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_000045 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 +17x +10=0, let its roots be α and β. What is α²+β²? | {
"A": "63.25",
"B": "62.25",
"C": "49.8",
"D": "-62.25"
} | B | 62.25 | By Vieta's relations, α+β = -17/2 and αβ = 10/2. Then α²+β²=(α+β)²−2αβ = (-17/2)²−2(10/2) = 62.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 62.25, not 63.25.",
"B": "Correct. The worked calculation gives 62.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 62.25, not 49.8.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_001197 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ +3x² -8x+7. Evaluate f′(-3). | {
"A": "-136",
"B": "68",
"C": "136",
"D": "134"
} | C | 136 | Differentiate: f′(x)=3(6)x²+2(3)x+(-8). At x=-3, f′(-3)=3(6)(-3)²+2(3)(-3)+(-8)=136. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 136, not -136.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 136, not 68.",
"C": "Correct. The worked calculation gives 136.",
"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_005953 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.7 atm at 249 K. What is its pressure at 764 K? | {
"A": "6.21325 atm",
"B": "8.28434 atm",
"C": "4.14217 atm",
"D": "9.28434 atm"
} | B | 8.28434 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.7)(764)/(249)=8.28434 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.28434 atm, not 6.21325 atm.",
"B": "Correct. The worked calculation gives 8.28434 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.28434 atm, not 4.14217 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_008449 | 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 0.46 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.9568 K",
"B": "2.9568 K",
"C": "1.09568 K",
"D": "1.4352 K"
} | A | 0.9568 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.52×0.46=0.9568 K. | {
"A": "Correct. The worked calculation gives 0.9568 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9568 K, not 2.9568 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9568 K, not 1.09568 K.",
"D": "Incorrect. Substituting the sta... | [
"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_000517 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -11 and common difference 10. Find the sum of its first 16 terms. | {
"A": "1025",
"B": "1024",
"C": "819.2",
"D": "1026"
} | B | 1024 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-11, d=10, n=16: Sₙ=16/2[2(-11)+(16−1)(10)]=1024. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1024, not 1025.",
"B": "Correct. The worked calculation gives 1024.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1024, not 819.2.",
"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_005203 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +4 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "33.75 N",
"B": "54 N",
"C": "36 N",
"D": "45 N"
} | D | 45 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(4×10⁻⁶)/(4×10⁻²)²=45 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45 N, not 33.75 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 45 N, not 54 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 45 N, not 36 N.",
"D": "C... | [
"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_002864 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-7, 2, 2) and v=(2, -2, 0), calculate u·v. | {
"A": "-19",
"B": "-18",
"C": "-13.5",
"D": "-20"
} | B | -18 | The dot product is the sum of corresponding component products: (-7)(2)+(2)(-2)+(2)(0)=-18. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -18, not -19.",
"B": "Correct. The worked calculation gives -18.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -18, not -13.5.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_009193 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.44 V, transfers 3 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.5582 V",
"B": "1.5582 V",
"C": "3.5582 V",
"D": "1.15582 V"
} | B | 1.5582 V | Apply the Nernst equation: E=1.44−(0.0591/3)(-6)=1.5582 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.5582 V, not 2.5582 V.",
"B": "Correct. The worked calculation gives 1.5582 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.5582 V, not 3.5582 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_004024 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 18 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.43. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "45.08 N",
"B": "36.864 N",
"C": "23.04 N",
"D": "46.08 N"
} | D | 46.08 N | Net force=mg(sinθ−μcosθ)=18×10×(0.6−0.43×0.8)=46.08 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 46.08 N, not 45.08 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 46.08 N, not 36.864 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 46.08 N, not 23.0... | [
"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_006920 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 30 mol H₂ and 15 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "24 mol",
"B": "4 mol",
"C": "30 mol",
"D": "32 mol"
} | C | 30 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 30 mol H₂O; O₂ can produce 30 mol H₂O. The limiting condition is neither; stoichiometric; product=30 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 30 mol, not 24 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30 mol, not 4 mol.",
"C": "Correct. The worked calculation gives 30 mol.",
"D": "Incorrect. Substituting the stated values i... | [
"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_007023 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 12 mol of gas at 374 K and 0.79 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "466.16686 L",
"B": "559.40023 L",
"C": "465.16686 L",
"D": "932.33371 L"
} | A | 466.16686 L | PV=nRT, so V=nRT/P=(12)(0.082057)(374)/(0.79)=466.16686 L. | {
"A": "Correct. The worked calculation gives 466.16686 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 466.16686 L, not 559.40023 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 466.16686 L, not 465.16686 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002858 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(3, -4, -3) and v=(9, 6, 5), calculate u·v. | {
"A": "-0.2",
"B": "-12",
"C": "-9",
"D": "12"
} | B | -12 | The dot product is the sum of corresponding component products: (3)(9)+(-4)(6)+(-3)(5)=-12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -12, not -0.2.",
"B": "Correct. The worked calculation gives -12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -12, not -9.",
"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_009664 | 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_14H_24X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "5",
"B": "3",
"C": "2",
"D": "4"
} | C | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×14+2+0−24−2)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"C": "Correct. The worked calculation gives 2.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007549 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 98 mL of 0.10 M HCl is mixed with 90 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "4.37107",
"B": "-2.37107",
"C": "2.37107",
"D": "1.18553"
} | C | 2.37107 | Excess H⁺ moles=0.10×(98−90)/1000=0.000800 mol. Total volume=0.188 L, so [H⁺]=0.004255 M and pH=−log₁₀[H⁺]=2.37107. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.37107, not 4.37107.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.37107, not -2.37107.",
"C": "Correct. The worked calculation gives 2.37107.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002443 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, 8], [6, -3]]. | {
"A": "-69",
"B": "69",
"C": "-34.5",
"D": "-55.2"
} | A | -69 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(-3)−(8)(6)=-69. | {
"A": "Correct. The worked calculation gives -69.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -69, not 69.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -69, not -34.5.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_008111 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 4 A for 1697 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "2.23336 g",
"B": "3.23336 g",
"C": "-0.76664 g",
"D": "5.23336 g"
} | A | 2.23336 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×1697/(2×96500)=2.23336 g. | {
"A": "Correct. The worked calculation gives 2.23336 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.23336 g, not 3.23336 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.23336 g, not -0.76664 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_007289 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 13 mol of gas at 228 K and 0.06 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "8107.2316 L",
"B": "4053.6158 L",
"C": "4051.6158 L",
"D": "4054.6158 L"
} | B | 4053.6158 L | PV=nRT, so V=nRT/P=(13)(0.082057)(228)/(0.06)=4053.6158 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4053.6158 L, not 8107.2316 L.",
"B": "Correct. The worked calculation gives 4053.6158 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4053.6158 L, not 4051.6158 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004777 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 6 Ω are connected in series; this combination is connected in parallel with a 13 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.50962 A",
"B": "1.88221 A",
"C": "2.50962 A",
"D": "-0.49038 A"
} | C | 2.50962 A | Series branch resistance=10+6=16 Ω. Parallel equivalent R_eq=(16×13)/(16+13)=7.17241 Ω. Total current I=V/R_eq=18/7.17241=2.50962 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.50962 A, not 1.50962 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.50962 A, not 1.88221 A.",
"C": "Correct. The worked calculation gives 2.50962 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_005998 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.4 atm at 191 K. What is its pressure at 719 K? | {
"A": "12.79895 atm",
"B": "10.79895 atm",
"C": "11.79895 atm",
"D": "14.79895 atm"
} | A | 12.79895 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.4)(719)/(191)=12.79895 atm. | {
"A": "Correct. The worked calculation gives 12.79895 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.79895 atm, not 10.79895 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.79895 atm, not 11.79895 atm.",
"D": "Incorrect. S... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008974 | 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 1.37 mol L⁻¹ and initially B is absent. At equilibrium, 20% of A has dissociated at constant volume. Find K_c. | {
"A": "0.2055",
"B": "0.411",
"C": "0.274",
"D": "1.0274"
} | C | 0.274 | Let α=0.2. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.37)(0.2)²/(1−0.2)=0.274. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.274, not 0.2055.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.274, not 0.411.",
"C": "Correct. The worked calculation gives 0.274.",
"D": "Incorrect. Substituting the stated values into... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009630 | 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_13N_1X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "1",
"B": "2",
"C": "0.75",
"D": "-1"
} | A | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×8+2+1−13−4)/2=1. | {
"A": "Correct. The worked calculation gives 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.75.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"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_009482 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_15H_29N_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "1.5",
"B": "-1",
"C": "2",
"D": "4"
} | C | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×15+2+1−29−0)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not -1.",
"C": "Correct. The worked calculation gives 2.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"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_009293 | 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 1 electrons, and has reaction quotient Q=10^2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.5159 V",
"B": "1.0318 V",
"C": "1.5477 V",
"D": "1.10318 V"
} | B | 1.0318 V | Apply the Nernst equation: E=1.15−(0.0591/1)(2)=1.0318 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0318 V, not 0.5159 V.",
"B": "Correct. The worked calculation gives 1.0318 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0318 V, not 1.5477 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_009763 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(Cl)_4]^+3, each Cl ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "5",
"B": "7",
"C": "6",
"D": "8"
} | B | 7 | Let the formal oxidation state of Cr be x. Charge balance gives x+(4)(−1)=+3; hence x=3+4=+7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 5.",
"B": "Correct. The worked calculation gives 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 6.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009827 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(Cl)_2]^+2, each Cl ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "1.4",
"B": "4",
"C": "2",
"D": "6"
} | B | 4 | Let the formal oxidation state of Co be x. Charge balance gives x+(2)(−1)=+2; hence x=2+2=+4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.4.",
"B": "Correct. The worked calculation gives 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001105 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=3x³ -6x² +10x+7. Evaluate f′(-3). | {
"A": "127",
"B": "95.25",
"C": "63.5",
"D": "13.7"
} | A | 127 | Differentiate: f′(x)=3(3)x²+2(-6)x+(10). At x=-3, f′(-3)=3(3)(-3)²+2(-6)(-3)+(10)=127. | {
"A": "Correct. The worked calculation gives 127.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 127, not 95.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 127, not 63.5.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_004297 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 23 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.19. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "103.04 N",
"B": "77.28 N",
"C": "102.04 N",
"D": "123.648 N"
} | A | 103.04 N | Net force=mg(sinθ−μcosθ)=23×10×(0.6−0.19×0.8)=103.04 N. | {
"A": "Correct. The worked calculation gives 103.04 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 103.04 N, not 77.28 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 103.04 N, not 102.04 N.",
"D": "Incorrect. Substituting the state... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001708 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 28 distinct elements? | {
"A": "13123110",
"B": "9842332.5",
"C": "26246220",
"D": "19684665"
} | A | 13123110 | Order does not matter, so the count is C(28,10)=28!/[10!(18)!]=13123110. | {
"A": "Correct. The worked calculation gives 13123110.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13123110, not 9842332.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13123110, not 26246220.",
"D": "Incorrect. Substituting the sta... | [
"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_009823 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(OH)_5]^-1, each OH ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "5",
"B": "2",
"C": "4",
"D": "3"
} | C | 4 | Let the formal oxidation state of Ni be x. Charge balance gives x+(5)(−1)=-1; hence x=-1+5=+4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"C": "Correct. The worked calculation gives 4.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003031 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(0-7i)/(10+2i). What is Re(z), the real part of z? | {
"A": "-0.20192",
"B": "-0.13462",
"C": "-3.13462",
"D": "0.86538"
} | B | -0.13462 | Multiply numerator and denominator by the conjugate (10-2i). Then Re(z)=(ac+bd)/(c²+d²)=((0)(10)+(-7)(2))/(10²+(2)²)=-0.13462. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.13462, not -0.20192.",
"B": "Correct. The worked calculation gives -0.13462.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.13462, not -3.13462.",
"D": "Incorrect. Substituting the stat... | [
"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_008810 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.53 mol L⁻¹ and initially B is absent. At equilibrium, 54% of A has dissociated at constant volume. Find K_c. | {
"A": "0.67195",
"B": "1.13439",
"C": "2.01584",
"D": "1.3439"
} | D | 1.3439 | Let α=0.54. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.53)(0.54)²/(1−0.54)=1.3439. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.3439, not 0.67195.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.3439, not 1.13439.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.3439, not 2.01584.... | [
"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_009479 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_17H_9N_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "11",
"B": "17",
"C": "10.5",
"D": "14"
} | D | 14 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×17+2+1−9−0)/2=14. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14, not 11.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14, not 17.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14, not 10.5.",
"D": "Correct. The w... | [
"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_008971 | 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 1.08 mol L⁻¹ and initially B is absent. At equilibrium, 48% of A has dissociated at constant volume. Find K_c. | {
"A": "4.91409",
"B": "1.91409",
"C": "1.19141",
"D": "-1.91409"
} | B | 1.91409 | Let α=0.48. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.08)(0.48)²/(1−0.48)=1.91409. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.91409, not 4.91409.",
"B": "Correct. The worked calculation gives 1.91409.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.91409, not 1.19141.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006298 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 14 cm in front of a thin convex lens of focal length 6 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-1.25",
"B": "1.75",
"C": "0.75",
"D": "0.375"
} | C | 0.75 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(14)(6)/(14−6)=10.5 cm. Thus |m|=v/u=10.5/14=0.75. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.75, not -1.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.75, not 1.75.",
"C": "Correct. The worked calculation gives 0.75.",
"D": "Incorrect. Substituting the stated values into the ... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002911 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-4, 5, 0) and v=(-1, 7, -6), calculate u·v. | {
"A": "39",
"B": "29.25",
"C": "4.9",
"D": "-39"
} | A | 39 | The dot product is the sum of corresponding component products: (-4)(-1)+(5)(7)+(0)(-6)=39. | {
"A": "Correct. The worked calculation gives 39.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39, not 29.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39, not 4.9.",
"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_006563 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 17 kg is attached to an ideal spring of force constant 1106 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.24796 s",
"B": "2.24796 s",
"C": "-0.75204 s",
"D": "-1.75204 s"
} | A | 0.24796 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(17/1106)=0.24796 s. | {
"A": "Correct. The worked calculation gives 0.24796 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.24796 s, not 2.24796 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.24796 s, not -0.75204 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_006501 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 8 kg is attached to an ideal spring of force constant 1153 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.33319 s",
"B": "-2.83341 s",
"C": "0.16659 s",
"D": "0.24989 s"
} | C | 0.16659 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(8/1153)=0.16659 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.16659 s, not 0.33319 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.16659 s, not -2.83341 s.",
"C": "Correct. The worked calculation gives 0.16659 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_009485 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_17H_18N_3X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "9",
"B": "7",
"C": "11",
"D": "8"
} | A | 9 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×17+2+3−18−3)/2=9. | {
"A": "Correct. The worked calculation gives 9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9, not 11.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005009 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +2 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "7 N",
"B": "6 N",
"C": "5 N",
"D": "3.75 N"
} | C | 5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(2×10⁻⁶)/(6×10⁻²)²=5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5 N, not 7 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5 N, not 6 N.",
"C": "Correct. The worked calculation gives 5 N.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_002296 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 4 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-1.63492",
"B": "0.36508",
"C": "0.73016",
"D": "0.54762"
} | B | 0.36508 | Favourable pairs = C(12,2)+C(4,2)+C(12,2)=138. Total pairs=C(28,2)=378. Therefore P=138/378=0.36508. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.36508, not -1.63492.",
"B": "Correct. The worked calculation gives 0.36508.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.36508, not 0.73016.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000431 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 5 and common difference 13. Find the sum of its first 30 terms. | {
"A": "5804",
"B": "4644",
"C": "8707.5",
"D": "5805"
} | D | 5805 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=5, d=13, n=30: Sₙ=30/2[2(5)+(30−1)(13)]=5805. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5805, not 5804.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5805, not 4644.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5805, not 8707.5.",
"D": "Co... | [
"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_001526 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (3x² -1x +3) dx. | {
"A": "215",
"B": "22.6",
"C": "324",
"D": "216"
} | D | 216 | An antiderivative is (3/3)x³+(-1/2)x²+(3)x. Evaluating between 0 and 6 gives (3/3)(6)³+(-1/2)(6)²+(3)(6)=216. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 216, not 215.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 216, not 22.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 216, not 324.",
"D": "Correct. ... | [
"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_006434 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 5 kg is attached to an ideal spring of force constant 636 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.17733 s",
"B": "-2.82267 s",
"C": "0.35466 s",
"D": "1.17733 s"
} | A | 0.17733 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(5/636)=0.17733 s. | {
"A": "Correct. The worked calculation gives 0.17733 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.17733 s, not -2.82267 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.17733 s, not 0.35466 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_003647 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 68 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "265.66421 m",
"B": "352.21895 m",
"C": "354.21895 m",
"D": "36.4219 m"
} | C | 354.21895 m | Range R=u²sin(2θ)/g. Substituting u=68, θ=25° and g=10 gives R=(68)²sin(50°)/10=354.21895 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 354.21895 m, not 265.66421 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 354.21895 m, not 352.21895 m.",
"C": "Correct. The worked calculation gives 354.21895 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000877 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio 4. What is the sum of its first 12 terms? | {
"A": "27962025",
"B": "2796203.5",
"C": "22369620",
"D": "27962027"
} | A | 27962025 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(4^12−1)/(4−1)=27962025. | {
"A": "Correct. The worked calculation gives 27962025.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 27962025, not 2796203.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 27962025, not 22369620.",
"D": "Incorrect. Substituting the sta... | [
"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_003870 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 10 m s⁻¹. A constant net force does 20 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "576 J",
"B": "720 J",
"C": "1440 J",
"D": "1080 J"
} | B | 720 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(10)²+(20)(11)=720 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 720 J, not 576 J.",
"B": "Correct. The worked calculation gives 720 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 720 J, not 1440 J.",
"D": "Incorrect. Substituting the stated values into... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008784 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.55 mol L⁻¹ and initially B is absent. At equilibrium, 62% of A has dissociated at constant volume. Find K_c. | {
"A": "-6.27179",
"B": "9.40768",
"C": "6.27179",
"D": "7.27179"
} | C | 6.27179 | Let α=0.62. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.55)(0.62)²/(1−0.62)=6.27179. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.27179, not -6.27179.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.27179, not 9.40768.",
"C": "Correct. The worked calculation gives 6.27179.",
"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_005571 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 3 μF capacitor is charged to a potential difference of 24 V. Calculate the energy stored, expressed in μJ. | {
"A": "864 μJ",
"B": "866 μJ",
"C": "691.2 μJ",
"D": "432 μJ"
} | A | 864 μJ | U=½CV². Since C=3 μF, U in μJ is ½×3×(24)²=864 μJ. | {
"A": "Correct. The worked calculation gives 864 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 864 μJ, not 866 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 864 μJ, not 691.2 μJ.",
"D": "Incorrect. Substituting the stated value... | [
"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_001532 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (2x² -2x -2) dx. | {
"A": "165.66667",
"B": "164.66667",
"C": "163.66667",
"D": "-165.66667"
} | A | 165.66667 | An antiderivative is (2/3)x³+(-2/2)x²+(-2)x. Evaluating between 0 and 7 gives (2/3)(7)³+(-2/2)(7)²+(-2)(7)=165.66667. | {
"A": "Correct. The worked calculation gives 165.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 165.66667, not 164.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 165.66667, not 163.66667.",
"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_006042 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 30 cm in front of a thin convex lens of focal length 13 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.76471",
"B": "1.76471",
"C": "1.52941",
"D": "2.76471"
} | A | 0.76471 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(30)(13)/(30−13)=22.94118 cm. Thus |m|=v/u=22.94118/30=0.76471. | {
"A": "Correct. The worked calculation gives 0.76471.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.76471, not 1.76471.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.76471, not 1.52941.",
"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_003811 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 12 m s⁻¹. A constant net force does 5 N of work over 17 m in the direction of motion. Find its final kinetic energy. | {
"A": "1138.8 J",
"B": "1898 J",
"C": "949 J",
"D": "-949 J"
} | C | 949 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(12)²+(5)(17)=949 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 949 J, not 1138.8 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 949 J, not 1898 J.",
"C": "Correct. The worked calculation gives 949 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_008015 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 3 A for 29868 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": "29.48111 g",
"B": "3.94811 g",
"C": "27.48111 g",
"D": "28.48111 g"
} | A | 29.48111 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×3×29868/(2×96500)=29.48111 g. | {
"A": "Correct. The worked calculation gives 29.48111 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 29.48111 g, not 3.94811 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29.48111 g, not 27.48111 g.",
"D": "Incorrect. Substituting... | [
"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_008755 | 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 0.83 mol L⁻¹ and initially B is absent. At equilibrium, 26% of A has dissociated at constant volume. Find K_c. | {
"A": "1.03033",
"B": "0.45493",
"C": "-1.69671",
"D": "0.30329"
} | D | 0.30329 | Let α=0.26. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.83)(0.26)²/(1−0.26)=0.30329. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30329, not 1.03033.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30329, not 0.45493.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30329, not -1.69... | [
"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_002430 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, 2], [1, 3]]. | {
"A": "21",
"B": "14.25",
"C": "22.8",
"D": "19"
} | D | 19 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(3)−(2)(1)=19. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19, not 21.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19, not 14.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19, not 22.8.",
"D": "Correct. Th... | [
"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_006567 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 25 kg is attached to an ideal spring of force constant 133 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.86711 s",
"B": "3.86711 s",
"C": "0.43355 s",
"D": "-0.86711 s"
} | A | 0.86711 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(25/133)=0.86711 s. | {
"A": "Correct. The worked calculation gives 0.86711 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.86711 s, not 3.86711 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.86711 s, not 0.43355 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000002 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 -7x -2=0, let its roots be α and β. What is α²+β²? | {
"A": "10.16667",
"B": "-6.77778",
"C": "6.77778",
"D": "13.55556"
} | C | 6.77778 | By Vieta's relations, α+β = 7/3 and αβ = -2/3. Then α²+β²=(α+β)²−2αβ = (7/3)²−2(-2/3) = 6.77778. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.77778, not 10.16667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.77778, not -6.77778.",
"C": "Correct. The worked calculation gives 6.77778.",
"D": "Incorrect. Substituting the stated ... | [
"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_008241 | 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 15 A for 18251 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": "90.07294 g",
"B": "-90.07294 g",
"C": "72.05835 g",
"D": "91.07294 g"
} | A | 90.07294 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×15×18251/(2×96500)=90.07294 g. | {
"A": "Correct. The worked calculation gives 90.07294 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 90.07294 g, not -90.07294 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 90.07294 g, not 72.05835 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000981 | 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 12 terms? | {
"A": "123032910",
"B": "30758227.5",
"C": "61516454",
"D": "61516455"
} | D | 61516455 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(4^12−1)/(4−1)=61516455. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 61516455, not 123032910.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 61516455, not 30758227.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 61516455, n... | [
"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_007746 | 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 90 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "5.625 mmol L⁻¹",
"B": "4.625 mmol L⁻¹",
"C": "3.625 mmol L⁻¹",
"D": "1.5625 mmol L⁻¹"
} | A | 5.625 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=90/2^4=5.625 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 5.625 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.625 mmol L⁻¹, not 4.625 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.625 mmol L⁻¹, not 3.625 mmol L⁻¹.",
"D": "In... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006515 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 7 kg is attached to an ideal spring of force constant 566 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.77758 s",
"B": "2.22242 s",
"C": "0.22242 s",
"D": "0.16681 s"
} | C | 0.22242 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(7/566)=0.22242 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.22242 s, not -2.77758 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.22242 s, not 2.22242 s.",
"C": "Correct. The worked calculation gives 0.22242 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_005689 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.4 atm at 267 K. What is its pressure at 479 K? | {
"A": "3.76742 atm",
"B": "2.51161 atm",
"C": "5.51161 atm",
"D": "-0.48839 atm"
} | B | 2.51161 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.4)(479)/(267)=2.51161 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.51161 atm, not 3.76742 atm.",
"B": "Correct. The worked calculation gives 2.51161 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.51161 atm, not 5.51161 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_001609 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (1x² +5x +2) dx. | {
"A": "67.33333",
"B": "7.93333",
"C": "69.33333",
"D": "-69.33333"
} | C | 69.33333 | An antiderivative is (1/3)x³+(5/2)x²+(2)x. Evaluating between 0 and 4 gives (1/3)(4)³+(5/2)(4)²+(2)(4)=69.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 69.33333, not 67.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 69.33333, not 7.93333.",
"C": "Correct. The worked calculation gives 69.33333.",
"D": "Incorrect. Substituting the state... | [
"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_006312 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 84 cm in front of a thin convex lens of focal length 18 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.27273",
"B": "0.27273",
"C": "-0.72727",
"D": "0.20455"
} | B | 0.27273 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(84)(18)/(84−18)=22.90909 cm. Thus |m|=v/u=22.90909/84=0.27273. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.27273, not 1.27273.",
"B": "Correct. The worked calculation gives 0.27273.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.27273, not -0.72727.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004954 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 12 Ω and 5 Ω are connected in series; this combination is connected in parallel with a 18 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.7451 A",
"B": "1.27451 A",
"C": "2.05882 A",
"D": "4.7451 A"
} | A | 2.7451 A | Series branch resistance=12+5=17 Ω. Parallel equivalent R_eq=(17×18)/(17+18)=8.74286 Ω. Total current I=V/R_eq=24/8.74286=2.7451 A. | {
"A": "Correct. The worked calculation gives 2.7451 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.7451 A, not 1.27451 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.7451 A, not 2.05882 A.",
"D": "Incorrect. Substituting the st... | [
"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_003913 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 9 m s⁻¹. A constant net force does 11 N of work over 3 m in the direction of motion. Find its final kinetic energy. | {
"A": "478.5 J",
"B": "239.25 J",
"C": "717.75 J",
"D": "957 J"
} | A | 478.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(9)²+(11)(3)=478.5 J. | {
"A": "Correct. The worked calculation gives 478.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 478.5 J, not 239.25 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 478.5 J, not 717.75 J.",
"D": "Incorrect. Substituting the stated ... | [
"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_003118 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(3+13i)/(5+5i). What is Re(z), the real part of z? | {
"A": "-1.6",
"B": "1.6",
"C": "0.6",
"D": "4.6"
} | B | 1.6 | Multiply numerator and denominator by the conjugate (5-5i). Then Re(z)=(ac+bd)/(c²+d²)=((3)(5)+(13)(5))/(5²+(5)²)=1.6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.6, not -1.6.",
"B": "Correct. The worked calculation gives 1.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.6, not 0.6.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_001027 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-3x³ -4x² -6x+7. Evaluate f′(4). | {
"A": "-218.4",
"B": "-182",
"C": "182",
"D": "-273"
} | B | -182 | Differentiate: f′(x)=3(-3)x²+2(-4)x+(-6). At x=4, f′(4)=3(-3)(4)²+2(-4)(4)+(-6)=-182. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -182, not -218.4.",
"B": "Correct. The worked calculation gives -182.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -182, not 182.",
"D": "Incorrect. Substituting the stated values into the ... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002132 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 12 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.32258",
"B": "-0.32258",
"C": "2.32258",
"D": "0.32258"
} | D | 0.32258 | Favourable pairs = C(8,2)+C(12,2)+C(12,2)=160. Total pairs=C(32,2)=496. Therefore P=160/496=0.32258. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32258, not 1.32258.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32258, not -0.32258.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32258, not 2.32... | [
"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_007395 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 47 mL of 0.10 M HCl is mixed with 45 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-0.33724",
"B": "2.66276",
"C": "3.99414",
"D": "1.26628"
} | B | 2.66276 | Excess H⁺ moles=0.10×(47−45)/1000=0.000200 mol. Total volume=0.092 L, so [H⁺]=0.002174 M and pH=−log₁₀[H⁺]=2.66276. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.66276, not -0.33724.",
"B": "Correct. The worked calculation gives 2.66276.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.66276, not 3.99414.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001189 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ +10x² +1x+7. Evaluate f′(5). | {
"A": "-238.8",
"B": "-197",
"C": "-199",
"D": "-298.5"
} | C | -199 | Differentiate: f′(x)=3(-4)x²+2(10)x+(1). At x=5, f′(5)=3(-4)(5)²+2(10)(5)+(1)=-199. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -199, not -238.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -199, not -197.",
"C": "Correct. The worked calculation gives -199.",
"D": "Incorrect. Substituting the stated values into the... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005112 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +8 μC and +7 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "43.65289 N",
"B": "42.65289 N",
"C": "41.65289 N",
"D": "20.82645 N"
} | C | 41.65289 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(8×10⁻⁶)(7×10⁻⁶)/(11×10⁻²)²=41.65289 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 41.65289 N, not 43.65289 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 41.65289 N, not 42.65289 N.",
"C": "Correct. The worked calculation gives 41.65289 N.",
"D": "Incorrect. Substitutin... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005245 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +5 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "199 N",
"B": "200 N",
"C": "240 N",
"D": "198 N"
} | B | 200 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(5×10⁻⁶)/(3×10⁻²)²=200 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 200 N, not 199 N.",
"B": "Correct. The worked calculation gives 200 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 200 N, not 240 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_000116 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +7x -6=0, let its roots be α and β. What is α²+β²? | {
"A": "14.16667",
"B": "11.44444",
"C": "9.44444",
"D": "4.72222"
} | C | 9.44444 | By Vieta's relations, α+β = -7/3 and αβ = -6/3. Then α²+β²=(α+β)²−2αβ = (-7/3)²−2(-6/3) = 9.44444. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.44444, not 14.16667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.44444, not 11.44444.",
"C": "Correct. The worked calculation gives 9.44444.",
"D": "Incorrect. Substituting the stated ... | [
"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_008285 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 9 A for 25298 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": "74.91092 g",
"B": "56.18319 g",
"C": "72.91092 g",
"D": "112.36638 g"
} | A | 74.91092 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×9×25298/(2×96500)=74.91092 g. | {
"A": "Correct. The worked calculation gives 74.91092 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 74.91092 g, not 56.18319 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 74.91092 g, not 72.91092 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003213 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(14+7i)/(11+4i). What is Re(z), the real part of z? | {
"A": "1.32847",
"B": "0.99635",
"C": "1.13285",
"D": "3.32847"
} | A | 1.32847 | Multiply numerator and denominator by the conjugate (11-4i). Then Re(z)=(ac+bd)/(c²+d²)=((14)(11)+(7)(4))/(11²+(4)²)=1.32847. | {
"A": "Correct. The worked calculation gives 1.32847.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.32847, not 0.99635.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.32847, not 1.13285.",
"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_002692 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(7, 6, -2) and v=(0, 3, 7), calculate u·v. | {
"A": "4",
"B": "5",
"C": "6",
"D": "7"
} | A | 4 | The dot product is the sum of corresponding component products: (7)(0)+(6)(3)+(-2)(7)=4. | {
"A": "Correct. The worked calculation gives 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 6.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_003996 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 7 m s⁻¹. A constant net force does 11 N of work over 8 m in the direction of motion. Find its final kinetic energy. | {
"A": "31.85 J",
"B": "306.5 J",
"C": "308.5 J",
"D": "310.5 J"
} | C | 308.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(7)²+(11)(8)=308.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 308.5 J, not 31.85 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 308.5 J, not 306.5 J.",
"C": "Correct. The worked calculation gives 308.5 J.",
"D": "Incorrect. Substituting the stated va... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004252 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.13. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "52.08 N",
"B": "70.44 N",
"C": "69.44 N",
"D": "-69.44 N"
} | C | 69.44 N | Net force=mg(sinθ−μcosθ)=14×10×(0.6−0.13×0.8)=69.44 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 69.44 N, not 52.08 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 69.44 N, not 70.44 N.",
"C": "Correct. The worked calculation gives 69.44 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_002532 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, 6], [1, -8]]. | {
"A": "-84",
"B": "-52.5",
"C": "-71",
"D": "-70"
} | D | -70 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(-8)−(6)(1)=-70. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -70, not -84.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -70, not -52.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -70, not -71.",
"D": "Correct.... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005946 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.4 atm at 435 K. What is its pressure at 738 K? | {
"A": "3.56276 atm",
"B": "3.37517 atm",
"C": "2.37517 atm",
"D": "4.37517 atm"
} | C | 2.37517 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.4)(738)/(435)=2.37517 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.37517 atm, not 3.56276 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.37517 atm, not 3.37517 atm.",
"C": "Correct. The worked calculation gives 2.37517 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_005368 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 11 μF capacitor is charged to a potential difference of 34 V. Calculate the energy stored, expressed in μJ. | {
"A": "6357 μJ",
"B": "6360 μJ",
"C": "12716 μJ",
"D": "6358 μJ"
} | D | 6358 μJ | U=½CV². Since C=11 μF, U in μJ is ½×11×(34)²=6358 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6358 μJ, not 6357 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6358 μJ, not 6360 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6358 μJ, not 12716... | [
"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_005075 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +9 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "225 N",
"B": "540 N",
"C": "450 N",
"D": "448 N"
} | C | 450 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(9×10⁻⁶)/(3×10⁻²)²=450 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 450 N, not 225 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 450 N, not 540 N.",
"C": "Correct. The worked calculation gives 450 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_003511 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 57 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "298.66541 m",
"B": "124.44392 m",
"C": "248.88784 m",
"D": "246.88784 m"
} | C | 248.88784 m | Range R=u²sin(2θ)/g. Substituting u=57, θ=25° and g=10 gives R=(57)²sin(50°)/10=248.88784 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 248.88784 m, not 298.66541 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 248.88784 m, not 124.44392 m.",
"C": "Correct. The worked calculation gives 248.88784 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009860 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(OH)_4]^-1, each OH ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "1.5",
"B": "3",
"C": "4.5",
"D": "-3"
} | B | 3 | Let the formal oxidation state of Pd be x. Charge balance gives x+(4)(−1)=-1; hence x=-1+4=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.5.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.5.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009702 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(OH)_4]^+0, each OH ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "2",
"B": "4",
"C": "7",
"D": "3"
} | B | 4 | Let the formal oxidation state of Co be x. Charge balance gives x+(4)(−1)=+0; hence x=0+4=+4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"B": "Correct. The worked calculation gives 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 7.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001689 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 6 elements can be selected from a set of 17 distinct elements? | {
"A": "18564",
"B": "12377",
"C": "1238.6",
"D": "12376"
} | D | 12376 | Order does not matter, so the count is C(17,6)=17!/[6!(11)!]=12376. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12376, not 18564.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12376, not 12377.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12376, not 1238.6.",
"D"... | [
"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_006303 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 29 cm in front of a thin convex lens of focal length 19 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "4.9",
"B": "0.95",
"C": "1.9",
"D": "3.9"
} | C | 1.9 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(29)(19)/(29−19)=55.1 cm. Thus |m|=v/u=55.1/29=1.9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.9, not 4.9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.9, not 0.95.",
"C": "Correct. The worked calculation gives 1.9.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_007917 | 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 91 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "11.375 mmol L⁻¹",
"B": "8.375 mmol L⁻¹",
"C": "10.375 mmol L⁻¹",
"D": "12.375 mmol L⁻¹"
} | A | 11.375 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=91/2^3=11.375 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 11.375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.375 mmol L⁻¹, not 8.375 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.375 mmol L⁻¹, not 10.375 mmol L⁻¹.",
"D":... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000599 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -2 and common difference 12. Find the sum of its first 30 terms. | {
"A": "6192",
"B": "3870",
"C": "5160",
"D": "5162"
} | C | 5160 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-2, d=12, n=30: Sₙ=30/2[2(-2)+(30−1)(12)]=5160. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5160, not 6192.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5160, not 3870.",
"C": "Correct. The worked calculation gives 5160.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003380 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 39 m s⁻¹ at 75° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "38.025 m",
"B": "76.05 m",
"C": "78.05 m",
"D": "57.0375 m"
} | B | 76.05 m | Range R=u²sin(2θ)/g. Substituting u=39, θ=75° and g=10 gives R=(39)²sin(150°)/10=76.05 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 76.05 m, not 38.025 m.",
"B": "Correct. The worked calculation gives 76.05 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 76.05 m, not 78.05 m.",
"D": "Incorrect. Substituting the stated v... | [
"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_009134 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.24 V, transfers 3 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.1415 V",
"B": "3.1415 V",
"C": "-1.8585 V",
"D": "1.11415 V"
} | A | 1.1415 V | Apply the Nernst equation: E=1.24−(0.0591/3)(5)=1.1415 V. | {
"A": "Correct. The worked calculation gives 1.1415 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1415 V, not 3.1415 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1415 V, not -1.8585 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004823 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 13 Ω are connected in series; this combination is connected in parallel with a 6 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "7.8 A",
"B": "8.8 A",
"C": "5.85 A",
"D": "10.8 A"
} | A | 7.8 A | Series branch resistance=7+13=20 Ω. Parallel equivalent R_eq=(20×6)/(20+6)=4.61538 Ω. Total current I=V/R_eq=36/4.61538=7.8 A. | {
"A": "Correct. The worked calculation gives 7.8 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.8 A, not 8.8 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.8 A, not 5.85 A.",
"D": "Incorrect. Substituting the stated values into... | [
"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_006304 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 141 cm in front of a thin convex lens of focal length 29 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.25893",
"B": "1.02589",
"C": "0.38839",
"D": "0.51786"
} | A | 0.25893 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(141)(29)/(141−29)=36.50893 cm. Thus |m|=v/u=36.50893/141=0.25893. | {
"A": "Correct. The worked calculation gives 0.25893.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25893, not 1.02589.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25893, not 0.38839.",
"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_002448 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, -8], [7, 6]]. | {
"A": "80",
"B": "120",
"C": "96",
"D": "64"
} | A | 80 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(6)−(-8)(7)=80. | {
"A": "Correct. The worked calculation gives 80.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 80, not 120.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 80, not 96.",
"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_005431 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 63 μF capacitor is charged to a potential difference of 5 V. Calculate the energy stored, expressed in μJ. | {
"A": "785.5 μJ",
"B": "79.75 μJ",
"C": "590.625 μJ",
"D": "787.5 μJ"
} | D | 787.5 μJ | U=½CV². Since C=63 μF, U in μJ is ½×63×(5)²=787.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 787.5 μJ, not 785.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 787.5 μJ, not 79.75 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 787.5 μJ, not ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006969 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 23 mol H₂ and 35 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "22 mol",
"B": "3.3 mol",
"C": "23 mol",
"D": "46 mol"
} | C | 23 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 23 mol H₂O; O₂ can produce 70 mol H₂O. The limiting condition is H₂; product=23 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 23 mol, not 22 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23 mol, not 3.3 mol.",
"C": "Correct. The worked calculation gives 23 mol.",
"D": "Incorrect. Substituting the stated values... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004240 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.39. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "15.84 N",
"B": "31.68 N",
"C": "38.016 N",
"D": "33.68 N"
} | B | 31.68 N | Net force=mg(sinθ−μcosθ)=11×10×(0.6−0.39×0.8)=31.68 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 31.68 N, not 15.84 N.",
"B": "Correct. The worked calculation gives 31.68 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 31.68 N, not 38.016 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_004458 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 9 kg and radius 4 m is acted on by a constant torque of 31 N m about its central axis. Find its angular acceleration. | {
"A": "0.43056 rad s⁻²",
"B": "0.64583 rad s⁻²",
"C": "-0.56944 rad s⁻²",
"D": "0.21528 rad s⁻²"
} | A | 0.43056 rad s⁻² | For a solid disc, I=½MR²=½(9)(4)²=72 kg m². Using τ=Iα, α=31/72=0.43056 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.43056 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.43056 rad s⁻², not 0.64583 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.43056 rad s⁻², not -0.56944 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_000129 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 +7x -1=0, let its roots be α and β. What is α²+β²? | {
"A": "0.64286",
"B": "1.28571",
"C": "1.92857",
"D": "1.12857"
} | B | 1.28571 | By Vieta's relations, α+β = -7/7 and αβ = -1/7. Then α²+β²=(α+β)²−2αβ = (-7/7)²−2(-1/7) = 1.28571. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.28571, not 0.64286.",
"B": "Correct. The worked calculation gives 1.28571.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.28571, not 1.92857.",
"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_000263 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 +5x +10=0, let its roots be α and β. What is α²+β²? | {
"A": "5",
"B": "7",
"C": "8",
"D": "-5"
} | A | 5 | By Vieta's relations, α+β = -5/1 and αβ = 10/1. Then α²+β²=(α+β)²−2αβ = (-5/1)²−2(10/1) = 5. | {
"A": "Correct. The worked calculation gives 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 8.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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 |
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