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_007963 | 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 15 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "1.40625 mmol L⁻¹",
"B": "-1.0625 mmol L⁻¹",
"C": "-2.0625 mmol L⁻¹",
"D": "0.9375 mmol L⁻¹"
} | D | 0.9375 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=15/2^4=0.9375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9375 mmol L⁻¹, not 1.40625 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9375 mmol L⁻¹, not -1.0625 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing... | [
"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_003588 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 80 m s⁻¹ at 15° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "320 m",
"B": "480 m",
"C": "321 m",
"D": "-320 m"
} | A | 320 m | Range R=u²sin(2θ)/g. Substituting u=80, θ=15° and g=10 gives R=(80)²sin(30°)/10=320 m. | {
"A": "Correct. The worked calculation gives 320 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 320 m, not 480 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 320 m, not 321 m.",
"D": "Incorrect. Substituting the stated values into ... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009858 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(OH)_3]^+0, each OH ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "0",
"B": "2.25",
"C": "3",
"D": "1.5"
} | C | 3 | Let the formal oxidation state of Cu be x. Charge balance gives x+(3)(−1)=+0; hence x=0+3=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"C": "Correct. The worked calculation gives 3.",
"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_008603 | 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 0.47 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.48128 K",
"B": "-0.48128 K",
"C": "2.48128 K",
"D": "1.04813 K"
} | A | 0.48128 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×0.47=0.48128 K. | {
"A": "Correct. The worked calculation gives 0.48128 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.48128 K, not -0.48128 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.48128 K, not 2.48128 K.",
"D": "Incorrect. Substituting th... | [
"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_002583 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, -2], [2, -2]]. | {
"A": "-8",
"B": "-3",
"C": "-7",
"D": "-4"
} | D | -4 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(-2)−(-2)(2)=-4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4, not -8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -4, not -3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -4, not -7.",
"D": "Correct. The wor... | [
"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_008861 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.93 mol L⁻¹ and initially B is absent. At equilibrium, 55% of A has dissociated at constant volume. Find K_c. | {
"A": "5.00133",
"B": "2.50067",
"C": "-0.49933",
"D": "0.50067"
} | B | 2.50067 | Let α=0.55. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.93)(0.55)²/(1−0.55)=2.50067. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.50067, not 5.00133.",
"B": "Correct. The worked calculation gives 2.50067.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.50067, not -0.49933.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003419 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 15 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "20.48557 m",
"B": "19.48557 m",
"C": "17.48557 m",
"D": "14.61418 m"
} | B | 19.48557 m | Range R=u²sin(2θ)/g. Substituting u=15, θ=60° and g=10 gives R=(15)²sin(120°)/10=19.48557 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19.48557 m, not 20.48557 m.",
"B": "Correct. The worked calculation gives 19.48557 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19.48557 m, not 17.48557 m.",
"D": "Incorrect. Substitutin... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004264 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 20 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.17. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "-92.8 N",
"B": "94.8 N",
"C": "92.8 N",
"D": "46.4 N"
} | C | 92.8 N | Net force=mg(sinθ−μcosθ)=20×10×(0.6−0.17×0.8)=92.8 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 92.8 N, not -92.8 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 92.8 N, not 94.8 N.",
"C": "Correct. The worked calculation gives 92.8 N.",
"D": "Incorrect. Substituting the stated values... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005177 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +1 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "2.11111 N",
"B": "0.55556 N",
"C": "4.11111 N",
"D": "1.11111 N"
} | D | 1.11111 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(1×10⁻⁶)/(9×10⁻²)²=1.11111 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.11111 N, not 2.11111 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.11111 N, not 0.55556 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.11111 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_005011 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +8 μC and +4 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "-35.55556 N",
"B": "53.33333 N",
"C": "34.55556 N",
"D": "35.55556 N"
} | D | 35.55556 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(8×10⁻⁶)(4×10⁻⁶)/(9×10⁻²)²=35.55556 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 35.55556 N, not -35.55556 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 35.55556 N, not 53.33333 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 35.55... | [
"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_007675 | 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 65 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "5.125 mmol L⁻¹",
"B": "1.8125 mmol L⁻¹",
"C": "8.125 mmol L⁻¹",
"D": "6.09375 mmol L⁻¹"
} | C | 8.125 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=65/2^3=8.125 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.125 mmol L⁻¹, not 5.125 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.125 mmol L⁻¹, not 1.8125 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 8.125 mmol L⁻¹.",
"D": "I... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005194 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +8 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "576 N",
"B": "720 N",
"C": "360 N",
"D": "480 N"
} | D | 480 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(8×10⁻⁶)/(3×10⁻²)²=480 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 480 N, not 576 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 480 N, not 720 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 480 N, not 360 N.",
"D":... | [
"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_005691 | 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 3.8 atm at 435 K. What is its pressure at 664 K? | {
"A": "5.80046 atm",
"B": "8.70069 atm",
"C": "3.80046 atm",
"D": "2.80046 atm"
} | A | 5.80046 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.8)(664)/(435)=5.80046 atm. | {
"A": "Correct. The worked calculation gives 5.80046 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.80046 atm, not 8.70069 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.80046 atm, not 3.80046 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_008264 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 14 A for 3184 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": "10.99965 g",
"B": "14.6662 g",
"C": "12.6662 g",
"D": "16.6662 g"
} | B | 14.6662 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×3184/(2×96500)=14.6662 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14.6662 g, not 10.99965 g.",
"B": "Correct. The worked calculation gives 14.6662 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14.6662 g, not 12.6662 g.",
"D": "Incorrect. Substituting th... | [
"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_001356 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (-4x² +4x +4) dx. | {
"A": "-36.33333",
"B": "-29.86667",
"C": "37.33333",
"D": "-37.33333"
} | D | -37.33333 | An antiderivative is (-4/3)x³+(4/2)x²+(4)x. Evaluating between 0 and 4 gives (-4/3)(4)³+(4/2)(4)²+(4)(4)=-37.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -37.33333, not -36.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -37.33333, not -29.86667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -37.33333,... | [
"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_007902 | 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 88 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "11 mmol L⁻¹",
"B": "16.5 mmol L⁻¹",
"C": "12 mmol L⁻¹",
"D": "2.1 mmol L⁻¹"
} | A | 11 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=88/2^3=11 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 11 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11 mmol L⁻¹, not 16.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11 mmol L⁻¹, not 12 mmol L⁻¹.",
"D": "Incorrect. Subs... | [
"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_001520 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (3x² +8x +5) dx. | {
"A": "147",
"B": "296",
"C": "148",
"D": "15.8"
} | C | 148 | An antiderivative is (3/3)x³+(8/2)x²+(5)x. Evaluating between 0 and 4 gives (3/3)(4)³+(8/2)(4)²+(5)(4)=148. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 148, not 147.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 148, not 296.",
"C": "Correct. The worked calculation gives 148.",
"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_008447 | 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 0.14 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.084 K",
"B": "0.063 K",
"C": "-1.916 K",
"D": "0.126 K"
} | A | 0.084 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.6×0.14=0.084 K. | {
"A": "Correct. The worked calculation gives 0.084 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.084 K, not 0.063 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.084 K, not -1.916 K.",
"D": "Incorrect. Substituting the stated v... | [
"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_000894 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio 3. What is the sum of its first 10 terms? | {
"A": "177146",
"B": "177144",
"C": "17715.4",
"D": "177143"
} | B | 177144 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(3^10−1)/(3−1)=177144. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 177144, not 177146.",
"B": "Correct. The worked calculation gives 177144.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 177144, not 17715.4.",
"D": "Incorrect. Substituting the stated values... | [
"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_003858 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 0 m s⁻¹. A constant net force does 11 N of work over 12 m in the direction of motion. Find its final kinetic energy. | {
"A": "134 J",
"B": "66 J",
"C": "158.4 J",
"D": "132 J"
} | D | 132 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(0)²+(11)(12)=132 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 132 J, not 134 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 132 J, not 66 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 132 J, not 158.4 J.",
"D"... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004256 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 17 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.32. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "-58.48 N",
"B": "56.48 N",
"C": "58.48 N",
"D": "70.176 N"
} | C | 58.48 N | Net force=mg(sinθ−μcosθ)=17×10×(0.6−0.32×0.8)=58.48 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 58.48 N, not -58.48 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 58.48 N, not 56.48 N.",
"C": "Correct. The worked calculation gives 58.48 N.",
"D": "Incorrect. Substituting the stated v... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008877 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.6 mol L⁻¹ and initially B is absent. At equilibrium, 66% of A has dissociated at constant volume. Find K_c. | {
"A": "5.07482",
"B": "2.07482",
"C": "0.07482",
"D": "3.07482"
} | D | 3.07482 | Let α=0.66. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.6)(0.66)²/(1−0.66)=3.07482. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.07482, not 5.07482.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.07482, not 2.07482.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.07482, not 0.074... | [
"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_008491 | 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 1.69 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.8788 K",
"B": "0.4394 K",
"C": "3.8788 K",
"D": "1.7576 K"
} | A | 0.8788 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.52×1.69=0.8788 K. | {
"A": "Correct. The worked calculation gives 0.8788 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8788 K, not 0.4394 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8788 K, not 3.8788 K.",
"D": "Incorrect. Substituting the stat... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004876 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 6 Ω are connected in series; this combination is connected in parallel with a 13 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.44615 A",
"B": "0.44615 A",
"C": "6.44615 A",
"D": "3.44615 A"
} | D | 3.44615 A | Series branch resistance=9+6=15 Ω. Parallel equivalent R_eq=(15×13)/(15+13)=6.96429 Ω. Total current I=V/R_eq=24/6.96429=3.44615 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.44615 A, not 4.44615 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.44615 A, not 0.44615 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.44615 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_007357 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 17 mL of 0.10 M HCl is mixed with 39 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "10.59423",
"B": "6.29712",
"C": "-12.59423",
"D": "12.59423"
} | D | 12.59423 | Excess OH⁻ moles=0.10×(39−17)/1000=0.002200 mol. Total volume=0.056 L, so [OH⁻]=0.039286 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.59423. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.59423, not 10.59423.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.59423, not 6.29712.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.59423, 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_005790 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.5 atm at 289 K. What is its pressure at 309 K? | {
"A": "1.16038 atm",
"B": "4.60381 atm",
"C": "1.60381 atm",
"D": "-1.39619 atm"
} | C | 1.60381 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.5)(309)/(289)=1.60381 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.60381 atm, not 1.16038 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.60381 atm, not 4.60381 atm.",
"C": "Correct. The worked calculation gives 1.60381 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_000277 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +14x -5=0, let its roots be α and β. What is α²+β²? | {
"A": "9.84",
"B": "4.92",
"C": "6.84",
"D": "11.84"
} | A | 9.84 | By Vieta's relations, α+β = -14/5 and αβ = -5/5. Then α²+β²=(α+β)²−2αβ = (-14/5)²−2(-5/5) = 9.84. | {
"A": "Correct. The worked calculation gives 9.84.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.84, not 4.92.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.84, not 6.84.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_001495 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (2x² -7x -2) dx. | {
"A": "-17.06667",
"B": "-42.66667",
"C": "-21.33333",
"D": "-1.13333"
} | C | -21.33333 | An antiderivative is (2/3)x³+(-7/2)x²+(-2)x. Evaluating between 0 and 4 gives (2/3)(4)³+(-7/2)(4)²+(-2)(4)=-21.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -21.33333, not -17.06667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -21.33333, not -42.66667.",
"C": "Correct. The worked calculation gives -21.33333.",
"D": "Incorrect. Substituting the... | [
"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_003813 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 10 m s⁻¹. A constant net force does 27 N of work over 17 m in the direction of motion. Find its final kinetic energy. | {
"A": "-909 J",
"B": "1090.8 J",
"C": "909 J",
"D": "727.2 J"
} | C | 909 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(10)²+(27)(17)=909 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 909 J, not -909 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 909 J, not 1090.8 J.",
"C": "Correct. The worked calculation gives 909 J.",
"D": "Incorrect. Substituting the stated values i... | [
"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_008918 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.12 mol L⁻¹ and initially B is absent. At equilibrium, 44% of A has dissociated at constant volume. Find K_c. | {
"A": "0.5488",
"B": "1.1616",
"C": "2.3232",
"D": "1.5488"
} | D | 1.5488 | Let α=0.44. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.12)(0.44)²/(1−0.44)=1.5488. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.5488, not 0.5488.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.5488, not 1.1616.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.5488, not 2.3232.",
... | [
"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_008497 | 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 1.35 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.62 K",
"B": "2.62 K",
"C": "-0.38 K",
"D": "3.24 K"
} | A | 1.62 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.6×1.35=1.62 K. | {
"A": "Correct. The worked calculation gives 1.62 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.62 K, not 2.62 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.62 K, not -0.38 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_004329 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 33 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.30. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "117.8 N",
"B": "118.8 N",
"C": "95.04 N",
"D": "120.8 N"
} | B | 118.8 N | Net force=mg(sinθ−μcosθ)=33×10×(0.6−0.30×0.8)=118.8 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 118.8 N, not 117.8 N.",
"B": "Correct. The worked calculation gives 118.8 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 118.8 N, not 95.04 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003533 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 52 m s⁻¹ at 50° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "266.29202 m",
"B": "268.29202 m",
"C": "-266.29202 m",
"D": "319.55042 m"
} | A | 266.29202 m | Range R=u²sin(2θ)/g. Substituting u=52, θ=50° and g=10 gives R=(52)²sin(100°)/10=266.29202 m. | {
"A": "Correct. The worked calculation gives 266.29202 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 266.29202 m, not 268.29202 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 266.29202 m, not -266.29202 m.",
"D": "Incorrect. Subst... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002568 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, -4], [7, -2]]. | {
"A": "2.4",
"B": "11",
"C": "14",
"D": "28"
} | C | 14 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(-2)−(-4)(7)=14. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14, not 2.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14, not 11.",
"C": "Correct. The worked calculation gives 14.",
"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_000601 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 18 and common difference 2. Find the sum of its first 35 terms. | {
"A": "910",
"B": "1820",
"C": "2730",
"D": "183"
} | B | 1820 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=18, d=2, n=35: Sₙ=35/2[2(18)+(35−1)(2)]=1820. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1820, not 910.",
"B": "Correct. The worked calculation gives 1820.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1820, not 2730.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_002311 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 5 blue and 10 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.49457",
"B": "3.32971",
"C": "0.32971",
"D": "2.32971"
} | C | 0.32971 | Favourable pairs = C(9,2)+C(5,2)+C(10,2)=91. Total pairs=C(24,2)=276. Therefore P=91/276=0.32971. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32971, not 0.49457.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32971, not 3.32971.",
"C": "Correct. The worked calculation gives 0.32971.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001784 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 2 elements can be selected from a set of 30 distinct elements? | {
"A": "437",
"B": "435",
"C": "326.25",
"D": "522"
} | B | 435 | Order does not matter, so the count is C(30,2)=30!/[2!(28)!]=435. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 435, not 437.",
"B": "Correct. The worked calculation gives 435.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 435, not 326.25.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_005272 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +8 μC and +4 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "576 N",
"B": "720 N",
"C": "1440 N",
"D": "722 N"
} | B | 720 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(8×10⁻⁶)(4×10⁻⁶)/(2×10⁻²)²=720 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 720 N, not 576 N.",
"B": "Correct. The worked calculation gives 720 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 720 N, not 1440 N.",
"D": "Incorrect. Substituting the stated values into... | [
"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_003909 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block initially moves at 0 m s⁻¹. A constant net force does 12 N of work over 19 m in the direction of motion. Find its final kinetic energy. | {
"A": "342 J",
"B": "182.4 J",
"C": "23.8 J",
"D": "228 J"
} | D | 228 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(15)(0)²+(12)(19)=228 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 228 J, not 342 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 228 J, not 182.4 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 228 J, not 23.8 J.",
"... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002861 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-1, -3, -3) and v=(9, 6, -1), calculate u·v. | {
"A": "-48",
"B": "-22",
"C": "-24",
"D": "-18"
} | C | -24 | The dot product is the sum of corresponding component products: (-1)(9)+(-3)(6)+(-3)(-1)=-24. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -24, not -48.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -24, not -22.",
"C": "Correct. The worked calculation gives -24.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000984 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio 4. What is the sum of its first 9 terms? | {
"A": "961191",
"B": "1441786.5",
"C": "961192",
"D": "480595.5"
} | A | 961191 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(4^9−1)/(4−1)=961191. | {
"A": "Correct. The worked calculation gives 961191.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 961191, not 1441786.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 961191, not 961192.",
"D": "Incorrect. Substituting the stated valu... | [
"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_001468 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (4x² +8x +3) dx. | {
"A": "159.33333",
"B": "129.06667",
"C": "161.33333",
"D": "80.66667"
} | C | 161.33333 | An antiderivative is (4/3)x³+(8/2)x²+(3)x. Evaluating between 0 and 4 gives (4/3)(4)³+(8/2)(4)²+(3)(4)=161.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 161.33333, not 159.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 161.33333, not 129.06667.",
"C": "Correct. The worked calculation gives 161.33333.",
"D": "Incorrect. Substituting the... | [
"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_000088 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 +10x -2=0, let its roots be α and β. What is α²+β²? | {
"A": "3.44444",
"B": "6.44444",
"C": "1.34444",
"D": "5.16667"
} | A | 3.44444 | By Vieta's relations, α+β = -10/6 and αβ = -2/6. Then α²+β²=(α+β)²−2αβ = (-10/6)²−2(-2/6) = 3.44444. | {
"A": "Correct. The worked calculation gives 3.44444.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.44444, not 6.44444.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.44444, not 1.34444.",
"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_009805 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(OH)_2]^-1, each OH ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "2",
"B": "1",
"C": "-1",
"D": "0"
} | B | 1 | Let the formal oxidation state of Mn be x. Charge balance gives x+(2)(−1)=-1; hence x=-1+2=+1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"B": "Correct. The worked calculation gives 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not -1.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003261 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-5-7i)/(5+3i). What is Re(z), the real part of z? | {
"A": "-2.70588",
"B": "1.64706",
"C": "-1.35294",
"D": "-1.01471"
} | C | -1.35294 | Multiply numerator and denominator by the conjugate (5-3i). Then Re(z)=(ac+bd)/(c²+d²)=((-5)(5)+(-7)(3))/(5²+(3)²)=-1.35294. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.35294, not -2.70588.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.35294, not 1.64706.",
"C": "Correct. The worked calculation gives -1.35294.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003122 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(2-2i)/(1+9i). What is Re(z), the real part of z? | {
"A": "0.80488",
"B": "-2.19512",
"C": "-0.19512",
"D": "-0.29268"
} | C | -0.19512 | Multiply numerator and denominator by the conjugate (1-9i). Then Re(z)=(ac+bd)/(c²+d²)=((2)(1)+(-2)(9))/(1²+(9)²)=-0.19512. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.19512, not 0.80488.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.19512, not -2.19512.",
"C": "Correct. The worked calculation gives -0.19512.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005883 | 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 5 atm at 271 K. What is its pressure at 482 K? | {
"A": "6.66974 atm",
"B": "17.78598 atm",
"C": "8.89299 atm",
"D": "13.33948 atm"
} | C | 8.89299 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(5)(482)/(271)=8.89299 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.89299 atm, not 6.66974 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.89299 atm, not 17.78598 atm.",
"C": "Correct. The worked calculation gives 8.89299 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_004369 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 15 kg and radius 6 m is acted on by a constant torque of 11 N m about its central axis. Find its angular acceleration. | {
"A": "-2.95926 rad s⁻²",
"B": "0.02037 rad s⁻²",
"C": "1.04074 rad s⁻²",
"D": "0.04074 rad s⁻²"
} | D | 0.04074 rad s⁻² | For a solid disc, I=½MR²=½(15)(6)²=270 kg m². Using τ=Iα, α=11/270=0.04074 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.04074 rad s⁻², not -2.95926 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.04074 rad s⁻², not 0.02037 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing ... | [
"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_002764 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(7, 5, -3) and v=(9, -6, 0), calculate u·v. | {
"A": "16.5",
"B": "26.4",
"C": "33",
"D": "66"
} | C | 33 | The dot product is the sum of corresponding component products: (7)(9)+(5)(-6)+(-3)(0)=33. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33, not 16.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33, not 26.4.",
"C": "Correct. The worked calculation gives 33.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_004630 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 13 kg and radius 5 m is acted on by a constant torque of 48 N m about its central axis. Find its angular acceleration. | {
"A": "0.22154 rad s⁻²",
"B": "0.59077 rad s⁻²",
"C": "0.29538 rad s⁻²",
"D": "0.14769 rad s⁻²"
} | C | 0.29538 rad s⁻² | For a solid disc, I=½MR²=½(13)(5)²=162.5 kg m². Using τ=Iα, α=48/162.5=0.29538 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29538 rad s⁻², not 0.22154 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29538 rad s⁻², not 0.59077 rad s⁻².",
"C": "Correct. The worked calculation gives 0.29538 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_004119 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 13 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.20. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "59.2 N",
"B": "57.2 N",
"C": "58.2 N",
"D": "68.64 N"
} | B | 57.2 N | Net force=mg(sinθ−μcosθ)=13×10×(0.6−0.20×0.8)=57.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 57.2 N, not 59.2 N.",
"B": "Correct. The worked calculation gives 57.2 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 57.2 N, not 58.2 N.",
"D": "Incorrect. Substituting the stated values ... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007918 | 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 32 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "1 mmol L⁻¹",
"B": "4 mmol L⁻¹",
"C": "6 mmol L⁻¹",
"D": "5 mmol L⁻¹"
} | B | 4 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=32/2^3=4 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4 mmol L⁻¹, not 1 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 4 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4 mmol L⁻¹, not 6 mmol L⁻¹.",
"D": "Incorrect. Substitutin... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001328 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ +5x² -4x+7. Evaluate f′(3). | {
"A": "134",
"B": "133",
"C": "160.8",
"D": "201"
} | A | 134 | Differentiate: f′(x)=3(4)x²+2(5)x+(-4). At x=3, f′(3)=3(4)(3)²+2(5)(3)+(-4)=134. | {
"A": "Correct. The worked calculation gives 134.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 134, not 133.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 134, not 160.8.",
"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_007797 | 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 11 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "-0.95703 mmol L⁻¹",
"B": "0.04297 mmol L⁻¹",
"C": "-1.95703 mmol L⁻¹",
"D": "0.03223 mmol L⁻¹"
} | B | 0.04297 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=11/2^8=0.04297 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.04297 mmol L⁻¹, not -0.95703 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.04297 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.04297 mmol L⁻¹, not -1.95703 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_006280 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 78 cm in front of a thin convex lens of focal length 16 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.3871",
"B": "-0.25806",
"C": "0.25806",
"D": "2.25806"
} | C | 0.25806 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(78)(16)/(78−16)=20.12903 cm. Thus |m|=v/u=20.12903/78=0.25806. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25806, not 0.3871.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25806, not -0.25806.",
"C": "Correct. The worked calculation gives 0.25806.",
"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_004437 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 12 kg and radius 5 m is acted on by a constant torque of 29 N m about its central axis. Find its angular acceleration. | {
"A": "0.09667 rad s⁻²",
"B": "-1.80667 rad s⁻²",
"C": "2.19333 rad s⁻²",
"D": "0.19333 rad s⁻²"
} | D | 0.19333 rad s⁻² | For a solid disc, I=½MR²=½(12)(5)²=150 kg m². Using τ=Iα, α=29/150=0.19333 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.19333 rad s⁻², not 0.09667 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.19333 rad s⁻², not -1.80667 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing ... | [
"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_000313 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 -6x +1=0, let its roots be α and β. What is α²+β²? | {
"A": "4.33333",
"B": "3.33333",
"C": "-3.33333",
"D": "2.5"
} | B | 3.33333 | By Vieta's relations, α+β = 6/3 and αβ = 1/3. Then α²+β²=(α+β)²−2αβ = (6/3)²−2(1/3) = 3.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.33333, not 4.33333.",
"B": "Correct. The worked calculation gives 3.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.33333, not -3.33333.",
"D": "Incorrect. Substituting the stated v... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005063 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +6 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "3.33333 N",
"B": "6.66667 N",
"C": "-6.66667 N",
"D": "3.66667 N"
} | B | 6.66667 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(6×10⁻⁶)/(9×10⁻²)²=6.66667 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.66667 N, not 3.33333 N.",
"B": "Correct. The worked calculation gives 6.66667 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.66667 N, not -6.66667 N.",
"D": "Incorrect. Substituting th... | [
"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_002017 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 12 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": "0.4386",
"B": "0.65789",
"C": "-0.5614",
"D": "1.04386"
} | A | 0.4386 | Favourable pairs = C(4,2)+C(12,2)+C(3,2)=75. Total pairs=C(19,2)=171. Therefore P=75/171=0.4386. | {
"A": "Correct. The worked calculation gives 0.4386.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.4386, not 0.65789.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.4386, not -0.5614.",
"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_006165 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 137 cm in front of a thin convex lens of focal length 28 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.25688",
"B": "-0.74312",
"C": "0.51376",
"D": "-0.25688"
} | A | 0.25688 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(137)(28)/(137−28)=35.19266 cm. Thus |m|=v/u=35.19266/137=0.25688. | {
"A": "Correct. The worked calculation gives 0.25688.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25688, not -0.74312.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25688, not 0.51376.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006551 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 14 kg is attached to an ideal spring of force constant 70 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.34164 s",
"B": "-2.10557 s",
"C": "0.89443 s",
"D": "0.44721 s"
} | C | 0.89443 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(14/70)=0.89443 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.89443 s, not 1.34164 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.89443 s, not -2.10557 s.",
"C": "Correct. The worked calculation gives 0.89443 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_002526 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, -1], [6, -7]]. | {
"A": "-57",
"B": "-42.75",
"C": "-56",
"D": "-45.6"
} | A | -57 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(-7)−(-1)(6)=-57. | {
"A": "Correct. The worked calculation gives -57.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -57, not -42.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -57, not -56.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_009581 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_8H_14N_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "6",
"B": "5",
"C": "2",
"D": "3"
} | D | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×8+2+2−14−0)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.",
"D": "Correct. The worked ca... | [
"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_000474 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -13 and common difference 13. Find the sum of its first 29 terms. | {
"A": "4903",
"B": "4901",
"C": "3675.75",
"D": "2450.5"
} | B | 4901 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-13, d=13, n=29: Sₙ=29/2[2(-13)+(29−1)(13)]=4901. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4901, not 4903.",
"B": "Correct. The worked calculation gives 4901.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4901, not 3675.75.",
"D": "Incorrect. Substituting the stated values into th... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005451 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 46 μF capacitor is charged to a potential difference of 39 V. Calculate the energy stored, expressed in μJ. | {
"A": "34984 μJ",
"B": "27986.4 μJ",
"C": "34981 μJ",
"D": "34983 μJ"
} | D | 34983 μJ | U=½CV². Since C=46 μF, U in μJ is ½×46×(39)²=34983 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 34983 μJ, not 34984 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 34983 μJ, not 27986.4 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 34983 μJ, no... | [
"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_002521 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 5], [1, -5]]. | {
"A": "-21",
"B": "-24",
"C": "-20",
"D": "-18"
} | C | -20 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(-5)−(5)(1)=-20. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -20, not -21.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -20, not -24.",
"C": "Correct. The worked calculation gives -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_002723 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-1, 7, 3) and v=(-2, 1, -4), calculate u·v. | {
"A": "-3",
"B": "-5",
"C": "-4.5",
"D": "-1.5"
} | A | -3 | The dot product is the sum of corresponding component products: (-1)(-2)+(7)(1)+(3)(-4)=-3. | {
"A": "Correct. The worked calculation gives -3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -3, not -5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -3, not -4.5.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008741 | 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 1.3 mol L⁻¹ and initially B is absent. At equilibrium, 71% of A has dissociated at constant volume. Find K_c. | {
"A": "-9.03903",
"B": "9.03903",
"C": "7.03903",
"D": "8.03903"
} | B | 9.03903 | Let α=0.71. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.3)(0.71)²/(1−0.71)=9.03903. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.03903, not -9.03903.",
"B": "Correct. The worked calculation gives 9.03903.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.03903, not 7.03903.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000880 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio 4. What is the sum of its first 8 terms? | {
"A": "196605",
"B": "196603",
"C": "196604",
"D": "98302.5"
} | A | 196605 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(4^8−1)/(4−1)=196605. | {
"A": "Correct. The worked calculation gives 196605.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 196605, not 196603.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 196605, not 196604.",
"D": "Incorrect. Substituting the stated values ... | [
"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_004432 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 2 m is acted on by a constant torque of 35 N m about its central axis. Find its angular acceleration. | {
"A": "2.5 rad s⁻²",
"B": "4.5 rad s⁻²",
"C": "-2.5 rad s⁻²",
"D": "5.5 rad s⁻²"
} | A | 2.5 rad s⁻² | For a solid disc, I=½MR²=½(7)(2)²=14 kg m². Using τ=Iα, α=35/14=2.5 rad s⁻². | {
"A": "Correct. The worked calculation gives 2.5 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.5 rad s⁻², not 4.5 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.5 rad s⁻², not -2.5 rad s⁻².",
"D": "Incorrect. Subst... | [
"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_007911 | 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 78 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "9.75 mmol L⁻¹",
"B": "29.25 mmol L⁻¹",
"C": "21.5 mmol L⁻¹",
"D": "19.5 mmol L⁻¹"
} | D | 19.5 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=78/2^2=19.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19.5 mmol L⁻¹, not 9.75 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19.5 mmol L⁻¹, not 29.25 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation... | [
"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_009744 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(CN)_6]^+2, each CN ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "5",
"B": "11",
"C": "8",
"D": "12"
} | C | 8 | Let the formal oxidation state of Fe be x. Charge balance gives x+(6)(−1)=+2; hence x=2+6=+8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 11.",
"C": "Correct. The worked calculation gives 8.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002151 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 8 blue and 7 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.0308",
"B": "0.30797",
"C": "0.46196",
"D": "0.23098"
} | B | 0.30797 | Favourable pairs = C(9,2)+C(8,2)+C(7,2)=85. Total pairs=C(24,2)=276. Therefore P=85/276=0.30797. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30797, not 1.0308.",
"B": "Correct. The worked calculation gives 0.30797.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30797, not 0.46196.",
"D": "Incorrect. Substituting the stated val... | [
"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_004860 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 11 Ω are connected in series; this combination is connected in parallel with a 4 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "16.2 A",
"B": "12.8 A",
"C": "21.6 A",
"D": "10.8 A"
} | D | 10.8 A | Series branch resistance=9+11=20 Ω. Parallel equivalent R_eq=(20×4)/(20+4)=3.33333 Ω. Total current I=V/R_eq=36/3.33333=10.8 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.8 A, not 16.2 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.8 A, not 12.8 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10.8 A, not 21.6 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_001098 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ -10x² -3x+7. Evaluate f′(-3). | {
"A": "-117",
"B": "-77",
"C": "-80",
"D": "-78"
} | D | -78 | Differentiate: f′(x)=3(-5)x²+2(-10)x+(-3). At x=-3, f′(-3)=3(-5)(-3)²+2(-10)(-3)+(-3)=-78. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -78, not -117.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -78, not -77.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -78, not -80.",
"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_002461 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, 2], [1, -5]]. | {
"A": "-37.6",
"B": "-3.7",
"C": "-23.5",
"D": "-47"
} | D | -47 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(-5)−(2)(1)=-47. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -47, not -37.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -47, not -3.7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -47, not -23.5.",
"D": "Corre... | [
"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_002252 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 8 blue and 10 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.3619",
"B": "2.3619",
"C": "-2.6381",
"D": "0.3619"
} | D | 0.3619 | Favourable pairs = C(3,2)+C(8,2)+C(10,2)=76. Total pairs=C(21,2)=210. Therefore P=76/210=0.3619. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3619, not 1.3619.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3619, not 2.3619.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3619, not -2.6381.",... | [
"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_004081 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 43 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.17. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "199.52 N",
"B": "200.52 N",
"C": "-199.52 N",
"D": "159.616 N"
} | A | 199.52 N | Net force=mg(sinθ−μcosθ)=43×10×(0.6−0.17×0.8)=199.52 N. | {
"A": "Correct. The worked calculation gives 199.52 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 199.52 N, not 200.52 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 199.52 N, not -199.52 N.",
"D": "Incorrect. Substituting the sta... | [
"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_000864 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio 3. What is the sum of its first 12 terms? | {
"A": "2125762",
"B": "2125760",
"C": "212577",
"D": "2550912"
} | B | 2125760 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(3^12−1)/(3−1)=2125760. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2125760, not 2125762.",
"B": "Correct. The worked calculation gives 2125760.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2125760, not 212577.",
"D": "Incorrect. Substituting the stated val... | [
"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_001116 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=1x³ +8x² -8x+7. Evaluate f′(3). | {
"A": "67",
"B": "65",
"C": "50.25",
"D": "69"
} | A | 67 | Differentiate: f′(x)=3(1)x²+2(8)x+(-8). At x=3, f′(3)=3(1)(3)²+2(8)(3)+(-8)=67. | {
"A": "Correct. The worked calculation gives 67.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 67, not 65.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 67, not 50.25.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_006409 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 14 kg is attached to an ideal spring of force constant 1013 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.76488 s",
"B": "0.47024 s",
"C": "3.23512 s",
"D": "0.23512 s"
} | D | 0.23512 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(14/1013)=0.23512 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.23512 s, not -1.76488 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.23512 s, not 0.47024 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.23512 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_002517 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, -4], [1, 3]]. | {
"A": "15",
"B": "19.5",
"C": "13",
"D": "11"
} | C | 13 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(3)−(-4)(1)=13. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13, not 15.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13, not 19.5.",
"C": "Correct. The worked calculation gives 13.",
"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_003415 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 119 m s⁻¹ at 75° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "710.05 m",
"B": "71.805 m",
"C": "1062.075 m",
"D": "708.05 m"
} | D | 708.05 m | Range R=u²sin(2θ)/g. Substituting u=119, θ=75° and g=10 gives R=(119)²sin(150°)/10=708.05 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 708.05 m, not 710.05 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 708.05 m, not 71.805 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 708.05 m, not ... | [
"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_000646 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 21 and common difference 10. Find the sum of its first 23 terms. | {
"A": "1506.5",
"B": "3013",
"C": "3012",
"D": "2259.75"
} | B | 3013 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=21, d=10, n=23: Sₙ=23/2[2(21)+(23−1)(10)]=3013. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3013, not 1506.5.",
"B": "Correct. The worked calculation gives 3013.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3013, not 3012.",
"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_002971 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(9, 0, -6) and v=(2, 7, -5), calculate u·v. | {
"A": "49",
"B": "48",
"C": "38.4",
"D": "46"
} | B | 48 | The dot product is the sum of corresponding component products: (9)(2)+(0)(7)+(-6)(-5)=48. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 48, not 49.",
"B": "Correct. The worked calculation gives 48.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 48, not 38.4.",
"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_000291 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +4x +6=0, let its roots be α and β. What is α²+β²? | {
"A": "-2.22222",
"B": "-4.44444",
"C": "-4.22222",
"D": "-1.22222"
} | A | -2.22222 | By Vieta's relations, α+β = -4/3 and αβ = 6/3. Then α²+β²=(α+β)²−2αβ = (-4/3)²−2(6/3) = -2.22222. | {
"A": "Correct. The worked calculation gives -2.22222.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2.22222, not -4.44444.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2.22222, not -4.22222.",
"D": "Incorrect. Substituting the stat... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006784 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 26 mol H₂ and 30 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "27 mol",
"B": "26 mol",
"C": "19.5 mol",
"D": "3.6 mol"
} | B | 26 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 26 mol H₂O; O₂ can produce 60 mol H₂O. The limiting condition is H₂; product=26 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 27 mol.",
"B": "Correct. The worked calculation gives 26 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 19.5 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_001649 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (-4x² +1x -2) dx. | {
"A": "-1.41667",
"B": "-2.125",
"C": "-2.83333",
"D": "-0.83333"
} | C | -2.83333 | An antiderivative is (-4/3)x³+(1/2)x²+(-2)x. Evaluating between 0 and 1 gives (-4/3)(1)³+(1/2)(1)²+(-2)(1)=-2.83333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2.83333, not -1.41667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2.83333, not -2.125.",
"C": "Correct. The worked calculation gives -2.83333.",
"D": "Incorrect. Substituting the stated... | [
"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_003214 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(7-4i)/(5+8i). What is Re(z), the real part of z? | {
"A": "0.03371",
"B": "0.06742",
"C": "1.03371",
"D": "-0.96629"
} | A | 0.03371 | Multiply numerator and denominator by the conjugate (5-8i). Then Re(z)=(ac+bd)/(c²+d²)=((7)(5)+(-4)(8))/(5²+(8)²)=0.03371. | {
"A": "Correct. The worked calculation gives 0.03371.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.03371, not 0.06742.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.03371, not 1.03371.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000327 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 -12x +9=0, let its roots be α and β. What is α²+β²? | {
"A": "11",
"B": "2",
"C": "20",
"D": "10"
} | D | 10 | By Vieta's relations, α+β = 12/3 and αβ = 9/3. Then α²+β²=(α+β)²−2αβ = (12/3)²−2(9/3) = 10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 11.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 20.",
"D": "Correct. The work... | [
"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_000017 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 -15x -12=0, let its roots be α and β. What is α²+β²? | {
"A": "199.2",
"B": "124.5",
"C": "249",
"D": "251"
} | C | 249 | By Vieta's relations, α+β = 15/1 and αβ = -12/1. Then α²+β²=(α+β)²−2αβ = (15/1)²−2(-12/1) = 249. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 249, not 199.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 249, not 124.5.",
"C": "Correct. The worked calculation gives 249.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_009121 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.77 V, transfers 2 electrons, and has reaction quotient Q=10^3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "3.68135 V",
"B": "0.34068 V",
"C": "1.06814 V",
"D": "0.68135 V"
} | D | 0.68135 V | Apply the Nernst equation: E=0.77−(0.0591/2)(3)=0.68135 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.68135 V, not 3.68135 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.68135 V, not 0.34068 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.68135 V,... | [
"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_000940 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio -2. What is the sum of its first 8 terms? | {
"A": "-850",
"B": "-1020",
"C": "-849",
"D": "-84"
} | A | -850 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(-2^8−1)/(-2−1)=-850. | {
"A": "Correct. The worked calculation gives -850.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -850, not -1020.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -850, not -849.",
"D": "Incorrect. Substituting the stated values into the ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007450 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 76 mL of 0.10 M HCl is mixed with 100 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "15.1347",
"B": "24.2694",
"C": "-12.1347",
"D": "12.1347"
} | D | 12.1347 | Excess OH⁻ moles=0.10×(100−76)/1000=0.002400 mol. Total volume=0.176 L, so [OH⁻]=0.013636 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.1347. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.1347, not 15.1347.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.1347, not 24.2694.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.1347, not -12.1... | [
"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_001284 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ -2x² +1x+7. Evaluate f′(-3). | {
"A": "-76",
"B": "-95",
"C": "-96",
"D": "-71.25"
} | B | -95 | Differentiate: f′(x)=3(-4)x²+2(-2)x+(1). At x=-3, f′(-3)=3(-4)(-3)²+2(-2)(-3)+(1)=-95. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -95, not -76.",
"B": "Correct. The worked calculation gives -95.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -95, not -96.",
"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_007645 | 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 90 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "11.88349",
"B": "-12.88349",
"C": "12.88349",
"D": "6.44175"
} | C | 12.88349 | Excess OH⁻ moles=0.10×(90−12)/1000=0.007800 mol. Total volume=0.102 L, so [OH⁻]=0.076471 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.88349. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.88349, not 11.88349.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.88349, not -12.88349.",
"C": "Correct. The worked calculation gives 12.88349.",
"D": "Incorrect. Substituting the sta... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005014 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +6 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "99.18367 N",
"B": "-99.18367 N",
"C": "101.18367 N",
"D": "198.36735 N"
} | A | 99.18367 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(6×10⁻⁶)/(7×10⁻²)²=99.18367 N. | {
"A": "Correct. The worked calculation gives 99.18367 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 99.18367 N, not -99.18367 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 99.18367 N, not 101.18367 N.",
"D": "Incorrect. Substitut... | [
"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_009065 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.15 V, transfers 3 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "4.0712 V",
"B": "1.6068 V",
"C": "1.0712 V",
"D": "-1.0712 V"
} | C | 1.0712 V | Apply the Nernst equation: E=1.15−(0.0591/3)(4)=1.0712 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0712 V, not 4.0712 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0712 V, not 1.6068 V.",
"C": "Correct. The worked calculation gives 1.0712 V.",
"D": "Incorrect. Substituting the stat... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004886 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 18 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.83333 A",
"B": "3.33333 A",
"C": "1.66667 A",
"D": "1.16667 A"
} | C | 1.66667 A | Series branch resistance=4+8=12 Ω. Parallel equivalent R_eq=(12×18)/(12+18)=7.2 Ω. Total current I=V/R_eq=12/7.2=1.66667 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.66667 A, not 0.83333 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.66667 A, not 3.33333 A.",
"C": "Correct. The worked calculation gives 1.66667 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_006309 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 24 cm in front of a thin convex lens of focal length 18 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "6",
"B": "3",
"C": "1",
"D": "4.5"
} | B | 3 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(24)(18)/(24−18)=72 cm. Thus |m|=v/u=72/24=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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 |
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