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_005350 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 22 μF capacitor is charged to a potential difference of 10 V. Calculate the energy stored, expressed in μJ. | {
"A": "1320 μJ",
"B": "825 μJ",
"C": "880 μJ",
"D": "1100 μJ"
} | D | 1100 μJ | U=½CV². Since C=22 μF, U in μJ is ½×22×(10)²=1100 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1100 μJ, not 1320 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1100 μJ, not 825 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1100 μJ, not 880 μJ... | [
"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_003667 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 58 m s⁻¹ at 30° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "291.33095 m",
"B": "293.33095 m",
"C": "349.59713 m",
"D": "582.66189 m"
} | A | 291.33095 m | Range R=u²sin(2θ)/g. Substituting u=58, θ=30° and g=10 gives R=(58)²sin(60°)/10=291.33095 m. | {
"A": "Correct. The worked calculation gives 291.33095 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 291.33095 m, not 293.33095 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 291.33095 m, not 349.59713 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001278 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ +0x² +12x+7. Evaluate f′(-1). | {
"A": "18",
"B": "28.8",
"C": "24",
"D": "26"
} | C | 24 | Differentiate: f′(x)=3(4)x²+2(0)x+(12). At x=-1, f′(-1)=3(4)(-1)²+2(0)(-1)+(12)=24. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24, not 18.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24, not 28.8.",
"C": "Correct. The worked calculation gives 24.",
"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_009995 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(Cl)_6]^+1, each Cl ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "8",
"B": "5.25",
"C": "7",
"D": "10"
} | C | 7 | Let the formal oxidation state of Co be x. Charge balance gives x+(6)(−1)=+1; hence x=1+6=+7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 5.25.",
"C": "Correct. The worked calculation gives 7.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006692 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 6 mol H₂ and 31 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "6 mol",
"B": "7 mol",
"C": "1.6 mol",
"D": "4.5 mol"
} | A | 6 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 6 mol H₂O; O₂ can produce 62 mol H₂O. The limiting condition is H₂; product=6 mol. | {
"A": "Correct. The worked calculation gives 6 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 7 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 1.6 mol.",
"D": "Incorrect. Substituting the stated values int... | [
"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_007841 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 67 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "1.52344 mmol L⁻¹",
"B": "-0.47656 mmol L⁻¹",
"C": "-2.47656 mmol L⁻¹",
"D": "0.52344 mmol L⁻¹"
} | D | 0.52344 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=67/2^7=0.52344 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.52344 mmol L⁻¹, not 1.52344 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.52344 mmol L⁻¹, not -0.47656 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the govern... | [
"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_007969 | 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 87 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "0.16992 mmol L⁻¹",
"B": "-0.33984 mmol L⁻¹",
"C": "0.33984 mmol L⁻¹",
"D": "-0.66016 mmol L⁻¹"
} | C | 0.33984 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=87/2^8=0.33984 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33984 mmol L⁻¹, not 0.16992 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33984 mmol L⁻¹, not -0.33984 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.33984 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_006230 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 80 cm in front of a thin convex lens of focal length 22 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "2.37931",
"B": "1.03793",
"C": "0.75862",
"D": "0.37931"
} | D | 0.37931 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(80)(22)/(80−22)=30.34483 cm. Thus |m|=v/u=30.34483/80=0.37931. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.37931, not 2.37931.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.37931, not 1.03793.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.37931, not 0.758... | [
"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_001684 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 4 elements can be selected from a set of 26 distinct elements? | {
"A": "11212.5",
"B": "14950",
"C": "29900",
"D": "-14950"
} | B | 14950 | Order does not matter, so the count is C(26,4)=26!/[4!(22)!]=14950. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14950, not 11212.5.",
"B": "Correct. The worked calculation gives 14950.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14950, not 29900.",
"D": "Incorrect. Substituting the stated values int... | [
"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_001149 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ +4x² +9x+7. Evaluate f′(3). | {
"A": "168",
"B": "201.6",
"C": "126",
"D": "336"
} | A | 168 | Differentiate: f′(x)=3(5)x²+2(4)x+(9). At x=3, f′(3)=3(5)(3)²+2(4)(3)+(9)=168. | {
"A": "Correct. The worked calculation gives 168.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 168, not 201.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 168, not 126.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008038 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 8 A for 13122 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": "-34.53874 g",
"B": "25.90405 g",
"C": "17.26937 g",
"D": "34.53874 g"
} | D | 34.53874 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×8×13122/(2×96500)=34.53874 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 34.53874 g, not -34.53874 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 34.53874 g, not 25.90405 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 34.53... | [
"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_007844 | 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 12 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "3.09375 mmol L⁻¹",
"B": "0.04688 mmol L⁻¹",
"C": "0.09375 mmol L⁻¹",
"D": "-0.09375 mmol L⁻¹"
} | C | 0.09375 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=12/2^7=0.09375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.09375 mmol L⁻¹, not 3.09375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.09375 mmol L⁻¹, not 0.04688 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.09375 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_004780 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 7 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.14286 A",
"B": "2.28571 A",
"C": "-1.14286 A",
"D": "1.11429 A"
} | A | 1.14286 A | Series branch resistance=13+8=21 Ω. Parallel equivalent R_eq=(21×7)/(21+7)=5.25 Ω. Total current I=V/R_eq=6/5.25=1.14286 A. | {
"A": "Correct. The worked calculation gives 1.14286 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.14286 A, not 2.28571 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.14286 A, not -1.14286 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_009440 | 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_1N_3X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "6",
"B": "7",
"C": "3",
"D": "8"
} | A | 6 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+3−1−4)/2=6. | {
"A": "Correct. The worked calculation gives 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005258 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +6 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "60.75 N",
"B": "-50.625 N",
"C": "50.625 N",
"D": "52.625 N"
} | C | 50.625 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(6×10⁻⁶)/(8×10⁻²)²=50.625 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 50.625 N, not 60.75 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 50.625 N, not -50.625 N.",
"C": "Correct. The worked calculation gives 50.625 N.",
"D": "Incorrect. Substituting the stat... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007275 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 17 mol of gas at 504 K and 0.48 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "1464.71745 L",
"B": "1465.71745 L",
"C": "2197.07618 L",
"D": "1466.71745 L"
} | A | 1464.71745 L | PV=nRT, so V=nRT/P=(17)(0.082057)(504)/(0.48)=1464.71745 L. | {
"A": "Correct. The worked calculation gives 1464.71745 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1464.71745 L, not 1465.71745 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1464.71745 L, not 2197.07618 L.",
"D": "Incorrect. S... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006654 | 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 407 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.62699 s",
"B": "0.3135 s",
"C": "-1.6865 s",
"D": "0.15675 s"
} | B | 0.3135 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(10/407)=0.3135 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3135 s, not 0.62699 s.",
"B": "Correct. The worked calculation gives 0.3135 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3135 s, not -1.6865 s.",
"D": "Incorrect. Substituting the st... | [
"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_006688 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 44 mol H₂ and 7 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "10.5 mol",
"B": "7 mol",
"C": "11 mol",
"D": "14 mol"
} | D | 14 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 44 mol H₂O; O₂ can produce 14 mol H₂O. The limiting condition is O₂; product=14 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14 mol, not 10.5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14 mol, not 7 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14 mol, not 11 mol.",... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000272 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -10x -6=0, let its roots be α and β. What is α²+β²? | {
"A": "33",
"B": "32",
"C": "31",
"D": "4.1"
} | C | 31 | By Vieta's relations, α+β = 10/2 and αβ = -6/2. Then α²+β²=(α+β)²−2αβ = (10/2)²−2(-6/2) = 31. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 31, not 33.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 31, not 32.",
"C": "Correct. The worked calculation gives 31.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004901 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 6 Ω and 11 Ω are connected in series; this combination is connected in parallel with a 7 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.81513 A",
"B": "4.21008 A",
"C": "0.60504 A",
"D": "1.21008 A"
} | D | 1.21008 A | Series branch resistance=6+11=17 Ω. Parallel equivalent R_eq=(17×7)/(17+7)=4.95833 Ω. Total current I=V/R_eq=6/4.95833=1.21008 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.21008 A, not 1.81513 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.21008 A, not 4.21008 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.21008 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_000095 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +12x -8=0, let its roots be α and β. What is α²+β²? | {
"A": "3.13333",
"B": "16",
"C": "22.33333",
"D": "21.33333"
} | D | 21.33333 | By Vieta's relations, α+β = -12/3 and αβ = -8/3. Then α²+β²=(α+β)²−2αβ = (-12/3)²−2(-8/3) = 21.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21.33333, not 3.13333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21.33333, not 16.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21.33333, not 22.3333... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002654 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, -7], [7, -1]]. | {
"A": "36",
"B": "-48",
"C": "48",
"D": "57.6"
} | C | 48 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(-1)−(-7)(7)=48. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 48, not 36.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 48, not -48.",
"C": "Correct. The worked calculation gives 48.",
"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_002813 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(5, -3, 8) and v=(5, -5, -1), calculate u·v. | {
"A": "25.6",
"B": "32",
"C": "33",
"D": "30"
} | B | 32 | The dot product is the sum of corresponding component products: (5)(5)+(-3)(-5)+(8)(-1)=32. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 32, not 25.6.",
"B": "Correct. The worked calculation gives 32.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 32, not 33.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005499 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 40 μF capacitor is charged to a potential difference of 40 V. Calculate the energy stored, expressed in μJ. | {
"A": "31999 μJ",
"B": "32000 μJ",
"C": "24000 μJ",
"D": "32001 μJ"
} | B | 32000 μJ | U=½CV². Since C=40 μF, U in μJ is ½×40×(40)²=32000 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 32000 μJ, not 31999 μJ.",
"B": "Correct. The worked calculation gives 32000 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 32000 μJ, not 24000 μJ.",
"D": "Incorrect. Substituting the stat... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001321 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=1x³ +9x² -5x+7. Evaluate f′(5). | {
"A": "240",
"B": "160",
"C": "162",
"D": "320"
} | B | 160 | Differentiate: f′(x)=3(1)x²+2(9)x+(-5). At x=5, f′(5)=3(1)(5)²+2(9)(5)+(-5)=160. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 160, not 240.",
"B": "Correct. The worked calculation gives 160.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 160, not 162.",
"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_004269 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.40. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "29.8 N",
"B": "46.2 N",
"C": "31.8 N",
"D": "30.8 N"
} | D | 30.8 N | Net force=mg(sinθ−μcosθ)=11×10×(0.6−0.40×0.8)=30.8 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 30.8 N, not 29.8 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30.8 N, not 46.2 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30.8 N, not 31.8 N.",
... | [
"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_007143 | 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 331 K and 2.38 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "116.12129 L",
"B": "12.41213 L",
"C": "91.29703 L",
"D": "114.12129 L"
} | D | 114.12129 L | PV=nRT, so V=nRT/P=(10)(0.082057)(331)/(2.38)=114.12129 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 114.12129 L, not 116.12129 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 114.12129 L, not 12.41213 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 114... | [
"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_002364 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, -3], [1, -8]]. | {
"A": "-42",
"B": "-21",
"C": "-20",
"D": "-16.8"
} | B | -21 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(-8)−(-3)(1)=-21. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -21, not -42.",
"B": "Correct. The worked calculation gives -21.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -21, not -20.",
"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_002301 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 8 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.51754",
"B": "3.34503",
"C": "-0.65497",
"D": "0.34503"
} | D | 0.34503 | Favourable pairs = C(8,2)+C(8,2)+C(3,2)=59. Total pairs=C(19,2)=171. Therefore P=59/171=0.34503. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34503, not 0.51754.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34503, not 3.34503.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34503, not -0.65... | [
"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_007629 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 39 mL of 0.10 M HCl is mixed with 60 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.32658",
"B": "24.65317",
"C": "13.32658",
"D": "6.16329"
} | A | 12.32658 | Excess OH⁻ moles=0.10×(60−39)/1000=0.002100 mol. Total volume=0.099 L, so [OH⁻]=0.021212 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.32658. | {
"A": "Correct. The worked calculation gives 12.32658.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.32658, not 24.65317.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.32658, not 13.32658.",
"D": "Incorrect. Substituting the stat... | [
"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_008362 | 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 1.9 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-5.7 K",
"B": "5.7 K",
"C": "8.7 K",
"D": "8.55 K"
} | B | 5.7 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×1.0×1.9=5.7 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.7 K, not -5.7 K.",
"B": "Correct. The worked calculation gives 5.7 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.7 K, not 8.7 K.",
"D": "Incorrect. Substituting the stated values into... | [
"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_001953 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 4 elements can be selected from a set of 70 distinct elements? | {
"A": "916893",
"B": "458447.5",
"C": "916895",
"D": "1100274"
} | C | 916895 | Order does not matter, so the count is C(70,4)=70!/[4!(66)!]=916895. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 916895, not 916893.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 916895, not 458447.5.",
"C": "Correct. The worked calculation gives 916895.",
"D": "Incorrect. Substituting the stated value... | [
"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_000442 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -14 and common difference 10. Find the sum of its first 22 terms. | {
"A": "4004",
"B": "2002",
"C": "1501.5",
"D": "1001"
} | B | 2002 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-14, d=10, n=22: Sₙ=22/2[2(-14)+(22−1)(10)]=2002. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2002, not 4004.",
"B": "Correct. The worked calculation gives 2002.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2002, not 1501.5.",
"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_000861 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio 2. What is the sum of its first 9 terms? | {
"A": "1022",
"B": "52.1",
"C": "613.2",
"D": "511"
} | D | 511 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(2^9−1)/(2−1)=511. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 511, not 1022.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 511, not 52.1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 511, not 613.2.",
"D": "Correc... | [
"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_000355 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -1 and common difference 7. Find the sum of its first 10 terms. | {
"A": "304",
"B": "305",
"C": "457.5",
"D": "306"
} | B | 305 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-1, d=7, n=10: Sₙ=10/2[2(-1)+(10−1)(7)]=305. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 305, not 304.",
"B": "Correct. The worked calculation gives 305.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 305, not 457.5.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_006737 | 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 26 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "12.5 mol",
"B": "25 mol",
"C": "23 mol",
"D": "-25 mol"
} | B | 25 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 25 mol H₂O; O₂ can produce 52 mol H₂O. The limiting condition is H₂; product=25 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 25 mol, not 12.5 mol.",
"B": "Correct. The worked calculation gives 25 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 25 mol, not 23 mol.",
"D": "Incorrect. Substituting the stated value... | [
"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_007648 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 77 mL of 0.10 M HCl is mixed with 63 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.5",
"B": "1.2",
"C": "2",
"D": "0"
} | C | 2 | Excess H⁺ moles=0.10×(77−63)/1000=0.001400 mol. Total volume=0.140 L, so [H⁺]=0.010000 M and pH=−log₁₀[H⁺]=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.2.",
"C": "Correct. The worked calculation gives 2.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_001939 | 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 29 distinct elements? | {
"A": "10015004",
"B": "10015005",
"C": "15022507.5",
"D": "-10015005"
} | B | 10015005 | Order does not matter, so the count is C(29,9)=29!/[9!(20)!]=10015005. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10015005, not 10015004.",
"B": "Correct. The worked calculation gives 10015005.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10015005, not 15022507.5.",
"D": "Incorrect. Substituting the st... | [
"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_005037 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +8 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "81 N",
"B": "-67.5 N",
"C": "33.75 N",
"D": "67.5 N"
} | D | 67.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(8×10⁻⁶)/(8×10⁻²)²=67.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 67.5 N, not 81 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 67.5 N, not -67.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 67.5 N, not 33.75 N.",
... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001103 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=1x³ -10x² +3x+7. Evaluate f′(-4). | {
"A": "-131",
"B": "65.5",
"C": "132",
"D": "131"
} | D | 131 | Differentiate: f′(x)=3(1)x²+2(-10)x+(3). At x=-4, f′(-4)=3(1)(-4)²+2(-10)(-4)+(3)=131. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 131, not -131.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 131, not 65.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 131, not 132.",
"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_005325 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +4 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "2.19008 N",
"B": "11.90083 N",
"C": "12.90083 N",
"D": "23.80165 N"
} | B | 11.90083 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(4×10⁻⁶)/(11×10⁻²)²=11.90083 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.90083 N, not 2.19008 N.",
"B": "Correct. The worked calculation gives 11.90083 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.90083 N, not 12.90083 N.",
"D": "Incorrect. Substituting... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009438 | 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_15H_10N_1X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "13",
"B": "12",
"C": "11",
"D": "5.5"
} | C | 11 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×15+2+1−10−1)/2=11. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11, not 13.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11, not 12.",
"C": "Correct. The worked calculation gives 11.",
"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_006132 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 40 cm in front of a thin convex lens of focal length 11 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.37931",
"B": "0.56897",
"C": "2.37931",
"D": "-0.37931"
} | A | 0.37931 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(40)(11)/(40−11)=15.17241 cm. Thus |m|=v/u=15.17241/40=0.37931. | {
"A": "Correct. The worked calculation gives 0.37931.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.37931, not 0.56897.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.37931, not 2.37931.",
"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_008139 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 4 A for 974 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": "2.28184 g",
"B": "0.28184 g",
"C": "2.56369 g",
"D": "1.28184 g"
} | D | 1.28184 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×974/(2×96500)=1.28184 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.28184 g, not 2.28184 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.28184 g, not 0.28184 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.28184 g,... | [
"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_003973 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 7 m s⁻¹. A constant net force does 18 N of work over 13 m in the direction of motion. Find its final kinetic energy. | {
"A": "681.75 J",
"B": "909 J",
"C": "363.6 J",
"D": "454.5 J"
} | D | 454.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(7)²+(18)(13)=454.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 454.5 J, not 681.75 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 454.5 J, not 909 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 454.5 J, not 363.6 ... | [
"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_007612 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 12 mL of 0.10 M HCl is mixed with 17 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-12.23657",
"B": "14.23657",
"C": "15.23657",
"D": "12.23657"
} | D | 12.23657 | Excess OH⁻ moles=0.10×(17−12)/1000=0.000500 mol. Total volume=0.029 L, so [OH⁻]=0.017241 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.23657. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.23657, not -12.23657.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.23657, not 14.23657.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.23657, not... | [
"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_001915 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 7 elements can be selected from a set of 70 distinct elements? | {
"A": "1798162080",
"B": "599387360",
"C": "1198774720",
"D": "1438529664"
} | C | 1198774720 | Order does not matter, so the count is C(70,7)=70!/[7!(63)!]=1198774720. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1198774720, not 1798162080.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1198774720, not 599387360.",
"C": "Correct. The worked calculation gives 1198774720.",
"D": "Incorrect. Substituting... | [
"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_002782 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(5, 3, 5) and v=(4, 5, 3), calculate u·v. | {
"A": "37.5",
"B": "48",
"C": "52",
"D": "50"
} | D | 50 | The dot product is the sum of corresponding component products: (5)(4)+(3)(5)+(5)(3)=50. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 50, not 37.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 50, not 48.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 50, not 52.",
"D": "Correct. The w... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001392 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (5x² -3x +5) dx. | {
"A": "336",
"B": "268.8",
"C": "672",
"D": "252"
} | A | 336 | An antiderivative is (5/3)x³+(-3/2)x²+(5)x. Evaluating between 0 and 6 gives (5/3)(6)³+(-3/2)(6)²+(5)(6)=336. | {
"A": "Correct. The worked calculation gives 336.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 336, not 268.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 336, not 672.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_006635 | 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 895 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "2.21141 s",
"B": "-0.21141 s",
"C": "0.31711 s",
"D": "0.21141 s"
} | D | 0.21141 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(10/895)=0.21141 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.21141 s, not 2.21141 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.21141 s, not -0.21141 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.21141 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_001491 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (4x² +7x -3) dx. | {
"A": "198",
"B": "397",
"C": "396",
"D": "475.2"
} | C | 396 | An antiderivative is (4/3)x³+(7/2)x²+(-3)x. Evaluating between 0 and 6 gives (4/3)(6)³+(7/2)(6)²+(-3)(6)=396. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 396, not 198.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 396, not 397.",
"C": "Correct. The worked calculation gives 396.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000150 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +8x +5=0, let its roots be α and β. What is α²+β²? | {
"A": "1.37778",
"B": "7.55556",
"C": "5.77778",
"D": "3.77778"
} | D | 3.77778 | By Vieta's relations, α+β = -8/3 and αβ = 5/3. Then α²+β²=(α+β)²−2αβ = (-8/3)²−2(5/3) = 3.77778. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.77778, not 1.37778.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.77778, not 7.55556.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.77778, not 5.777... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008197 | 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 25233 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": "76.71844 g",
"B": "74.71844 g",
"C": "73.71844 g",
"D": "149.43689 g"
} | B | 74.71844 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×9×25233/(2×96500)=74.71844 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 74.71844 g, not 76.71844 g.",
"B": "Correct. The worked calculation gives 74.71844 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 74.71844 g, not 73.71844 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_004691 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 6 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 14 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.56044 A",
"B": "5.56044 A",
"C": "2.56044 A",
"D": "4.56044 A"
} | A | 3.56044 A | Series branch resistance=6+7=13 Ω. Parallel equivalent R_eq=(13×14)/(13+14)=6.74074 Ω. Total current I=V/R_eq=24/6.74074=3.56044 A. | {
"A": "Correct. The worked calculation gives 3.56044 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.56044 A, not 5.56044 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.56044 A, not 2.56044 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002856 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(7, 0, -6) and v=(6, 8, -7), calculate u·v. | {
"A": "84",
"B": "42",
"C": "126",
"D": "82"
} | A | 84 | The dot product is the sum of corresponding component products: (7)(6)+(0)(8)+(-6)(-7)=84. | {
"A": "Correct. The worked calculation gives 84.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 84, not 42.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 84, not 126.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004651 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 10 kg and radius 6 m is acted on by a constant torque of 67 N m about its central axis. Find its angular acceleration. | {
"A": "0.18611 rad s⁻²",
"B": "0.37222 rad s⁻²",
"C": "0.27917 rad s⁻²",
"D": "-0.62778 rad s⁻²"
} | B | 0.37222 rad s⁻² | For a solid disc, I=½MR²=½(10)(6)²=180 kg m². Using τ=Iα, α=67/180=0.37222 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.37222 rad s⁻², not 0.18611 rad s⁻².",
"B": "Correct. The worked calculation gives 0.37222 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.37222 rad s⁻², not 0.27917 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_008392 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.75 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "4.5 K",
"B": "2.5 K",
"C": "1.125 K",
"D": "1.5 K"
} | D | 1.5 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×0.75=1.5 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.5 K, not 4.5 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.5 K, not 2.5 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.5 K, not 1.125 K.",
"D... | [
"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_004042 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 23 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.41. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "63.56 N",
"B": "50.048 N",
"C": "62.56 N",
"D": "46.92 N"
} | C | 62.56 N | Net force=mg(sinθ−μcosθ)=23×10×(0.6−0.41×0.8)=62.56 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 62.56 N, not 63.56 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 62.56 N, not 50.048 N.",
"C": "Correct. The worked calculation gives 62.56 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_000699 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 3 and common ratio 3. What is the sum of its first 10 terms? | {
"A": "88574",
"B": "88572",
"C": "88573",
"D": "177144"
} | B | 88572 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=3(3^10−1)/(3−1)=88572. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 88572, not 88574.",
"B": "Correct. The worked calculation gives 88572.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 88572, not 88573.",
"D": "Incorrect. Substituting the stated values into ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005385 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 70 μF capacitor is charged to a potential difference of 35 V. Calculate the energy stored, expressed in μJ. | {
"A": "42873 μJ",
"B": "42877 μJ",
"C": "64312.5 μJ",
"D": "42875 μJ"
} | D | 42875 μJ | U=½CV². Since C=70 μF, U in μJ is ½×70×(35)²=42875 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 42875 μJ, not 42873 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 42875 μJ, not 42877 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 42875 μJ, not ... | [
"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_001117 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-1x³ -9x² +6x+7. Evaluate f′(5). | {
"A": "-161",
"B": "-159",
"C": "159",
"D": "-190.8"
} | B | -159 | Differentiate: f′(x)=3(-1)x²+2(-9)x+(6). At x=5, f′(5)=3(-1)(5)²+2(-9)(5)+(6)=-159. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -159, not -161.",
"B": "Correct. The worked calculation gives -159.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -159, not 159.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_003834 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block initially moves at 8 m s⁻¹. A constant net force does 24 N of work over 12 m in the direction of motion. Find its final kinetic energy. | {
"A": "446 J",
"B": "896 J",
"C": "448 J",
"D": "224 J"
} | C | 448 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(5)(8)²+(24)(12)=448 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 448 J, not 446 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 448 J, not 896 J.",
"C": "Correct. The worked calculation gives 448 J.",
"D": "Incorrect. Substituting the stated values into ... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007162 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 18 mol of gas at 595 K and 0.76 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "1734.53382 L",
"B": "1156.35588 L",
"C": "1154.35588 L",
"D": "1155.35588 L"
} | B | 1156.35588 L | PV=nRT, so V=nRT/P=(18)(0.082057)(595)/(0.76)=1156.35588 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1156.35588 L, not 1734.53382 L.",
"B": "Correct. The worked calculation gives 1156.35588 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1156.35588 L, not 1154.35588 L.",
"D": "Incorrect. S... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006470 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 11 kg is attached to an ideal spring of force constant 532 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.28759 s",
"B": "0.14379 s",
"C": "-0.71241 s",
"D": "1.28759 s"
} | A | 0.28759 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(11/532)=0.28759 s. | {
"A": "Correct. The worked calculation gives 0.28759 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.28759 s, not 0.14379 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.28759 s, not -0.71241 s.",
"D": "Incorrect. Substituting th... | [
"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_008713 | 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, 20% of A has dissociated at constant volume. Find K_c. | {
"A": "-1.686",
"B": "0.314",
"C": "3.314",
"D": "0.2355"
} | B | 0.314 | Let α=0.2. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.57)(0.2)²/(1−0.2)=0.314. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.314, not -1.686.",
"B": "Correct. The worked calculation gives 0.314.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.314, not 3.314.",
"D": "Incorrect. Substituting the stated values into... | [
"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_001316 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=0x³ +9x² +0x+7. Evaluate f′(-4). | {
"A": "-108",
"B": "-71",
"C": "-72",
"D": "-73"
} | C | -72 | Differentiate: f′(x)=3(0)x²+2(9)x+(0). At x=-4, f′(-4)=3(0)(-4)²+2(9)(-4)+(0)=-72. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -72, not -108.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -72, not -71.",
"C": "Correct. The worked calculation gives -72.",
"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_005797 | 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 1.4 atm at 191 K. What is its pressure at 384 K? | {
"A": "2.11099 atm",
"B": "2.81466 atm",
"C": "1.28147 atm",
"D": "1.40733 atm"
} | B | 2.81466 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.4)(384)/(191)=2.81466 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.81466 atm, not 2.11099 atm.",
"B": "Correct. The worked calculation gives 2.81466 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.81466 atm, not 1.28147 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_003829 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block initially moves at 1 m s⁻¹. A constant net force does 6 N of work over 14 m in the direction of motion. Find its final kinetic energy. | {
"A": "173 J",
"B": "-86.5 J",
"C": "86.5 J",
"D": "103.8 J"
} | C | 86.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(5)(1)²+(6)(14)=86.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 86.5 J, not 173 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 86.5 J, not -86.5 J.",
"C": "Correct. The worked calculation gives 86.5 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_003642 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 40 m s⁻¹ at 30° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "138.56406 m",
"B": "277.12813 m",
"C": "166.27688 m",
"D": "103.92305 m"
} | A | 138.56406 m | Range R=u²sin(2θ)/g. Substituting u=40, θ=30° and g=10 gives R=(40)²sin(60°)/10=138.56406 m. | {
"A": "Correct. The worked calculation gives 138.56406 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 138.56406 m, not 277.12813 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 138.56406 m, not 166.27688 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000230 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +4x -3=0, let its roots be α and β. What is α²+β²? | {
"A": "3.77778",
"B": "1.88889",
"C": "7.55556",
"D": "2.77778"
} | A | 3.77778 | By Vieta's relations, α+β = -4/3 and αβ = -3/3. Then α²+β²=(α+β)²−2αβ = (-4/3)²−2(-3/3) = 3.77778. | {
"A": "Correct. The worked calculation gives 3.77778.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.77778, not 1.88889.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.77778, not 7.55556.",
"D": "Incorrect. Substituting the stated va... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008209 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 13 A for 9449 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": "41.41528 g",
"B": "80.83056 g",
"C": "40.41528 g",
"D": "20.20764 g"
} | C | 40.41528 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×9449/(2×96500)=40.41528 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 40.41528 g, not 41.41528 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 40.41528 g, not 80.83056 g.",
"C": "Correct. The worked calculation gives 40.41528 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_007002 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 6 mol H₂ and 22 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "12 mol",
"B": "9 mol",
"C": "-6 mol",
"D": "6 mol"
} | D | 6 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 6 mol H₂O; O₂ can produce 44 mol H₂O. The limiting condition is H₂; product=6 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 12 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 9 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not -6 mol.",
"D... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001389 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (-2x² -2x +6) dx. | {
"A": "-216",
"B": "-144",
"C": "144",
"D": "-72"
} | B | -144 | An antiderivative is (-2/3)x³+(-2/2)x²+(6)x. Evaluating between 0 and 6 gives (-2/3)(6)³+(-2/2)(6)²+(6)(6)=-144. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -144, not -216.",
"B": "Correct. The worked calculation gives -144.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -144, not 144.",
"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_008455 | 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 1.68 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-1.32 K",
"B": "1.68 K",
"C": "1.26 K",
"D": "-0.32 K"
} | B | 1.68 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×1.0×1.68=1.68 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.68 K, not -1.32 K.",
"B": "Correct. The worked calculation gives 1.68 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.68 K, not 1.26 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005241 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +4 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "22.04082 N",
"B": "3.20408 N",
"C": "23.04082 N",
"D": "11.02041 N"
} | A | 22.04082 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(4×10⁻⁶)/(7×10⁻²)²=22.04082 N. | {
"A": "Correct. The worked calculation gives 22.04082 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22.04082 N, not 3.20408 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22.04082 N, not 23.04082 N.",
"D": "Incorrect. Substituting... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005751 | 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 1.9 atm at 356 K. What is its pressure at 633 K? | {
"A": "-3.37837 atm",
"B": "4.37837 atm",
"C": "1.68919 atm",
"D": "3.37837 atm"
} | D | 3.37837 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.9)(633)/(356)=3.37837 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.37837 atm, not -3.37837 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.37837 atm, not 4.37837 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3... | [
"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_008098 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 3 A for 7875 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": "9.77299 g",
"B": "6.77299 g",
"C": "7.77299 g",
"D": "15.54598 g"
} | C | 7.77299 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×3×7875/(2×96500)=7.77299 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.77299 g, not 9.77299 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.77299 g, not 6.77299 g.",
"C": "Correct. The worked calculation gives 7.77299 g.",
"D": "Incorrect. Substituting the... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002873 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-1, 5, 1) and v=(-7, 7, -4), calculate u·v. | {
"A": "38",
"B": "30.4",
"C": "40",
"D": "37"
} | A | 38 | The dot product is the sum of corresponding component products: (-1)(-7)+(5)(7)+(1)(-4)=38. | {
"A": "Correct. The worked calculation gives 38.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 38, not 30.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 38, not 40.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005639 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 26 μF capacitor is charged to a potential difference of 6 V. Calculate the energy stored, expressed in μJ. | {
"A": "466 μJ",
"B": "234 μJ",
"C": "702 μJ",
"D": "468 μJ"
} | D | 468 μJ | U=½CV². Since C=26 μF, U in μJ is ½×26×(6)²=468 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 468 μJ, not 466 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 468 μJ, not 234 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 468 μJ, not 702 μJ.",
... | [
"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_007751 | 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 120 minutes? | {
"A": "-1.23438 mmol L⁻¹",
"B": "0.76562 mmol L⁻¹",
"C": "-0.23438 mmol L⁻¹",
"D": "-2.23438 mmol L⁻¹"
} | B | 0.76562 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=49/2^6=0.76562 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.76562 mmol L⁻¹, not -1.23438 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.76562 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.76562 mmol L⁻¹, not -0.23438 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_005225 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +7 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "5.68595 N",
"B": "48.8595 N",
"C": "46.8595 N",
"D": "56.2314 N"
} | C | 46.8595 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(7×10⁻⁶)/(11×10⁻²)²=46.8595 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 46.8595 N, not 5.68595 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 46.8595 N, not 48.8595 N.",
"C": "Correct. The worked calculation gives 46.8595 N.",
"D": "Incorrect. Substituting the... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002445 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, -8], [1, -6]]. | {
"A": "-55.2",
"B": "-92",
"C": "-46",
"D": "-45"
} | C | -46 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(-6)−(-8)(1)=-46. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -46, not -55.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -46, not -92.",
"C": "Correct. The worked calculation gives -46.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_007493 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 59 mL of 0.10 M HCl is mixed with 83 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "14.22792",
"B": "9.17094",
"C": "18.34188",
"D": "12.22792"
} | D | 12.22792 | Excess OH⁻ moles=0.10×(83−59)/1000=0.002400 mol. Total volume=0.142 L, so [OH⁻]=0.016901 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.22792. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.22792, not 14.22792.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.22792, not 9.17094.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.22792, not 1... | [
"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_001323 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ +4x² +2x+7. Evaluate f′(-2). | {
"A": "34",
"B": "-34",
"C": "68",
"D": "33"
} | A | 34 | Differentiate: f′(x)=3(4)x²+2(4)x+(2). At x=-2, f′(-2)=3(4)(-2)²+2(4)(-2)+(2)=34. | {
"A": "Correct. The worked calculation gives 34.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 34, not -34.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 34, not 68.",
"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_009562 | 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_8N_3X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "5",
"C": "4",
"D": "7"
} | C | 4 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+3−8−1)/2=4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 5.",
"C": "Correct. The worked calculation gives 4.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004163 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 35 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.23. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "291.2 N",
"B": "-145.6 N",
"C": "145.6 N",
"D": "143.6 N"
} | C | 145.6 N | Net force=mg(sinθ−μcosθ)=35×10×(0.6−0.23×0.8)=145.6 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 145.6 N, not 291.2 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 145.6 N, not -145.6 N.",
"C": "Correct. The worked calculation gives 145.6 N.",
"D": "Incorrect. Substituting the stated v... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005864 | 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 3 atm at 370 K. What is its pressure at 500 K? | {
"A": "8.10811 atm",
"B": "4.05405 atm",
"C": "5.05405 atm",
"D": "6.05405 atm"
} | B | 4.05405 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3)(500)/(370)=4.05405 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.05405 atm, not 8.10811 atm.",
"B": "Correct. The worked calculation gives 4.05405 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.05405 atm, not 5.05405 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_004707 | 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 9 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.42105 A",
"B": "2.94737 A",
"C": "0.94737 A",
"D": "5.94737 A"
} | B | 2.94737 A | Series branch resistance=7+12=19 Ω. Parallel equivalent R_eq=(19×9)/(19+9)=6.10714 Ω. Total current I=V/R_eq=18/6.10714=2.94737 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.94737 A, not 4.42105 A.",
"B": "Correct. The worked calculation gives 2.94737 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.94737 A, not 0.94737 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002923 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(9, 6, 2) and v=(5, 7, 0), calculate u·v. | {
"A": "174",
"B": "43.5",
"C": "-87",
"D": "87"
} | D | 87 | The dot product is the sum of corresponding component products: (9)(5)+(6)(7)+(2)(0)=87. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 87, not 174.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 87, not 43.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 87, not -87.",
"D": "Correct. The... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005702 | 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 3.4 atm at 305 K. What is its pressure at 501 K? | {
"A": "5.58492 atm",
"B": "-5.58492 atm",
"C": "4.18869 atm",
"D": "2.58492 atm"
} | A | 5.58492 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.4)(501)/(305)=5.58492 atm. | {
"A": "Correct. The worked calculation gives 5.58492 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.58492 atm, not -5.58492 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.58492 atm, not 4.18869 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_006783 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 17 mol H₂ and 3 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "3 mol",
"B": "4.5 mol",
"C": "5 mol",
"D": "6 mol"
} | D | 6 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 17 mol H₂O; O₂ can produce 6 mol H₂O. The limiting condition is O₂; product=6 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 3 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 4.5 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 5 mol.",
"D... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002255 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 8 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.3834",
"B": "1.03834",
"C": "-1.6166",
"D": "0.7668"
} | A | 0.3834 | Favourable pairs = C(3,2)+C(8,2)+C(12,2)=97. Total pairs=C(23,2)=253. Therefore P=97/253=0.3834. | {
"A": "Correct. The worked calculation gives 0.3834.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3834, not 1.03834.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3834, not -1.6166.",
"D": "Incorrect. Substituting the stated value... | [
"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_000642 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 23 and common difference 2. Find the sum of its first 24 terms. | {
"A": "1104",
"B": "1102",
"C": "1106",
"D": "1656"
} | A | 1104 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=23, d=2, n=24: Sₙ=24/2[2(23)+(24−1)(2)]=1104. | {
"A": "Correct. The worked calculation gives 1104.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1104, not 1102.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1104, not 1106.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009054 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.68 V, transfers 1 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.9755 V",
"B": "1.46325 V",
"C": "1.9755 V",
"D": "-0.0245 V"
} | A | 0.9755 V | Apply the Nernst equation: E=0.68−(0.0591/1)(-5)=0.9755 V. | {
"A": "Correct. The worked calculation gives 0.9755 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9755 V, not 1.46325 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9755 V, not 1.9755 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_007344 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 50 mL of 0.10 M HCl is mixed with 92 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "11.47096",
"B": "14.47096",
"C": "12.47096",
"D": "10.47096"
} | C | 12.47096 | Excess OH⁻ moles=0.10×(92−50)/1000=0.004200 mol. Total volume=0.142 L, so [OH⁻]=0.029577 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.47096. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.47096, not 11.47096.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.47096, not 14.47096.",
"C": "Correct. The worked calculation gives 12.47096.",
"D": "Incorrect. Substituting the stat... | [
"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_007565 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 96 mL of 0.10 M HCl is mixed with 73 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.18662",
"B": "2.79924",
"C": "1.86616",
"D": "2.86616"
} | C | 1.86616 | Excess H⁺ moles=0.10×(96−73)/1000=0.002300 mol. Total volume=0.169 L, so [H⁺]=0.013609 M and pH=−log₁₀[H⁺]=1.86616. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.86616, not 1.18662.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.86616, not 2.79924.",
"C": "Correct. The worked calculation gives 1.86616.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001723 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 33 distinct elements? | {
"A": "23734.6",
"B": "237336",
"C": "189868.8",
"D": "178002"
} | B | 237336 | Order does not matter, so the count is C(33,5)=33!/[5!(28)!]=237336. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 237336, not 23734.6.",
"B": "Correct. The worked calculation gives 237336.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 237336, not 189868.8.",
"D": "Incorrect. Substituting the stated valu... | [
"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_001231 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ -2x² -6x+7. Evaluate f′(5). | {
"A": "328.8",
"B": "205.5",
"C": "275",
"D": "274"
} | D | 274 | Differentiate: f′(x)=3(4)x²+2(-2)x+(-6). At x=5, f′(5)=3(4)(5)²+2(-2)(5)+(-6)=274. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 274, not 328.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 274, not 205.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 274, not 275.",
"D": "Correc... | [
"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_002498 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 0], [6, -4]]. | {
"A": "-24",
"B": "-15",
"C": "-10",
"D": "-12"
} | D | -12 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(-4)−(0)(6)=-12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -12, not -24.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -12, not -15.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -12, not -10.",
"D": "Correct. T... | [
"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_007770 | 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 71 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "0.27734 mmol L⁻¹",
"B": "0.55469 mmol L⁻¹",
"C": "-2.44531 mmol L⁻¹",
"D": "1.05547 mmol L⁻¹"
} | B | 0.55469 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=71/2^7=0.55469 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.55469 mmol L⁻¹, not 0.27734 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.55469 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.55469 mmol L⁻¹, not -2.44531 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 |
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