156"
} | D | 61035156 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(5^12−1)/(5−1)=61035156. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 61035156, not 61035158.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 61035156, not 91552734.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 61035156, not ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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