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_008409 | 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 0.72 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.10592 K",
"B": "-0.89408 K",
"C": "-1.89408 K",
"D": "1.10592 K"
} | D | 1.10592 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.512×0.72=1.10592 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.10592 K, not 0.10592 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.10592 K, not -0.89408 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.10592 K... | [
"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_002785 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(2, 7, -6) and v=(-2, -1, 5), calculate u·v. | {
"A": "-82",
"B": "-41",
"C": "-39",
"D": "-42"
} | B | -41 | The dot product is the sum of corresponding component products: (2)(-2)+(7)(-1)+(-6)(5)=-41. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -41, not -82.",
"B": "Correct. The worked calculation gives -41.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -41, not -39.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006285 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 121 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": "-0.32967",
"B": "1.03297",
"C": "0.32967",
"D": "-2.67033"
} | C | 0.32967 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(121)(30)/(121−30)=39.89011 cm. Thus |m|=v/u=39.89011/121=0.32967. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32967, not -0.32967.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32967, not 1.03297.",
"C": "Correct. The worked calculation gives 0.32967.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005064 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +2 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "7.66667 N",
"B": "4.66667 N",
"C": "1.66667 N",
"D": "6.66667 N"
} | D | 6.66667 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(2×10⁻⁶)/(9×10⁻²)²=6.66667 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.66667 N, not 7.66667 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.66667 N, not 4.66667 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.66667 N,... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009347 | 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_1N_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "6.75",
"B": "-9",
"C": "11",
"D": "9"
} | D | 9 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×8+2+1−1−0)/2=9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9, not 6.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9, not -9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9, not 11.",
"D": "Correct. The work... | [
"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_009889 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(CN)_3]^-4, each CN ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "-2",
"B": "-3",
"C": "-1",
"D": "-4"
} | C | -1 | Let the formal oxidation state of Pt be x. Charge balance gives x+(3)(−1)=-4; hence x=-4+3=-1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1, not -3.",
"C": "Correct. The worked calculation gives -1.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_001791 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 6 elements can be selected from a set of 58 distinct elements? | {
"A": "4047536.8",
"B": "20237679",
"C": "40475359",
"D": "40475358"
} | D | 40475358 | Order does not matter, so the count is C(58,6)=58!/[6!(52)!]=40475358. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 40475358, not 4047536.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 40475358, not 20237679.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 40475358, not... | [
"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_002929 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-2, -6, 6) and v=(0, -3, 6), calculate u·v. | {
"A": "6.4",
"B": "53",
"C": "52",
"D": "54"
} | D | 54 | The dot product is the sum of corresponding component products: (-2)(0)+(-6)(-3)+(6)(6)=54. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 54, not 6.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 54, not 53.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 54, not 52.",
"D": "Correct. The wo... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003322 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(10-11i)/(3+7i). What is Re(z), the real part of z? | {
"A": "-3.81034",
"B": "1.18966",
"C": "-0.81034",
"D": "0.81034"
} | C | -0.81034 | Multiply numerator and denominator by the conjugate (3-7i). Then Re(z)=(ac+bd)/(c²+d²)=((10)(3)+(-11)(7))/(3²+(7)²)=-0.81034. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.81034, not -3.81034.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.81034, not 1.18966.",
"C": "Correct. The worked calculation gives -0.81034.",
"D": "Incorrect. Substituting the state... | [
"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_003247 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-9-10i)/(5+5i). What is Re(z), the real part of z? | {
"A": "-2.9",
"B": "-2.85",
"C": "-0.9",
"D": "-1.9"
} | D | -1.9 | Multiply numerator and denominator by the conjugate (5-5i). Then Re(z)=(ac+bd)/(c²+d²)=((-9)(5)+(-10)(5))/(5²+(5)²)=-1.9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.9, not -2.9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.9, not -2.85.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.9, not -0.9.",
"D": "Cor... | [
"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_005879 | 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 4.3 atm at 295 K. What is its pressure at 710 K? | {
"A": "15.52373 atm",
"B": "10.34915 atm",
"C": "12.34915 atm",
"D": "-10.34915 atm"
} | B | 10.34915 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.3)(710)/(295)=10.34915 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.34915 atm, not 15.52373 atm.",
"B": "Correct. The worked calculation gives 10.34915 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10.34915 atm, not 12.34915 atm.",
"D": "Incorrect. S... | [
"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_002909 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(5, -2, -5) and v=(-2, -7, -7), calculate u·v. | {
"A": "39",
"B": "41",
"C": "19.5",
"D": "46.8"
} | A | 39 | The dot product is the sum of corresponding component products: (5)(-2)+(-2)(-7)+(-5)(-7)=39. | {
"A": "Correct. The worked calculation gives 39.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39, not 41.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39, not 19.5.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"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_007877 | 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 49 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "0.38281 mmol L⁻¹",
"B": "0.14355 mmol L⁻¹",
"C": "1.19141 mmol L⁻¹",
"D": "0.19141 mmol L⁻¹"
} | D | 0.19141 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=49/2^8=0.19141 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.19141 mmol L⁻¹, not 0.38281 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.19141 mmol L⁻¹, not 0.14355 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governi... | [
"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_004968 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 2 Ω and 6 Ω are connected in series; this combination is connected in parallel with a 19 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "5.26316 A",
"B": "3.19737 A",
"C": "1.42632 A",
"D": "4.26316 A"
} | D | 4.26316 A | Series branch resistance=2+6=8 Ω. Parallel equivalent R_eq=(8×19)/(8+19)=5.62963 Ω. Total current I=V/R_eq=24/5.62963=4.26316 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.26316 A, not 5.26316 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.26316 A, not 3.19737 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.26316 A,... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000083 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 -12x +5=0, let its roots be α and β. What is α²+β²? | {
"A": "4.5",
"B": "3.25",
"C": "-6.5",
"D": "6.5"
} | D | 6.5 | By Vieta's relations, α+β = 12/4 and αβ = 5/4. Then α²+β²=(α+β)²−2αβ = (12/4)²−2(5/4) = 6.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.5, not 4.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.5, not 3.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.5, not -6.5.",
"D": "Correct.... | [
"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_005532 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 17 μF capacitor is charged to a potential difference of 24 V. Calculate the energy stored, expressed in μJ. | {
"A": "7344 μJ",
"B": "4897 μJ",
"C": "4896 μJ",
"D": "490.6 μJ"
} | C | 4896 μJ | U=½CV². Since C=17 μF, U in μJ is ½×17×(24)²=4896 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4896 μJ, not 7344 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4896 μJ, not 4897 μJ.",
"C": "Correct. The worked calculation gives 4896 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_004017 | 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 0.25. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "134.4 N",
"B": "168 N",
"C": "201.6 N",
"D": "126 N"
} | B | 168 N | Net force=mg(sinθ−μcosθ)=42×10×(0.6−0.25×0.8)=168 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 168 N, not 134.4 N.",
"B": "Correct. The worked calculation gives 168 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 168 N, not 201.6 N.",
"D": "Incorrect. Substituting the stated values i... | [
"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_007273 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 1 mol of gas at 264 K and 1.6 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "13.5394 L",
"B": "2.35394 L",
"C": "12.5394 L",
"D": "27.07881 L"
} | A | 13.5394 L | PV=nRT, so V=nRT/P=(1)(0.082057)(264)/(1.6)=13.5394 L. | {
"A": "Correct. The worked calculation gives 13.5394 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13.5394 L, not 2.35394 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13.5394 L, not 12.5394 L.",
"D": "Incorrect. Substituting the... | [
"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_007967 | 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 22 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "-1.65625 mmol L⁻¹",
"B": "0.34375 mmol L⁻¹",
"C": "0.25781 mmol L⁻¹",
"D": "1.34375 mmol L⁻¹"
} | B | 0.34375 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=22/2^6=0.34375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34375 mmol L⁻¹, not -1.65625 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.34375 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34375 mmol L⁻¹, not 0.25781 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_004351 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 13 kg and radius 2 m is acted on by a constant torque of 24 N m about its central axis. Find its angular acceleration. | {
"A": "0.92308 rad s⁻²",
"B": "1.09231 rad s⁻²",
"C": "3.92308 rad s⁻²",
"D": "-2.07692 rad s⁻²"
} | A | 0.92308 rad s⁻² | For a solid disc, I=½MR²=½(13)(2)²=26 kg m². Using τ=Iα, α=24/26=0.92308 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.92308 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.92308 rad s⁻², not 1.09231 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.92308 rad s⁻², not 3.92308 rad s⁻².",
"D"... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001168 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ -5x² +12x+7. Evaluate f′(-4). | {
"A": "244",
"B": "195.2",
"C": "242",
"D": "292.8"
} | A | 244 | Differentiate: f′(x)=3(4)x²+2(-5)x+(12). At x=-4, f′(-4)=3(4)(-4)²+2(-5)(-4)+(12)=244. | {
"A": "Correct. The worked calculation gives 244.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 244, not 195.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 244, not 242.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000530 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 24 and common difference 10. Find the sum of its first 12 terms. | {
"A": "1896",
"B": "711",
"C": "758.4",
"D": "948"
} | D | 948 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=24, d=10, n=12: Sₙ=12/2[2(24)+(12−1)(10)]=948. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 948, not 1896.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 948, not 711.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 948, not 758.4.",
"D": "Correct... | [
"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_007299 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 15 mol of gas at 181 K and 0.54 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "42.25644 L",
"B": "825.12872 L",
"C": "412.56436 L",
"D": "618.84654 L"
} | C | 412.56436 L | PV=nRT, so V=nRT/P=(15)(0.082057)(181)/(0.54)=412.56436 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 412.56436 L, not 42.25644 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 412.56436 L, not 825.12872 L.",
"C": "Correct. The worked calculation gives 412.56436 L.",
"D": "Incorrect. Substit... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001570 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (-3x² +7x +4) dx. | {
"A": "10",
"B": "5",
"C": "1.8",
"D": "8"
} | D | 8 | An antiderivative is (-3/3)x³+(7/2)x²+(4)x. Evaluating between 0 and 4 gives (-3/3)(4)³+(7/2)(4)²+(4)(4)=8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 1.8.",
"D": "Correct. The worked... | [
"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_000555 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -6 and common difference 13. Find the sum of its first 28 terms. | {
"A": "475.6",
"B": "5695.2",
"C": "4746",
"D": "4745"
} | C | 4746 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-6, d=13, n=28: Sₙ=28/2[2(-6)+(28−1)(13)]=4746. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4746, not 475.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4746, not 5695.2.",
"C": "Correct. The worked calculation gives 4746.",
"D": "Incorrect. Substituting the stated values into th... | [
"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_002233 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 9 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": "1.03161",
"B": "0.31613",
"C": "-2.68387",
"D": "0.15806"
} | B | 0.31613 | Favourable pairs = C(10,2)+C(9,2)+C(12,2)=147. Total pairs=C(31,2)=465. Therefore P=147/465=0.31613. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31613, not 1.03161.",
"B": "Correct. The worked calculation gives 0.31613.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31613, not -2.68387.",
"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_000019 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 +4x +2=0, let its roots be α and β. What is α²+β²? | {
"A": "-0.11111",
"B": "-0.16667",
"C": "-0.22222",
"D": "0.97778"
} | C | -0.22222 | By Vieta's relations, α+β = -4/6 and αβ = 2/6. Then α²+β²=(α+β)²−2αβ = (-4/6)²−2(2/6) = -0.22222. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.22222, not -0.11111.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.22222, not -0.16667.",
"C": "Correct. The worked calculation gives -0.22222.",
"D": "Incorrect. Substituting the stat... | [
"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_008769 | 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 1.21 mol L⁻¹ and initially B is absent. At equilibrium, 40% of A has dissociated at constant volume. Find K_c. | {
"A": "1.29067",
"B": "2.58133",
"C": "1.936",
"D": "-1.70933"
} | A | 1.29067 | Let α=0.4. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.21)(0.4)²/(1−0.4)=1.29067. | {
"A": "Correct. The worked calculation gives 1.29067.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.29067, not 2.58133.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.29067, not 1.936.",
"D": "Incorrect. Substituting the stated valu... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007461 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 49 mL of 0.10 M HCl is mixed with 27 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "3.53839",
"B": "1.53839",
"C": "1.15379",
"D": "2.53839"
} | B | 1.53839 | Excess H⁺ moles=0.10×(49−27)/1000=0.002200 mol. Total volume=0.076 L, so [H⁺]=0.028947 M and pH=−log₁₀[H⁺]=1.53839. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.53839, not 3.53839.",
"B": "Correct. The worked calculation gives 1.53839.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.53839, not 1.15379.",
"D": "Incorrect. Substituting the stated va... | [
"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_006717 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 28 mol H₂ and 34 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "56 mol",
"B": "27 mol",
"C": "29 mol",
"D": "28 mol"
} | D | 28 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 28 mol H₂O; O₂ can produce 68 mol H₂O. The limiting condition is H₂; product=28 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28 mol, not 56 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28 mol, not 27 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28 mol, not 29 mol.",
... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007280 | 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 472 K and 0.36 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "1533.09828 L",
"B": "2044.13104 L",
"C": "3066.19657 L",
"D": "4088.26209 L"
} | B | 2044.13104 L | PV=nRT, so V=nRT/P=(19)(0.082057)(472)/(0.36)=2044.13104 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2044.13104 L, not 1533.09828 L.",
"B": "Correct. The worked calculation gives 2044.13104 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2044.13104 L, not 3066.19657 L.",
"D": "Incorrect. S... | [
"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_003029 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-13+15i)/(9+2i). What is Re(z), the real part of z? | {
"A": "-3.02353",
"B": "-1.02353",
"C": "1.02353",
"D": "0.97647"
} | B | -1.02353 | Multiply numerator and denominator by the conjugate (9-2i). Then Re(z)=(ac+bd)/(c²+d²)=((-13)(9)+(15)(2))/(9²+(2)²)=-1.02353. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.02353, not -3.02353.",
"B": "Correct. The worked calculation gives -1.02353.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.02353, not 1.02353.",
"D": "Incorrect. Substituting the state... | [
"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_006090 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 16 cm in front of a thin convex lens of focal length 9 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.28571",
"B": "-1.71429",
"C": "-1.28571",
"D": "2.57143"
} | A | 1.28571 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(16)(9)/(16−9)=20.57143 cm. Thus |m|=v/u=20.57143/16=1.28571. | {
"A": "Correct. The worked calculation gives 1.28571.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.28571, not -1.71429.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.28571, not -1.28571.",
"D": "Incorrect. Substituting the stated ... | [
"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_006992 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 39 mol H₂ and 33 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "41 mol",
"B": "40 mol",
"C": "39 mol",
"D": "78 mol"
} | C | 39 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 39 mol H₂O; O₂ can produce 66 mol H₂O. The limiting condition is H₂; product=39 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 39 mol, not 41 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39 mol, not 40 mol.",
"C": "Correct. The worked calculation gives 39 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002161 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 3 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.03971",
"B": "0.39706",
"C": "-2.60294",
"D": "0.59559"
} | B | 0.39706 | Favourable pairs = C(10,2)+C(3,2)+C(4,2)=54. Total pairs=C(17,2)=136. Therefore P=54/136=0.39706. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.39706, not 1.03971.",
"B": "Correct. The worked calculation gives 0.39706.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.39706, not -2.60294.",
"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_009153 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.26 V, transfers 1 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "4.4373 V",
"B": "3.4373 V",
"C": "1.4373 V",
"D": "2.4373 V"
} | C | 1.4373 V | Apply the Nernst equation: E=1.26−(0.0591/1)(-3)=1.4373 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.4373 V, not 4.4373 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4373 V, not 3.4373 V.",
"C": "Correct. The worked calculation gives 1.4373 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_009372 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_18H_36N_1X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "0",
"B": "-3",
"C": "2",
"D": "-2"
} | A | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+1−36−3)/2=0. | {
"A": "Correct. The worked calculation gives 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 2.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_006751 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 40 mol H₂ and 14 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "28 mol",
"B": "56 mol",
"C": "14 mol",
"D": "21 mol"
} | A | 28 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 40 mol H₂O; O₂ can produce 28 mol H₂O. The limiting condition is O₂; product=28 mol. | {
"A": "Correct. The worked calculation gives 28 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28 mol, not 56 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28 mol, not 14 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000934 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio -2. What is the sum of its first 5 terms? | {
"A": "55",
"B": "41.25",
"C": "66",
"D": "27.5"
} | A | 55 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(-2^5−1)/(-2−1)=55. | {
"A": "Correct. The worked calculation gives 55.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 55, not 41.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 55, not 66.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_009314 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.70 V, transfers 3 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.07955 V",
"B": "-1.2803 V",
"C": "1.4394 V",
"D": "0.7197 V"
} | D | 0.7197 V | Apply the Nernst equation: E=0.70−(0.0591/3)(-1)=0.7197 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7197 V, not 1.07955 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7197 V, not -1.2803 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7197 V, no... | [
"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_008507 | 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 0.86 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "5.16 K",
"B": "3.44 K",
"C": "5.44 K",
"D": "4.44 K"
} | B | 3.44 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×1.0×0.86=3.44 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.44 K, not 5.16 K.",
"B": "Correct. The worked calculation gives 3.44 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.44 K, not 5.44 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_009930 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(OH)_5]^+2, each OH ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "5",
"B": "9",
"C": "7",
"D": "10"
} | C | 7 | Let the formal oxidation state of Co be x. Charge balance gives x+(5)(−1)=+2; hence x=2+5=+7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 9.",
"C": "Correct. The worked calculation gives 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_003878 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 7 m s⁻¹. A constant net force does 19 N of work over 16 m in the direction of motion. Find its final kinetic energy. | {
"A": "448.5 J",
"B": "598 J",
"C": "599 J",
"D": "60.8 J"
} | B | 598 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(7)²+(19)(16)=598 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 598 J, not 448.5 J.",
"B": "Correct. The worked calculation gives 598 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 598 J, not 599 J.",
"D": "Incorrect. Substituting the stated values int... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002668 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, -1], [9, 6]]. | {
"A": "2.5",
"B": "7.5",
"C": "15",
"D": "22.5"
} | C | 15 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(6)−(-1)(9)=15. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15, not 2.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15, not 7.5.",
"C": "Correct. The worked calculation gives 15.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003339 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(15-7i)/(6+11i). What is Re(z), the real part of z? | {
"A": "0.0621",
"B": "0.0828",
"C": "0.16561",
"D": "1.0828"
} | B | 0.0828 | Multiply numerator and denominator by the conjugate (6-11i). Then Re(z)=(ac+bd)/(c²+d²)=((15)(6)+(-7)(11))/(6²+(11)²)=0.0828. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.0828, not 0.0621.",
"B": "Correct. The worked calculation gives 0.0828.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.0828, not 0.16561.",
"D": "Incorrect. Substituting the stated values... | [
"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_008522 | 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 0.49 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-1.96 K",
"B": "1.47 K",
"C": "1.96 K",
"D": "0.96 K"
} | C | 1.96 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×1.0×0.49=1.96 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.96 K, not -1.96 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.96 K, not 1.47 K.",
"C": "Correct. The worked calculation gives 1.96 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_008228 | 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 28672 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": "132.06947 g",
"B": "264.13894 g",
"C": "-132.06947 g",
"D": "158.48337 g"
} | A | 132.06947 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×28672/(2×96500)=132.06947 g. | {
"A": "Correct. The worked calculation gives 132.06947 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 132.06947 g, not 264.13894 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 132.06947 g, not -132.06947 g.",
"D": "Incorrect. Subst... | [
"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_000719 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio -2. What is the sum of its first 12 terms? | {
"A": "-6825",
"B": "-6826",
"C": "-13650",
"D": "6825"
} | A | -6825 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(-2^12−1)/(-2−1)=-6825. | {
"A": "Correct. The worked calculation gives -6825.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -6825, not -6826.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -6825, not -13650.",
"D": "Incorrect. Substituting the stated values into... | [
"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_001066 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=3x³ +8x² +9x+7. Evaluate f′(1). | {
"A": "-34",
"B": "34",
"C": "36",
"D": "33"
} | B | 34 | Differentiate: f′(x)=3(3)x²+2(8)x+(9). At x=1, f′(1)=3(3)(1)²+2(8)(1)+(9)=34. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 34, not -34.",
"B": "Correct. The worked calculation gives 34.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 34, not 36.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007664 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 99 mL of 0.10 M HCl is mixed with 35 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.32092",
"B": "-0.67908",
"C": "1.98139",
"D": "4.32092"
} | A | 1.32092 | Excess H⁺ moles=0.10×(99−35)/1000=0.006400 mol. Total volume=0.134 L, so [H⁺]=0.047761 M and pH=−log₁₀[H⁺]=1.32092. | {
"A": "Correct. The worked calculation gives 1.32092.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.32092, not -0.67908.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.32092, not 1.98139.",
"D": "Incorrect. Substituting the stated v... | [
"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_009188 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.96 V, transfers 2 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.7827 V",
"B": "3.7827 V",
"C": "0.39135 V",
"D": "0.7827 V"
} | D | 0.7827 V | Apply the Nernst equation: E=0.96−(0.0591/2)(6)=0.7827 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7827 V, not 2.7827 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7827 V, not 3.7827 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7827 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_008964 | 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 1.1 mol L⁻¹ and initially B is absent. At equilibrium, 18% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.17385",
"B": "0.17385",
"C": "0.13039",
"D": "-2.82615"
} | B | 0.17385 | Let α=0.18. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.1)(0.18)²/(1−0.18)=0.17385. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.17385, not -0.17385.",
"B": "Correct. The worked calculation gives 0.17385.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.17385, not 0.13039.",
"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_001049 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ +3x² -11x+7. Evaluate f′(2). | {
"A": "-48",
"B": "-70.5",
"C": "-47",
"D": "-37.6"
} | C | -47 | Differentiate: f′(x)=3(-4)x²+2(3)x+(-11). At x=2, f′(2)=3(-4)(2)²+2(3)(2)+(-11)=-47. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -47, not -48.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -47, not -70.5.",
"C": "Correct. The worked calculation gives -47.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009790 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(OH)_2]^-2, each OH ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "1",
"B": "-1",
"C": "-3",
"D": "0"
} | D | 0 | Let the formal oxidation state of Cu be x. Charge balance gives x+(2)(−1)=-2; hence x=-2+2=+0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not -1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"D": "Correct. The worked ... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005218 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +3 μC are separated by 5 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "96.2 N",
"B": "97.2 N",
"C": "116.64 N",
"D": "77.76 N"
} | B | 97.2 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(3×10⁻⁶)/(5×10⁻²)²=97.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 97.2 N, not 96.2 N.",
"B": "Correct. The worked calculation gives 97.2 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 97.2 N, not 116.64 N.",
"D": "Incorrect. Substituting the stated value... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007510 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 43 mL of 0.10 M HCl is mixed with 40 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "4.44196",
"B": "1.83147",
"C": "2.44196",
"D": "-0.55804"
} | C | 2.44196 | Excess H⁺ moles=0.10×(43−40)/1000=0.000300 mol. Total volume=0.083 L, so [H⁺]=0.003614 M and pH=−log₁₀[H⁺]=2.44196. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.44196, not 4.44196.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.44196, not 1.83147.",
"C": "Correct. The worked calculation gives 2.44196.",
"D": "Incorrect. Substituting the stated va... | [
"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_008665 | 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 0.26 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "3.04 K",
"B": "1.04 K",
"C": "0.04 K",
"D": "-1.04 K"
} | B | 1.04 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×1.0×0.26=1.04 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.04 K, not 3.04 K.",
"B": "Correct. The worked calculation gives 1.04 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.04 K, not 0.04 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_007382 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 63 mL of 0.10 M HCl is mixed with 96 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "24.63423",
"B": "9.23784",
"C": "12.31712",
"D": "15.31712"
} | C | 12.31712 | Excess OH⁻ moles=0.10×(96−63)/1000=0.003300 mol. Total volume=0.159 L, so [OH⁻]=0.020755 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.31712. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.31712, not 24.63423.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.31712, not 9.23784.",
"C": "Correct. The worked calculation gives 12.31712.",
"D": "Incorrect. Substituting the state... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005434 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 5 μF capacitor is charged to a potential difference of 21 V. Calculate the energy stored, expressed in μJ. | {
"A": "1653.75 μJ",
"B": "1102.5 μJ",
"C": "111.25 μJ",
"D": "826.875 μJ"
} | B | 1102.5 μJ | U=½CV². Since C=5 μF, U in μJ is ½×5×(21)²=1102.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1102.5 μJ, not 1653.75 μJ.",
"B": "Correct. The worked calculation gives 1102.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1102.5 μJ, not 111.25 μJ.",
"D": "Incorrect. Substituting th... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004829 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 20 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "-3.51429 A",
"B": "6.51429 A",
"C": "3.51429 A",
"D": "7.02857 A"
} | C | 3.51429 A | Series branch resistance=13+8=21 Ω. Parallel equivalent R_eq=(21×20)/(21+20)=10.2439 Ω. Total current I=V/R_eq=36/10.2439=3.51429 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.51429 A, not -3.51429 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.51429 A, not 6.51429 A.",
"C": "Correct. The worked calculation gives 3.51429 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009624 | 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_17H_29N_3X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "2.25",
"B": "3",
"C": "1.3",
"D": "6"
} | B | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×17+2+3−29−4)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009668 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(OH)_6]^+3, each OH ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "13.5",
"B": "7",
"C": "9",
"D": "1.9"
} | C | 9 | Let the formal oxidation state of Cr be x. Charge balance gives x+(6)(−1)=+3; hence x=3+6=+9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9, not 13.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9, not 7.",
"C": "Correct. The worked calculation gives 9.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003757 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block initially moves at 6 m s⁻¹. A constant net force does 15 N of work over 14 m in the direction of motion. Find its final kinetic energy. | {
"A": "576 J",
"B": "478 J",
"C": "480 J",
"D": "479 J"
} | C | 480 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(15)(6)²+(15)(14)=480 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 480 J, not 576 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 480 J, not 478 J.",
"C": "Correct. The worked calculation gives 480 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_008611 | 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 0.98 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": "2.5096 K",
"B": "0.5096 K",
"C": "0.7644 K",
"D": "0.3822 K"
} | B | 0.5096 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.52×0.98=0.5096 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5096 K, not 2.5096 K.",
"B": "Correct. The worked calculation gives 0.5096 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5096 K, not 0.7644 K.",
"D": "Incorrect. Substituting the stat... | [
"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_006210 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 79 cm in front of a thin convex lens of focal length 28 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.54902",
"B": "0.54902",
"C": "-1.45098",
"D": "0.27451"
} | B | 0.54902 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(79)(28)/(79−28)=43.37255 cm. Thus |m|=v/u=43.37255/79=0.54902. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.54902, not -0.54902.",
"B": "Correct. The worked calculation gives 0.54902.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.54902, not -1.45098.",
"D": "Incorrect. Substituting the stated ... | [
"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_009017 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.37 V, transfers 1 electrons, and has reaction quotient Q=10^2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.2518 V",
"B": "1.2518 V",
"C": "3.2518 V",
"D": "1.12518 V"
} | B | 1.2518 V | Apply the Nernst equation: E=1.37−(0.0591/1)(2)=1.2518 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.2518 V, not -1.2518 V.",
"B": "Correct. The worked calculation gives 1.2518 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2518 V, not 3.2518 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_000879 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio -2. What is the sum of its first 6 terms? | {
"A": "-252",
"B": "-168",
"C": "-169",
"D": "-166"
} | B | -168 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(-2^6−1)/(-2−1)=-168. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -168, not -252.",
"B": "Correct. The worked calculation gives -168.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -168, not -169.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_001712 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 6 elements can be selected from a set of 90 distinct elements? | {
"A": "622614631",
"B": "622614629",
"C": "622614628",
"D": "622614630"
} | D | 622614630 | Order does not matter, so the count is C(90,6)=90!/[6!(84)!]=622614630. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 622614630, not 622614631.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 622614630, not 622614629.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 622614630,... | [
"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_008583 | 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 1.17 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.59904 K",
"B": "0.29952 K",
"C": "0.44928 K",
"D": "2.59904 K"
} | A | 0.59904 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.512×1.17=0.59904 K. | {
"A": "Correct. The worked calculation gives 0.59904 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.59904 K, not 0.29952 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.59904 K, not 0.44928 K.",
"D": "Incorrect. Substituting the... | [
"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_004014 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.29. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "32.384 N",
"B": "20.24 N",
"C": "40.48 N",
"D": "38.48 N"
} | C | 40.48 N | Net force=mg(sinθ−μcosθ)=11×10×(0.6−0.29×0.8)=40.48 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 40.48 N, not 32.384 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 40.48 N, not 20.24 N.",
"C": "Correct. The worked calculation gives 40.48 N.",
"D": "Incorrect. Substituting the stated v... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001096 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ -9x² +2x+7. Evaluate f′(2). | {
"A": "-94",
"B": "-93",
"C": "94",
"D": "-96"
} | A | -94 | Differentiate: f′(x)=3(-5)x²+2(-9)x+(2). At x=2, f′(2)=3(-5)(2)²+2(-9)(2)+(2)=-94. | {
"A": "Correct. The worked calculation gives -94.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -94, not -93.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -94, not 94.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000668 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 3 and common difference 7. Find the sum of its first 15 terms. | {
"A": "780",
"B": "782",
"C": "781",
"D": "778"
} | A | 780 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=3, d=7, n=15: Sₙ=15/2[2(3)+(15−1)(7)]=780. | {
"A": "Correct. The worked calculation gives 780.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 780, not 782.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 780, not 781.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009393 | 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_1N_1X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "9",
"B": "-6",
"C": "6",
"D": "7"
} | C | 6 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+1−1−4)/2=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not -6.",
"C": "Correct. The worked calculation gives 6.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_002446 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, -8], [6, 8]]. | {
"A": "6.6",
"B": "56",
"C": "112",
"D": "54"
} | B | 56 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(8)−(-8)(6)=56. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 56, not 6.6.",
"B": "Correct. The worked calculation gives 56.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 56, not 112.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008744 | 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 0.56 mol L⁻¹ and initially B is absent. At equilibrium, 12% of A has dissociated at constant volume. Find K_c. | {
"A": "3.03665",
"B": "-1.96335",
"C": "-2.96335",
"D": "0.03665"
} | D | 0.03665 | Let α=0.12. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.56)(0.12)²/(1−0.12)=0.03665. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.03665, not 3.03665.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.03665, not -1.96335.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.03665, not -2.9... | [
"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_007104 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 17 mol of gas at 271 K and 0.15 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "2519.24399 L",
"B": "2518.24399 L",
"C": "-2520.24399 L",
"D": "2520.24399 L"
} | D | 2520.24399 L | PV=nRT, so V=nRT/P=(17)(0.082057)(271)/(0.15)=2520.24399 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2520.24399 L, not 2519.24399 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2520.24399 L, not 2518.24399 L.",
"C": "Incorrect. Substituting the stated values into the governing relation give... | [
"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_001295 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ +9x² -11x+7. Evaluate f′(4). | {
"A": "523.5",
"B": "351",
"C": "349",
"D": "347"
} | C | 349 | Differentiate: f′(x)=3(6)x²+2(9)x+(-11). At x=4, f′(4)=3(6)(4)²+2(9)(4)+(-11)=349. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 349, not 523.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 349, not 351.",
"C": "Correct. The worked calculation gives 349.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007362 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 25 mL of 0.10 M HCl is mixed with 87 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.74317",
"B": "25.48635",
"C": "-12.74317",
"D": "9.55738"
} | A | 12.74317 | Excess OH⁻ moles=0.10×(87−25)/1000=0.006200 mol. Total volume=0.112 L, so [OH⁻]=0.055357 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.74317. | {
"A": "Correct. The worked calculation gives 12.74317.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.74317, not 25.48635.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.74317, not -12.74317.",
"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_008925 | 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 1.83 mol L⁻¹ and initially B is absent. At equilibrium, 58% of A has dissociated at constant volume. Find K_c. | {
"A": "-5.86297",
"B": "2.86297",
"C": "8.79446",
"D": "5.86297"
} | D | 5.86297 | Let α=0.58. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.83)(0.58)²/(1−0.58)=5.86297. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.86297, not -5.86297.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.86297, not 2.86297.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.86297, not 8.79... | [
"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_004787 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 11 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 11 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "-5.16746 A",
"B": "7.16746 A",
"C": "5.16746 A",
"D": "1.51675 A"
} | C | 5.16746 A | Series branch resistance=11+8=19 Ω. Parallel equivalent R_eq=(19×11)/(19+11)=6.96667 Ω. Total current I=V/R_eq=36/6.96667=5.16746 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.16746 A, not -5.16746 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.16746 A, not 7.16746 A.",
"C": "Correct. The worked calculation gives 5.16746 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002419 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, 7], [1, 0]]. | {
"A": "-7",
"B": "-9",
"C": "-10.5",
"D": "0.3"
} | A | -7 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(0)−(7)(1)=-7. | {
"A": "Correct. The worked calculation gives -7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -7, not -9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -7, not -10.5.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_007744 | 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 67 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "-16.75 mmol L⁻¹",
"B": "16.75 mmol L⁻¹",
"C": "18.75 mmol L⁻¹",
"D": "20.1 mmol L⁻¹"
} | B | 16.75 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=67/2^2=16.75 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16.75 mmol L⁻¹, not -16.75 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 16.75 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16.75 mmol L⁻¹, not 18.75 mmol L⁻¹.",
"D": "I... | [
"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_006546 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 16 kg is attached to an ideal spring of force constant 104 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.78446 s",
"B": "1.07845 s",
"C": "0.39223 s",
"D": "1.56893 s"
} | A | 0.78446 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(16/104)=0.78446 s. | {
"A": "Correct. The worked calculation gives 0.78446 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.78446 s, not 1.07845 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.78446 s, not 0.39223 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_003111 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-1+4i)/(3+9i). What is Re(z), the real part of z? | {
"A": "0.36667",
"B": "1.03667",
"C": "0.55",
"D": "-2.63333"
} | A | 0.36667 | Multiply numerator and denominator by the conjugate (3-9i). Then Re(z)=(ac+bd)/(c²+d²)=((-1)(3)+(4)(9))/(3²+(9)²)=0.36667. | {
"A": "Correct. The worked calculation gives 0.36667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36667, not 1.03667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.36667, not 0.55.",
"D": "Incorrect. Substituting the stated value... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004083 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 6 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": "55.68 N",
"B": "41.76 N",
"C": "27.84 N",
"D": "33.408 N"
} | C | 27.84 N | Net force=mg(sinθ−μcosθ)=6×10×(0.6−0.17×0.8)=27.84 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 27.84 N, not 55.68 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 27.84 N, not 41.76 N.",
"C": "Correct. The worked calculation gives 27.84 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001018 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=0x³ +5x² -3x+7. Evaluate f′(-2). | {
"A": "-23",
"B": "-21",
"C": "-27.6",
"D": "-18.4"
} | A | -23 | Differentiate: f′(x)=3(0)x²+2(5)x+(-3). At x=-2, f′(-2)=3(0)(-2)²+2(5)(-2)+(-3)=-23. | {
"A": "Correct. The worked calculation gives -23.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -23, not -21.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -23, not -27.6.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000985 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio -3. What is the sum of its first 5 terms? | {
"A": "-671",
"B": "670",
"C": "671",
"D": "68.1"
} | C | 671 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(-3^5−1)/(-3−1)=671. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 671, not -671.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 671, not 670.",
"C": "Correct. The worked calculation gives 671.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_006251 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 52 cm in front of a thin convex lens of focal length 22 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-1.26667",
"B": "-0.73333",
"C": "0.55",
"D": "0.73333"
} | D | 0.73333 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(52)(22)/(52−22)=38.13333 cm. Thus |m|=v/u=38.13333/52=0.73333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.73333, not -1.26667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.73333, not -0.73333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.73333, not 0.5... | [
"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_007803 | 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 39 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "0.60938 mmol L⁻¹",
"B": "-0.78125 mmol L⁻¹",
"C": "1.21875 mmol L⁻¹",
"D": "3.21875 mmol L⁻¹"
} | C | 1.21875 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=39/2^5=1.21875 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.21875 mmol L⁻¹, not 0.60938 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.21875 mmol L⁻¹, not -0.78125 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 1.21875 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_009243 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.00 V, transfers 3 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.0985 V",
"B": "2.0985 V",
"C": "0.82388 V",
"D": "-1.0985 V"
} | A | 1.0985 V | Apply the Nernst equation: E=1.00−(0.0591/3)(-5)=1.0985 V. | {
"A": "Correct. The worked calculation gives 1.0985 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0985 V, not 2.0985 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0985 V, not 0.82388 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_004415 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 3 kg and radius 2 m is acted on by a constant torque of 25 N m about its central axis. Find its angular acceleration. | {
"A": "1.16667 rad s⁻²",
"B": "5.16667 rad s⁻²",
"C": "4.16667 rad s⁻²",
"D": "7.16667 rad s⁻²"
} | C | 4.16667 rad s⁻² | For a solid disc, I=½MR²=½(3)(2)²=6 kg m². Using τ=Iα, α=25/6=4.16667 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.16667 rad s⁻², not 1.16667 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.16667 rad s⁻², not 5.16667 rad s⁻².",
"C": "Correct. The worked calculation gives 4.16667 rad s⁻².",
"D"... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007336 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 1 mol of gas at 281 K and 1.84 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "25.06306 L",
"B": "12.53153 L",
"C": "6.26577 L",
"D": "18.7973 L"
} | B | 12.53153 L | PV=nRT, so V=nRT/P=(1)(0.082057)(281)/(1.84)=12.53153 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.53153 L, not 25.06306 L.",
"B": "Correct. The worked calculation gives 12.53153 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.53153 L, not 6.26577 L.",
"D": "Incorrect. Substituting... | [
"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_007150 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 8 mol of gas at 500 K and 1.46 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "224.8137 L",
"B": "-224.8137 L",
"C": "226.8137 L",
"D": "449.6274 L"
} | A | 224.8137 L | PV=nRT, so V=nRT/P=(8)(0.082057)(500)/(1.46)=224.8137 L. | {
"A": "Correct. The worked calculation gives 224.8137 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 224.8137 L, not -224.8137 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 224.8137 L, not 226.8137 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_000839 | 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 12 terms? | {
"A": "91552734",
"B": "183105468",
"C": "274658202",
"D": "137329101"
} | B | 183105468 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=3(5^12−1)/(5−1)=183105468. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 183105468, not 91552734.",
"B": "Correct. The worked calculation gives 183105468.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 183105468, not 274658202.",
"D": "Incorrect. Substituting 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_003871 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 3 kg block initially moves at 11 m s⁻¹. A constant net force does 9 N of work over 17 m in the direction of motion. Find its final kinetic energy. | {
"A": "334.5 J",
"B": "336.5 J",
"C": "34.45 J",
"D": "335.5 J"
} | A | 334.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(3)(11)²+(9)(17)=334.5 J. | {
"A": "Correct. The worked calculation gives 334.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 334.5 J, not 336.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 334.5 J, not 34.45 J.",
"D": "Incorrect. Substituting the stated va... | [
"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_007780 | 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 94 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "0.73438 mmol L⁻¹",
"B": "1.10156 mmol L⁻¹",
"C": "1.46875 mmol L⁻¹",
"D": "1.73438 mmol L⁻¹"
} | A | 0.73438 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=94/2^7=0.73438 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 0.73438 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.73438 mmol L⁻¹, not 1.10156 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.73438 mmol L⁻¹, not 1.46875 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_004364 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 6 m is acted on by a constant torque of 17 N m about its central axis. Find its angular acceleration. | {
"A": "-0.86508 rad s⁻²",
"B": "0.13492 rad s⁻²",
"C": "0.10119 rad s⁻²",
"D": "-2.86508 rad s⁻²"
} | B | 0.13492 rad s⁻² | For a solid disc, I=½MR²=½(7)(6)²=126 kg m². Using τ=Iα, α=17/126=0.13492 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.13492 rad s⁻², not -0.86508 rad s⁻².",
"B": "Correct. The worked calculation gives 0.13492 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.13492 rad s⁻², not 0.10119 rad s⁻².",
"D... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002755 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, 7, -1) and v=(6, 6, 0), calculate u·v. | {
"A": "50",
"B": "49",
"C": "48",
"D": "72"
} | C | 48 | The dot product is the sum of corresponding component products: (1)(6)+(7)(6)+(-1)(0)=48. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 48, not 50.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 48, not 49.",
"C": "Correct. The worked calculation gives 48.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002504 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, -1], [7, -5]]. | {
"A": "-9.75",
"B": "-16",
"C": "-6.5",
"D": "-13"
} | D | -13 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(-5)−(-1)(7)=-13. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -13, not -9.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -13, not -16.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -13, not -6.5.",
"D": "Correct... | [
"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_005216 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +8 μC and +5 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "75.46939 N",
"B": "146.93878 N",
"C": "58.77551 N",
"D": "73.46939 N"
} | D | 73.46939 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(8×10⁻⁶)(5×10⁻⁶)/(7×10⁻²)²=73.46939 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 73.46939 N, not 75.46939 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 73.46939 N, not 146.93878 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 73.46... | [
"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 |
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