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_001210 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=2x³ +1x² +5x+7. Evaluate f′(2). | {
"A": "39.6",
"B": "33",
"C": "34",
"D": "35"
} | B | 33 | Differentiate: f′(x)=3(2)x²+2(1)x+(5). At x=2, f′(2)=3(2)(2)²+2(1)(2)+(5)=33. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33, not 39.6.",
"B": "Correct. The worked calculation gives 33.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 33, not 34.",
"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_000749 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio 3. What is the sum of its first 9 terms? | {
"A": "88569",
"B": "-59046",
"C": "5905.6",
"D": "59046"
} | D | 59046 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(3^9−1)/(3−1)=59046. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 59046, not 88569.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 59046, not -59046.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 59046, not 5905.6.",
"D... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005664 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 31 μF capacitor is charged to a potential difference of 4 V. Calculate the energy stored, expressed in μJ. | {
"A": "250 μJ",
"B": "246 μJ",
"C": "248 μJ",
"D": "249 μJ"
} | C | 248 μJ | U=½CV². Since C=31 μF, U in μJ is ½×31×(4)²=248 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 248 μJ, not 250 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 248 μJ, not 246 μJ.",
"C": "Correct. The worked calculation gives 248 μJ.",
"D": "Incorrect. Substituting the stated values ... | [
"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_001700 | 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 70 distinct elements? | {
"A": "65033528562",
"B": "65033528559",
"C": "65033528560",
"D": "130067057120"
} | C | 65033528560 | Order does not matter, so the count is C(70,9)=70!/[9!(61)!]=65033528560. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 65033528560, not 65033528562.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 65033528560, not 65033528559.",
"C": "Correct. The worked calculation gives 65033528560.",
"D": "Incorrect. Substi... | [
"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_001680 | 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 80 distinct elements? | {
"A": "2528",
"B": "3160",
"C": "3161",
"D": "3159"
} | B | 3160 | Order does not matter, so the count is C(80,2)=80!/[2!(78)!]=3160. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3160, not 2528.",
"B": "Correct. The worked calculation gives 3160.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3160, not 3161.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_006157 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 67 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": "0.34",
"B": "-1.66",
"C": "2.34",
"D": "-0.66"
} | A | 0.34 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(67)(17)/(67−17)=22.78 cm. Thus |m|=v/u=22.78/67=0.34. | {
"A": "Correct. The worked calculation gives 0.34.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34, not -1.66.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34, not 2.34.",
"D": "Incorrect. Substituting the stated values into the ... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008330 | 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 18291 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": "55.16221 g",
"B": "108.32442 g",
"C": "43.32977 g",
"D": "54.16221 g"
} | D | 54.16221 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×9×18291/(2×96500)=54.16221 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 54.16221 g, not 55.16221 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 54.16221 g, not 108.32442 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 54.16... | [
"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_008775 | 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 0.51 mol L⁻¹ and initially B is absent. At equilibrium, 25% of A has dissociated at constant volume. Find K_c. | {
"A": "1.17",
"B": "0.17",
"C": "0.1275",
"D": "0.255"
} | B | 0.17 | Let α=0.25. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.51)(0.25)²/(1−0.25)=0.17. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.17, not 1.17.",
"B": "Correct. The worked calculation gives 0.17.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.17, not 0.1275.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_004290 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 15 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": "50.4 N",
"B": "48.4 N",
"C": "-50.4 N",
"D": "40.32 N"
} | A | 50.4 N | Net force=mg(sinθ−μcosθ)=15×10×(0.6−0.33×0.8)=50.4 N. | {
"A": "Correct. The worked calculation gives 50.4 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 50.4 N, not 48.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 50.4 N, not -50.4 N.",
"D": "Incorrect. Substituting the stated values... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008845 | 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 1.57 mol L⁻¹ and initially B is absent. At equilibrium, 18% of A has dissociated at constant volume. Find K_c. | {
"A": "1.24814",
"B": "0.12407",
"C": "0.24814",
"D": "1.02481"
} | C | 0.24814 | Let α=0.18. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.57)(0.18)²/(1−0.18)=0.24814. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.24814, not 1.24814.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.24814, not 0.12407.",
"C": "Correct. The worked calculation gives 0.24814.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002085 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 9 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": "-2.64737",
"B": "-0.35263",
"C": "0.17632",
"D": "0.35263"
} | D | 0.35263 | Favourable pairs = C(3,2)+C(9,2)+C(8,2)=67. Total pairs=C(20,2)=190. Therefore P=67/190=0.35263. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35263, not -2.64737.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35263, not -0.35263.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35263, not 0.1... | [
"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_006490 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 10 kg is attached to an ideal spring of force constant 137 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.27017 s",
"B": "-2.45966 s",
"C": "3.54034 s",
"D": "0.54034 s"
} | D | 0.54034 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(10/137)=0.54034 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.54034 s, not 0.27017 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.54034 s, not -2.45966 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.54034 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000511 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 22 and common difference 8. Find the sum of its first 13 terms. | {
"A": "911",
"B": "92",
"C": "910",
"D": "728"
} | C | 910 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=22, d=8, n=13: Sₙ=13/2[2(22)+(13−1)(8)]=910. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 910, not 911.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 910, not 92.",
"C": "Correct. The worked calculation gives 910.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001249 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-1x³ -8x² -10x+7. Evaluate f′(-2). | {
"A": "10",
"B": "2",
"C": "11",
"D": "7.5"
} | A | 10 | Differentiate: f′(x)=3(-1)x²+2(-8)x+(-10). At x=-2, f′(-2)=3(-1)(-2)²+2(-8)(-2)+(-10)=10. | {
"A": "Correct. The worked calculation gives 10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 11.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_004071 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 18 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.39. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "41.472 N",
"B": "51.84 N",
"C": "52.84 N",
"D": "-51.84 N"
} | B | 51.84 N | Net force=mg(sinθ−μcosθ)=18×10×(0.6−0.39×0.8)=51.84 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 51.84 N, not 41.472 N.",
"B": "Correct. The worked calculation gives 51.84 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 51.84 N, not 52.84 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_007691 | 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 44 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "4.75 mmol L⁻¹",
"B": "2.75 mmol L⁻¹",
"C": "4.125 mmol L⁻¹",
"D": "3.75 mmol L⁻¹"
} | B | 2.75 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=44/2^4=2.75 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.75 mmol L⁻¹, not 4.75 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 2.75 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.75 mmol L⁻¹, not 4.125 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_009591 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_11H_4N_3X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "7",
"B": "12",
"C": "5",
"D": "10"
} | D | 10 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+3−4−3)/2=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 5.",
"D": "Correct. The worke... | [
"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_006865 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 9 mol H₂ and 35 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "6 mol",
"B": "9 mol",
"C": "6.75 mol",
"D": "8 mol"
} | B | 9 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 9 mol H₂O; O₂ can produce 70 mol H₂O. The limiting condition is H₂; product=9 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9 mol, not 6 mol.",
"B": "Correct. The worked calculation gives 9 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9 mol, not 6.75 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_006936 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 25 mol H₂ and 13 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "24 mol",
"B": "3.5 mol",
"C": "25 mol",
"D": "-25 mol"
} | C | 25 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 25 mol H₂O; O₂ can produce 26 mol H₂O. The limiting condition is H₂; product=25 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 25 mol, not 24 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 25 mol, not 3.5 mol.",
"C": "Correct. The worked calculation gives 25 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_000652 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 4 and common difference 5. Find the sum of its first 33 terms. | {
"A": "2770",
"B": "5544",
"C": "2773",
"D": "2772"
} | D | 2772 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=4, d=5, n=33: Sₙ=33/2[2(4)+(33−1)(5)]=2772. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2772, not 2770.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2772, not 5544.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2772, not 2773.",
"D": "Corr... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004371 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 9 kg and radius 6 m is acted on by a constant torque of 69 N m about its central axis. Find its angular acceleration. | {
"A": "-2.57407 rad s⁻²",
"B": "0.42593 rad s⁻²",
"C": "0.21296 rad s⁻²",
"D": "0.31944 rad s⁻²"
} | B | 0.42593 rad s⁻² | For a solid disc, I=½MR²=½(9)(6)²=162 kg m². Using τ=Iα, α=69/162=0.42593 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.42593 rad s⁻², not -2.57407 rad s⁻².",
"B": "Correct. The worked calculation gives 0.42593 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.42593 rad s⁻², not 0.21296 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_008091 | 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 27372 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": "121.57848 g",
"B": "81.05232 g",
"C": "60.78924 g",
"D": "80.05232 g"
} | B | 81.05232 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×9×27372/(2×96500)=81.05232 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 81.05232 g, not 121.57848 g.",
"B": "Correct. The worked calculation gives 81.05232 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 81.05232 g, not 60.78924 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_009987 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(CN)_5]^-4, each CN ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "1",
"B": "2",
"C": "-1",
"D": "0.75"
} | A | 1 | Let the formal oxidation state of Pd be x. Charge balance gives x+(5)(−1)=-4; hence x=-4+5=+1. | {
"A": "Correct. The worked calculation gives 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not -1.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002107 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 7 red, 8 blue and 9 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.30797",
"B": "-0.69203",
"C": "0.61594",
"D": "0.23098"
} | A | 0.30797 | Favourable pairs = C(7,2)+C(8,2)+C(9,2)=85. Total pairs=C(24,2)=276. Therefore P=85/276=0.30797. | {
"A": "Correct. The worked calculation gives 0.30797.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30797, not -0.69203.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30797, not 0.61594.",
"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_003437 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 91 m s⁻¹ at 65° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "317.1807 m",
"B": "634.3614 m",
"C": "635.3614 m",
"D": "-634.3614 m"
} | B | 634.3614 m | Range R=u²sin(2θ)/g. Substituting u=91, θ=65° and g=10 gives R=(91)²sin(130°)/10=634.3614 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 634.3614 m, not 317.1807 m.",
"B": "Correct. The worked calculation gives 634.3614 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 634.3614 m, not 635.3614 m.",
"D": "Incorrect. Substitutin... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001451 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (-2x² +3x +2) dx. | {
"A": "-6.8",
"B": "-93.6",
"C": "-78",
"D": "-77"
} | C | -78 | An antiderivative is (-2/3)x³+(3/2)x²+(2)x. Evaluating between 0 and 6 gives (-2/3)(6)³+(3/2)(6)²+(2)(6)=-78. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -78, not -6.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -78, not -93.6.",
"C": "Correct. The worked calculation gives -78.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_002335 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 9 blue and 9 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.15761",
"B": "0.47283",
"C": "0.31522",
"D": "1.03152"
} | C | 0.31522 | Favourable pairs = C(6,2)+C(9,2)+C(9,2)=87. Total pairs=C(24,2)=276. Therefore P=87/276=0.31522. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31522, not 0.15761.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31522, not 0.47283.",
"C": "Correct. The worked calculation gives 0.31522.",
"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_007804 | 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 72 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "2.25 mmol L⁻¹",
"B": "0.5625 mmol L⁻¹",
"C": "-0.875 mmol L⁻¹",
"D": "1.125 mmol L⁻¹"
} | D | 1.125 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=72/2^6=1.125 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.125 mmol L⁻¹, not 2.25 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.125 mmol L⁻¹, not 0.5625 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relat... | [
"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_005661 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 47 μF capacitor is charged to a potential difference of 18 V. Calculate the energy stored, expressed in μJ. | {
"A": "762.4 μJ",
"B": "5710.5 μJ",
"C": "7616 μJ",
"D": "7614 μJ"
} | D | 7614 μJ | U=½CV². Since C=47 μF, U in μJ is ½×47×(18)²=7614 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7614 μJ, not 762.4 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7614 μJ, not 5710.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7614 μJ, not 76... | [
"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_007884 | 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 40 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "1.03125 mmol L⁻¹",
"B": "-2.6875 mmol L⁻¹",
"C": "0.3125 mmol L⁻¹",
"D": "3.3125 mmol L⁻¹"
} | C | 0.3125 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=40/2^7=0.3125 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3125 mmol L⁻¹, not 1.03125 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3125 mmol L⁻¹, not -2.6875 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.3125 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_008261 | 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 6197 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "14.68015 g",
"B": "18.35018 g",
"C": "27.52528 g",
"D": "-18.35018 g"
} | B | 18.35018 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×9×6197/(2×96500)=18.35018 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18.35018 g, not 14.68015 g.",
"B": "Correct. The worked calculation gives 18.35018 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18.35018 g, not 27.52528 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005755 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.5 atm at 321 K. What is its pressure at 616 K? | {
"A": "8.63551 atm",
"B": "11.63551 atm",
"C": "9.63551 atm",
"D": "17.27103 atm"
} | A | 8.63551 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.5)(616)/(321)=8.63551 atm. | {
"A": "Correct. The worked calculation gives 8.63551 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.63551 atm, not 11.63551 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.63551 atm, not 9.63551 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_009635 | 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_6H_13N_1X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "2",
"B": "3",
"C": "-1",
"D": "0"
} | D | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+1−13−2)/2=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not -1.",
"D": "Correct. The worked c... | [
"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_009196 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.49 V, transfers 1 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.7855 V",
"B": "-1.7855 V",
"C": "0.7855 V",
"D": "2.67825 V"
} | A | 1.7855 V | Apply the Nernst equation: E=1.49−(0.0591/1)(-5)=1.7855 V. | {
"A": "Correct. The worked calculation gives 1.7855 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.7855 V, not -1.7855 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.7855 V, not 0.7855 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_002118 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 5 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.34632",
"B": "-0.65368",
"C": "2.34632",
"D": "1.34632"
} | A | 0.34632 | Favourable pairs = C(6,2)+C(5,2)+C(11,2)=80. Total pairs=C(22,2)=231. Therefore P=80/231=0.34632. | {
"A": "Correct. The worked calculation gives 0.34632.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34632, not -0.65368.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34632, not 2.34632.",
"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_007613 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 33 mL of 0.10 M HCl is mixed with 20 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-1.61033",
"B": "1.61033",
"C": "4.61033",
"D": "-1.38967"
} | B | 1.61033 | Excess H⁺ moles=0.10×(33−20)/1000=0.001300 mol. Total volume=0.053 L, so [H⁺]=0.024528 M and pH=−log₁₀[H⁺]=1.61033. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.61033, not -1.61033.",
"B": "Correct. The worked calculation gives 1.61033.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.61033, not 4.61033.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003693 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 3 kg block initially moves at 1 m s⁻¹. A constant net force does 25 N of work over 19 m in the direction of motion. Find its final kinetic energy. | {
"A": "953 J",
"B": "357.375 J",
"C": "571.8 J",
"D": "476.5 J"
} | D | 476.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(3)(1)²+(25)(19)=476.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 476.5 J, not 953 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 476.5 J, not 357.375 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 476.5 J, not 571.8... | [
"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_001729 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 6 elements can be selected from a set of 22 distinct elements? | {
"A": "37306.5",
"B": "-74613",
"C": "74613",
"D": "111919.5"
} | C | 74613 | Order does not matter, so the count is C(22,6)=22!/[6!(16)!]=74613. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 74613, not 37306.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 74613, not -74613.",
"C": "Correct. The worked calculation gives 74613.",
"D": "Incorrect. Substituting the stated values in... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001118 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-1x³ +2x² +10x+7. Evaluate f′(5). | {
"A": "-43",
"B": "-3.5",
"C": "-47",
"D": "-45"
} | D | -45 | Differentiate: f′(x)=3(-1)x²+2(2)x+(10). At x=5, f′(5)=3(-1)(5)²+2(2)(5)+(10)=-45. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -45, not -43.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -45, not -3.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -45, not -47.",
"D": "Correct. ... | [
"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_003210 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-12+7i)/(2+4i). What is Re(z), the real part of z? | {
"A": "0.2",
"B": "-1.8",
"C": "-0.8",
"D": "1.02"
} | A | 0.2 | Multiply numerator and denominator by the conjugate (2-4i). Then Re(z)=(ac+bd)/(c²+d²)=((-12)(2)+(7)(4))/(2²+(4)²)=0.2. | {
"A": "Correct. The worked calculation gives 0.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.2, not -1.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.2, not -0.8.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_004390 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 3 kg and radius 3 m is acted on by a constant torque of 100 N m about its central axis. Find its angular acceleration. | {
"A": "-7.40741 rad s⁻²",
"B": "14.81481 rad s⁻²",
"C": "7.40741 rad s⁻²",
"D": "9.40741 rad s⁻²"
} | C | 7.40741 rad s⁻² | For a solid disc, I=½MR²=½(3)(3)²=13.5 kg m². Using τ=Iα, α=100/13.5=7.40741 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.40741 rad s⁻², not -7.40741 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.40741 rad s⁻², not 14.81481 rad s⁻².",
"C": "Correct. The worked calculation gives 7.40741 rad s⁻².",
"... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003874 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 9 m s⁻¹. A constant net force does 19 N of work over 20 m in the direction of motion. Find its final kinetic energy. | {
"A": "588.75 J",
"B": "1177.5 J",
"C": "785 J",
"D": "786 J"
} | C | 785 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(9)²+(19)(20)=785 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 785 J, not 588.75 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 785 J, not 1177.5 J.",
"C": "Correct. The worked calculation gives 785 J.",
"D": "Incorrect. Substituting the stated values... | [
"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_006022 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 64 cm in front of a thin convex lens of focal length 16 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.33333",
"B": "-0.66667",
"C": "3.33333",
"D": "0.5"
} | A | 0.33333 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(64)(16)/(64−16)=21.33333 cm. Thus |m|=v/u=21.33333/64=0.33333. | {
"A": "Correct. The worked calculation gives 0.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not -0.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not 3.33333.",
"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_001270 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ -9x² -10x+7. Evaluate f′(4). | {
"A": "206",
"B": "205",
"C": "-206",
"D": "208"
} | A | 206 | Differentiate: f′(x)=3(6)x²+2(-9)x+(-10). At x=4, f′(4)=3(6)(4)²+2(-9)(4)+(-10)=206. | {
"A": "Correct. The worked calculation gives 206.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 206, not 205.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 206, not -206.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008070 | 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 6 A for 29553 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": "116.68076 g",
"B": "60.34038 g",
"C": "29.17019 g",
"D": "58.34038 g"
} | D | 58.34038 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×6×29553/(2×96500)=58.34038 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 58.34038 g, not 116.68076 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 58.34038 g, not 60.34038 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 58.34... | [
"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_004863 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 12 Ω are connected in series; this combination is connected in parallel with a 19 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "-3.15789 A",
"B": "1.15789 A",
"C": "2.15789 A",
"D": "3.15789 A"
} | D | 3.15789 A | Series branch resistance=7+12=19 Ω. Parallel equivalent R_eq=(19×19)/(19+19)=9.5 Ω. Total current I=V/R_eq=30/9.5=3.15789 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.15789 A, not -3.15789 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.15789 A, not 1.15789 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.15789 A... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007208 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 16 mol of gas at 638 K and 0.96 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "654.40458 L",
"B": "873.53943 L",
"C": "872.53943 L",
"D": "698.03155 L"
} | C | 872.53943 L | PV=nRT, so V=nRT/P=(16)(0.082057)(638)/(0.96)=872.53943 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 872.53943 L, not 654.40458 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 872.53943 L, not 873.53943 L.",
"C": "Correct. The worked calculation gives 872.53943 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_003026 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(9+6i)/(5+4i). What is Re(z), the real part of z? | {
"A": "3.36585",
"B": "1.68293",
"C": "2.52439",
"D": "4.68293"
} | B | 1.68293 | Multiply numerator and denominator by the conjugate (5-4i). Then Re(z)=(ac+bd)/(c²+d²)=((9)(5)+(6)(4))/(5²+(4)²)=1.68293. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.68293, not 3.36585.",
"B": "Correct. The worked calculation gives 1.68293.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.68293, not 2.52439.",
"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_008734 | 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 0.72 mol L⁻¹ and initially B is absent. At equilibrium, 41% of A has dissociated at constant volume. Find K_c. | {
"A": "0.82056",
"B": "1.82056",
"C": "-0.17944",
"D": "0.41028"
} | A | 0.82056 | Let α=0.41. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.72)(0.41)²/(1−0.41)=0.82056. | {
"A": "Correct. The worked calculation gives 0.82056.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.82056, not 1.82056.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.82056, not -0.17944.",
"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_003296 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(13-6i)/(2+3i). What is Re(z), the real part of z? | {
"A": "0.92308",
"B": "3.61538",
"C": "-2.38462",
"D": "0.61538"
} | D | 0.61538 | Multiply numerator and denominator by the conjugate (2-3i). Then Re(z)=(ac+bd)/(c²+d²)=((13)(2)+(-6)(3))/(2²+(3)²)=0.61538. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.61538, not 0.92308.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.61538, not 3.61538.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.61538, not -2.38... | [
"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_001215 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=0x³ -5x² +3x+7. Evaluate f′(3). | {
"A": "-27",
"B": "-26",
"C": "-29",
"D": "-13.5"
} | A | -27 | Differentiate: f′(x)=3(0)x²+2(-5)x+(3). At x=3, f′(3)=3(0)(3)²+2(-5)(3)+(3)=-27. | {
"A": "Correct. The worked calculation gives -27.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -27, not -26.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -27, not -29.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006324 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 19 cm in front of a thin convex lens of focal length 13 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "4.33333",
"B": "-0.83333",
"C": "2.16667",
"D": "5.16667"
} | C | 2.16667 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(19)(13)/(19−13)=41.16667 cm. Thus |m|=v/u=41.16667/19=2.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.16667, not 4.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.16667, not -0.83333.",
"C": "Correct. The worked calculation gives 2.16667.",
"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_003215 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(8+5i)/(8+10i). What is Re(z), the real part of z? | {
"A": "2.69512",
"B": "0.69512",
"C": "-0.30488",
"D": "1.04268"
} | B | 0.69512 | Multiply numerator and denominator by the conjugate (8-10i). Then Re(z)=(ac+bd)/(c²+d²)=((8)(8)+(5)(10))/(8²+(10)²)=0.69512. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.69512, not 2.69512.",
"B": "Correct. The worked calculation gives 0.69512.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.69512, not -0.30488.",
"D": "Incorrect. Substituting the stated v... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006923 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 3 mol H₂ and 2 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "6 mol",
"B": "5 mol",
"C": "3 mol",
"D": "-3 mol"
} | C | 3 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 3 mol H₂O; O₂ can produce 4 mol H₂O. The limiting condition is H₂; product=3 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3 mol, not 6 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3 mol, not 5 mol.",
"C": "Correct. The worked calculation gives 3 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_002612 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, -1], [3, -2]]. | {
"A": "-9",
"B": "-13.5",
"C": "0.1",
"D": "-6"
} | A | -9 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(-2)−(-1)(3)=-9. | {
"A": "Correct. The worked calculation gives -9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -9, not -13.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -9, not 0.1.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_007054 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 10 mol of gas at 279 K and 1.71 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "132.88247 L",
"B": "100.41186 L",
"C": "133.88247 L",
"D": "267.76495 L"
} | C | 133.88247 L | PV=nRT, so V=nRT/P=(10)(0.082057)(279)/(1.71)=133.88247 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 133.88247 L, not 132.88247 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 133.88247 L, not 100.41186 L.",
"C": "Correct. The worked calculation gives 133.88247 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_008561 | 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 1.63 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "2.66912 K",
"B": "-1.33088 K",
"C": "2.50368 K",
"D": "1.66912 K"
} | D | 1.66912 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×1.63=1.66912 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.66912 K, not 2.66912 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.66912 K, not -1.33088 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.66912 K... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001556 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (-3x² -2x +2) dx. | {
"A": "-168",
"B": "-140",
"C": "-70",
"D": "-210"
} | B | -140 | An antiderivative is (-3/3)x³+(-2/2)x²+(2)x. Evaluating between 0 and 5 gives (-3/3)(5)³+(-2/2)(5)²+(2)(5)=-140. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -140, not -168.",
"B": "Correct. The worked calculation gives -140.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -140, not -70.",
"D": "Incorrect. Substituting the stated values into the go... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002349 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, 0], [9, -5]]. | {
"A": "-46",
"B": "-45",
"C": "-43",
"D": "-36"
} | B | -45 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(-5)−(0)(9)=-45. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -45, not -46.",
"B": "Correct. The worked calculation gives -45.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -45, not -43.",
"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_007180 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 11 mol of gas at 245 K and 1.88 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "116.62958 L",
"B": "58.81479 L",
"C": "117.62958 L",
"D": "176.44437 L"
} | C | 117.62958 L | PV=nRT, so V=nRT/P=(11)(0.082057)(245)/(1.88)=117.62958 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 117.62958 L, not 116.62958 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 117.62958 L, not 58.81479 L.",
"C": "Correct. The worked calculation gives 117.62958 L.",
"D": "Incorrect. Substit... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006092 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 14 cm in front of a thin convex lens of focal length 5 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-2.44444",
"B": "1.11111",
"C": "0.55556",
"D": "0.83333"
} | C | 0.55556 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(14)(5)/(14−5)=7.77778 cm. Thus |m|=v/u=7.77778/14=0.55556. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.55556, not -2.44444.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.55556, not 1.11111.",
"C": "Correct. The worked calculation gives 0.55556.",
"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_007826 | 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 84 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "4.625 mmol L⁻¹",
"B": "5.625 mmol L⁻¹",
"C": "2.625 mmol L⁻¹",
"D": "1.3125 mmol L⁻¹"
} | C | 2.625 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=84/2^5=2.625 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.625 mmol L⁻¹, not 4.625 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.625 mmol L⁻¹, not 5.625 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 2.625 mmol L⁻¹.",
"D": "In... | [
"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_000542 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 16 and common difference 5. Find the sum of its first 10 terms. | {
"A": "288.75",
"B": "386",
"C": "385",
"D": "770"
} | C | 385 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=16, d=5, n=10: Sₙ=10/2[2(16)+(10−1)(5)]=385. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 385, not 288.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 385, not 386.",
"C": "Correct. The worked calculation gives 385.",
"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_001421 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (5x² +1x -4) dx. | {
"A": "49.33333",
"B": "74",
"C": "78.93333",
"D": "98.66667"
} | D | 98.66667 | An antiderivative is (5/3)x³+(1/2)x²+(-4)x. Evaluating between 0 and 4 gives (5/3)(4)³+(1/2)(4)²+(-4)(4)=98.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 98.66667, not 49.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 98.66667, not 74.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 98.66667, not 78.933... | [
"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_005592 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 43 μF capacitor is charged to a potential difference of 40 V. Calculate the energy stored, expressed in μJ. | {
"A": "-34400 μJ",
"B": "34398 μJ",
"C": "34400 μJ",
"D": "34402 μJ"
} | C | 34400 μJ | U=½CV². Since C=43 μF, U in μJ is ½×43×(40)²=34400 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 34400 μJ, not -34400 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 34400 μJ, not 34398 μJ.",
"C": "Correct. The worked calculation gives 34400 μJ.",
"D": "Incorrect. Substituting the sta... | [
"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_004156 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 47 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.28. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "174.72 N",
"B": "88.36 N",
"C": "176.72 N",
"D": "132.54 N"
} | C | 176.72 N | Net force=mg(sinθ−μcosθ)=47×10×(0.6−0.28×0.8)=176.72 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 176.72 N, not 174.72 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 176.72 N, not 88.36 N.",
"C": "Correct. The worked calculation gives 176.72 N.",
"D": "Incorrect. Substituting the state... | [
"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_009909 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(OH)_3]^-2, each OH ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "1",
"B": "1.5",
"C": "0.5",
"D": "3"
} | A | 1 | Let the formal oxidation state of Co be x. Charge balance gives x+(3)(−1)=-2; hence x=-2+3=+1. | {
"A": "Correct. The worked calculation gives 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.5.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004452 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 1 m is acted on by a constant torque of 96 N m about its central axis. Find its angular acceleration. | {
"A": "36 rad s⁻²",
"B": "3.4 rad s⁻²",
"C": "24 rad s⁻²",
"D": "48 rad s⁻²"
} | C | 24 rad s⁻² | For a solid disc, I=½MR²=½(8)(1)²=4 kg m². Using τ=Iα, α=96/4=24 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24 rad s⁻², not 36 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24 rad s⁻², not 3.4 rad s⁻².",
"C": "Correct. The worked calculation gives 24 rad s⁻².",
"D": "Incorrect. Substituti... | [
"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_006907 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 26 mol H₂ and 21 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "26 mol",
"B": "-26 mol",
"C": "24 mol",
"D": "13 mol"
} | A | 26 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 26 mol H₂O; O₂ can produce 42 mol H₂O. The limiting condition is H₂; product=26 mol. | {
"A": "Correct. The worked calculation gives 26 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not -26 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 24 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_009899 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(OH)_6]^+2, each OH ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "12",
"B": "4",
"C": "8",
"D": "11"
} | C | 8 | Let the formal oxidation state of Fe be x. Charge balance gives x+(6)(−1)=+2; hence x=2+6=+8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 12.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 4.",
"C": "Correct. The worked calculation gives 8.",
"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_001327 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-3x³ +10x² -11x+7. Evaluate f′(5). | {
"A": "-108.8",
"B": "136",
"C": "-136",
"D": "-272"
} | C | -136 | Differentiate: f′(x)=3(-3)x²+2(10)x+(-11). At x=5, f′(5)=3(-3)(5)²+2(10)(5)+(-11)=-136. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -136, not -108.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -136, not 136.",
"C": "Correct. The worked calculation gives -136.",
"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_002538 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, -2], [9, -4]]. | {
"A": "-18",
"B": "-9",
"C": "-17",
"D": "-16"
} | A | -18 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(-4)−(-2)(9)=-18. | {
"A": "Correct. The worked calculation gives -18.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -18, not -9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -18, not -17.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_009863 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(CN)_5]^+1, each CN ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "3",
"B": "4.5",
"C": "6",
"D": "7"
} | C | 6 | Let the formal oxidation state of Ni be x. Charge balance gives x+(5)(−1)=+1; hence x=1+5=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.5.",
"C": "Correct. The worked calculation gives 6.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009205 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.14 V, transfers 1 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.2146 V",
"B": "1.1781 V",
"C": "3.7854 V",
"D": "0.7854 V"
} | D | 0.7854 V | Apply the Nernst equation: E=1.14−(0.0591/1)(6)=0.7854 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7854 V, not -0.2146 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7854 V, not 1.1781 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7854 V, not... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000432 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 27 and common difference 5. Find the sum of its first 28 terms. | {
"A": "265.6",
"B": "2646",
"C": "3175.2",
"D": "3969"
} | B | 2646 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=27, d=5, n=28: Sₙ=28/2[2(27)+(28−1)(5)]=2646. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2646, not 265.6.",
"B": "Correct. The worked calculation gives 2646.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2646, not 3175.2.",
"D": "Incorrect. Substituting the stated values into th... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007404 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 80 mL of 0.10 M HCl is mixed with 25 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.28083",
"B": "-1.71917",
"C": "1.12808",
"D": "0.64041"
} | A | 1.28083 | Excess H⁺ moles=0.10×(80−25)/1000=0.005500 mol. Total volume=0.105 L, so [H⁺]=0.052381 M and pH=−log₁₀[H⁺]=1.28083. | {
"A": "Correct. The worked calculation gives 1.28083.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.28083, not -1.71917.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.28083, not 1.12808.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006198 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 20 cm in front of a thin convex lens of focal length 14 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "2.33333",
"B": "5.33333",
"C": "3.33333",
"D": "-0.66667"
} | A | 2.33333 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(20)(14)/(20−14)=46.66667 cm. Thus |m|=v/u=46.66667/20=2.33333. | {
"A": "Correct. The worked calculation gives 2.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.33333, not 5.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.33333, not 3.33333.",
"D": "Incorrect. Substituting the stated va... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002510 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, -5], [8, 1]]. | {
"A": "47",
"B": "55.2",
"C": "46",
"D": "69"
} | C | 46 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(1)−(-5)(8)=46. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 46, not 47.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 46, not 55.2.",
"C": "Correct. The worked calculation gives 46.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009797 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(CN)_4]^+1, each CN ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "6",
"B": "7.5",
"C": "5",
"D": "10"
} | C | 5 | Let the formal oxidation state of Pd 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 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.5.",
"C": "Correct. The worked calculation gives 5.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007777 | 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 18 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "-1.71875 mmol L⁻¹",
"B": "0.42188 mmol L⁻¹",
"C": "0.28125 mmol L⁻¹",
"D": "0.14062 mmol L⁻¹"
} | C | 0.28125 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=18/2^6=0.28125 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.28125 mmol L⁻¹, not -1.71875 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.28125 mmol L⁻¹, not 0.42188 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.28125 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_007821 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 94 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "2.9375 mmol L⁻¹",
"B": "5.875 mmol L⁻¹",
"C": "5.9375 mmol L⁻¹",
"D": "1.9375 mmol L⁻¹"
} | A | 2.9375 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=94/2^5=2.9375 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 2.9375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.9375 mmol L⁻¹, not 5.875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.9375 mmol L⁻¹, not 5.9375 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_005683 | 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 4.1 atm at 368 K. What is its pressure at 429 K? | {
"A": "7.16943 atm",
"B": "5.77962 atm",
"C": "6.77962 atm",
"D": "4.77962 atm"
} | D | 4.77962 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.1)(429)/(368)=4.77962 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.77962 atm, not 7.16943 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.77962 atm, not 5.77962 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.... | [
"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_004819 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 14 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 4 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.01786 A",
"B": "2.67857 A",
"C": "-0.32143 A",
"D": "0.67857 A"
} | B | 2.67857 A | Series branch resistance=14+7=21 Ω. Parallel equivalent R_eq=(21×4)/(21+4)=3.36 Ω. Total current I=V/R_eq=9/3.36=2.67857 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.67857 A, not 4.01786 A.",
"B": "Correct. The worked calculation gives 2.67857 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.67857 A, not -0.32143 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003542 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 117 m s⁻¹ at 50° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1347.10333 m",
"B": "1348.10333 m",
"C": "135.81033 m",
"D": "1350.10333 m"
} | B | 1348.10333 m | Range R=u²sin(2θ)/g. Substituting u=117, θ=50° and g=10 gives R=(117)²sin(100°)/10=1348.10333 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1348.10333 m, not 1347.10333 m.",
"B": "Correct. The worked calculation gives 1348.10333 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1348.10333 m, not 135.81033 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_004331 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 40 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.29. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "73.6 N",
"B": "147.2 N",
"C": "110.4 N",
"D": "176.64 N"
} | B | 147.2 N | Net force=mg(sinθ−μcosθ)=40×10×(0.6−0.29×0.8)=147.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 147.2 N, not 73.6 N.",
"B": "Correct. The worked calculation gives 147.2 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 147.2 N, not 110.4 N.",
"D": "Incorrect. Substituting the stated val... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005801 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.6 atm at 273 K. What is its pressure at 335 K? | {
"A": "5.64469 atm",
"B": "7.64469 atm",
"C": "6.64469 atm",
"D": "4.23352 atm"
} | A | 5.64469 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.6)(335)/(273)=5.64469 atm. | {
"A": "Correct. The worked calculation gives 5.64469 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.64469 atm, not 7.64469 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.64469 atm, not 6.64469 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_007345 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 68 mL of 0.10 M HCl is mixed with 90 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "18.21565",
"B": "12.14377",
"C": "9.14377",
"D": "2.21438"
} | B | 12.14377 | Excess OH⁻ moles=0.10×(90−68)/1000=0.002200 mol. Total volume=0.158 L, so [OH⁻]=0.013924 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.14377. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.14377, not 18.21565.",
"B": "Correct. The worked calculation gives 12.14377.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.14377, not 9.14377.",
"D": "Incorrect. Substituting the state... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004983 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 2 Ω and 12 Ω are connected in series; this combination is connected in parallel with a 9 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "-0.90476 A",
"B": "0.82143 A",
"C": "1.09524 A",
"D": "-1.09524 A"
} | C | 1.09524 A | Series branch resistance=2+12=14 Ω. Parallel equivalent R_eq=(14×9)/(14+9)=5.47826 Ω. Total current I=V/R_eq=6/5.47826=1.09524 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.09524 A, not -0.90476 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.09524 A, not 0.82143 A.",
"C": "Correct. The worked calculation gives 1.09524 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009430 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_18H_19N_2X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "10",
"B": "2",
"C": "-10",
"D": "20"
} | A | 10 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+2−19−1)/2=10. | {
"A": "Correct. The worked calculation gives 10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not -10.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005856 | 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 4.1 atm at 341 K. What is its pressure at 628 K? | {
"A": "1.75507 atm",
"B": "7.55073 atm",
"C": "6.55073 atm",
"D": "11.3261 atm"
} | B | 7.55073 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.1)(628)/(341)=7.55073 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.55073 atm, not 1.75507 atm.",
"B": "Correct. The worked calculation gives 7.55073 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.55073 atm, not 6.55073 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_008692 | 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 0.89 mol L⁻¹ and initially B is absent. At equilibrium, 15% of A has dissociated at constant volume. Find K_c. | {
"A": "0.18847",
"B": "0.07068",
"C": "0.09424",
"D": "-2.90576"
} | C | 0.09424 | Let α=0.15. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.89)(0.15)²/(1−0.15)=0.09424. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.09424, not 0.18847.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.09424, not 0.07068.",
"C": "Correct. The worked calculation gives 0.09424.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003009 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-2+10i)/(6+6i). What is Re(z), the real part of z? | {
"A": "2.66667",
"B": "0.66667",
"C": "3.66667",
"D": "-0.66667"
} | B | 0.66667 | Multiply numerator and denominator by the conjugate (6-6i). Then Re(z)=(ac+bd)/(c²+d²)=((-2)(6)+(10)(6))/(6²+(6)²)=0.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.66667, not 2.66667.",
"B": "Correct. The worked calculation gives 0.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.66667, not 3.66667.",
"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_005756 | 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 1.5 atm at 418 K. What is its pressure at 480 K? | {
"A": "2.72249 atm",
"B": "2.58373 atm",
"C": "-1.72249 atm",
"D": "1.72249 atm"
} | D | 1.72249 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.5)(480)/(418)=1.72249 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.72249 atm, not 2.72249 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.72249 atm, not 2.58373 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.... | [
"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_007069 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 20 mol of gas at 192 K and 2.94 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "108.17649 L",
"B": "105.17649 L",
"C": "107.17649 L",
"D": "128.61179 L"
} | C | 107.17649 L | PV=nRT, so V=nRT/P=(20)(0.082057)(192)/(2.94)=107.17649 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 107.17649 L, not 108.17649 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 107.17649 L, not 105.17649 L.",
"C": "Correct. The worked calculation gives 107.17649 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_005631 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 46 μF capacitor is charged to a potential difference of 2 V. Calculate the energy stored, expressed in μJ. | {
"A": "91 μJ",
"B": "92 μJ",
"C": "110.4 μJ",
"D": "94 μJ"
} | B | 92 μJ | U=½CV². Since C=46 μF, U in μJ is ½×46×(2)²=92 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 92 μJ, not 91 μJ.",
"B": "Correct. The worked calculation gives 92 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 92 μJ, not 110.4 μJ.",
"D": "Incorrect. Substituting the stated values in... | [
"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_000366 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -18 and common difference 12. Find the sum of its first 29 terms. | {
"A": "4350",
"B": "4348",
"C": "3262.5",
"D": "3480"
} | A | 4350 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-18, d=12, n=29: Sₙ=29/2[2(-18)+(29−1)(12)]=4350. | {
"A": "Correct. The worked calculation gives 4350.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4350, not 4348.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4350, not 3262.5.",
"D": "Incorrect. Substituting the stated values into the... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007122 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 15 mol of gas at 232 K and 1.99 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "15.34967 L",
"B": "143.49666 L",
"C": "141.49666 L",
"D": "71.74833 L"
} | B | 143.49666 L | PV=nRT, so V=nRT/P=(15)(0.082057)(232)/(1.99)=143.49666 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 143.49666 L, not 15.34967 L.",
"B": "Correct. The worked calculation gives 143.49666 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 143.49666 L, not 141.49666 L.",
"D": "Incorrect. Substit... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007674 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 49 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "-3.0625 mmol L⁻¹",
"B": "4.0625 mmol L⁻¹",
"C": "3.0625 mmol L⁻¹",
"D": "6.125 mmol L⁻¹"
} | C | 3.0625 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=49/2^4=3.0625 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.0625 mmol L⁻¹, not -3.0625 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.0625 mmol L⁻¹, not 4.0625 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 3.0625 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_003459 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 86 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "512.40991 m",
"B": "642.51239 m",
"C": "320.25619 m",
"D": "640.51239 m"
} | D | 640.51239 m | Range R=u²sin(2θ)/g. Substituting u=86, θ=60° and g=10 gives R=(86)²sin(120°)/10=640.51239 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 640.51239 m, not 512.40991 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 640.51239 m, not 642.51239 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 64... | [
"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_005996 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.8 atm at 297 K. What is its pressure at 407 K? | {
"A": "3.28889 atm",
"B": "3.57778 atm",
"C": "6.57778 atm",
"D": "9.86667 atm"
} | C | 6.57778 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.8)(407)/(297)=6.57778 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.57778 atm, not 3.28889 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.57778 atm, not 3.57778 atm.",
"C": "Correct. The worked calculation gives 6.57778 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 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.