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_008789 | 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 1.52 mol L⁻¹ and initially B is absent. At equilibrium, 54% of A has dissociated at constant volume. Find K_c. | {
"A": "5.78129",
"B": "7.70838",
"C": "1.9271",
"D": "3.85419"
} | D | 3.85419 | Let α=0.54. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.52)(0.54)²/(1−0.54)=3.85419. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.85419, not 5.78129.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.85419, not 7.70838.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.85419, not 1.927... | [
"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_009773 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(OH)_5]^+3, each OH ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "5",
"B": "8",
"C": "11",
"D": "6"
} | B | 8 | Let the formal oxidation state of Ni be x. Charge balance gives x+(5)(−1)=+3; hence x=3+5=+8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 5.",
"B": "Correct. The worked calculation gives 8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 11.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003600 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 12 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "12.03104 m",
"B": "11.03104 m",
"C": "-11.03104 m",
"D": "9.03104 m"
} | B | 11.03104 m | Range R=u²sin(2θ)/g. Substituting u=12, θ=25° and g=10 gives R=(12)²sin(50°)/10=11.03104 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.03104 m, not 12.03104 m.",
"B": "Correct. The worked calculation gives 11.03104 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.03104 m, not -11.03104 m.",
"D": "Incorrect. Substituti... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009676 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(OH)_4]^+1, each OH ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "2",
"B": "7",
"C": "8",
"D": "5"
} | D | 5 | Let the formal oxidation state of Mn be x. Charge balance gives x+(4)(−1)=+1; hence x=1+4=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 8.",
"D": "Correct. The worked ca... | [
"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_006908 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 19 mol H₂ and 7 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "14 mol",
"B": "13 mol",
"C": "12 mol",
"D": "15 mol"
} | A | 14 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 19 mol H₂O; O₂ can produce 14 mol H₂O. The limiting condition is O₂; product=14 mol. | {
"A": "Correct. The worked calculation gives 14 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14 mol, not 13 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14 mol, not 12 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_002217 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 3 blue and 7 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.03896",
"B": "3.38961",
"C": "0.38961",
"D": "-0.38961"
} | C | 0.38961 | Favourable pairs = C(12,2)+C(3,2)+C(7,2)=90. Total pairs=C(22,2)=231. Therefore P=90/231=0.38961. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.38961, not 1.03896.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.38961, not 3.38961.",
"C": "Correct. The worked calculation gives 0.38961.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009543 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_7H_2N_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "-8",
"B": "9",
"C": "8",
"D": "6"
} | C | 8 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+2−2−0)/2=8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not -8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 9.",
"C": "Correct. The worked calculation gives 8.",
"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_006194 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 70 cm in front of a thin convex lens of focal length 15 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.20455",
"B": "0.27273",
"C": "-1.72727",
"D": "0.54545"
} | B | 0.27273 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(70)(15)/(70−15)=19.09091 cm. Thus |m|=v/u=19.09091/70=0.27273. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.27273, not 0.20455.",
"B": "Correct. The worked calculation gives 0.27273.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.27273, not -1.72727.",
"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_001079 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ +6x² -6x+7. Evaluate f′(4). | {
"A": "175.5",
"B": "233",
"C": "234",
"D": "-234"
} | C | 234 | Differentiate: f′(x)=3(4)x²+2(6)x+(-6). At x=4, f′(4)=3(4)(4)²+2(6)(4)+(-6)=234. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 234, not 175.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 234, not 233.",
"C": "Correct. The worked calculation gives 234.",
"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_009307 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.62 V, transfers 1 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.2654 V",
"B": "3.2654 V",
"C": "-0.7346 V",
"D": "-2.7346 V"
} | A | 0.2654 V | Apply the Nernst equation: E=0.62−(0.0591/1)(6)=0.2654 V. | {
"A": "Correct. The worked calculation gives 0.2654 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.2654 V, not 3.2654 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.2654 V, not -0.7346 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_003910 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block initially moves at 8 m s⁻¹. A constant net force does 20 N of work over 2 m in the direction of motion. Find its final kinetic energy. | {
"A": "624 J",
"B": "519 J",
"C": "780 J",
"D": "520 J"
} | D | 520 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(15)(8)²+(20)(2)=520 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 520 J, not 624 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 520 J, not 519 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 520 J, not 780 J.",
"D":... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008867 | 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 0.53 mol L⁻¹ and initially B is absent. At equilibrium, 61% of A has dissociated at constant volume. Find K_c. | {
"A": "3.0227",
"B": "2.0227",
"C": "4.04539",
"D": "3.03405"
} | B | 2.0227 | Let α=0.61. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.53)(0.61)²/(1−0.61)=2.0227. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.0227, not 3.0227.",
"B": "Correct. The worked calculation gives 2.0227.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.0227, not 4.04539.",
"D": "Incorrect. Substituting the stated values... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002220 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 11 blue and 9 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.52717",
"B": "-0.64855",
"C": "0.35145",
"D": "3.35145"
} | C | 0.35145 | Favourable pairs = C(4,2)+C(11,2)+C(9,2)=97. Total pairs=C(24,2)=276. Therefore P=97/276=0.35145. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35145, not 0.52717.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35145, not -0.64855.",
"C": "Correct. The worked calculation gives 0.35145.",
"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_009038 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.02 V, transfers 2 electrons, and has reaction quotient Q=10^-4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.5691 V",
"B": "1.1382 V",
"C": "0.1382 V",
"D": "0.85365 V"
} | B | 1.1382 V | Apply the Nernst equation: E=1.02−(0.0591/2)(-4)=1.1382 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.1382 V, not 0.5691 V.",
"B": "Correct. The worked calculation gives 1.1382 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1382 V, not 0.1382 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_008828 | 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 1.27 mol L⁻¹ and initially B is absent. At equilibrium, 37% of A has dissociated at constant volume. Find K_c. | {
"A": "1.10389",
"B": "1.65584",
"C": "-0.89611",
"D": "4.10389"
} | A | 1.10389 | Let α=0.37. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.27)(0.37)²/(1−0.37)=1.10389. | {
"A": "Correct. The worked calculation gives 1.10389.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.10389, not 1.65584.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.10389, not -0.89611.",
"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_005172 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +4 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "112.5 N",
"B": "111.5 N",
"C": "114.5 N",
"D": "12.25 N"
} | A | 112.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(4×10⁻⁶)/(4×10⁻²)²=112.5 N. | {
"A": "Correct. The worked calculation gives 112.5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 112.5 N, not 111.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 112.5 N, not 114.5 N.",
"D": "Incorrect. Substituting the stated va... | [
"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_007688 | 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 29 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "4.25 mmol L⁻¹",
"B": "7.25 mmol L⁻¹",
"C": "3.625 mmol L⁻¹",
"D": "-7.25 mmol L⁻¹"
} | B | 7.25 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=29/2^2=7.25 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.25 mmol L⁻¹, not 4.25 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 7.25 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.25 mmol L⁻¹, not 3.625 mmol L⁻¹.",
"D": "Incorr... | [
"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_001217 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-2x³ -6x² -1x+7. Evaluate f′(5). | {
"A": "-20.1",
"B": "-211",
"C": "-209",
"D": "-168.8"
} | B | -211 | Differentiate: f′(x)=3(-2)x²+2(-6)x+(-1). At x=5, f′(5)=3(-2)(5)²+2(-6)(5)+(-1)=-211. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -211, not -20.1.",
"B": "Correct. The worked calculation gives -211.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -211, not -209.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_008489 | 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 1.41 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.7332 K",
"B": "3.7332 K",
"C": "1.0998 K",
"D": "-0.7332 K"
} | A | 0.7332 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.52×1.41=0.7332 K. | {
"A": "Correct. The worked calculation gives 0.7332 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7332 K, not 3.7332 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7332 K, not 1.0998 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_009585 | 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_5H_8N_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "-3",
"B": "3",
"C": "6",
"D": "1"
} | B | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×5+2+2−8−0)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not -3.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 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_002560 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, -1], [6, 2]]. | {
"A": "24",
"B": "12",
"C": "48",
"D": "36"
} | A | 24 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(2)−(-1)(6)=24. | {
"A": "Correct. The worked calculation gives 24.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24, not 12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24, not 48.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003147 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(10+8i)/(5+9i). What is Re(z), the real part of z? | {
"A": "0.86321",
"B": "2.15094",
"C": "1.15094",
"D": "4.15094"
} | C | 1.15094 | Multiply numerator and denominator by the conjugate (5-9i). Then Re(z)=(ac+bd)/(c²+d²)=((10)(5)+(8)(9))/(5²+(9)²)=1.15094. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.15094, not 0.86321.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.15094, not 2.15094.",
"C": "Correct. The worked calculation gives 1.15094.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008961 | 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 1.12 mol L⁻¹ and initially B is absent. At equilibrium, 54% of A has dissociated at constant volume. Find K_c. | {
"A": "2.83993",
"B": "2.12995",
"C": "-0.16007",
"D": "1.83993"
} | A | 2.83993 | Let α=0.54. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.12)(0.54)²/(1−0.54)=2.83993. | {
"A": "Correct. The worked calculation gives 2.83993.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.83993, not 2.12995.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.83993, not -0.16007.",
"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_008946 | 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 1.55 mol L⁻¹ and initially B is absent. At equilibrium, 45% of A has dissociated at constant volume. Find K_c. | {
"A": "1.22827",
"B": "0.28273",
"C": "5.28273",
"D": "2.28273"
} | D | 2.28273 | Let α=0.45. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.55)(0.45)²/(1−0.45)=2.28273. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.28273, not 1.22827.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.28273, not 0.28273.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.28273, not 5.282... | [
"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_002196 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 12 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": "2.31818",
"B": "0.47727",
"C": "-0.31818",
"D": "0.31818"
} | D | 0.31818 | Favourable pairs = C(9,2)+C(12,2)+C(12,2)=168. Total pairs=C(33,2)=528. Therefore P=168/528=0.31818. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31818, not 2.31818.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31818, not 0.47727.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31818, not -0.31... | [
"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_007229 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 12 mol of gas at 285 K and 2.39 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "116.42048 L",
"B": "140.90457 L",
"C": "117.42048 L",
"D": "119.42048 L"
} | C | 117.42048 L | PV=nRT, so V=nRT/P=(12)(0.082057)(285)/(2.39)=117.42048 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 117.42048 L, not 116.42048 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 117.42048 L, not 140.90457 L.",
"C": "Correct. The worked calculation gives 117.42048 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005718 | 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 4.7 atm at 250 K. What is its pressure at 406 K? | {
"A": "1.76328 atm",
"B": "6.6328 atm",
"C": "7.6328 atm",
"D": "4.6328 atm"
} | C | 7.6328 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.7)(406)/(250)=7.6328 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.6328 atm, not 1.76328 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.6328 atm, not 6.6328 atm.",
"C": "Correct. The worked calculation gives 7.6328 atm.",
"D": "Incorrect. Substituti... | [
"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_000783 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio -3. What is the sum of its first 11 terms? | {
"A": "88574",
"B": "44287",
"C": "44286",
"D": "53144.4"
} | B | 44287 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(-3^11−1)/(-3−1)=44287. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 44287, not 88574.",
"B": "Correct. The worked calculation gives 44287.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 44287, not 44286.",
"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_003202 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-7-14i)/(2+6i). What is Re(z), the real part of z? | {
"A": "-1.45",
"B": "-2.45",
"C": "-0.45",
"D": "-3.675"
} | B | -2.45 | Multiply numerator and denominator by the conjugate (2-6i). Then Re(z)=(ac+bd)/(c²+d²)=((-7)(2)+(-14)(6))/(2²+(6)²)=-2.45. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2.45, not -1.45.",
"B": "Correct. The worked calculation gives -2.45.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2.45, not -0.45.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_000446 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -7 and common difference 9. Find the sum of its first 33 terms. | {
"A": "3616.8",
"B": "3390.75",
"C": "4521",
"D": "6781.5"
} | C | 4521 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-7, d=9, n=33: Sₙ=33/2[2(-7)+(33−1)(9)]=4521. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4521, not 3616.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4521, not 3390.75.",
"C": "Correct. The worked calculation gives 4521.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_006924 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 46 mol H₂ and 16 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "48 mol",
"B": "64 mol",
"C": "32 mol",
"D": "31 mol"
} | C | 32 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 46 mol H₂O; O₂ can produce 32 mol H₂O. The limiting condition is O₂; product=32 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 32 mol, not 48 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 32 mol, not 64 mol.",
"C": "Correct. The worked calculation gives 32 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_001813 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 9 elements can be selected from a set of 16 distinct elements? | {
"A": "17160",
"B": "9152",
"C": "11440",
"D": "11438"
} | C | 11440 | Order does not matter, so the count is C(16,9)=16!/[9!(7)!]=11440. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11440, not 17160.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11440, not 9152.",
"C": "Correct. The worked calculation gives 11440.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_001353 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (4x² -1x +5) dx. | {
"A": "374.26667",
"B": "701.75",
"C": "467.83333",
"D": "350.875"
} | C | 467.83333 | An antiderivative is (4/3)x³+(-1/2)x²+(5)x. Evaluating between 0 and 7 gives (4/3)(7)³+(-1/2)(7)²+(5)(7)=467.83333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 467.83333, not 374.26667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 467.83333, not 701.75.",
"C": "Correct. The worked calculation gives 467.83333.",
"D": "Incorrect. Substituting the st... | [
"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_003942 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 6 m s⁻¹. A constant net force does 12 N of work over 3 m in the direction of motion. Find its final kinetic energy. | {
"A": "180 J",
"B": "-180 J",
"C": "179 J",
"D": "178 J"
} | A | 180 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(6)²+(12)(3)=180 J. | {
"A": "Correct. The worked calculation gives 180 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 180 J, not -180 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 180 J, not 179 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_002775 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, 4, -7) and v=(-3, 0, 2), calculate u·v. | {
"A": "-27",
"B": "-25",
"C": "-28",
"D": "-26"
} | D | -26 | The dot product is the sum of corresponding component products: (4)(-3)+(4)(0)+(-7)(2)=-26. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -26, not -27.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -26, not -25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -26, not -28.",
"D": "Correct. T... | [
"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_001858 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 12 elements can be selected from a set of 39 distinct elements? | {
"A": "3910797438",
"B": "3910797436",
"C": "1955398718",
"D": "-3910797436"
} | B | 3910797436 | Order does not matter, so the count is C(39,12)=39!/[12!(27)!]=3910797436. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3910797436, not 3910797438.",
"B": "Correct. The worked calculation gives 3910797436.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3910797436, not 1955398718.",
"D": "Incorrect. Substitutin... | [
"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_007759 | 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 16 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "1 mmol L⁻¹",
"B": "2 mmol L⁻¹",
"C": "4 mmol L⁻¹",
"D": "0 mmol L⁻¹"
} | B | 2 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=16/2^3=2 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2 mmol L⁻¹, not 1 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 2 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2 mmol L⁻¹, not 4 mmol L⁻¹.",
"D": "Incorrect. Substitutin... | [
"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_002155 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 3 blue and 8 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.03417",
"B": "0.34167",
"C": "-1.65833",
"D": "-2.65833"
} | B | 0.34167 | Favourable pairs = C(5,2)+C(3,2)+C(8,2)=41. Total pairs=C(16,2)=120. Therefore P=41/120=0.34167. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34167, not 1.03417.",
"B": "Correct. The worked calculation gives 0.34167.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34167, not -1.65833.",
"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_008990 | 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 mol L⁻¹ and initially B is absent. At equilibrium, 27% of A has dissociated at constant volume. Find K_c. | {
"A": "0.39945",
"B": "-0.60055",
"C": "-1.60055",
"D": "2.39945"
} | A | 0.39945 | Let α=0.27. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1)(0.27)²/(1−0.27)=0.39945. | {
"A": "Correct. The worked calculation gives 0.39945.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.39945, not -0.60055.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.39945, not -1.60055.",
"D": "Incorrect. Substituting the stated ... | [
"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_007895 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 46 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "1.4375 mmol L⁻¹",
"B": "-1.4375 mmol L⁻¹",
"C": "2.875 mmol L⁻¹",
"D": "2.15625 mmol L⁻¹"
} | A | 1.4375 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=46/2^5=1.4375 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 1.4375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4375 mmol L⁻¹, not -1.4375 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.4375 mmol L⁻¹, not 2.875 mmol L⁻¹.",
"D"... | [
"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_000472 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 11 and common difference 8. Find the sum of its first 13 terms. | {
"A": "767",
"B": "575.25",
"C": "765",
"D": "-767"
} | A | 767 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=11, d=8, n=13: Sₙ=13/2[2(11)+(13−1)(8)]=767. | {
"A": "Correct. The worked calculation gives 767.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 767, not 575.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 767, not 765.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_002966 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(0, -1, 6) and v=(9, 6, -2), calculate u·v. | {
"A": "-14.4",
"B": "-18",
"C": "-0.8",
"D": "-13.5"
} | B | -18 | The dot product is the sum of corresponding component products: (0)(9)+(-1)(6)+(6)(-2)=-18. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -18, not -14.4.",
"B": "Correct. The worked calculation gives -18.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -18, not -0.8.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_004786 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 9 Ω are connected in series; this combination is connected in parallel with a 20 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.52308 A",
"B": "0.76154 A",
"C": "1.07615 A",
"D": "1.76154 A"
} | B | 0.76154 A | Series branch resistance=4+9=13 Ω. Parallel equivalent R_eq=(13×20)/(13+20)=7.87879 Ω. Total current I=V/R_eq=6/7.87879=0.76154 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.76154 A, not 1.52308 A.",
"B": "Correct. The worked calculation gives 0.76154 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.76154 A, not 1.07615 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007889 | 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 98 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "3.45 mmol L⁻¹",
"B": "12.25 mmol L⁻¹",
"C": "24.5 mmol L⁻¹",
"D": "19.6 mmol L⁻¹"
} | C | 24.5 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=98/2^2=24.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24.5 mmol L⁻¹, not 3.45 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24.5 mmol L⁻¹, not 12.25 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 24.5 mmol L⁻¹.",
"D": "Incorr... | [
"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_000166 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 +10x -10=0, let its roots be α and β. What is α²+β²? | {
"A": "6.11111",
"B": "9.16667",
"C": "7.11111",
"D": "9.11111"
} | A | 6.11111 | By Vieta's relations, α+β = -10/6 and αβ = -10/6. Then α²+β²=(α+β)²−2αβ = (-10/6)²−2(-10/6) = 6.11111. | {
"A": "Correct. The worked calculation gives 6.11111.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.11111, not 9.16667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.11111, not 7.11111.",
"D": "Incorrect. Substituting the stated va... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000070 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 -2x -12=0, let its roots be α and β. What is α²+β²? | {
"A": "28",
"B": "21",
"C": "56",
"D": "3.8"
} | A | 28 | By Vieta's relations, α+β = 2/1 and αβ = -12/1. Then α²+β²=(α+β)²−2αβ = (2/1)²−2(-12/1) = 28. | {
"A": "Correct. The worked calculation gives 28.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28, not 21.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28, not 56.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_004355 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 12 kg and radius 6 m is acted on by a constant torque of 48 N m about its central axis. Find its angular acceleration. | {
"A": "1.02222 rad s⁻²",
"B": "3.22222 rad s⁻²",
"C": "0.22222 rad s⁻²",
"D": "0.16667 rad s⁻²"
} | C | 0.22222 rad s⁻² | For a solid disc, I=½MR²=½(12)(6)²=216 kg m². Using τ=Iα, α=48/216=0.22222 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.22222 rad s⁻², not 1.02222 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.22222 rad s⁻², not 3.22222 rad s⁻².",
"C": "Correct. The worked calculation gives 0.22222 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_007839 | 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 74 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "3.46875 mmol L⁻¹",
"B": "4.625 mmol L⁻¹",
"C": "1.625 mmol L⁻¹",
"D": "5.625 mmol L⁻¹"
} | B | 4.625 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=74/2^4=4.625 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.625 mmol L⁻¹, not 3.46875 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 4.625 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.625 mmol L⁻¹, not 1.625 mmol L⁻¹.",
"D": "... | [
"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_005052 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +9 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "31.4 N",
"B": "32.4 N",
"C": "-32.4 N",
"D": "4.24 N"
} | B | 32.4 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(9×10⁻⁶)/(10×10⁻²)²=32.4 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 32.4 N, not 31.4 N.",
"B": "Correct. The worked calculation gives 32.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 32.4 N, not -32.4 N.",
"D": "Incorrect. Substituting the stated values... | [
"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_004108 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 50 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.35. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "320 N",
"B": "240 N",
"C": "160 N",
"D": "120 N"
} | C | 160 N | Net force=mg(sinθ−μcosθ)=50×10×(0.6−0.35×0.8)=160 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 160 N, not 320 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 160 N, not 240 N.",
"C": "Correct. The worked calculation gives 160 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_002484 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, -8], [4, -8]]. | {
"A": "-32",
"B": "-64",
"C": "-33",
"D": "-38.4"
} | A | -32 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(-8)−(-8)(4)=-32. | {
"A": "Correct. The worked calculation gives -32.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -32, not -64.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -32, not -33.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_002843 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(0, 6, 9) and v=(0, 5, 6), calculate u·v. | {
"A": "9.4",
"B": "84",
"C": "86",
"D": "42"
} | B | 84 | The dot product is the sum of corresponding component products: (0)(0)+(6)(5)+(9)(6)=84. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 84, not 9.4.",
"B": "Correct. The worked calculation gives 84.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 84, not 86.",
"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_008426 | 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 0.94 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.9776 K",
"B": "-2.0224 K",
"C": "-1.0224 K",
"D": "0.9776 K"
} | D | 0.9776 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×0.94=0.9776 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9776 K, not -0.9776 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9776 K, not -2.0224 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9776 K, no... | [
"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_009969 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(OH)_5]^+0, each OH ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "7",
"B": "-5",
"C": "5",
"D": "8"
} | C | 5 | Let the formal oxidation state of Fe be x. Charge balance gives x+(5)(−1)=+0; hence x=0+5=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not -5.",
"C": "Correct. The worked calculation gives 5.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006993 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 5 mol H₂ and 6 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "5 mol",
"B": "6 mol",
"C": "8 mol",
"D": "7.5 mol"
} | A | 5 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 5 mol H₂O; O₂ can produce 12 mol H₂O. The limiting condition is H₂; product=5 mol. | {
"A": "Correct. The worked calculation gives 5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5 mol, not 6 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5 mol, not 8 mol.",
"D": "Incorrect. Substituting the stated values into ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004063 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 35 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.33. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "119.6 N",
"B": "-117.6 N",
"C": "117.6 N",
"D": "58.8 N"
} | C | 117.6 N | Net force=mg(sinθ−μcosθ)=35×10×(0.6−0.33×0.8)=117.6 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 117.6 N, not 119.6 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 117.6 N, not -117.6 N.",
"C": "Correct. The worked calculation gives 117.6 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_001921 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 2 elements can be selected from a set of 59 distinct elements? | {
"A": "855.5",
"B": "1711",
"C": "2566.5",
"D": "1712"
} | B | 1711 | Order does not matter, so the count is C(59,2)=59!/[2!(57)!]=1711. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1711, not 855.5.",
"B": "Correct. The worked calculation gives 1711.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1711, not 2566.5.",
"D": "Incorrect. Substituting the stated values into th... | [
"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_003341 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 102 m s⁻¹ at 70° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "666.75623 m",
"B": "501.56717 m",
"C": "802.50747 m",
"D": "668.75623 m"
} | D | 668.75623 m | Range R=u²sin(2θ)/g. Substituting u=102, θ=70° and g=10 gives R=(102)²sin(140°)/10=668.75623 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 668.75623 m, not 666.75623 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 668.75623 m, not 501.56717 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 66... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007358 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 98 mL of 0.10 M HCl is mixed with 72 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.81548",
"B": "3.81548",
"C": "1.81548",
"D": "0.81548"
} | C | 1.81548 | Excess H⁺ moles=0.10×(98−72)/1000=0.002600 mol. Total volume=0.170 L, so [H⁺]=0.015294 M and pH=−log₁₀[H⁺]=1.81548. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.81548, not 2.81548.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.81548, not 3.81548.",
"C": "Correct. The worked calculation gives 1.81548.",
"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_002922 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-5, -3, -6) and v=(1, -6, 9), calculate u·v. | {
"A": "-82",
"B": "-40",
"C": "41",
"D": "-41"
} | D | -41 | The dot product is the sum of corresponding component products: (-5)(1)+(-3)(-6)+(-6)(9)=-41. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -41, not -82.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -41, not -40.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -41, not 41.",
"D": "Correct. Th... | [
"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_007622 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 65 mL of 0.10 M HCl is mixed with 50 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "0.88461",
"B": "0.9423",
"C": "1.88461",
"D": "-1.11539"
} | C | 1.88461 | Excess H⁺ moles=0.10×(65−50)/1000=0.001500 mol. Total volume=0.115 L, so [H⁺]=0.013043 M and pH=−log₁₀[H⁺]=1.88461. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.88461, not 0.88461.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.88461, not 0.9423.",
"C": "Correct. The worked calculation gives 1.88461.",
"D": "Incorrect. Substituting the stated val... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003018 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(3-7i)/(1+7i). What is Re(z), the real part of z? | {
"A": "-1.92",
"B": "-0.46",
"C": "-3.92",
"D": "-0.92"
} | D | -0.92 | Multiply numerator and denominator by the conjugate (1-7i). Then Re(z)=(ac+bd)/(c²+d²)=((3)(1)+(-7)(7))/(1²+(7)²)=-0.92. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.92, not -1.92.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.92, not -0.46.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.92, not -3.92.",
"D":... | [
"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_008600 | 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 1.48 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "3.03104 K",
"B": "2.03104 K",
"C": "1.3031 K",
"D": "1.03104 K"
} | A | 3.03104 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.512×1.48=3.03104 K. | {
"A": "Correct. The worked calculation gives 3.03104 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.03104 K, not 2.03104 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.03104 K, not 1.3031 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_005612 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 38 μF capacitor is charged to a potential difference of 31 V. Calculate the energy stored, expressed in μJ. | {
"A": "36518 μJ",
"B": "18259 μJ",
"C": "14607.2 μJ",
"D": "18258 μJ"
} | B | 18259 μJ | U=½CV². Since C=38 μF, U in μJ is ½×38×(31)²=18259 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18259 μJ, not 36518 μJ.",
"B": "Correct. The worked calculation gives 18259 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18259 μJ, not 14607.2 μJ.",
"D": "Incorrect. Substituting the st... | [
"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_003019 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-9-6i)/(7+5i). What is Re(z), the real part of z? | {
"A": "-4.25676",
"B": "-0.62838",
"C": "-2.25676",
"D": "-1.25676"
} | D | -1.25676 | Multiply numerator and denominator by the conjugate (7-5i). Then Re(z)=(ac+bd)/(c²+d²)=((-9)(7)+(-6)(5))/(7²+(5)²)=-1.25676. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.25676, not -4.25676.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.25676, not -0.62838.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.25676, not ... | [
"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_004642 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 11 kg and radius 6 m is acted on by a constant torque of 5 N m about its central axis. Find its angular acceleration. | {
"A": "0.02525 rad s⁻²",
"B": "0.01263 rad s⁻²",
"C": "-2.97475 rad s⁻²",
"D": "1.00253 rad s⁻²"
} | A | 0.02525 rad s⁻² | For a solid disc, I=½MR²=½(11)(6)²=198 kg m². Using τ=Iα, α=5/198=0.02525 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.02525 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.02525 rad s⁻², not 0.01263 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.02525 rad s⁻², not -2.97475 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_006684 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 6 mol H₂ and 27 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "4.5 mol",
"B": "-6 mol",
"C": "6 mol",
"D": "9 mol"
} | C | 6 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 6 mol H₂O; O₂ can produce 54 mol H₂O. The limiting condition is H₂; product=6 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 4.5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not -6 mol.",
"C": "Correct. The worked calculation gives 6 mol.",
"D": "Incorrect. Substituting the stated values in... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004743 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 12 Ω are connected in series; this combination is connected in parallel with a 3 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.5625 A",
"B": "3.5625 A",
"C": "-3.5625 A",
"D": "1.35625 A"
} | B | 3.5625 A | Series branch resistance=4+12=16 Ω. Parallel equivalent R_eq=(16×3)/(16+3)=2.52632 Ω. Total current I=V/R_eq=9/2.52632=3.5625 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.5625 A, not 1.5625 A.",
"B": "Correct. The worked calculation gives 3.5625 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.5625 A, not -3.5625 A.",
"D": "Incorrect. Substituting the sta... | [
"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_008385 | 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 1.52 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "5.56 K",
"B": "4.56 K",
"C": "2.28 K",
"D": "6.84 K"
} | B | 4.56 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×1.0×1.52=4.56 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.56 K, not 5.56 K.",
"B": "Correct. The worked calculation gives 4.56 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.56 K, not 2.28 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_002743 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(2, 7, 9) and v=(-2, 3, 0), calculate u·v. | {
"A": "16",
"B": "8.5",
"C": "-17",
"D": "17"
} | D | 17 | The dot product is the sum of corresponding component products: (2)(-2)+(7)(3)+(9)(0)=17. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 17, not 16.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17, not 8.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17, not -17.",
"D": "Correct. The w... | [
"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_009441 | 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_13H_7N_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "9",
"B": "11",
"C": "13",
"D": "14"
} | B | 11 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×13+2+1−7−0)/2=11. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11, not 9.",
"B": "Correct. The worked calculation gives 11.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11, not 13.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008259 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 8 A for 22650 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": "59.61762 g",
"B": "44.71321 g",
"C": "-59.61762 g",
"D": "29.80881 g"
} | A | 59.61762 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×8×22650/(2×96500)=59.61762 g. | {
"A": "Correct. The worked calculation gives 59.61762 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 59.61762 g, not 44.71321 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 59.61762 g, not -59.61762 g.",
"D": "Incorrect. Substituti... | [
"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_003371 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 108 m s⁻¹ at 18° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1028.38908 m",
"B": "684.59272 m",
"C": "685.59272 m",
"D": "69.55927 m"
} | C | 685.59272 m | Range R=u²sin(2θ)/g. Substituting u=108, θ=18° and g=10 gives R=(108)²sin(36°)/10=685.59272 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 685.59272 m, not 1028.38908 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 685.59272 m, not 684.59272 m.",
"C": "Correct. The worked calculation gives 685.59272 m.",
"D": "Incorrect. Subst... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008291 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 9 A for 12495 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "-36.99944 g",
"B": "36.99944 g",
"C": "34.99944 g",
"D": "18.49972 g"
} | B | 36.99944 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×9×12495/(2×96500)=36.99944 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 36.99944 g, not -36.99944 g.",
"B": "Correct. The worked calculation gives 36.99944 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 36.99944 g, not 34.99944 g.",
"D": "Incorrect. Substituti... | [
"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_003945 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 9 m s⁻¹. A constant net force does 25 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "449.25 J",
"B": "600 J",
"C": "479.2 J",
"D": "599 J"
} | D | 599 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(9)²+(25)(11)=599 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 599 J, not 449.25 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 599 J, not 600 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 599 J, not 479.2 J.",
... | [
"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_007454 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 19 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": "12.55137",
"B": "9.41353",
"C": "9.55137",
"D": "15.55137"
} | A | 12.55137 | Excess OH⁻ moles=0.10×(40−19)/1000=0.002100 mol. Total volume=0.059 L, so [OH⁻]=0.035593 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.55137. | {
"A": "Correct. The worked calculation gives 12.55137.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.55137, not 9.41353.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.55137, not 9.55137.",
"D": "Incorrect. Substituting the stated... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006314 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 84 cm in front of a thin convex lens of focal length 20 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.3125",
"B": "-1.6875",
"C": "2.3125",
"D": "0.15625"
} | A | 0.3125 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(84)(20)/(84−20)=26.25 cm. Thus |m|=v/u=26.25/84=0.3125. | {
"A": "Correct. The worked calculation gives 0.3125.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3125, not -1.6875.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3125, not 2.3125.",
"D": "Incorrect. Substituting the stated values... | [
"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_007022 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 6 mol of gas at 235 K and 2.56 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "44.19546 L",
"B": "-45.19546 L",
"C": "33.89659 L",
"D": "45.19546 L"
} | D | 45.19546 L | PV=nRT, so V=nRT/P=(6)(0.082057)(235)/(2.56)=45.19546 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45.19546 L, not 44.19546 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 45.19546 L, not -45.19546 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 45.19... | [
"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_005665 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 79 μF capacitor is charged to a potential difference of 32 V. Calculate the energy stored, expressed in μJ. | {
"A": "40447 μJ",
"B": "40448 μJ",
"C": "20224 μJ",
"D": "40450 μJ"
} | B | 40448 μJ | U=½CV². Since C=79 μF, U in μJ is ½×79×(32)²=40448 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 40448 μJ, not 40447 μJ.",
"B": "Correct. The worked calculation gives 40448 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 40448 μJ, not 20224 μJ.",
"D": "Incorrect. Substituting the stat... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001127 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ -9x² -4x+7. Evaluate f′(2). | {
"A": "19",
"B": "30",
"C": "20",
"D": "-20"
} | C | 20 | Differentiate: f′(x)=3(5)x²+2(-9)x+(-4). At x=2, f′(2)=3(5)(2)²+2(-9)(2)+(-4)=20. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20, not 19.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20, not 30.",
"C": "Correct. The worked calculation gives 20.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_005963 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.7 atm at 383 K. What is its pressure at 723 K? | {
"A": "-1.67859 atm",
"B": "1.13214 atm",
"C": "1.32141 atm",
"D": "-1.32141 atm"
} | C | 1.32141 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.7)(723)/(383)=1.32141 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.32141 atm, not -1.67859 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.32141 atm, not 1.13214 atm.",
"C": "Correct. The worked calculation gives 1.32141 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001254 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=0x³ -5x² +4x+7. Evaluate f′(-3). | {
"A": "34",
"B": "27.2",
"C": "36",
"D": "17"
} | A | 34 | Differentiate: f′(x)=3(0)x²+2(-5)x+(4). At x=-3, f′(-3)=3(0)(-3)²+2(-5)(-3)+(4)=34. | {
"A": "Correct. The worked calculation gives 34.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 34, not 27.2.",
"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_002238 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 7 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": "2.38961",
"B": "-1.61039",
"C": "0.38961",
"D": "-0.61039"
} | C | 0.38961 | Favourable pairs = C(3,2)+C(7,2)+C(12,2)=90. Total pairs=C(22,2)=231. Therefore P=90/231=0.38961. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.38961, not 2.38961.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.38961, not -1.61039.",
"C": "Correct. The worked calculation gives 0.38961.",
"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_003352 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 104 m s⁻¹ at 50° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1067.16807 m",
"B": "1065.16807 m",
"C": "798.87605 m",
"D": "1066.16807 m"
} | B | 1065.16807 m | Range R=u²sin(2θ)/g. Substituting u=104, θ=50° and g=10 gives R=(104)²sin(100°)/10=1065.16807 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1065.16807 m, not 1067.16807 m.",
"B": "Correct. The worked calculation gives 1065.16807 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1065.16807 m, not 798.87605 m.",
"D": "Incorrect. Su... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001893 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 68 distinct elements? | {
"A": "3696004884",
"B": "8870411721.6",
"C": "7392009768",
"D": "739200977.8"
} | C | 7392009768 | Order does not matter, so the count is C(68,8)=68!/[8!(60)!]=7392009768. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7392009768, not 3696004884.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7392009768, not 8870411721.6.",
"C": "Correct. The worked calculation gives 7392009768.",
"D": "Incorrect. Substitut... | [
"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_003499 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 56 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "313.6 m",
"B": "311.6 m",
"C": "312.6 m",
"D": "32.36 m"
} | A | 313.6 m | Range R=u²sin(2θ)/g. Substituting u=56, θ=45° and g=10 gives R=(56)²sin(90°)/10=313.6 m. | {
"A": "Correct. The worked calculation gives 313.6 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 313.6 m, not 311.6 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 313.6 m, not 312.6 m.",
"D": "Incorrect. Substituting the stated va... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008556 | 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 0.4 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.312 K",
"B": "1.624 K",
"C": "-0.376 K",
"D": "0.624 K"
} | D | 0.624 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.52×0.4=0.624 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.624 K, not 0.312 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.624 K, not 1.624 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.624 K, not -0.37... | [
"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_000228 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -14x -9=0, let its roots be α and β. What is α²+β²? | {
"A": "69.6",
"B": "58",
"C": "-58",
"D": "116"
} | B | 58 | By Vieta's relations, α+β = 14/2 and αβ = -9/2. Then α²+β²=(α+β)²−2αβ = (14/2)²−2(-9/2) = 58. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 58, not 69.6.",
"B": "Correct. The worked calculation gives 58.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 58, not -58.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_002465 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 5], [2, 6]]. | {
"A": "5",
"B": "1.8",
"C": "8",
"D": "-8"
} | C | 8 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(6)−(5)(2)=8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 1.8.",
"C": "Correct. The worked calculation gives 8.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005826 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2 atm at 310 K. What is its pressure at 784 K? | {
"A": "5.05806 atm",
"B": "3.79355 atm",
"C": "2.05806 atm",
"D": "4.05806 atm"
} | A | 5.05806 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2)(784)/(310)=5.05806 atm. | {
"A": "Correct. The worked calculation gives 5.05806 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.05806 atm, not 3.79355 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.05806 atm, not 2.05806 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006422 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 17 kg is attached to an ideal spring of force constant 136 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.70711 s",
"B": "3.70711 s",
"C": "1.41421 s",
"D": "0.35355 s"
} | A | 0.70711 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(17/136)=0.70711 s. | {
"A": "Correct. The worked calculation gives 0.70711 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.70711 s, not 3.70711 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.70711 s, not 1.41421 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_007823 | 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 55 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "1.02148 mmol L⁻¹",
"B": "0.21484 mmol L⁻¹",
"C": "-0.78516 mmol L⁻¹",
"D": "0.10742 mmol L⁻¹"
} | B | 0.21484 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=55/2^8=0.21484 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.21484 mmol L⁻¹, not 1.02148 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.21484 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.21484 mmol L⁻¹, not -0.78516 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_000393 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -2 and common difference 11. Find the sum of its first 19 terms. | {
"A": "185.3",
"B": "921.5",
"C": "2211.6",
"D": "1843"
} | D | 1843 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-2, d=11, n=19: Sₙ=19/2[2(-2)+(19−1)(11)]=1843. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1843, not 185.3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1843, not 921.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1843, not 2211.6.",
"D": "... | [
"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_006237 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 32 cm in front of a thin convex lens of focal length 17 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.7",
"B": "1.13333",
"C": "1.11333",
"D": "-0.86667"
} | B | 1.13333 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(32)(17)/(32−17)=36.26667 cm. Thus |m|=v/u=36.26667/32=1.13333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.13333, not 1.7.",
"B": "Correct. The worked calculation gives 1.13333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.13333, not 1.11333.",
"D": "Incorrect. Substituting the stated values... | [
"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_009301 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.99 V, transfers 3 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.9112 V",
"B": "1.3668 V",
"C": "-2.0888 V",
"D": "2.9112 V"
} | A | 0.9112 V | Apply the Nernst equation: E=0.99−(0.0591/3)(4)=0.9112 V. | {
"A": "Correct. The worked calculation gives 0.9112 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9112 V, not 1.3668 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9112 V, not -2.0888 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_005091 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +8 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "23.80165 N",
"B": "47.60331 N",
"C": "22.80165 N",
"D": "21.80165 N"
} | A | 23.80165 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(8×10⁻⁶)/(11×10⁻²)²=23.80165 N. | {
"A": "Correct. The worked calculation gives 23.80165 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23.80165 N, not 47.60331 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23.80165 N, not 22.80165 N.",
"D": "Incorrect. Substitutin... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008422 | 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 1.62 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": "4.48 K",
"B": "6.48 K",
"C": "4.86 K",
"D": "-6.48 K"
} | B | 6.48 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×1.0×1.62=6.48 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.48 K, not 4.48 K.",
"B": "Correct. The worked calculation gives 6.48 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.48 K, not 4.86 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_009942 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(Cl)_3]^+3, each Cl ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "-6",
"B": "8",
"C": "4.5",
"D": "6"
} | D | 6 | Let the formal oxidation state of Ni be x. Charge balance gives x+(3)(−1)=+3; hence x=3+3=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not -6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.5.",
"D": "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_002200 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 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": "3.34462",
"B": "1.03446",
"C": "0.34462",
"D": "0.25846"
} | C | 0.34462 | Favourable pairs = C(5,2)+C(9,2)+C(12,2)=112. Total pairs=C(26,2)=325. Therefore P=112/325=0.34462. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34462, not 3.34462.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34462, not 1.03446.",
"C": "Correct. The worked calculation gives 0.34462.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008812 | 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 1.86 mol L⁻¹ and initially B is absent. At equilibrium, 37% of A has dissociated at constant volume. Find K_c. | {
"A": "1.61672",
"B": "4.61672",
"C": "-0.38328",
"D": "3.23345"
} | A | 1.61672 | Let α=0.37. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.86)(0.37)²/(1−0.37)=1.61672. | {
"A": "Correct. The worked calculation gives 1.61672.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.61672, not 4.61672.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.61672, not -0.38328.",
"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 |
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