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_007757 | 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 96 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "24 mmol L⁻¹",
"B": "23 mmol L⁻¹",
"C": "48 mmol L⁻¹",
"D": "22 mmol L⁻¹"
} | A | 24 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=96/2^2=24 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 24 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24 mmol L⁻¹, not 23 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24 mmol L⁻¹, not 48 mmol L⁻¹.",
"D": "Incorrect. Substi... | [
"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_002344 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, -7], [7, -4]]. | {
"A": "42",
"B": "16.8",
"C": "10.5",
"D": "21"
} | D | 21 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(-4)−(-7)(7)=21. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21, not 42.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21, not 16.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21, not 10.5.",
"D": "Correct. The... | [
"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_004913 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 14 Ω and 3 Ω are connected in series; this combination is connected in parallel with a 12 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.27941 A",
"B": "-1.14706 A",
"C": "0.85294 A",
"D": "1.85294 A"
} | C | 0.85294 A | Series branch resistance=14+3=17 Ω. Parallel equivalent R_eq=(17×12)/(17+12)=7.03448 Ω. Total current I=V/R_eq=6/7.03448=0.85294 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.85294 A, not 1.27941 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.85294 A, not -1.14706 A.",
"C": "Correct. The worked calculation gives 0.85294 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007904 | 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 55 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "1.71875 mmol L⁻¹",
"B": "0.85938 mmol L⁻¹",
"C": "0.42969 mmol L⁻¹",
"D": "-0.85938 mmol L⁻¹"
} | B | 0.85938 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=55/2^6=0.85938 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.85938 mmol L⁻¹, not 1.71875 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.85938 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.85938 mmol L⁻¹, not 0.42969 mmol L⁻¹.",
... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001454 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (-2x² +0x +6) dx. | {
"A": "1.53333",
"B": "5.33333",
"C": "3.33333",
"D": "4"
} | B | 5.33333 | An antiderivative is (-2/3)x³+(0/2)x²+(6)x. Evaluating between 0 and 1 gives (-2/3)(1)³+(0/2)(1)²+(6)(1)=5.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.33333, not 1.53333.",
"B": "Correct. The worked calculation gives 5.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.33333, not 3.33333.",
"D": "Incorrect. Substituting the stated va... | [
"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_005367 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 15 μF capacitor is charged to a potential difference of 34 V. Calculate the energy stored, expressed in μJ. | {
"A": "8670 μJ",
"B": "8669 μJ",
"C": "4335 μJ",
"D": "6502.5 μJ"
} | A | 8670 μJ | U=½CV². Since C=15 μF, U in μJ is ½×15×(34)²=8670 μJ. | {
"A": "Correct. The worked calculation gives 8670 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8670 μJ, not 8669 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8670 μJ, not 4335 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"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_008026 | 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 11 A for 16841 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": "60.95046 g",
"B": "73.14055 g",
"C": "-60.95046 g",
"D": "61.95046 g"
} | A | 60.95046 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×16841/(2×96500)=60.95046 g. | {
"A": "Correct. The worked calculation gives 60.95046 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 60.95046 g, not 73.14055 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 60.95046 g, not -60.95046 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_008006 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 13 A for 10887 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": "46.5659 g",
"B": "44.5659 g",
"C": "23.28295 g",
"D": "55.87908 g"
} | A | 46.5659 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×10887/(2×96500)=46.5659 g. | {
"A": "Correct. The worked calculation gives 46.5659 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 46.5659 g, not 44.5659 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 46.5659 g, not 23.28295 g.",
"D": "Incorrect. Substituting th... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005746 | 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 0.4 atm at 232 K. What is its pressure at 542 K? | {
"A": "2.93448 atm",
"B": "-2.06552 atm",
"C": "0.93448 atm",
"D": "-0.93448 atm"
} | C | 0.93448 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.4)(542)/(232)=0.93448 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.93448 atm, not 2.93448 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.93448 atm, not -2.06552 atm.",
"C": "Correct. The worked calculation gives 0.93448 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004486 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 15 kg and radius 5 m is acted on by a constant torque of 26 N m about its central axis. Find its angular acceleration. | {
"A": "0.104 rad s⁻²",
"B": "0.06933 rad s⁻²",
"C": "-0.13867 rad s⁻²",
"D": "0.13867 rad s⁻²"
} | D | 0.13867 rad s⁻² | For a solid disc, I=½MR²=½(15)(5)²=187.5 kg m². Using τ=Iα, α=26/187.5=0.13867 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.13867 rad s⁻², not 0.104 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.13867 rad s⁻², not 0.06933 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing rel... | [
"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_001806 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 12 elements can be selected from a set of 41 distinct elements? | {
"A": "11847982380",
"B": "6318923936",
"C": "7898654920",
"D": "15797309840"
} | C | 7898654920 | Order does not matter, so the count is C(41,12)=41!/[12!(29)!]=7898654920. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7898654920, not 11847982380.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7898654920, not 6318923936.",
"C": "Correct. The worked calculation gives 7898654920.",
"D": "Incorrect. Substituti... | [
"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_003552 | 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 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "925.60561 m",
"B": "694.95421 m",
"C": "1853.21123 m",
"D": "926.60561 m"
} | D | 926.60561 m | Range R=u²sin(2θ)/g. Substituting u=97, θ=40° and g=10 gives R=(97)²sin(80°)/10=926.60561 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 926.60561 m, not 925.60561 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 926.60561 m, not 694.95421 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 92... | [
"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_007051 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 17 mol of gas at 304 K and 2.41 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "211.15547 L",
"B": "173.96289 L",
"C": "175.96289 L",
"D": "177.96289 L"
} | C | 175.96289 L | PV=nRT, so V=nRT/P=(17)(0.082057)(304)/(2.41)=175.96289 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 175.96289 L, not 211.15547 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 175.96289 L, not 173.96289 L.",
"C": "Correct. The worked calculation gives 175.96289 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_006589 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 24 kg is attached to an ideal spring of force constant 1183 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.4273 s",
"B": "-0.71513 s",
"C": "0.21365 s",
"D": "0.28487 s"
} | D | 0.28487 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(24/1183)=0.28487 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.28487 s, not 0.4273 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.28487 s, not -0.71513 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.28487 s,... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001827 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 7 elements can be selected from a set of 27 distinct elements? | {
"A": "666022.5",
"B": "888030",
"C": "710424",
"D": "1332045"
} | B | 888030 | Order does not matter, so the count is C(27,7)=27!/[7!(20)!]=888030. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 888030, not 666022.5.",
"B": "Correct. The worked calculation gives 888030.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 888030, not 710424.",
"D": "Incorrect. Substituting the stated value... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008065 | 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 15497 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": "72.38255 g",
"B": "53.53692 g",
"C": "35.69128 g",
"D": "71.38255 g"
} | D | 71.38255 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×15497/(2×96500)=71.38255 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 71.38255 g, not 72.38255 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 71.38255 g, not 53.53692 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 71.382... | [
"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_007009 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 13 mol of gas at 349 K and 2.73 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "14.63709 L",
"B": "163.6451 L",
"C": "136.37092 L",
"D": "68.18546 L"
} | C | 136.37092 L | PV=nRT, so V=nRT/P=(13)(0.082057)(349)/(2.73)=136.37092 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 136.37092 L, not 14.63709 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 136.37092 L, not 163.6451 L.",
"C": "Correct. The worked calculation gives 136.37092 L.",
"D": "Incorrect. Substitu... | [
"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_003615 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 83 m s⁻¹ at 65° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "-527.72802 m",
"B": "791.59203 m",
"C": "633.27362 m",
"D": "527.72802 m"
} | D | 527.72802 m | Range R=u²sin(2θ)/g. Substituting u=83, θ=65° and g=10 gives R=(83)²sin(130°)/10=527.72802 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 527.72802 m, not -527.72802 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 527.72802 m, not 791.59203 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5... | [
"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_002589 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 6], [5, 2]]. | {
"A": "-22",
"B": "-26.4",
"C": "-1.2",
"D": "-11"
} | A | -22 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(2)−(6)(5)=-22. | {
"A": "Correct. The worked calculation gives -22.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -22, not -26.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -22, not -1.2.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007171 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 10 mol of gas at 218 K and 0.21 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "1022.19577 L",
"B": "849.82981 L",
"C": "850.82981 L",
"D": "851.82981 L"
} | D | 851.82981 L | PV=nRT, so V=nRT/P=(10)(0.082057)(218)/(0.21)=851.82981 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 851.82981 L, not 1022.19577 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 851.82981 L, not 849.82981 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8... | [
"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_007595 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 12 mL of 0.10 M HCl is mixed with 57 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-12.81436",
"B": "6.40718",
"C": "2.28144",
"D": "12.81436"
} | D | 12.81436 | Excess OH⁻ moles=0.10×(57−12)/1000=0.004500 mol. Total volume=0.069 L, so [OH⁻]=0.065217 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.81436. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.81436, not -12.81436.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.81436, not 6.40718.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.81436, not ... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006358 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 15 kg is attached to an ideal spring of force constant 886 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.73977 s",
"B": "0.26023 s",
"C": "-2.73977 s",
"D": "-1.73977 s"
} | B | 0.26023 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(15/886)=0.26023 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.26023 s, not -0.73977 s.",
"B": "Correct. The worked calculation gives 0.26023 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.26023 s, not -2.73977 s.",
"D": "Incorrect. Substituting t... | [
"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_004675 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 20 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.53333 A",
"B": "-2.53333 A",
"C": "2.53333 A",
"D": "3.8 A"
} | C | 2.53333 A | Series branch resistance=4+14=18 Ω. Parallel equivalent R_eq=(18×20)/(18+20)=9.47368 Ω. Total current I=V/R_eq=24/9.47368=2.53333 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.53333 A, not 0.53333 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.53333 A, not -2.53333 A.",
"C": "Correct. The worked calculation gives 2.53333 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009600 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_18H_5N_3X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "20.4",
"B": "8.5",
"C": "17",
"D": "16"
} | C | 17 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+3−5−2)/2=17. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 17, not 20.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17, not 8.5.",
"C": "Correct. The worked calculation gives 17.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_000691 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 12 and common ratio 2. What is the sum of its first 8 terms? | {
"A": "2295",
"B": "3672",
"C": "1530",
"D": "3060"
} | D | 3060 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=12(2^8−1)/(2−1)=3060. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3060, not 2295.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3060, not 3672.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3060, not 1530.",
"D": "Corr... | [
"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_006288 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 51 cm in front of a thin convex lens of focal length 20 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.64516",
"B": "0.48387",
"C": "0.64516",
"D": "-1.35484"
} | C | 0.64516 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(51)(20)/(51−20)=32.90323 cm. Thus |m|=v/u=32.90323/51=0.64516. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.64516, not 1.64516.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.64516, not 0.48387.",
"C": "Correct. The worked calculation gives 0.64516.",
"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_002807 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-5, 6, -2) and v=(-6, -1, -2), calculate u·v. | {
"A": "42",
"B": "28",
"C": "29",
"D": "33.6"
} | B | 28 | The dot product is the sum of corresponding component products: (-5)(-6)+(6)(-1)+(-2)(-2)=28. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28, not 42.",
"B": "Correct. The worked calculation gives 28.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28, not 29.",
"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_004381 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 12 kg and radius 1 m is acted on by a constant torque of 8 N m about its central axis. Find its angular acceleration. | {
"A": "1.33333 rad s⁻²",
"B": "1.13333 rad s⁻²",
"C": "3.33333 rad s⁻²",
"D": "-0.66667 rad s⁻²"
} | A | 1.33333 rad s⁻² | For a solid disc, I=½MR²=½(12)(1)²=6 kg m². Using τ=Iα, α=8/6=1.33333 rad s⁻². | {
"A": "Correct. The worked calculation gives 1.33333 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.33333 rad s⁻², not 1.13333 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.33333 rad s⁻², not 3.33333 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_002645 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, -4], [3, -1]]. | {
"A": "6.75",
"B": "9",
"C": "1.9",
"D": "11"
} | B | 9 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(-1)−(-4)(3)=9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9, not 6.75.",
"B": "Correct. The worked calculation gives 9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9, not 1.9.",
"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_000995 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio 4. What is the sum of its first 7 terms? | {
"A": "4095.75",
"B": "8191.5",
"C": "5461",
"D": "5462"
} | C | 5461 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(4^7−1)/(4−1)=5461. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5461, not 4095.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5461, not 8191.5.",
"C": "Correct. The worked calculation gives 5461.",
"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_004322 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.13. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "27.776 N",
"B": "26.04 N",
"C": "-34.72 N",
"D": "34.72 N"
} | D | 34.72 N | Net force=mg(sinθ−μcosθ)=7×10×(0.6−0.13×0.8)=34.72 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 34.72 N, not 27.776 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 34.72 N, not 26.04 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 34.72 N, not -34.... | [
"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_004996 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 12 Ω and 9 Ω are connected in series; this combination is connected in parallel with a 19 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.6015 A",
"B": "1.20301 A",
"C": "-0.3985 A",
"D": "0.6015 A"
} | D | 0.6015 A | Series branch resistance=12+9=21 Ω. Parallel equivalent R_eq=(21×19)/(21+19)=9.975 Ω. Total current I=V/R_eq=6/9.975=0.6015 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6015 A, not 3.6015 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6015 A, not 1.20301 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.6015 A, not... | [
"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_006788 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 12 mol H₂ and 25 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "12 mol",
"B": "14 mol",
"C": "15 mol",
"D": "13 mol"
} | A | 12 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 12 mol H₂O; O₂ can produce 50 mol H₂O. The limiting condition is H₂; product=12 mol. | {
"A": "Correct. The worked calculation gives 12 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 14 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 15 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000084 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 -18x +8=0, let its roots be α and β. What is α²+β²? | {
"A": "309",
"B": "31.8",
"C": "308",
"D": "307"
} | C | 308 | By Vieta's relations, α+β = 18/1 and αβ = 8/1. Then α²+β²=(α+β)²−2αβ = (18/1)²−2(8/1) = 308. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 308, not 309.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 308, not 31.8.",
"C": "Correct. The worked calculation gives 308.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_003094 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-1-4i)/(11+6i). What is Re(z), the real part of z? | {
"A": "-0.22293",
"B": "-0.11146",
"C": "-0.44586",
"D": "0.77707"
} | A | -0.22293 | Multiply numerator and denominator by the conjugate (11-6i). Then Re(z)=(ac+bd)/(c²+d²)=((-1)(11)+(-4)(6))/(11²+(6)²)=-0.22293. | {
"A": "Correct. The worked calculation gives -0.22293.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.22293, not -0.11146.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.22293, not -0.44586.",
"D": "Incorrect. Substituting the stat... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005464 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 6 μF capacitor is charged to a potential difference of 30 V. Calculate the energy stored, expressed in μJ. | {
"A": "2701 μJ",
"B": "2700 μJ",
"C": "2025 μJ",
"D": "2699 μJ"
} | B | 2700 μJ | U=½CV². Since C=6 μF, U in μJ is ½×6×(30)²=2700 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2700 μJ, not 2701 μJ.",
"B": "Correct. The worked calculation gives 2700 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2700 μJ, not 2025 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"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_006153 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 60 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": "0.27273",
"B": "1.03636",
"C": "0.36364",
"D": "0.72727"
} | C | 0.36364 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(60)(16)/(60−16)=21.81818 cm. Thus |m|=v/u=21.81818/60=0.36364. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.36364, not 0.27273.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36364, not 1.03636.",
"C": "Correct. The worked calculation gives 0.36364.",
"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_003331 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(9+13i)/(1+10i). What is Re(z), the real part of z? | {
"A": "2.37624",
"B": "-1.37624",
"C": "1.37624",
"D": "-0.62376"
} | C | 1.37624 | Multiply numerator and denominator by the conjugate (1-10i). Then Re(z)=(ac+bd)/(c²+d²)=((9)(1)+(13)(10))/(1²+(10)²)=1.37624. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.37624, not 2.37624.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.37624, not -1.37624.",
"C": "Correct. The worked calculation gives 1.37624.",
"D": "Incorrect. Substituting the stated v... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001084 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=1x³ +6x² -7x+7. Evaluate f′(5). | {
"A": "126",
"B": "128",
"C": "-128",
"D": "153.6"
} | B | 128 | Differentiate: f′(x)=3(1)x²+2(6)x+(-7). At x=5, f′(5)=3(1)(5)²+2(6)(5)+(-7)=128. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 128, not 126.",
"B": "Correct. The worked calculation gives 128.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 128, not -128.",
"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_003893 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 4 m s⁻¹. A constant net force does 15 N of work over 7 m in the direction of motion. Find its final kinetic energy. | {
"A": "17.1 J",
"B": "322 J",
"C": "241.5 J",
"D": "161 J"
} | D | 161 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(4)²+(15)(7)=161 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 161 J, not 17.1 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 161 J, not 322 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 161 J, not 241.5 J.",
"... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003775 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 0 m s⁻¹. A constant net force does 6 N of work over 12 m in the direction of motion. Find its final kinetic energy. | {
"A": "73 J",
"B": "71 J",
"C": "86.4 J",
"D": "72 J"
} | D | 72 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(0)²+(6)(12)=72 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 72 J, not 73 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 72 J, not 71 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 72 J, not 86.4 J.",
"D": "Co... | [
"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_004639 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 11 kg and radius 4 m is acted on by a constant torque of 15 N m about its central axis. Find its angular acceleration. | {
"A": "0.25568 rad s⁻²",
"B": "1.01705 rad s⁻²",
"C": "2.17045 rad s⁻²",
"D": "0.17045 rad s⁻²"
} | D | 0.17045 rad s⁻² | For a solid disc, I=½MR²=½(11)(4)²=88 kg m². Using τ=Iα, α=15/88=0.17045 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.17045 rad s⁻², not 0.25568 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.17045 rad s⁻², not 1.01705 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing r... | [
"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_009743 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(OH)_2]^-2, each OH ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "-2",
"B": "1",
"C": "-3",
"D": "0"
} | D | 0 | Let the formal oxidation state of Ni be x. Charge balance gives x+(2)(−1)=-2; hence x=-2+2=+0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"D": "Correct. The worked ... | [
"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_009288 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.51 V, transfers 2 electrons, and has reaction quotient Q=10^0. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.51 V",
"B": "-1.49 V",
"C": "1.051 V",
"D": "0.51 V"
} | D | 0.51 V | Apply the Nernst equation: E=0.51−(0.0591/2)(0)=0.51 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.51 V, not -0.51 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.51 V, not -1.49 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.51 V, not 1.051 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_004684 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 2 Ω are connected in series; this combination is connected in parallel with a 14 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.14286 A",
"B": "1.42857 A",
"C": "7.28571 A",
"D": "4.28571 A"
} | D | 4.28571 A | Series branch resistance=4+2=6 Ω. Parallel equivalent R_eq=(6×14)/(6+14)=4.2 Ω. Total current I=V/R_eq=18/4.2=4.28571 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.28571 A, not 2.14286 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.28571 A, not 1.42857 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.28571 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_007928 | 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 37 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "-1.85547 mmol L⁻¹",
"B": "0.14453 mmol L⁻¹",
"C": "-0.85547 mmol L⁻¹",
"D": "-0.14453 mmol L⁻¹"
} | B | 0.14453 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=37/2^8=0.14453 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.14453 mmol L⁻¹, not -1.85547 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.14453 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.14453 mmol L⁻¹, not -0.85547 mmol L⁻¹."... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003577 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 74 m s⁻¹ at 70° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "422.38859 m",
"B": "351.9905 m",
"C": "527.98574 m",
"D": "352.9905 m"
} | B | 351.9905 m | Range R=u²sin(2θ)/g. Substituting u=74, θ=70° and g=10 gives R=(74)²sin(140°)/10=351.9905 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 351.9905 m, not 422.38859 m.",
"B": "Correct. The worked calculation gives 351.9905 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 351.9905 m, not 527.98574 m.",
"D": "Incorrect. Substitut... | [
"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_004654 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 3 m is acted on by a constant torque of 7 N m about its central axis. Find its angular acceleration. | {
"A": "2.31111 rad s⁻²",
"B": "-0.31111 rad s⁻²",
"C": "-2.68889 rad s⁻²",
"D": "0.31111 rad s⁻²"
} | D | 0.31111 rad s⁻² | For a solid disc, I=½MR²=½(5)(3)²=22.5 kg m². Using τ=Iα, α=7/22.5=0.31111 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31111 rad s⁻², not 2.31111 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31111 rad s⁻², not -0.31111 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing ... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004466 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 3 kg and radius 2 m is acted on by a constant torque of 73 N m about its central axis. Find its angular acceleration. | {
"A": "15.16667 rad s⁻²",
"B": "12.16667 rad s⁻²",
"C": "18.25 rad s⁻²",
"D": "9.16667 rad s⁻²"
} | B | 12.16667 rad s⁻² | For a solid disc, I=½MR²=½(3)(2)²=6 kg m². Using τ=Iα, α=73/6=12.16667 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.16667 rad s⁻², not 15.16667 rad s⁻².",
"B": "Correct. The worked calculation gives 12.16667 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.16667 rad s⁻², not 18.25 rad s⁻².",
"... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006533 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 8 kg is attached to an ideal spring of force constant 931 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.13905 s",
"B": "-0.1854 s",
"C": "0.1854 s",
"D": "1.1854 s"
} | C | 0.1854 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(8/931)=0.1854 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.1854 s, not 0.13905 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.1854 s, not -0.1854 s.",
"C": "Correct. The worked calculation gives 0.1854 s.",
"D": "Incorrect. Substituting the st... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005309 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +8 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "17.77778 N",
"B": "14.22222 N",
"C": "26.66667 N",
"D": "35.55556 N"
} | A | 17.77778 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(8×10⁻⁶)/(9×10⁻²)²=17.77778 N. | {
"A": "Correct. The worked calculation gives 17.77778 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17.77778 N, not 14.22222 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17.77778 N, not 26.66667 N.",
"D": "Incorrect. Substitutin... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007600 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 14 mL of 0.10 M HCl is mixed with 86 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "10.85733",
"B": "12.85733",
"C": "2.28573",
"D": "25.71466"
} | B | 12.85733 | Excess OH⁻ moles=0.10×(86−14)/1000=0.007200 mol. Total volume=0.100 L, so [OH⁻]=0.072000 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.85733. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.85733, not 10.85733.",
"B": "Correct. The worked calculation gives 12.85733.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.85733, not 2.28573.",
"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_007012 | 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 566 K and 0.94 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "49.40879 L",
"B": "97.81758 L",
"C": "98.81758 L",
"D": "10.88176 L"
} | C | 98.81758 L | PV=nRT, so V=nRT/P=(2)(0.082057)(566)/(0.94)=98.81758 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 98.81758 L, not 49.40879 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 98.81758 L, not 97.81758 L.",
"C": "Correct. The worked calculation gives 98.81758 L.",
"D": "Incorrect. Substitutin... | [
"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_008079 | 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 27802 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": "137.20935 g",
"B": "274.4187 g",
"C": "136.20935 g",
"D": "205.81403 g"
} | A | 137.20935 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×15×27802/(2×96500)=137.20935 g. | {
"A": "Correct. The worked calculation gives 137.20935 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 137.20935 g, not 274.4187 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 137.20935 g, not 136.20935 g.",
"D": "Incorrect. Substit... | [
"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_009313 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.05 V, transfers 1 electrons, and has reaction quotient Q=10^1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "3.9909 V",
"B": "0.9909 V",
"C": "1.9818 V",
"D": "0.49545 V"
} | B | 0.9909 V | Apply the Nernst equation: E=1.05−(0.0591/1)(1)=0.9909 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9909 V, not 3.9909 V.",
"B": "Correct. The worked calculation gives 0.9909 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9909 V, not 1.9818 V.",
"D": "Incorrect. Substituting the stat... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006510 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 6 kg is attached to an ideal spring of force constant 955 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.15853 s",
"B": "-2.84147 s",
"C": "1.01585 s",
"D": "0.15853 s"
} | D | 0.15853 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(6/955)=0.15853 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.15853 s, not 1.15853 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.15853 s, not -2.84147 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.15853 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006600 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 14 kg is attached to an ideal spring of force constant 220 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.50452 s",
"B": "-0.49548 s",
"C": "1.50452 s",
"D": "0.37839 s"
} | A | 0.50452 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(14/220)=0.50452 s. | {
"A": "Correct. The worked calculation gives 0.50452 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.50452 s, not -0.49548 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.50452 s, not 1.50452 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_004800 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 10 Ω are connected in series; this combination is connected in parallel with a 11 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.51515 A",
"B": "0.75758 A",
"C": "1.75758 A",
"D": "0.87879 A"
} | C | 1.75758 A | Series branch resistance=8+10=18 Ω. Parallel equivalent R_eq=(18×11)/(18+11)=6.82759 Ω. Total current I=V/R_eq=12/6.82759=1.75758 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.75758 A, not 3.51515 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.75758 A, not 0.75758 A.",
"C": "Correct. The worked calculation gives 1.75758 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_001904 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 11 elements can be selected from a set of 25 distinct elements? | {
"A": "4457399",
"B": "4457400",
"C": "6686100",
"D": "-4457400"
} | B | 4457400 | Order does not matter, so the count is C(25,11)=25!/[11!(14)!]=4457400. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4457400, not 4457399.",
"B": "Correct. The worked calculation gives 4457400.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4457400, not 6686100.",
"D": "Incorrect. Substituting the stated va... | [
"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_002272 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 11 blue and 9 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-1.67385",
"B": "0.32615",
"C": "0.16308",
"D": "0.48923"
} | B | 0.32615 | Favourable pairs = C(6,2)+C(11,2)+C(9,2)=106. Total pairs=C(26,2)=325. Therefore P=106/325=0.32615. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32615, not -1.67385.",
"B": "Correct. The worked calculation gives 0.32615.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32615, not 0.16308.",
"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_003224 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(7-7i)/(2+2i). What is Re(z), the real part of z? | {
"A": "-1",
"B": "0",
"C": "1",
"D": "2"
} | B | 0 | Multiply numerator and denominator by the conjugate (2-2i). Then Re(z)=(ac+bd)/(c²+d²)=((7)(2)+(-7)(2))/(2²+(2)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 1.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_008956 | 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 1.32 mol L⁻¹ and initially B is absent. At equilibrium, 11% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.92822",
"B": "2.07178",
"C": "1.00718",
"D": "0.07178"
} | D | 0.07178 | Let α=0.11. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.32)(0.11)²/(1−0.11)=0.07178. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.07178, not -0.92822.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.07178, not 2.07178.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.07178, not 1.00... | [
"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_005223 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +4 μC are separated by 12 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "17 N",
"B": "7.5 N",
"C": "22.5 N",
"D": "15 N"
} | D | 15 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(4×10⁻⁶)/(12×10⁻²)²=15 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15 N, not 17 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15 N, not 7.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15 N, not 22.5 N.",
"D": "C... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007713 | 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 28 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "1.75 mmol L⁻¹",
"B": "3.5 mmol L⁻¹",
"C": "1.175 mmol L⁻¹",
"D": "0.75 mmol L⁻¹"
} | A | 1.75 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=28/2^4=1.75 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 1.75 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.75 mmol L⁻¹, not 3.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.75 mmol L⁻¹, not 1.175 mmol L⁻¹.",
"D": "Incorre... | [
"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_003676 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block initially moves at 4 m s⁻¹. A constant net force does 28 N of work over 10 m in the direction of motion. Find its final kinetic energy. | {
"A": "-296 J",
"B": "30.6 J",
"C": "296 J",
"D": "295 J"
} | C | 296 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(2)(4)²+(28)(10)=296 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 296 J, not -296 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 296 J, not 30.6 J.",
"C": "Correct. The worked calculation gives 296 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_008503 | 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 1.97 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "3.94 K",
"B": "4.94 K",
"C": "1.97 K",
"D": "7.88 K"
} | A | 3.94 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×1.97=3.94 K. | {
"A": "Correct. The worked calculation gives 3.94 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.94 K, not 4.94 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.94 K, not 1.97 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_005483 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 47 μF capacitor is charged to a potential difference of 40 V. Calculate the energy stored, expressed in μJ. | {
"A": "56400 μJ",
"B": "37600 μJ",
"C": "37598 μJ",
"D": "75200 μJ"
} | B | 37600 μJ | U=½CV². Since C=47 μF, U in μJ is ½×47×(40)²=37600 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 37600 μJ, not 56400 μJ.",
"B": "Correct. The worked calculation gives 37600 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 37600 μJ, not 37598 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_005253 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +5 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "36.15625 N",
"B": "34.15625 N",
"C": "35.15625 N",
"D": "52.73438 N"
} | C | 35.15625 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(5×10⁻⁶)/(8×10⁻²)²=35.15625 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 35.15625 N, not 36.15625 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 35.15625 N, not 34.15625 N.",
"C": "Correct. The worked calculation gives 35.15625 N.",
"D": "Incorrect. Substitutin... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002892 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-7, -1, 5) and v=(-2, -3, 4), calculate u·v. | {
"A": "37",
"B": "74",
"C": "35",
"D": "18.5"
} | A | 37 | The dot product is the sum of corresponding component products: (-7)(-2)+(-1)(-3)+(5)(4)=37. | {
"A": "Correct. The worked calculation gives 37.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 37, not 74.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 37, not 35.",
"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_005515 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 62 μF capacitor is charged to a potential difference of 31 V. Calculate the energy stored, expressed in μJ. | {
"A": "29791 μJ",
"B": "29790 μJ",
"C": "22343.25 μJ",
"D": "44686.5 μJ"
} | A | 29791 μJ | U=½CV². Since C=62 μF, U in μJ is ½×62×(31)²=29791 μJ. | {
"A": "Correct. The worked calculation gives 29791 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 29791 μJ, not 29790 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29791 μJ, not 22343.25 μJ.",
"D": "Incorrect. Substituting the s... | [
"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_002835 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(3, 1, -1) and v=(5, 4, 2), calculate u·v. | {
"A": "19",
"B": "2.7",
"C": "15",
"D": "17"
} | D | 17 | The dot product is the sum of corresponding component products: (3)(5)+(1)(4)+(-1)(2)=17. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 17, not 19.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17, not 2.7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17, not 15.",
"D": "Correct. The wo... | [
"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_004203 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 45 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.28. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "126.9 N",
"B": "168.2 N",
"C": "169.2 N",
"D": "-169.2 N"
} | C | 169.2 N | Net force=mg(sinθ−μcosθ)=45×10×(0.6−0.28×0.8)=169.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 169.2 N, not 126.9 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 169.2 N, not 168.2 N.",
"C": "Correct. The worked calculation gives 169.2 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_009542 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_14H_17N_1X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "2.5",
"B": "-5",
"C": "5",
"D": "1.5"
} | C | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×14+2+1−17−4)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not -5.",
"C": "Correct. The worked calculation gives 5.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006671 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 12 mol H₂ and 12 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "14 mol",
"B": "13 mol",
"C": "12 mol",
"D": "10 mol"
} | C | 12 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 12 mol H₂O; O₂ can produce 24 mol H₂O. The limiting condition is H₂; product=12 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 14 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 13 mol.",
"C": "Correct. The worked calculation gives 12 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000771 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio -3. What is the sum of its first 10 terms? | {
"A": "-59048",
"B": "-59050",
"C": "-5903.8",
"D": "-59046"
} | A | -59048 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(-3^10−1)/(-3−1)=-59048. | {
"A": "Correct. The worked calculation gives -59048.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -59048, not -59050.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -59048, not -5903.8.",
"D": "Incorrect. Substituting the stated values... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003920 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 10 m s⁻¹. A constant net force does 15 N of work over 3 m in the direction of motion. Find its final kinetic energy. | {
"A": "497 J",
"B": "594 J",
"C": "247.5 J",
"D": "495 J"
} | D | 495 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(10)²+(15)(3)=495 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 495 J, not 497 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 495 J, not 594 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 495 J, not 247.5 J.",
"D... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009713 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(Cl)_4]^+0, each Cl ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "2",
"B": "1",
"C": "4",
"D": "3"
} | C | 4 | Let the formal oxidation state of Co be x. Charge balance gives x+(4)(−1)=+0; hence x=0+4=+4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.",
"C": "Correct. The worked calculation gives 4.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002057 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 12 blue and 10 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "3.36",
"B": "1.036",
"C": "2.36",
"D": "0.36"
} | D | 0.36 | Favourable pairs = C(4,2)+C(12,2)+C(10,2)=117. Total pairs=C(26,2)=325. Therefore P=117/325=0.36. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.36, not 3.36.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36, not 1.036.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.36, not 2.36.",
"D": "Cor... | [
"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_007326 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 16 mol of gas at 634 K and 0.76 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "876.19601 L",
"B": "1095.24501 L",
"C": "821.43376 L",
"D": "1096.24501 L"
} | B | 1095.24501 L | PV=nRT, so V=nRT/P=(16)(0.082057)(634)/(0.76)=1095.24501 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1095.24501 L, not 876.19601 L.",
"B": "Correct. The worked calculation gives 1095.24501 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1095.24501 L, not 821.43376 L.",
"D": "Incorrect. Sub... | [
"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_008616 | 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 0.69 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.62 K",
"B": "0.38 K",
"C": "1.38 K",
"D": "-1.62 K"
} | C | 1.38 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×0.69=1.38 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.38 K, not -0.62 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.38 K, not 0.38 K.",
"C": "Correct. The worked calculation gives 1.38 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002921 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-4, 9, -3) and v=(3, -2, -5), calculate u·v. | {
"A": "-15",
"B": "15",
"C": "-22.5",
"D": "-17"
} | A | -15 | The dot product is the sum of corresponding component products: (-4)(3)+(9)(-2)+(-3)(-5)=-15. | {
"A": "Correct. The worked calculation gives -15.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -15, not 15.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -15, not -22.5.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_005142 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +3 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "22.33333 N",
"B": "17.5 N",
"C": "28 N",
"D": "23.33333 N"
} | D | 23.33333 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(3×10⁻⁶)/(9×10⁻²)²=23.33333 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 23.33333 N, not 22.33333 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23.33333 N, not 17.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23.33333 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_000518 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 2 and common difference 3. Find the sum of its first 20 terms. | {
"A": "608",
"B": "62",
"C": "611",
"D": "610"
} | D | 610 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=2, d=3, n=20: Sₙ=20/2[2(2)+(20−1)(3)]=610. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 610, not 608.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 610, not 62.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 610, not 611.",
"D": "Correct. Th... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009089 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.22 V, transfers 2 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.92775 V",
"B": "1.10722 V",
"C": "1.07225 V",
"D": "-0.92775 V"
} | C | 1.07225 V | Apply the Nernst equation: E=1.22−(0.0591/2)(5)=1.07225 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.07225 V, not -1.92775 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.07225 V, not 1.10722 V.",
"C": "Correct. The worked calculation gives 1.07225 V.",
"D": "Incorrect. Substituting th... | [
"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_008553 | 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 1.67 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.67 K",
"B": "1.167 K",
"C": "1.2525 K",
"D": "-1.67 K"
} | A | 1.67 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×1.0×1.67=1.67 K. | {
"A": "Correct. The worked calculation gives 1.67 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.67 K, not 1.167 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.67 K, not 1.2525 K.",
"D": "Incorrect. Substituting the stated valu... | [
"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_007144 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 9 mol of gas at 182 K and 2.57 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "41.83949 L",
"B": "62.75924 L",
"C": "52.29936 L",
"D": "53.29936 L"
} | C | 52.29936 L | PV=nRT, so V=nRT/P=(9)(0.082057)(182)/(2.57)=52.29936 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 52.29936 L, not 41.83949 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 52.29936 L, not 62.75924 L.",
"C": "Correct. The worked calculation gives 52.29936 L.",
"D": "Incorrect. Substitutin... | [
"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_008311 | 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 2 A for 8612 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": "4.66696 g",
"B": "5.66696 g",
"C": "1.5667 g",
"D": "8.50045 g"
} | B | 5.66696 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×2×8612/(2×96500)=5.66696 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.66696 g, not 4.66696 g.",
"B": "Correct. The worked calculation gives 5.66696 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.66696 g, not 1.5667 g.",
"D": "Incorrect. Substituting the ... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000625 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -18 and common difference 9. Find the sum of its first 34 terms. | {
"A": "4435",
"B": "3549.6",
"C": "4437",
"D": "4439"
} | C | 4437 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-18, d=9, n=34: Sₙ=34/2[2(-18)+(34−1)(9)]=4437. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4437, not 4435.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4437, not 3549.6.",
"C": "Correct. The worked calculation gives 4437.",
"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_001724 | 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 67 distinct elements? | {
"A": "47905",
"B": "47907",
"C": "35928.75",
"D": "4791.5"
} | A | 47905 | Order does not matter, so the count is C(67,3)=67!/[3!(64)!]=47905. | {
"A": "Correct. The worked calculation gives 47905.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 47905, not 47907.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 47905, not 35928.75.",
"D": "Incorrect. Substituting the stated values in... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009527 | 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_7H_3N_1X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "-5",
"C": "5",
"D": "6"
} | C | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+1−3−4)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not -5.",
"C": "Correct. The worked calculation gives 5.",
"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_009948 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(OH)_2]^-4, each OH ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "-5",
"B": "-2",
"C": "1",
"D": "-3"
} | B | -2 | Let the formal oxidation state of Cu be x. Charge balance gives x+(2)(−1)=-4; hence x=-4+2=-2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2, not -5.",
"B": "Correct. The worked calculation gives -2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2, not 1.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006415 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 14 kg is attached to an ideal spring of force constant 757 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.72801 s",
"B": "0.13599 s",
"C": "0.27199 s",
"D": "-2.72801 s"
} | C | 0.27199 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(14/757)=0.27199 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.27199 s, not -1.72801 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.27199 s, not 0.13599 s.",
"C": "Correct. The worked calculation gives 0.27199 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_003169 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(5+3i)/(11+5i). What is Re(z), the real part of z? | {
"A": "1.04795",
"B": "-2.52055",
"C": "-0.47945",
"D": "0.47945"
} | D | 0.47945 | Multiply numerator and denominator by the conjugate (11-5i). Then Re(z)=(ac+bd)/(c²+d²)=((5)(11)+(3)(5))/(11²+(5)²)=0.47945. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.47945, not 1.04795.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.47945, not -2.52055.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.47945, not -0.4... | [
"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_005275 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +2 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "4.375 N",
"B": "25.3125 N",
"C": "33.75 N",
"D": "50.625 N"
} | C | 33.75 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(2×10⁻⁶)/(4×10⁻²)²=33.75 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33.75 N, not 4.375 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33.75 N, not 25.3125 N.",
"C": "Correct. The worked calculation gives 33.75 N.",
"D": "Incorrect. Substituting the stated ... | [
"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_001271 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-3x³ +10x² -8x+7. Evaluate f′(-3). | {
"A": "-13.9",
"B": "-149",
"C": "-111.75",
"D": "-74.5"
} | B | -149 | Differentiate: f′(x)=3(-3)x²+2(10)x+(-8). At x=-3, f′(-3)=3(-3)(-3)²+2(10)(-3)+(-8)=-149. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -149, not -13.9.",
"B": "Correct. The worked calculation gives -149.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -149, not -111.75.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_007043 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 16 mol of gas at 484 K and 1.37 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "461.83168 L",
"B": "463.83168 L",
"C": "927.66337 L",
"D": "462.83168 L"
} | B | 463.83168 L | PV=nRT, so V=nRT/P=(16)(0.082057)(484)/(1.37)=463.83168 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 463.83168 L, not 461.83168 L.",
"B": "Correct. The worked calculation gives 463.83168 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 463.83168 L, not 927.66337 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_007897 | 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 81 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "48.6 mmol L⁻¹",
"B": "40.5 mmol L⁻¹",
"C": "-40.5 mmol L⁻¹",
"D": "32.4 mmol L⁻¹"
} | B | 40.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=81/2^1=40.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 40.5 mmol L⁻¹, not 48.6 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 40.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 40.5 mmol L⁻¹, not -40.5 mmol L⁻¹.",
"D": "Incorr... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000534 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 19 and common difference 13. Find the sum of its first 12 terms. | {
"A": "1086",
"B": "1087",
"C": "868.8",
"D": "109.6"
} | A | 1086 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=19, d=13, n=12: Sₙ=12/2[2(19)+(12−1)(13)]=1086. | {
"A": "Correct. The worked calculation gives 1086.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1086, not 1087.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1086, not 868.8.",
"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_006183 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 111 cm in front of a thin convex lens of focal length 28 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.33735",
"B": "3.33735",
"C": "-1.66265",
"D": "0.50602"
} | A | 0.33735 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(111)(28)/(111−28)=37.44578 cm. Thus |m|=v/u=37.44578/111=0.33735. | {
"A": "Correct. The worked calculation gives 0.33735.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33735, not 3.33735.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33735, not -1.66265.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002763 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, 8, -1) and v=(6, -6, -3), calculate u·v. | {
"A": "-16.8",
"B": "-15.75",
"C": "-1.1",
"D": "-21"
} | D | -21 | The dot product is the sum of corresponding component products: (4)(6)+(8)(-6)+(-1)(-3)=-21. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -21, not -16.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -21, not -15.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -21, not -1.1.",
"D": "Corr... | [
"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 |
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