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_007029 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 2 mol of gas at 596 K and 0.72 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "135.84992 L",
"B": "108.67994 L",
"C": "101.88744 L",
"D": "-135.84992 L"
} | A | 135.84992 L | PV=nRT, so V=nRT/P=(2)(0.082057)(596)/(0.72)=135.84992 L. | {
"A": "Correct. The worked calculation gives 135.84992 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 135.84992 L, not 108.67994 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 135.84992 L, not 101.88744 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_003117 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-3+15i)/(7+4i). What is Re(z), the real part of z? | {
"A": "0.9",
"B": "0.6",
"C": "1.6",
"D": "1.2"
} | B | 0.6 | Multiply numerator and denominator by the conjugate (7-4i). Then Re(z)=(ac+bd)/(c²+d²)=((-3)(7)+(15)(4))/(7²+(4)²)=0.6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6, not 0.9.",
"B": "Correct. The worked calculation gives 0.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.6, not 1.6.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_008571 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.42 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "2.90816 K",
"B": "1.29082 K",
"C": "4.90816 K",
"D": "2.18112 K"
} | A | 2.90816 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.512×1.42=2.90816 K. | {
"A": "Correct. The worked calculation gives 2.90816 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.90816 K, not 1.29082 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.90816 K, not 4.90816 K.",
"D": "Incorrect. Substituting the... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001225 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=7x³ +4x² -5x+7. Evaluate f′(4). | {
"A": "435.6",
"B": "363",
"C": "365",
"D": "726"
} | B | 363 | Differentiate: f′(x)=3(7)x²+2(4)x+(-5). At x=4, f′(4)=3(7)(4)²+2(4)(4)+(-5)=363. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 363, not 435.6.",
"B": "Correct. The worked calculation gives 363.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 363, not 365.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003717 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 4 m s⁻¹. A constant net force does 17 N of work over 8 m in the direction of motion. Find its final kinetic energy. | {
"A": "156 J",
"B": "208 J",
"C": "206 J",
"D": "416 J"
} | B | 208 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(4)²+(17)(8)=208 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 208 J, not 156 J.",
"B": "Correct. The worked calculation gives 208 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 208 J, not 206 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_007067 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 6 mol of gas at 467 K and 2.25 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "103.18832 L",
"B": "102.18832 L",
"C": "104.18832 L",
"D": "51.09416 L"
} | B | 102.18832 L | PV=nRT, so V=nRT/P=(6)(0.082057)(467)/(2.25)=102.18832 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 102.18832 L, not 103.18832 L.",
"B": "Correct. The worked calculation gives 102.18832 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 102.18832 L, not 104.18832 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_004491 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 2 m is acted on by a constant torque of 29 N m about its central axis. Find its angular acceleration. | {
"A": "0.07143 rad s⁻²",
"B": "2.07143 rad s⁻²",
"C": "1.55357 rad s⁻²",
"D": "4.14286 rad s⁻²"
} | B | 2.07143 rad s⁻² | For a solid disc, I=½MR²=½(7)(2)²=14 kg m². Using τ=Iα, α=29/14=2.07143 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.07143 rad s⁻², not 0.07143 rad s⁻².",
"B": "Correct. The worked calculation gives 2.07143 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.07143 rad s⁻², not 1.55357 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_005071 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +8 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "80 N",
"B": "82 N",
"C": "96 N",
"D": "-80 N"
} | A | 80 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(8×10⁻⁶)/(6×10⁻²)²=80 N. | {
"A": "Correct. The worked calculation gives 80 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 80 N, not 82 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 80 N, not 96 N.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_009287 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.27 V, transfers 3 electrons, and has reaction quotient Q=10^0. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.73 V",
"B": "-1.27 V",
"C": "4.27 V",
"D": "1.27 V"
} | D | 1.27 V | Apply the Nernst equation: E=1.27−(0.0591/3)(0)=1.27 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.27 V, not -1.73 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.27 V, not -1.27 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.27 V, not 4.27 V."... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007106 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 1 mol of gas at 207 K and 2.57 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "9.91389 L",
"B": "5.60926 L",
"C": "1.66093 L",
"D": "6.60926 L"
} | D | 6.60926 L | PV=nRT, so V=nRT/P=(1)(0.082057)(207)/(2.57)=6.60926 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.60926 L, not 9.91389 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.60926 L, not 5.60926 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.60926 L,... | [
"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_005293 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +1 μC are separated by 12 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "0.625 N",
"B": "2.625 N",
"C": "-1.375 N",
"D": "3.625 N"
} | A | 0.625 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(1×10⁻⁶)/(12×10⁻²)²=0.625 N. | {
"A": "Correct. The worked calculation gives 0.625 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.625 N, not 2.625 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.625 N, not -1.375 N.",
"D": "Incorrect. Substituting the stated v... | [
"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_008389 | 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 0.56 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": "1.7472 K",
"B": "3.1648 K",
"C": "1.1648 K",
"D": "1.11648 K"
} | C | 1.1648 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.52×0.56=1.1648 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.1648 K, not 1.7472 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1648 K, not 3.1648 K.",
"C": "Correct. The worked calculation gives 1.1648 K.",
"D": "Incorrect. Substituting the stat... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000453 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 11 and common difference 14. Find the sum of its first 35 terms. | {
"A": "8713",
"B": "10458",
"C": "8715",
"D": "13072.5"
} | C | 8715 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=11, d=14, n=35: Sₙ=35/2[2(11)+(35−1)(14)]=8715. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8715, not 8713.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8715, not 10458.",
"C": "Correct. The worked calculation gives 8715.",
"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_001004 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=3x³ -5x² +1x+7. Evaluate f′(5). | {
"A": "18.6",
"B": "176",
"C": "177",
"D": "175"
} | B | 176 | Differentiate: f′(x)=3(3)x²+2(-5)x+(1). At x=5, f′(5)=3(3)(5)²+2(-5)(5)+(1)=176. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 176, not 18.6.",
"B": "Correct. The worked calculation gives 176.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 176, not 177.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008788 | 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 0.37 mol L⁻¹ and initially B is absent. At equilibrium, 39% of A has dissociated at constant volume. Find K_c. | {
"A": "0.36903",
"B": "-2.63097",
"C": "3.36903",
"D": "-0.36903"
} | A | 0.36903 | Let α=0.39. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.37)(0.39)²/(1−0.39)=0.36903. | {
"A": "Correct. The worked calculation gives 0.36903.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36903, not -2.63097.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.36903, not 3.36903.",
"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_000515 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -4 and common difference 14. Find the sum of its first 31 terms. | {
"A": "3193",
"B": "6387",
"C": "6386",
"D": "9579"
} | C | 6386 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-4, d=14, n=31: Sₙ=31/2[2(-4)+(31−1)(14)]=6386. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6386, not 3193.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6386, not 6387.",
"C": "Correct. The worked calculation gives 6386.",
"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_008299 | 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 18170 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": "2.79346 g",
"B": "13.45098 g",
"C": "17.93464 g",
"D": "15.93464 g"
} | C | 17.93464 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×3×18170/(2×96500)=17.93464 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 17.93464 g, not 2.79346 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17.93464 g, not 13.45098 g.",
"C": "Correct. The worked calculation gives 17.93464 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_005357 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 61 μF capacitor is charged to a potential difference of 36 V. Calculate the energy stored, expressed in μJ. | {
"A": "39530 μJ",
"B": "39528 μJ",
"C": "19764 μJ",
"D": "39526 μJ"
} | B | 39528 μJ | U=½CV². Since C=61 μF, U in μJ is ½×61×(36)²=39528 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 39528 μJ, not 39530 μJ.",
"B": "Correct. The worked calculation gives 39528 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39528 μJ, not 19764 μJ.",
"D": "Incorrect. Substituting the stat... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008221 | 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 7 A for 12380 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "34.21498 g",
"B": "14.25624 g",
"C": "28.51249 g",
"D": "29.51249 g"
} | C | 28.51249 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×7×12380/(2×96500)=28.51249 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28.51249 g, not 34.21498 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28.51249 g, not 14.25624 g.",
"C": "Correct. The worked calculation gives 28.51249 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_000935 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 3. What is the sum of its first 9 terms? | {
"A": "98410",
"B": "78728",
"C": "98408",
"D": "-98410"
} | A | 98410 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(3^9−1)/(3−1)=98410. | {
"A": "Correct. The worked calculation gives 98410.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 98410, not 78728.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 98410, not 98408.",
"D": "Incorrect. Substituting the stated values into ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007422 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 50 mL of 0.10 M HCl is mixed with 44 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "3.19498",
"B": "2.19498",
"C": "4.38995",
"D": "-2.19498"
} | B | 2.19498 | Excess H⁺ moles=0.10×(50−44)/1000=0.000600 mol. Total volume=0.094 L, so [H⁺]=0.006383 M and pH=−log₁₀[H⁺]=2.19498. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.19498, not 3.19498.",
"B": "Correct. The worked calculation gives 2.19498.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.19498, not 4.38995.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005067 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +1 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "5.5 N",
"B": "4.5 N",
"C": "3.375 N",
"D": "2.25 N"
} | B | 4.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(1×10⁻⁶)/(10×10⁻²)²=4.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.5 N, not 5.5 N.",
"B": "Correct. The worked calculation gives 4.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.5 N, not 3.375 N.",
"D": "Incorrect. Substituting the stated values int... | [
"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_003027 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(9+12i)/(8+6i). What is Re(z), the real part of z? | {
"A": "2.16",
"B": "-1.56",
"C": "1.44",
"D": "2.88"
} | C | 1.44 | Multiply numerator and denominator by the conjugate (8-6i). Then Re(z)=(ac+bd)/(c²+d²)=((9)(8)+(12)(6))/(8²+(6)²)=1.44. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.44, not 2.16.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.44, not -1.56.",
"C": "Correct. The worked calculation gives 1.44.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_004101 | 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 0.16. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "130.272 N",
"B": "110.56 N",
"C": "108.56 N",
"D": "86.848 N"
} | C | 108.56 N | Net force=mg(sinθ−μcosθ)=23×10×(0.6−0.16×0.8)=108.56 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 108.56 N, not 130.272 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 108.56 N, not 110.56 N.",
"C": "Correct. The worked calculation gives 108.56 N.",
"D": "Incorrect. Substituting the sta... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003953 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 12 m s⁻¹. A constant net force does 24 N of work over 6 m in the direction of motion. Find its final kinetic energy. | {
"A": "87.4 J",
"B": "432 J",
"C": "864 J",
"D": "1728 J"
} | C | 864 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(12)²+(24)(6)=864 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 864 J, not 87.4 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 864 J, not 432 J.",
"C": "Correct. The worked calculation gives 864 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_002647 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, -8], [7, 0]]. | {
"A": "55",
"B": "42",
"C": "56",
"D": "-56"
} | C | 56 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(0)−(-8)(7)=56. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 56, not 55.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 56, not 42.",
"C": "Correct. The worked calculation gives 56.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006091 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 43 cm in front of a thin convex lens of focal length 16 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.59259",
"B": "1.18519",
"C": "1.59259",
"D": "1.05926"
} | A | 0.59259 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(43)(16)/(43−16)=25.48148 cm. Thus |m|=v/u=25.48148/43=0.59259. | {
"A": "Correct. The worked calculation gives 0.59259.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.59259, not 1.18519.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.59259, not 1.59259.",
"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_003914 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 3 m s⁻¹. A constant net force does 12 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "177 J",
"B": "132.75 J",
"C": "175 J",
"D": "179 J"
} | A | 177 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(3)²+(12)(11)=177 J. | {
"A": "Correct. The worked calculation gives 177 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 177 J, not 132.75 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 177 J, not 175 J.",
"D": "Incorrect. Substituting the stated values in... | [
"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_007026 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 14 mol of gas at 508 K and 1.06 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "550.55602 L",
"B": "-550.55602 L",
"C": "412.91702 L",
"D": "56.0556 L"
} | A | 550.55602 L | PV=nRT, so V=nRT/P=(14)(0.082057)(508)/(1.06)=550.55602 L. | {
"A": "Correct. The worked calculation gives 550.55602 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 550.55602 L, not -550.55602 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 550.55602 L, not 412.91702 L.",
"D": "Incorrect. Subst... | [
"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_007628 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 40 mL of 0.10 M HCl is mixed with 32 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "3.90849",
"B": "2.93136",
"C": "2.95424",
"D": "1.95424"
} | D | 1.95424 | Excess H⁺ moles=0.10×(40−32)/1000=0.000800 mol. Total volume=0.072 L, so [H⁺]=0.011111 M and pH=−log₁₀[H⁺]=1.95424. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.95424, not 3.90849.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.95424, not 2.93136.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.95424, not 2.954... | [
"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_001223 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=3x³ +9x² +12x+7. Evaluate f′(1). | {
"A": "40",
"B": "39",
"C": "19.5",
"D": "29.25"
} | B | 39 | Differentiate: f′(x)=3(3)x²+2(9)x+(12). At x=1, f′(1)=3(3)(1)²+2(9)(1)+(12)=39. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 39, not 40.",
"B": "Correct. The worked calculation gives 39.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39, not 19.5.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003521 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 56 m s⁻¹ at 70° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "302.36729 m",
"B": "201.57819 m",
"C": "-201.57819 m",
"D": "100.7891 m"
} | B | 201.57819 m | Range R=u²sin(2θ)/g. Substituting u=56, θ=70° and g=10 gives R=(56)²sin(140°)/10=201.57819 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 201.57819 m, not 302.36729 m.",
"B": "Correct. The worked calculation gives 201.57819 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 201.57819 m, not -201.57819 m.",
"D": "Incorrect. Subst... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002035 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 11 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.38154",
"B": "0.38154",
"C": "0.19077",
"D": "-2.61846"
} | B | 0.38154 | Favourable pairs = C(12,2)+C(11,2)+C(3,2)=124. Total pairs=C(26,2)=325. Therefore P=124/325=0.38154. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.38154, not -0.38154.",
"B": "Correct. The worked calculation gives 0.38154.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.38154, not 0.19077.",
"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_005093 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +6 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "137 N",
"B": "202.5 N",
"C": "14.5 N",
"D": "135 N"
} | D | 135 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(6×10⁻⁶)/(4×10⁻²)²=135 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 135 N, not 137 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 135 N, not 202.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 135 N, not 14.5 N.",
"... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009594 | 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_0X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "14",
"B": "16",
"C": "7",
"D": "-14"
} | A | 14 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×15+2+0−0−4)/2=14. | {
"A": "Correct. The worked calculation gives 14.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14, not 16.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14, not 7.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005504 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 46 μF capacitor is charged to a potential difference of 16 V. Calculate the energy stored, expressed in μJ. | {
"A": "5888 μJ",
"B": "4710.4 μJ",
"C": "5887 μJ",
"D": "8832 μJ"
} | A | 5888 μJ | U=½CV². Since C=46 μF, U in μJ is ½×46×(16)²=5888 μJ. | {
"A": "Correct. The worked calculation gives 5888 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5888 μJ, not 4710.4 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5888 μJ, not 5887 μJ.",
"D": "Incorrect. Substituting the stated ... | [
"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_006016 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 91 cm in front of a thin convex lens of focal length 25 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.18939",
"B": "0.56818",
"C": "0.37879",
"D": "1.37879"
} | C | 0.37879 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(91)(25)/(91−25)=34.4697 cm. Thus |m|=v/u=34.4697/91=0.37879. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.37879, not 0.18939.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.37879, not 0.56818.",
"C": "Correct. The worked calculation gives 0.37879.",
"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_004814 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 14 Ω and 9 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": "1.78261 A",
"B": "3.37681 A",
"C": "4.75362 A",
"D": "2.37681 A"
} | D | 2.37681 A | Series branch resistance=14+9=23 Ω. Parallel equivalent R_eq=(23×18)/(23+18)=10.09756 Ω. Total current I=V/R_eq=24/10.09756=2.37681 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.37681 A, not 1.78261 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.37681 A, not 3.37681 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.37681 A,... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004818 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 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": "3.33333 A",
"B": "5.33333 A",
"C": "2.5 A",
"D": "5 A"
} | A | 3.33333 A | Series branch resistance=7+5=12 Ω. Parallel equivalent R_eq=(12×18)/(12+18)=7.2 Ω. Total current I=V/R_eq=24/7.2=3.33333 A. | {
"A": "Correct. The worked calculation gives 3.33333 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.33333 A, not 5.33333 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.33333 A, not 2.5 A.",
"D": "Incorrect. Substituting the sta... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009975 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(Cl)_4]^-4, each Cl ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "-3",
"B": "-2",
"C": "0",
"D": "2"
} | C | 0 | Let the formal oxidation state of Fe be x. Charge balance gives x+(4)(−1)=-4; hence x=-4+4=+0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"C": "Correct. The worked calculation gives 0.",
"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_006498 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 19 kg is attached to an ideal spring of force constant 605 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.35443 s",
"B": "1.03544 s",
"C": "2.35443 s",
"D": "0.17721 s"
} | A | 0.35443 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(19/605)=0.35443 s. | {
"A": "Correct. The worked calculation gives 0.35443 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35443 s, not 1.03544 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35443 s, not 2.35443 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_009901 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(CN)_5]^+1, each CN ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "3",
"B": "7",
"C": "12",
"D": "6"
} | D | 6 | Let the formal oxidation state of Fe be x. Charge balance gives x+(5)(−1)=+1; hence x=1+5=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 12.",
"D": "Correct. The worked c... | [
"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_005584 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 67 μF capacitor is charged to a potential difference of 8 V. Calculate the energy stored, expressed in μJ. | {
"A": "215.4 μJ",
"B": "2144 μJ",
"C": "2572.8 μJ",
"D": "4288 μJ"
} | B | 2144 μJ | U=½CV². Since C=67 μF, U in μJ is ½×67×(8)²=2144 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2144 μJ, not 215.4 μJ.",
"B": "Correct. The worked calculation gives 2144 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2144 μJ, not 2572.8 μJ.",
"D": "Incorrect. Substituting the stated... | [
"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_005650 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 67 μF capacitor is charged to a potential difference of 5 V. Calculate the energy stored, expressed in μJ. | {
"A": "418.75 μJ",
"B": "1005 μJ",
"C": "837.5 μJ",
"D": "839.5 μJ"
} | C | 837.5 μJ | U=½CV². Since C=67 μF, U in μJ is ½×67×(5)²=837.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 837.5 μJ, not 418.75 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 837.5 μJ, not 1005 μJ.",
"C": "Correct. The worked calculation gives 837.5 μJ.",
"D": "Incorrect. Substituting the stat... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000802 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio 2. What is the sum of its first 11 terms? | {
"A": "9211.5",
"B": "18423",
"C": "18425",
"D": "18424"
} | B | 18423 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(2^11−1)/(2−1)=18423. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18423, not 9211.5.",
"B": "Correct. The worked calculation gives 18423.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18423, not 18425.",
"D": "Incorrect. Substituting the stated values into... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003756 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block initially moves at 6 m s⁻¹. A constant net force does 30 N of work over 7 m in the direction of motion. Find its final kinetic energy. | {
"A": "248 J",
"B": "246 J",
"C": "123 J",
"D": "247 J"
} | B | 246 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(2)(6)²+(30)(7)=246 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 246 J, not 248 J.",
"B": "Correct. The worked calculation gives 246 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 246 J, not 123 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_002973 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-6, 6, 0) and v=(4, 5, -1), calculate u·v. | {
"A": "9",
"B": "3",
"C": "5",
"D": "6"
} | D | 6 | The dot product is the sum of corresponding component products: (-6)(4)+(6)(5)+(0)(-1)=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 5.",
"D": "Correct. The worked ca... | [
"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_003999 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 3 kg block initially moves at 2 m s⁻¹. A constant net force does 6 N of work over 14 m in the direction of motion. Find its final kinetic energy. | {
"A": "89 J",
"B": "72 J",
"C": "180 J",
"D": "90 J"
} | D | 90 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(3)(2)²+(6)(14)=90 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 90 J, not 89 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 90 J, not 72 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 90 J, not 180 J.",
"D": "Cor... | [
"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_005248 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 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": "24 N",
"B": "29 N",
"C": "-30 N",
"D": "30 N"
} | D | 30 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(2×10⁻⁶)/(6×10⁻²)²=30 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 30 N, not 24 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30 N, not 29 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30 N, not -30 N.",
"D": "Cor... | [
"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_000760 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio 2. What is the sum of its first 8 terms? | {
"A": "3060",
"B": "1530",
"C": "1531",
"D": "1836"
} | B | 1530 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(2^8−1)/(2−1)=1530. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1530, not 3060.",
"B": "Correct. The worked calculation gives 1530.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1530, not 1531.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_003808 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 6 m s⁻¹. A constant net force does 24 N of work over 8 m in the direction of motion. Find its final kinetic energy. | {
"A": "372 J",
"B": "38.2 J",
"C": "-372 J",
"D": "297.6 J"
} | A | 372 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(6)²+(24)(8)=372 J. | {
"A": "Correct. The worked calculation gives 372 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 372 J, not 38.2 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 372 J, not -372 J.",
"D": "Incorrect. Substituting the stated values int... | [
"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_007771 | 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 75 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "18.75 mmol L⁻¹",
"B": "2.875 mmol L⁻¹",
"C": "14.0625 mmol L⁻¹",
"D": "19.75 mmol L⁻¹"
} | A | 18.75 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=75/2^2=18.75 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 18.75 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18.75 mmol L⁻¹, not 2.875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18.75 mmol L⁻¹, not 14.0625 mmol L⁻¹.",
"D": "... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002870 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(9, 6, -6) and v=(0, -3, -6), calculate u·v. | {
"A": "9",
"B": "2.8",
"C": "20",
"D": "18"
} | D | 18 | The dot product is the sum of corresponding component products: (9)(0)+(6)(-3)+(-6)(-6)=18. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18, not 9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18, not 2.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18, not 20.",
"D": "Correct. The wor... | [
"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_008919 | 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 1.51 mol L⁻¹ and initially B is absent. At equilibrium, 39% of A has dissociated at constant volume. Find K_c. | {
"A": "1.50604",
"B": "0.50604",
"C": "2.50604",
"D": "-1.49396"
} | A | 1.50604 | Let α=0.39. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.51)(0.39)²/(1−0.39)=1.50604. | {
"A": "Correct. The worked calculation gives 1.50604.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.50604, not 0.50604.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.50604, not 2.50604.",
"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_002279 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 12 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-1.66462",
"B": "-0.66462",
"C": "0.33538",
"D": "2.33538"
} | C | 0.33538 | Favourable pairs = C(8,2)+C(12,2)+C(6,2)=109. Total pairs=C(26,2)=325. Therefore P=109/325=0.33538. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33538, not -1.66462.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33538, not -0.66462.",
"C": "Correct. The worked calculation gives 0.33538.",
"D": "Incorrect. Substituting the stated ... | [
"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_009727 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(CN)_6]^-4, each CN ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "1",
"B": "2",
"C": "0",
"D": "3"
} | B | 2 | Let the formal oxidation state of Co be x. Charge balance gives x+(6)(−1)=-4; hence x=-4+6=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 0.",
"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_004522 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 14 kg and radius 4 m is acted on by a constant torque of 78 N m about its central axis. Find its angular acceleration. | {
"A": "-2.30357 rad s⁻²",
"B": "1.39286 rad s⁻²",
"C": "0.69643 rad s⁻²",
"D": "3.69643 rad s⁻²"
} | C | 0.69643 rad s⁻² | For a solid disc, I=½MR²=½(14)(4)²=112 kg m². Using τ=Iα, α=78/112=0.69643 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.69643 rad s⁻², not -2.30357 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.69643 rad s⁻², not 1.39286 rad s⁻².",
"C": "Correct. The worked calculation gives 0.69643 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_005397 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 53 μF capacitor is charged to a potential difference of 20 V. Calculate the energy stored, expressed in μJ. | {
"A": "10600 μJ",
"B": "10602 μJ",
"C": "-10600 μJ",
"D": "21200 μJ"
} | A | 10600 μJ | U=½CV². Since C=53 μF, U in μJ is ½×53×(20)²=10600 μJ. | {
"A": "Correct. The worked calculation gives 10600 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10600 μJ, not 10602 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10600 μJ, not -10600 μJ.",
"D": "Incorrect. Substituting the sta... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009784 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(Cl)_4]^-4, each Cl ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "1",
"B": "-3",
"C": "2",
"D": "0"
} | D | 0 | Let the formal oxidation state of Ni be x. Charge balance gives x+(4)(−1)=-4; hence x=-4+4=+0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 2.",
"D": "Correct. The worked c... | [
"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_005754 | 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 1.1 atm at 426 K. What is its pressure at 751 K? | {
"A": "3.9392 atm",
"B": "0.9696 atm",
"C": "1.4544 atm",
"D": "1.9392 atm"
} | D | 1.9392 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.1)(751)/(426)=1.9392 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.9392 atm, not 3.9392 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.9392 atm, not 0.9696 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.9392... | [
"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_003278 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-12+3i)/(6+6i). What is Re(z), the real part of z? | {
"A": "-3.75",
"B": "0.925",
"C": "-0.75",
"D": "-2.75"
} | C | -0.75 | Multiply numerator and denominator by the conjugate (6-6i). Then Re(z)=(ac+bd)/(c²+d²)=((-12)(6)+(3)(6))/(6²+(6)²)=-0.75. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.75, not -3.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.75, not 0.925.",
"C": "Correct. The worked calculation gives -0.75.",
"D": "Incorrect. Substituting the stated values into ... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003403 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 92 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "733.0039 m",
"B": "586.40312 m",
"C": "732.0039 m",
"D": "731.0039 m"
} | A | 733.0039 m | Range R=u²sin(2θ)/g. Substituting u=92, θ=60° and g=10 gives R=(92)²sin(120°)/10=733.0039 m. | {
"A": "Correct. The worked calculation gives 733.0039 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 733.0039 m, not 586.40312 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 733.0039 m, not 732.0039 m.",
"D": "Incorrect. Substituti... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009377 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_6H_10X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "1",
"B": "0",
"C": "-2",
"D": "3"
} | B | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+0−10−4)/2=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"B": "Correct. The worked calculation gives 0.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"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_004251 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 33 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.39. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "95.04 N",
"B": "94.04 N",
"C": "93.04 N",
"D": "-95.04 N"
} | A | 95.04 N | Net force=mg(sinθ−μcosθ)=33×10×(0.6−0.39×0.8)=95.04 N. | {
"A": "Correct. The worked calculation gives 95.04 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 95.04 N, not 94.04 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 95.04 N, not 93.04 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008333 | 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 29547 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": "-145.82133 g",
"B": "72.91067 g",
"C": "291.64267 g",
"D": "145.82133 g"
} | D | 145.82133 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×15×29547/(2×96500)=145.82133 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 145.82133 g, not -145.82133 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 145.82133 g, not 72.91067 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14... | [
"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_009132 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.95 V, transfers 3 electrons, and has reaction quotient Q=10^2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.0894 V",
"B": "0.9106 V",
"C": "1.8212 V",
"D": "1.3659 V"
} | B | 0.9106 V | Apply the Nernst equation: E=0.95−(0.0591/3)(2)=0.9106 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9106 V, not -0.0894 V.",
"B": "Correct. The worked calculation gives 0.9106 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9106 V, not 1.8212 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_001677 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 3 elements can be selected from a set of 23 distinct elements? | {
"A": "2125.2",
"B": "1771",
"C": "1773",
"D": "1416.8"
} | B | 1771 | Order does not matter, so the count is C(23,3)=23!/[3!(20)!]=1771. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1771, not 2125.2.",
"B": "Correct. The worked calculation gives 1771.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1771, not 1773.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_000012 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 -16x +8=0, let its roots be α and β. What is α²+β²? | {
"A": "12",
"B": "2.2",
"C": "13",
"D": "11"
} | A | 12 | By Vieta's relations, α+β = 16/4 and αβ = 8/4. Then α²+β²=(α+β)²−2αβ = (16/4)²−2(8/4) = 12. | {
"A": "Correct. The worked calculation gives 12.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12, not 2.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12, not 13.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"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_008337 | 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 0.55 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.99 K",
"B": "1.32 K",
"C": "2.32 K",
"D": "0.66 K"
} | B | 1.32 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.6×0.55=1.32 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.32 K, not 0.99 K.",
"B": "Correct. The worked calculation gives 1.32 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.32 K, not 2.32 K.",
"D": "Incorrect. Substituting the stated values ... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000132 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 +14x -6=0, let its roots be α and β. What is α²+β²? | {
"A": "14.25",
"B": "11.4375",
"C": "15.25",
"D": "12.2"
} | C | 15.25 | By Vieta's relations, α+β = -14/4 and αβ = -6/4. Then α²+β²=(α+β)²−2αβ = (-14/4)²−2(-6/4) = 15.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15.25, not 14.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15.25, not 11.4375.",
"C": "Correct. The worked calculation gives 15.25.",
"D": "Incorrect. Substituting the stated values int... | [
"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_002275 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 7 red, 11 blue and 5 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.33992",
"B": "-0.33992",
"C": "-2.66008",
"D": "0.67984"
} | A | 0.33992 | Favourable pairs = C(7,2)+C(11,2)+C(5,2)=86. Total pairs=C(23,2)=253. Therefore P=86/253=0.33992. | {
"A": "Correct. The worked calculation gives 0.33992.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33992, not -0.33992.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33992, not -2.66008.",
"D": "Incorrect. Substituting the stated ... | [
"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_009208 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.45 V, transfers 1 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.82155 V",
"B": "2.0954 V",
"C": "0.5477 V",
"D": "1.0954 V"
} | D | 1.0954 V | Apply the Nernst equation: E=1.45−(0.0591/1)(6)=1.0954 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0954 V, not 0.82155 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0954 V, not 2.0954 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0954 V, not... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008886 | 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 1.81 mol L⁻¹ and initially B is absent. At equilibrium, 46% of A has dissociated at constant volume. Find K_c. | {
"A": "4.83701",
"B": "3.83701",
"C": "2.83701",
"D": "1.4185"
} | C | 2.83701 | Let α=0.46. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.81)(0.46)²/(1−0.46)=2.83701. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.83701, not 4.83701.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.83701, not 3.83701.",
"C": "Correct. The worked calculation gives 2.83701.",
"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_001294 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ +9x² -9x+7. Evaluate f′(-4). | {
"A": "208",
"B": "103.5",
"C": "310.5",
"D": "207"
} | D | 207 | Differentiate: f′(x)=3(6)x²+2(9)x+(-9). At x=-4, f′(-4)=3(6)(-4)²+2(9)(-4)+(-9)=207. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 207, not 208.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 207, not 103.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 207, not 310.5.",
"D": "Correc... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007472 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 67 mL of 0.10 M HCl is mixed with 29 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.40249",
"B": "-0.59751",
"C": "1.40249",
"D": "-1.40249"
} | C | 1.40249 | Excess H⁺ moles=0.10×(67−29)/1000=0.003800 mol. Total volume=0.096 L, so [H⁺]=0.039583 M and pH=−log₁₀[H⁺]=1.40249. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.40249, not 2.40249.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.40249, not -0.59751.",
"C": "Correct. The worked calculation gives 1.40249.",
"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_001148 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ +10x² +4x+7. Evaluate f′(3). | {
"A": "-33",
"B": "-66",
"C": "-44",
"D": "-52.8"
} | C | -44 | Differentiate: f′(x)=3(-4)x²+2(10)x+(4). At x=3, f′(3)=3(-4)(3)²+2(10)(3)+(4)=-44. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -44, not -33.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -44, not -66.",
"C": "Correct. The worked calculation gives -44.",
"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_008106 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 14 A for 23224 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": "104.9748 g",
"B": "108.9748 g",
"C": "53.4874 g",
"D": "106.9748 g"
} | D | 106.9748 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×23224/(2×96500)=106.9748 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 106.9748 g, not 104.9748 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 106.9748 g, not 108.9748 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 106.97... | [
"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_001255 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ +5x² -8x+7. Evaluate f′(-2). | {
"A": "-88",
"B": "-105.6",
"C": "-90",
"D": "88"
} | A | -88 | Differentiate: f′(x)=3(-5)x²+2(5)x+(-8). At x=-2, f′(-2)=3(-5)(-2)²+2(5)(-2)+(-8)=-88. | {
"A": "Correct. The worked calculation gives -88.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -88, not -105.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -88, not -90.",
"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_003498 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 97 m s⁻¹ at 75° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "469.45 m",
"B": "470.45 m",
"C": "940.9 m",
"D": "48.045 m"
} | B | 470.45 m | Range R=u²sin(2θ)/g. Substituting u=97, θ=75° and g=10 gives R=(97)²sin(150°)/10=470.45 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 470.45 m, not 469.45 m.",
"B": "Correct. The worked calculation gives 470.45 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 470.45 m, not 940.9 m.",
"D": "Incorrect. Substituting the state... | [
"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_006418 | 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 601 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.59209 s",
"B": "0.61186 s",
"C": "0.40791 s",
"D": "-0.40791 s"
} | C | 0.40791 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(25/601)=0.40791 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.40791 s, not -1.59209 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.40791 s, not 0.61186 s.",
"C": "Correct. The worked calculation gives 0.40791 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_004704 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 6 Ω and 3 Ω are connected in series; this combination is connected in parallel with a 16 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.08333 A",
"B": "1.20833 A",
"C": "3.08333 A",
"D": "-2.08333 A"
} | A | 2.08333 A | Series branch resistance=6+3=9 Ω. Parallel equivalent R_eq=(9×16)/(9+16)=5.76 Ω. Total current I=V/R_eq=12/5.76=2.08333 A. | {
"A": "Correct. The worked calculation gives 2.08333 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.08333 A, not 1.20833 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.08333 A, not 3.08333 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_001557 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (-1x² +7x +6) dx. | {
"A": "9.16667",
"B": "7.16667",
"C": "18.33333",
"D": "1.91667"
} | A | 9.16667 | An antiderivative is (-1/3)x³+(7/2)x²+(6)x. Evaluating between 0 and 1 gives (-1/3)(1)³+(7/2)(1)²+(6)(1)=9.16667. | {
"A": "Correct. The worked calculation gives 9.16667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.16667, not 7.16667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.16667, not 18.33333.",
"D": "Incorrect. Substituting the stated v... | [
"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_002731 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(0, 3, 6) and v=(-1, -5, -3), calculate u·v. | {
"A": "-33",
"B": "-66",
"C": "-39.6",
"D": "-49.5"
} | A | -33 | The dot product is the sum of corresponding component products: (0)(-1)+(3)(-5)+(6)(-3)=-33. | {
"A": "Correct. The worked calculation gives -33.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -33, not -66.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -33, not -39.6.",
"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_002746 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(3, 4, 4) and v=(3, 7, -1), calculate u·v. | {
"A": "35",
"B": "66",
"C": "33",
"D": "24.75"
} | C | 33 | The dot product is the sum of corresponding component products: (3)(3)+(4)(7)+(4)(-1)=33. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33, not 35.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33, not 66.",
"C": "Correct. The worked calculation gives 33.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_004765 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 12 Ω are connected in series; this combination is connected in parallel with a 16 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "-2.385 A",
"B": "1.23 A",
"C": "0.615 A",
"D": "0.9225 A"
} | C | 0.615 A | Series branch resistance=13+12=25 Ω. Parallel equivalent R_eq=(25×16)/(25+16)=9.7561 Ω. Total current I=V/R_eq=6/9.7561=0.615 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.615 A, not -2.385 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.615 A, not 1.23 A.",
"C": "Correct. The worked calculation gives 0.615 A.",
"D": "Incorrect. Substituting the stated va... | [
"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_007490 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 49 mL of 0.10 M HCl is mixed with 81 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.39121",
"B": "2.23912",
"C": "15.39121",
"D": "9.39121"
} | A | 12.39121 | Excess OH⁻ moles=0.10×(81−49)/1000=0.003200 mol. Total volume=0.130 L, so [OH⁻]=0.024615 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.39121. | {
"A": "Correct. The worked calculation gives 12.39121.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.39121, not 2.23912.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.39121, not 15.39121.",
"D": "Incorrect. Substituting the state... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004293 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 30 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.15. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "288 N",
"B": "144 N",
"C": "172.8 N",
"D": "-144 N"
} | B | 144 N | Net force=mg(sinθ−μcosθ)=30×10×(0.6−0.15×0.8)=144 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 144 N, not 288 N.",
"B": "Correct. The worked calculation gives 144 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 144 N, not 172.8 N.",
"D": "Incorrect. Substituting the stated values int... | [
"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_001967 | 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 42 distinct elements? | {
"A": "4196628.8",
"B": "5245784",
"C": "3934339.5",
"D": "5245786"
} | D | 5245786 | Order does not matter, so the count is C(42,6)=42!/[6!(36)!]=5245786. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5245786, not 4196628.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5245786, not 5245784.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5245786, not 393... | [
"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_002331 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 11 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.32615",
"B": "3.32615",
"C": "2.32615",
"D": "-0.67385"
} | A | 0.32615 | Favourable pairs = C(9,2)+C(11,2)+C(6,2)=106. Total pairs=C(26,2)=325. Therefore P=106/325=0.32615. | {
"A": "Correct. The worked calculation gives 0.32615.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32615, not 3.32615.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32615, not 2.32615.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007253 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 8 mol of gas at 344 K and 1.79 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "127.15691 L",
"B": "126.15691 L",
"C": "252.31381 L",
"D": "124.15691 L"
} | B | 126.15691 L | PV=nRT, so V=nRT/P=(8)(0.082057)(344)/(1.79)=126.15691 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 126.15691 L, not 127.15691 L.",
"B": "Correct. The worked calculation gives 126.15691 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 126.15691 L, not 252.31381 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_000169 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 +3x -4=0, let its roots be α and β. What is α²+β²? | {
"A": "17",
"B": "-17",
"C": "20.4",
"D": "2.7"
} | A | 17 | By Vieta's relations, α+β = -3/1 and αβ = -4/1. Then α²+β²=(α+β)²−2αβ = (-3/1)²−2(-4/1) = 17. | {
"A": "Correct. The worked calculation gives 17.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17, not -17.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17, not 20.4.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008334 | 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 2884 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "14.23321 g",
"B": "21.34982 g",
"C": "-14.23321 g",
"D": "2.42332 g"
} | A | 14.23321 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×15×2884/(2×96500)=14.23321 g. | {
"A": "Correct. The worked calculation gives 14.23321 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14.23321 g, not 21.34982 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14.23321 g, not -14.23321 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_007672 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 16 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "3.0625 mmol L⁻¹",
"B": "0.125 mmol L⁻¹",
"C": "0.0625 mmol L⁻¹",
"D": "1.0625 mmol L⁻¹"
} | C | 0.0625 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=16/2^8=0.0625 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.0625 mmol L⁻¹, not 3.0625 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.0625 mmol L⁻¹, not 0.125 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.0625 mmol L⁻¹.",
"D":... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006879 | 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 4 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "9 mol",
"B": "8 mol",
"C": "10 mol",
"D": "16 mol"
} | B | 8 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 30 mol H₂O; O₂ can produce 8 mol H₂O. The limiting condition is O₂; product=8 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8 mol, not 9 mol.",
"B": "Correct. The worked calculation gives 8 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8 mol, not 10 mol.",
"D": "Incorrect. Substituting the stated values into... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008947 | 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 0.52 mol L⁻¹ and initially B is absent. At equilibrium, 15% of A has dissociated at constant volume. Find K_c. | {
"A": "0.05506",
"B": "1.00551",
"C": "0.08259",
"D": "0.11012"
} | A | 0.05506 | Let α=0.15. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.52)(0.15)²/(1−0.15)=0.05506. | {
"A": "Correct. The worked calculation gives 0.05506.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.05506, not 1.00551.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.05506, not 0.08259.",
"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_000422 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 28 and common difference 6. Find the sum of its first 11 terms. | {
"A": "638",
"B": "478.5",
"C": "765.6",
"D": "639"
} | A | 638 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=28, d=6, n=11: Sₙ=11/2[2(28)+(11−1)(6)]=638. | {
"A": "Correct. The worked calculation gives 638.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 638, not 478.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 638, not 765.6.",
"D": "Incorrect. Substituting the stated values into the go... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005267 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +8 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "236.25 N",
"B": "315 N",
"C": "630 N",
"D": "472.5 N"
} | B | 315 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(8×10⁻⁶)/(4×10⁻²)²=315 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 315 N, not 236.25 N.",
"B": "Correct. The worked calculation gives 315 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 315 N, not 630 N.",
"D": "Incorrect. Substituting the stated values in... | [
"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_001494 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (5x² -1x -3) dx. | {
"A": "324",
"B": "326",
"C": "648",
"D": "243"
} | A | 324 | An antiderivative is (5/3)x³+(-1/2)x²+(-3)x. Evaluating between 0 and 6 gives (5/3)(6)³+(-1/2)(6)²+(-3)(6)=324. | {
"A": "Correct. The worked calculation gives 324.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 324, not 326.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 324, not 648.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007277 | 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 214 K and 2.96 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "56.95199 L",
"B": "8.119 L",
"C": "-71.18999 L",
"D": "71.18999 L"
} | D | 71.18999 L | PV=nRT, so V=nRT/P=(12)(0.082057)(214)/(2.96)=71.18999 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 71.18999 L, not 56.95199 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 71.18999 L, not 8.119 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 71.18999 ... | [
"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_005421 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 48 μF capacitor is charged to a potential difference of 22 V. Calculate the energy stored, expressed in μJ. | {
"A": "-11616 μJ",
"B": "8712 μJ",
"C": "23232 μJ",
"D": "11616 μJ"
} | D | 11616 μJ | U=½CV². Since C=48 μF, U in μJ is ½×48×(22)²=11616 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11616 μJ, not -11616 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11616 μJ, not 8712 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11616 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 |
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