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_004601 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 15 kg and radius 1 m is acted on by a constant torque of 53 N m about its central axis. Find its angular acceleration. | {
"A": "5.3 rad s⁻²",
"B": "7.06667 rad s⁻²",
"C": "-7.06667 rad s⁻²",
"D": "14.13333 rad s⁻²"
} | B | 7.06667 rad s⁻² | For a solid disc, I=½MR²=½(15)(1)²=7.5 kg m². Using τ=Iα, α=53/7.5=7.06667 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.06667 rad s⁻², not 5.3 rad s⁻².",
"B": "Correct. The worked calculation gives 7.06667 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.06667 rad s⁻², not -7.06667 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_000796 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio -2. What is the sum of its first 9 terms? | {
"A": "1368",
"B": "684",
"C": "1026",
"D": "-1368"
} | A | 1368 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(-2^9−1)/(-2−1)=1368. | {
"A": "Correct. The worked calculation gives 1368.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1368, not 684.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1368, not 1026.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_001516 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (6x² +7x +3) dx. | {
"A": "354.5",
"B": "282",
"C": "528.75",
"D": "352.5"
} | D | 352.5 | An antiderivative is (6/3)x³+(7/2)x²+(3)x. Evaluating between 0 and 5 gives (6/3)(5)³+(7/2)(5)²+(3)(5)=352.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 352.5, not 354.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 352.5, not 282.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 352.5, not 528.75.",
"D": ... | [
"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_008710 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.91 mol L⁻¹ and initially B is absent. At equilibrium, 72% of A has dissociated at constant volume. Find K_c. | {
"A": "6.7392",
"B": "10.1088",
"C": "13.4784",
"D": "5.7392"
} | A | 6.7392 | Let α=0.72. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.91)(0.72)²/(1−0.72)=6.7392. | {
"A": "Correct. The worked calculation gives 6.7392.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.7392, not 10.1088.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.7392, not 13.4784.",
"D": "Incorrect. Substituting the stated value... | [
"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_006739 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 46 mol H₂ and 9 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "17 mol",
"B": "18 mol",
"C": "16 mol",
"D": "9 mol"
} | B | 18 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 46 mol H₂O; O₂ can produce 18 mol H₂O. The limiting condition is O₂; product=18 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18 mol, not 17 mol.",
"B": "Correct. The worked calculation gives 18 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18 mol, not 16 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_006731 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 27 mol H₂ and 34 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "21.6 mol",
"B": "27 mol",
"C": "54 mol",
"D": "20.25 mol"
} | B | 27 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 27 mol H₂O; O₂ can produce 68 mol H₂O. The limiting condition is H₂; product=27 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 27 mol, not 21.6 mol.",
"B": "Correct. The worked calculation gives 27 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 27 mol, not 54 mol.",
"D": "Incorrect. Substituting the stated value... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003902 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block initially moves at 6 m s⁻¹. A constant net force does 28 N of work over 19 m in the direction of motion. Find its final kinetic energy. | {
"A": "786 J",
"B": "627.2 J",
"C": "588 J",
"D": "784 J"
} | D | 784 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(14)(6)²+(28)(19)=784 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 784 J, not 786 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 784 J, not 627.2 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 784 J, not 588 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_006381 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 18 kg is attached to an ideal spring of force constant 172 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.48525 s",
"B": "0.647 s",
"C": "2.647 s",
"D": "-2.353 s"
} | B | 0.647 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(18/172)=0.647 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.647 s, not 0.48525 s.",
"B": "Correct. The worked calculation gives 0.647 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.647 s, not 2.647 s.",
"D": "Incorrect. Substituting the stated ... | [
"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_009767 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(Cl)_6]^+0, each Cl ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "5",
"B": "6",
"C": "9",
"D": "3"
} | B | 6 | Let the formal oxidation state of Fe be x. Charge balance gives x+(6)(−1)=+0; hence x=0+6=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 5.",
"B": "Correct. The worked calculation gives 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"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_007903 | 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 14 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "1.4375 mmol L⁻¹",
"B": "0.4375 mmol L⁻¹",
"C": "1.04375 mmol L⁻¹",
"D": "0.32812 mmol L⁻¹"
} | B | 0.4375 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=14/2^5=0.4375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.4375 mmol L⁻¹, not 1.4375 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.4375 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.4375 mmol L⁻¹, not 1.04375 mmol L⁻¹.",
"D... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001658 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (-1x² +0x -4) dx. | {
"A": "-23",
"B": "-20",
"C": "21",
"D": "-21"
} | D | -21 | An antiderivative is (-1/3)x³+(0/2)x²+(-4)x. Evaluating between 0 and 3 gives (-1/3)(3)³+(0/2)(3)²+(-4)(3)=-21. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -21, not -23.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -21, not -20.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -21, not 21.",
"D": "Correct. Th... | [
"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_007015 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 15 mol of gas at 497 K and 2.31 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "266.82032 L",
"B": "317.78438 L",
"C": "27.48203 L",
"D": "264.82032 L"
} | D | 264.82032 L | PV=nRT, so V=nRT/P=(15)(0.082057)(497)/(2.31)=264.82032 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 264.82032 L, not 266.82032 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 264.82032 L, not 317.78438 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26... | [
"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_006562 | 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 347 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.60259 s",
"B": "0.40173 s",
"C": "-0.59827 s",
"D": "1.40173 s"
} | B | 0.40173 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(14/347)=0.40173 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.40173 s, not 0.60259 s.",
"B": "Correct. The worked calculation gives 0.40173 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.40173 s, not -0.59827 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_001911 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 4 elements can be selected from a set of 13 distinct elements? | {
"A": "858",
"B": "714",
"C": "1430",
"D": "715"
} | D | 715 | Order does not matter, so the count is C(13,4)=13!/[4!(9)!]=715. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 715, not 858.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 715, not 714.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 715, not 1430.",
"D": "Correct. ... | [
"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_002851 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-7, 2, 2) and v=(5, 0, 0), calculate u·v. | {
"A": "-26.25",
"B": "-42",
"C": "-33",
"D": "-35"
} | D | -35 | The dot product is the sum of corresponding component products: (-7)(5)+(2)(0)+(2)(0)=-35. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -35, not -26.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -35, not -42.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -35, not -33.",
"D": "Correct... | [
"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_005622 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 7 μF capacitor is charged to a potential difference of 37 V. Calculate the energy stored, expressed in μJ. | {
"A": "480.15 μJ",
"B": "4791.5 μJ",
"C": "4792.5 μJ",
"D": "3833.2 μJ"
} | B | 4791.5 μJ | U=½CV². Since C=7 μF, U in μJ is ½×7×(37)²=4791.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4791.5 μJ, not 480.15 μJ.",
"B": "Correct. The worked calculation gives 4791.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4791.5 μJ, not 4792.5 μJ.",
"D": "Incorrect. Substituting the... | [
"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_004551 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 4 kg and radius 2 m is acted on by a constant torque of 42 N m about its central axis. Find its angular acceleration. | {
"A": "2.625 rad s⁻²",
"B": "7.25 rad s⁻²",
"C": "5.25 rad s⁻²",
"D": "6.25 rad s⁻²"
} | C | 5.25 rad s⁻² | For a solid disc, I=½MR²=½(4)(2)²=8 kg m². Using τ=Iα, α=42/8=5.25 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.25 rad s⁻², not 2.625 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.25 rad s⁻², not 7.25 rad s⁻².",
"C": "Correct. The worked calculation gives 5.25 rad s⁻².",
"D": "Incorrect. ... | [
"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_008679 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.64 mol L⁻¹ and initially B is absent. At equilibrium, 31% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.35654",
"B": "0.53482",
"C": "-1.64346",
"D": "0.35654"
} | D | 0.35654 | Let α=0.31. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.64)(0.31)²/(1−0.31)=0.35654. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35654, not -0.35654.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35654, not 0.53482.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35654, not -1.6... | [
"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_001336 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=7x³ -9x² -2x+7. Evaluate f′(-1). | {
"A": "29.6",
"B": "74",
"C": "36",
"D": "37"
} | D | 37 | Differentiate: f′(x)=3(7)x²+2(-9)x+(-2). At x=-1, f′(-1)=3(7)(-1)²+2(-9)(-1)+(-2)=37. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 37, not 29.6.",
"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 36.",
"D": "Correct. The w... | [
"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_008088 | 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 5 A for 22833 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": "28.17154 g",
"B": "38.56206 g",
"C": "37.56206 g",
"D": "-37.56206 g"
} | C | 37.56206 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×5×22833/(2×96500)=37.56206 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 37.56206 g, not 28.17154 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 37.56206 g, not 38.56206 g.",
"C": "Correct. The worked calculation gives 37.56206 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003793 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 4 m s⁻¹. A constant net force does 12 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "212 J",
"B": "214 J",
"C": "169.6 J",
"D": "22.2 J"
} | A | 212 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(4)²+(12)(11)=212 J. | {
"A": "Correct. The worked calculation gives 212 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 212 J, not 214 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 212 J, not 169.6 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_002585 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, 1], [8, 0]]. | {
"A": "-5",
"B": "-16",
"C": "-6",
"D": "-8"
} | D | -8 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(0)−(1)(8)=-8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -8, not -5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -8, not -16.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -8, not -6.",
"D": "Correct. The wo... | [
"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_006442 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 7 kg is attached to an ideal spring of force constant 65 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "3.65633 s",
"B": "0.65633 s",
"C": "1.06563 s",
"D": "-1.34367 s"
} | B | 0.65633 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(7/65)=0.65633 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.65633 s, not 3.65633 s.",
"B": "Correct. The worked calculation gives 0.65633 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.65633 s, not 1.06563 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001527 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (-4x² +0x +7) dx. | {
"A": "6.66667",
"B": "2.5",
"C": "3.33333",
"D": "2.33333"
} | C | 3.33333 | An antiderivative is (-4/3)x³+(0/2)x²+(7)x. Evaluating between 0 and 2 gives (-4/3)(2)³+(0/2)(2)²+(7)(2)=3.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.33333, not 6.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.33333, not 2.5.",
"C": "Correct. The worked calculation gives 3.33333.",
"D": "Incorrect. Substituting the stated values... | [
"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_008933 | 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 1.39 mol L⁻¹ and initially B is absent. At equilibrium, 36% of A has dissociated at constant volume. Find K_c. | {
"A": "1.68885",
"B": "4.1259",
"C": "1.1259",
"D": "2.1259"
} | C | 1.1259 | Let α=0.36. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.39)(0.36)²/(1−0.36)=1.1259. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.1259, not 1.68885.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1259, not 4.1259.",
"C": "Correct. The worked calculation gives 1.1259.",
"D": "Incorrect. Substituting the stated values... | [
"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_007781 | 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 39 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "0.60938 mmol L⁻¹",
"B": "0.30469 mmol L⁻¹",
"C": "0.45703 mmol L⁻¹",
"D": "0.15234 mmol L⁻¹"
} | B | 0.30469 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=39/2^7=0.30469 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30469 mmol L⁻¹, not 0.60938 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.30469 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30469 mmol L⁻¹, not 0.45703 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_009845 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(Cl)_4]^-2, each Cl ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "-2",
"B": "2",
"C": "1.5",
"D": "4"
} | B | 2 | Let the formal oxidation state of Fe be x. Charge balance gives x+(4)(−1)=-2; hence x=-2+4=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.5.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006554 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 17 kg is attached to an ideal spring of force constant 289 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.48507 s",
"B": "3.48507 s",
"C": "0.24254 s",
"D": "1.04851 s"
} | A | 0.48507 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(17/289)=0.48507 s. | {
"A": "Correct. The worked calculation gives 0.48507 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.48507 s, not 3.48507 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.48507 s, not 0.24254 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005010 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +7 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "56 N",
"B": "70 N",
"C": "69 N",
"D": "105 N"
} | B | 70 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(7×10⁻⁶)/(6×10⁻²)²=70 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 70 N, not 56 N.",
"B": "Correct. The worked calculation gives 70 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 70 N, not 69 N.",
"D": "Incorrect. Substituting the stated values into the g... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002086 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 7 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-1.67033",
"B": "0.16484",
"C": "0.32967",
"D": "2.32967"
} | C | 0.32967 | Favourable pairs = C(3,2)+C(7,2)+C(4,2)=30. Total pairs=C(14,2)=91. Therefore P=30/91=0.32967. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32967, not -1.67033.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32967, not 0.16484.",
"C": "Correct. The worked calculation gives 0.32967.",
"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_009138 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.43 V, transfers 1 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.9246 V",
"B": "1.0754 V",
"C": "1.6131 V",
"D": "-1.9246 V"
} | B | 1.0754 V | Apply the Nernst equation: E=1.43−(0.0591/1)(6)=1.0754 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0754 V, not -0.9246 V.",
"B": "Correct. The worked calculation gives 1.0754 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0754 V, not 1.6131 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005621 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 12 μF capacitor is charged to a potential difference of 27 V. Calculate the energy stored, expressed in μJ. | {
"A": "-4374 μJ",
"B": "4376 μJ",
"C": "8748 μJ",
"D": "4374 μJ"
} | D | 4374 μJ | U=½CV². Since C=12 μF, U in μJ is ½×12×(27)²=4374 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4374 μJ, not -4374 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4374 μJ, not 4376 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4374 μJ, not 8748... | [
"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_000600 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 28 and common difference 8. Find the sum of its first 33 terms. | {
"A": "4118.4",
"B": "5150",
"C": "515.8",
"D": "5148"
} | D | 5148 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=28, d=8, n=33: Sₙ=33/2[2(28)+(33−1)(8)]=5148. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5148, not 4118.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5148, not 5150.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5148, not 515.8.",
"D": "C... | [
"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_006450 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 1 kg is attached to an ideal spring of force constant 364 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "2.10483 s",
"B": "3.10483 s",
"C": "0.10483 s",
"D": "-0.10483 s"
} | C | 0.10483 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(1/364)=0.10483 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.10483 s, not 2.10483 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.10483 s, not 3.10483 s.",
"C": "Correct. The worked calculation gives 0.10483 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004885 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 13 Ω are connected in series; this combination is connected in parallel with a 8 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.575 A",
"B": "1.18125 A",
"C": "1.575 A",
"D": "-1.425 A"
} | C | 1.575 A | Series branch resistance=7+13=20 Ω. Parallel equivalent R_eq=(20×8)/(20+8)=5.71429 Ω. Total current I=V/R_eq=9/5.71429=1.575 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.575 A, not 2.575 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.575 A, not 1.18125 A.",
"C": "Correct. The worked calculation gives 1.575 A.",
"D": "Incorrect. Substituting the stated ... | [
"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_002704 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(0, 0, -4) and v=(0, 0, 5), calculate u·v. | {
"A": "-16",
"B": "20",
"C": "-19",
"D": "-20"
} | D | -20 | The dot product is the sum of corresponding component products: (0)(0)+(0)(0)+(-4)(5)=-20. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -20, not -16.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -20, not 20.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -20, not -19.",
"D": "Correct. Th... | [
"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_006517 | 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 1042 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.84823 s",
"B": "0.07588 s",
"C": "0.15177 s",
"D": "0.22765 s"
} | C | 0.15177 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(6/1042)=0.15177 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.15177 s, not -2.84823 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.15177 s, not 0.07588 s.",
"C": "Correct. The worked calculation gives 0.15177 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_003165 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(1+3i)/(1+11i). What is Re(z), the real part of z? | {
"A": "0.27869",
"B": "0.13934",
"C": "-0.72131",
"D": "1.02787"
} | A | 0.27869 | Multiply numerator and denominator by the conjugate (1-11i). Then Re(z)=(ac+bd)/(c²+d²)=((1)(1)+(3)(11))/(1²+(11)²)=0.27869. | {
"A": "Correct. The worked calculation gives 0.27869.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.27869, not 0.13934.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.27869, not -0.72131.",
"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_004604 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 4 kg and radius 2 m is acted on by a constant torque of 80 N m about its central axis. Find its angular acceleration. | {
"A": "20 rad s⁻²",
"B": "9 rad s⁻²",
"C": "10 rad s⁻²",
"D": "11 rad s⁻²"
} | C | 10 rad s⁻² | For a solid disc, I=½MR²=½(4)(2)²=8 kg m². Using τ=Iα, α=80/8=10 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10 rad s⁻², not 20 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10 rad s⁻², not 9 rad s⁻².",
"C": "Correct. The worked calculation gives 10 rad s⁻².",
"D": "Incorrect. Substituting... | [
"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_003640 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 95 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1172.38189 m",
"B": "781.58793 m",
"C": "780.58793 m",
"D": "1563.17585 m"
} | B | 781.58793 m | Range R=u²sin(2θ)/g. Substituting u=95, θ=60° and g=10 gives R=(95)²sin(120°)/10=781.58793 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 781.58793 m, not 1172.38189 m.",
"B": "Correct. The worked calculation gives 781.58793 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 781.58793 m, not 780.58793 m.",
"D": "Incorrect. Subst... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001831 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 68 distinct elements? | {
"A": "29075238421.8",
"B": "290752384208",
"C": "290752384206",
"D": "232601907366.39999"
} | B | 290752384208 | Order does not matter, so the count is C(68,10)=68!/[10!(58)!]=290752384208. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 290752384208, not 29075238421.8.",
"B": "Correct. The worked calculation gives 290752384208.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 290752384208, not 290752384206.",
"D": "Incorrect. ... | [
"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_009456 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_17H_15X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "11",
"B": "15",
"C": "8",
"D": "10"
} | D | 10 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×17+2+0−15−1)/2=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 11.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 15.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 8.",
"D": "Correct. The work... | [
"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_007925 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 12 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "0.1875 mmol L⁻¹",
"B": "-0.375 mmol L⁻¹",
"C": "0.375 mmol L⁻¹",
"D": "3.375 mmol L⁻¹"
} | C | 0.375 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=12/2^5=0.375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.375 mmol L⁻¹, not 0.1875 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.375 mmol L⁻¹, not -0.375 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.375 mmol L⁻¹.",
"D": "... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002442 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, 4], [8, 3]]. | {
"A": "-28",
"B": "-58",
"C": "-23.2",
"D": "-29"
} | D | -29 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(3)−(4)(8)=-29. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -29, not -28.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -29, not -58.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -29, not -23.2.",
"D": "Correct.... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002791 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-4, -5, 7) and v=(-1, -5, 9), calculate u·v. | {
"A": "92",
"B": "73.6",
"C": "138",
"D": "46"
} | A | 92 | The dot product is the sum of corresponding component products: (-4)(-1)+(-5)(-5)+(7)(9)=92. | {
"A": "Correct. The worked calculation gives 92.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 92, not 73.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 92, not 138.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_000111 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +0x +11=0, let its roots be α and β. What is α²+β²? | {
"A": "-2.2",
"B": "-4.4",
"C": "-6.6",
"D": "0.56"
} | B | -4.4 | By Vieta's relations, α+β = 0/5 and αβ = 11/5. Then α²+β²=(α+β)²−2αβ = (0/5)²−2(11/5) = -4.4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4.4, not -2.2.",
"B": "Correct. The worked calculation gives -4.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -4.4, not -6.6.",
"D": "Incorrect. Substituting the stated values into the g... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005160 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +4 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "-28.125 N",
"B": "14.0625 N",
"C": "28.125 N",
"D": "21.09375 N"
} | C | 28.125 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(4×10⁻⁶)/(8×10⁻²)²=28.125 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28.125 N, not -28.125 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28.125 N, not 14.0625 N.",
"C": "Correct. The worked calculation gives 28.125 N.",
"D": "Incorrect. Substituting the st... | [
"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_004999 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 8 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.675 A",
"B": "3.375 A",
"C": "6.75 A",
"D": "10.125 A"
} | C | 6.75 A | Series branch resistance=8+8=16 Ω. Parallel equivalent R_eq=(16×8)/(16+8)=5.33333 Ω. Total current I=V/R_eq=36/5.33333=6.75 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.75 A, not 1.675 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.75 A, not 3.375 A.",
"C": "Correct. The worked calculation gives 6.75 A.",
"D": "Incorrect. Substituting the stated value... | [
"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_003601 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 118 m s⁻¹ at 65° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1599.96042 m",
"B": "1066.64028 m",
"C": "107.66403 m",
"D": "1067.64028 m"
} | B | 1066.64028 m | Range R=u²sin(2θ)/g. Substituting u=118, θ=65° and g=10 gives R=(118)²sin(130°)/10=1066.64028 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1066.64028 m, not 1599.96042 m.",
"B": "Correct. The worked calculation gives 1066.64028 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1066.64028 m, not 107.66403 m.",
"D": "Incorrect. Su... | [
"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_004510 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 5 m is acted on by a constant torque of 95 N m about its central axis. Find its angular acceleration. | {
"A": "3.08571 rad s⁻²",
"B": "0.54286 rad s⁻²",
"C": "0.08571 rad s⁻²",
"D": "1.08571 rad s⁻²"
} | D | 1.08571 rad s⁻² | For a solid disc, I=½MR²=½(7)(5)²=87.5 kg m². Using τ=Iα, α=95/87.5=1.08571 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.08571 rad s⁻², not 3.08571 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.08571 rad s⁻², not 0.54286 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_002302 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 12 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.36182",
"B": "-0.63818",
"C": "-2.63818",
"D": "-0.36182"
} | A | 0.36182 | Favourable pairs = C(4,2)+C(12,2)+C(11,2)=127. Total pairs=C(27,2)=351. Therefore P=127/351=0.36182. | {
"A": "Correct. The worked calculation gives 0.36182.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36182, not -0.63818.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.36182, not -2.63818.",
"D": "Incorrect. Substituting the stated ... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004879 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 11 Ω are connected in series; this combination is connected in parallel with a 16 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.98214 A",
"B": "2.97321 A",
"C": "1.98214 A",
"D": "-0.01786 A"
} | C | 1.98214 A | Series branch resistance=10+11=21 Ω. Parallel equivalent R_eq=(21×16)/(21+16)=9.08108 Ω. Total current I=V/R_eq=18/9.08108=1.98214 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.98214 A, not 2.98214 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.98214 A, not 2.97321 A.",
"C": "Correct. The worked calculation gives 1.98214 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_009580 | 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_16H_5N_1X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "13",
"B": "11",
"C": "26",
"D": "14"
} | A | 13 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×16+2+1−5−4)/2=13. | {
"A": "Correct. The worked calculation gives 13.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13, not 11.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13, not 26.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006097 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 42 cm in front of a thin convex lens of focal length 11 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.70968",
"B": "2.35484",
"C": "0.26613",
"D": "0.35484"
} | D | 0.35484 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(42)(11)/(42−11)=14.90323 cm. Thus |m|=v/u=14.90323/42=0.35484. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35484, not 0.70968.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35484, not 2.35484.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35484, not 0.266... | [
"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_001928 | 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 88 distinct elements? | {
"A": "38407210034169.60156",
"B": "16003004180904",
"C": "48009012542712",
"D": "32006008361808"
} | D | 32006008361808 | Order does not matter, so the count is C(88,11)=88!/[11!(77)!]=32006008361808. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 32006008361808, not 38407210034169.60156.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 32006008361808, not 16003004180904.",
"C": "Incorrect. Substituting the stated values into the governing... | [
"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_005540 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 39 μF capacitor is charged to a potential difference of 8 V. Calculate the energy stored, expressed in μJ. | {
"A": "1872 μJ",
"B": "125.8 μJ",
"C": "1246 μJ",
"D": "1248 μJ"
} | D | 1248 μJ | U=½CV². Since C=39 μF, U in μJ is ½×39×(8)²=1248 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1248 μJ, not 1872 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1248 μJ, not 125.8 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1248 μJ, not 1246... | [
"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_001139 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ +5x² +10x+7. Evaluate f′(0). | {
"A": "15",
"B": "9",
"C": "10",
"D": "5"
} | C | 10 | Differentiate: f′(x)=3(4)x²+2(5)x+(10). At x=0, f′(0)=3(4)(0)²+2(5)(0)+(10)=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 15.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 9.",
"C": "Correct. The worked calculation gives 10.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_004247 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 10 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": "75.2 N",
"B": "35.6 N",
"C": "37.6 N",
"D": "45.12 N"
} | C | 37.6 N | Net force=mg(sinθ−μcosθ)=10×10×(0.6−0.28×0.8)=37.6 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 37.6 N, not 75.2 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 37.6 N, not 35.6 N.",
"C": "Correct. The worked calculation gives 37.6 N.",
"D": "Incorrect. Substituting the stated values ... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001281 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=3x³ -6x² -1x+7. Evaluate f′(2). | {
"A": "-11",
"B": "9",
"C": "2.1",
"D": "11"
} | D | 11 | Differentiate: f′(x)=3(3)x²+2(-6)x+(-1). At x=2, f′(2)=3(3)(2)²+2(-6)(2)+(-1)=11. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11, not -11.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11, not 9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11, not 2.1.",
"D": "Correct. The wo... | [
"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_002699 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-7, 5, -6) and v=(-2, 1, 3), calculate u·v. | {
"A": "1.5",
"B": "1",
"C": "4",
"D": "-1"
} | B | 1 | The dot product is the sum of corresponding component products: (-7)(-2)+(5)(1)+(-6)(3)=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.5.",
"B": "Correct. The worked calculation gives 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 4.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_000640 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 6 and common difference 15. Find the sum of its first 13 terms. | {
"A": "936",
"B": "2496",
"C": "1248",
"D": "1246"
} | C | 1248 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=6, d=15, n=13: Sₙ=13/2[2(6)+(13−1)(15)]=1248. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1248, not 936.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1248, not 2496.",
"C": "Correct. The worked calculation gives 1248.",
"D": "Incorrect. Substituting the stated values into the go... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000156 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 +17x -9=0, let its roots be α and β. What is α²+β²? | {
"A": "14.02778",
"B": "13.02778",
"C": "10.02778",
"D": "11.02778"
} | D | 11.02778 | By Vieta's relations, α+β = -17/6 and αβ = -9/6. Then α²+β²=(α+β)²−2αβ = (-17/6)²−2(-9/6) = 11.02778. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.02778, not 14.02778.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.02778, not 13.02778.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.02778, not ... | [
"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_003250 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-15+9i)/(6+3i). What is Re(z), the real part of z? | {
"A": "-1.4",
"B": "0.86",
"C": "-2.1",
"D": "-3.4"
} | A | -1.4 | Multiply numerator and denominator by the conjugate (6-3i). Then Re(z)=(ac+bd)/(c²+d²)=((-15)(6)+(9)(3))/(6²+(3)²)=-1.4. | {
"A": "Correct. The worked calculation gives -1.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.4, not 0.86.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.4, not -2.1.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_002540 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, -7], [2, -7]]. | {
"A": "5",
"B": "7",
"C": "6",
"D": "10.5"
} | B | 7 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(-7)−(-7)(2)=7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 5.",
"B": "Correct. The worked calculation gives 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 6.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_002420 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, -3], [4, 0]]. | {
"A": "15",
"B": "13",
"C": "12",
"D": "9"
} | C | 12 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(0)−(-3)(4)=12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12, not 15.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12, not 13.",
"C": "Correct. The worked calculation gives 12.",
"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_008739 | 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 1.24 mol L⁻¹ and initially B is absent. At equilibrium, 19% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.22106",
"B": "0.44211",
"C": "1.22106",
"D": "0.22106"
} | D | 0.22106 | Let α=0.19. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.24)(0.19)²/(1−0.19)=0.22106. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.22106, not -0.22106.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.22106, not 0.44211.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.22106, not 1.22... | [
"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_000510 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 30 and common difference 14. Find the sum of its first 22 terms. | {
"A": "3894",
"B": "3893",
"C": "2920.5",
"D": "1947"
} | A | 3894 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=30, d=14, n=22: Sₙ=22/2[2(30)+(22−1)(14)]=3894. | {
"A": "Correct. The worked calculation gives 3894.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3894, not 3893.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3894, not 2920.5.",
"D": "Incorrect. Substituting the stated values into the... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005730 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.2 atm at 284 K. What is its pressure at 726 K? | {
"A": "1.06761 atm",
"B": "4.06761 atm",
"C": "1.30676 atm",
"D": "3.06761 atm"
} | D | 3.06761 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.2)(726)/(284)=3.06761 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.06761 atm, not 1.06761 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.06761 atm, not 4.06761 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000751 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio 4. What is the sum of its first 5 terms? | {
"A": "273.8",
"B": "2728",
"C": "1364",
"D": "5456"
} | B | 2728 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(4^5−1)/(4−1)=2728. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2728, not 273.8.",
"B": "Correct. The worked calculation gives 2728.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2728, not 1364.",
"D": "Incorrect. Substituting the stated values into the ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000493 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 19 and common difference 10. Find the sum of its first 28 terms. | {
"A": "4312",
"B": "432.2",
"C": "4314",
"D": "-4312"
} | A | 4312 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=19, d=10, n=28: Sₙ=28/2[2(19)+(28−1)(10)]=4312. | {
"A": "Correct. The worked calculation gives 4312.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4312, not 432.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4312, not 4314.",
"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_001403 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (-4x² +6x -4) dx. | {
"A": "-163.2",
"B": "-204",
"C": "-19.4",
"D": "-205"
} | B | -204 | An antiderivative is (-4/3)x³+(6/2)x²+(-4)x. Evaluating between 0 and 6 gives (-4/3)(6)³+(6/2)(6)²+(-4)(6)=-204. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -204, not -163.2.",
"B": "Correct. The worked calculation gives -204.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -204, not -19.4.",
"D": "Incorrect. Substituting the stated values into th... | [
"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_002488 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, -3], [8, -4]]. | {
"A": "4",
"B": "-3",
"C": "-6",
"D": "-4"
} | D | -4 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(-4)−(-3)(8)=-4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4, not 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -4, not -3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -4, not -6.",
"D": "Correct. The work... | [
"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_003865 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 8 m s⁻¹. A constant net force does 18 N of work over 17 m in the direction of motion. Find its final kinetic energy. | {
"A": "44.4 J",
"B": "520.8 J",
"C": "436 J",
"D": "434 J"
} | D | 434 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(8)²+(18)(17)=434 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 434 J, not 44.4 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 434 J, not 520.8 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 434 J, not 436 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_003939 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 13 kg block initially moves at 0 m s⁻¹. A constant net force does 15 N of work over 4 m in the direction of motion. Find its final kinetic energy. | {
"A": "7 J",
"B": "59 J",
"C": "60 J",
"D": "61 J"
} | C | 60 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(13)(0)²+(15)(4)=60 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 60 J, not 7 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 60 J, not 59 J.",
"C": "Correct. The worked calculation gives 60 J.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_005778 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.3 atm at 222 K. What is its pressure at 344 K? | {
"A": "-5.11351 atm",
"B": "5.11351 atm",
"C": "3.83514 atm",
"D": "6.11351 atm"
} | B | 5.11351 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.3)(344)/(222)=5.11351 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.11351 atm, not -5.11351 atm.",
"B": "Correct. The worked calculation gives 5.11351 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.11351 atm, not 3.83514 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_000994 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio -2. What is the sum of its first 12 terms? | {
"A": "-21840",
"B": "-10919",
"C": "-10920",
"D": "-10918"
} | C | -10920 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(-2^12−1)/(-2−1)=-10920. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -10920, not -21840.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -10920, not -10919.",
"C": "Correct. The worked calculation gives -10920.",
"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_003634 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 114 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1949.4 m",
"B": "1301.6 m",
"C": "1298.6 m",
"D": "1299.6 m"
} | D | 1299.6 m | Range R=u²sin(2θ)/g. Substituting u=114, θ=45° and g=10 gives R=(114)²sin(90°)/10=1299.6 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1299.6 m, not 1949.4 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1299.6 m, not 1301.6 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1299.6 m, not ... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002202 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 12 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.36",
"B": "1.036",
"C": "-1.64",
"D": "0.72"
} | A | 0.36 | Favourable pairs = C(10,2)+C(12,2)+C(4,2)=117. Total pairs=C(26,2)=325. Therefore P=117/325=0.36. | {
"A": "Correct. The worked calculation gives 0.36.",
"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 -1.64.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_007670 | 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 48 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "2.375 mmol L⁻¹",
"B": "0.75 mmol L⁻¹",
"C": "0.375 mmol L⁻¹",
"D": "0.5625 mmol L⁻¹"
} | C | 0.375 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=48/2^7=0.375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.375 mmol L⁻¹, not 2.375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.375 mmol L⁻¹, not 0.75 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.375 mmol L⁻¹.",
"D": "Inc... | [
"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_006180 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 31 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": "-1.93333",
"B": "2.13333",
"C": "1.06667",
"D": "1.10667"
} | C | 1.06667 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(31)(16)/(31−16)=33.06667 cm. Thus |m|=v/u=33.06667/31=1.06667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.06667, not -1.93333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.06667, not 2.13333.",
"C": "Correct. The worked calculation gives 1.06667.",
"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_008319 | 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 5 A for 20914 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "34.40516 g",
"B": "36.40516 g",
"C": "27.52412 g",
"D": "25.80387 g"
} | A | 34.40516 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×5×20914/(2×96500)=34.40516 g. | {
"A": "Correct. The worked calculation gives 34.40516 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 34.40516 g, not 36.40516 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 34.40516 g, not 27.52412 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009715 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(OH)_6]^+3, each OH ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "12",
"B": "8",
"C": "6.75",
"D": "9"
} | D | 9 | Let the formal oxidation state of Co be x. Charge balance gives x+(6)(−1)=+3; hence x=3+6=+9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9, not 12.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9, not 8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9, not 6.75.",
"D": "Correct. The worke... | [
"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_005782 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.4 atm at 201 K. What is its pressure at 698 K? | {
"A": "1.83343 atm",
"B": "-8.33433 atm",
"C": "8.33433 atm",
"D": "7.33433 atm"
} | C | 8.33433 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.4)(698)/(201)=8.33433 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.33433 atm, not 1.83343 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.33433 atm, not -8.33433 atm.",
"C": "Correct. The worked calculation gives 8.33433 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_009462 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_6H_3X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "6",
"B": "5",
"C": "2.5",
"D": "-5"
} | B | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+0−3−1)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 6.",
"B": "Correct. The worked calculation gives 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.5.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_002562 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, -7], [7, 0]]. | {
"A": "98",
"B": "49",
"C": "73.5",
"D": "47"
} | B | 49 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(0)−(-7)(7)=49. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 49, not 98.",
"B": "Correct. The worked calculation gives 49.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 49, not 73.5.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001146 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ -7x² +6x+7. Evaluate f′(2). | {
"A": "-65.6",
"B": "-82",
"C": "-123",
"D": "-41"
} | B | -82 | Differentiate: f′(x)=3(-5)x²+2(-7)x+(6). At x=2, f′(2)=3(-5)(2)²+2(-7)(2)+(6)=-82. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -82, not -65.6.",
"B": "Correct. The worked calculation gives -82.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -82, not -123.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005116 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +8 μC are separated by 12 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "-15 N",
"B": "15 N",
"C": "14 N",
"D": "2.5 N"
} | B | 15 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(8×10⁻⁶)/(12×10⁻²)²=15 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15 N, not -15 N.",
"B": "Correct. The worked calculation gives 15 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15 N, not 14 N.",
"D": "Incorrect. Substituting the stated values into the ... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003335 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-4+9i)/(3+11i). What is Re(z), the real part of z? | {
"A": "1.33846",
"B": "-0.66923",
"C": "0.66923",
"D": "3.66923"
} | C | 0.66923 | Multiply numerator and denominator by the conjugate (3-11i). Then Re(z)=(ac+bd)/(c²+d²)=((-4)(3)+(9)(11))/(3²+(11)²)=0.66923. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.66923, not 1.33846.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.66923, not -0.66923.",
"C": "Correct. The worked calculation gives 0.66923.",
"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_003051 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(8+5i)/(5+6i). What is Re(z), the real part of z? | {
"A": "1.14754",
"B": "4.14754",
"C": "0.14754",
"D": "-1.14754"
} | A | 1.14754 | Multiply numerator and denominator by the conjugate (5-6i). Then Re(z)=(ac+bd)/(c²+d²)=((8)(5)+(5)(6))/(5²+(6)²)=1.14754. | {
"A": "Correct. The worked calculation gives 1.14754.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.14754, not 4.14754.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.14754, not 0.14754.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000121 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 -1x -8=0, let its roots be α and β. What is α²+β²? | {
"A": "-0.69388",
"B": "1.23061",
"C": "-2.30612",
"D": "2.30612"
} | D | 2.30612 | By Vieta's relations, α+β = 1/7 and αβ = -8/7. Then α²+β²=(α+β)²−2αβ = (1/7)²−2(-8/7) = 2.30612. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.30612, not -0.69388.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.30612, not 1.23061.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.30612, not -2.3... | [
"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_002991 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(8, 5, 8) and v=(-5, -5, 6), calculate u·v. | {
"A": "-16",
"B": "17",
"C": "-0.7",
"D": "-17"
} | D | -17 | The dot product is the sum of corresponding component products: (8)(-5)+(5)(-5)+(8)(6)=-17. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -17, not -16.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -17, not 17.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -17, not -0.7.",
"D": "Correct. T... | [
"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_008735 | 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 1.88 mol L⁻¹ and initially B is absent. At equilibrium, 47% of A has dissociated at constant volume. Find K_c. | {
"A": "1.56714",
"B": "0.13428",
"C": "3.13428",
"D": "1.13428"
} | C | 3.13428 | Let α=0.47. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.88)(0.47)²/(1−0.47)=3.13428. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.13428, not 1.56714.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.13428, not 0.13428.",
"C": "Correct. The worked calculation gives 3.13428.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001128 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=3x³ -4x² -8x+7. Evaluate f′(0). | {
"A": "-16",
"B": "-11",
"C": "-8",
"D": "-9"
} | C | -8 | Differentiate: f′(x)=3(3)x²+2(-4)x+(-8). At x=0, f′(0)=3(3)(0)²+2(-4)(0)+(-8)=-8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -8, not -16.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -8, not -11.",
"C": "Correct. The worked calculation gives -8.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"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_002316 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 9 blue and 10 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.15806",
"B": "0.63226",
"C": "-0.31613",
"D": "0.31613"
} | D | 0.31613 | Favourable pairs = C(12,2)+C(9,2)+C(10,2)=147. Total pairs=C(31,2)=465. Therefore P=147/465=0.31613. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31613, not 0.15806.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31613, not 0.63226.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31613, not -0.31... | [
"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_009523 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_17H_8N_1X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "9.75",
"B": "13",
"C": "19.5",
"D": "6.5"
} | B | 13 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×17+2+1−8−3)/2=13. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13, not 9.75.",
"B": "Correct. The worked calculation gives 13.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13, not 19.5.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_000197 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 +12x +4=0, let its roots be α and β. What is α²+β²? | {
"A": "135",
"B": "136",
"C": "204",
"D": "138"
} | B | 136 | By Vieta's relations, α+β = -12/1 and αβ = 4/1. Then α²+β²=(α+β)²−2αβ = (-12/1)²−2(4/1) = 136. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 136, not 135.",
"B": "Correct. The worked calculation gives 136.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 136, not 204.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_009060 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.58 V, transfers 1 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.2254 V",
"B": "0.3381 V",
"C": "0.2254 V",
"D": "-0.2254 V"
} | C | 0.2254 V | Apply the Nernst equation: E=0.58−(0.0591/1)(6)=0.2254 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.2254 V, not 1.2254 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.2254 V, not 0.3381 V.",
"C": "Correct. The worked calculation gives 0.2254 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_001913 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 9 elements can be selected from a set of 89 distinct elements? | {
"A": "508501820613.59998",
"B": "635627275767",
"C": "762752730920.40002",
"D": "-635627275767"
} | B | 635627275767 | Order does not matter, so the count is C(89,9)=89!/[9!(80)!]=635627275767. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 635627275767, not 508501820613.59998.",
"B": "Correct. The worked calculation gives 635627275767.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 635627275767, not 762752730920.40002.",
"D": "... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000990 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio 5. What is the sum of its first 9 terms? | {
"A": "4101560.4",
"B": "5126950.5",
"C": "3417967",
"D": "2563475.25"
} | C | 3417967 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(5^9−1)/(5−1)=3417967. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3417967, not 4101560.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3417967, not 5126950.5.",
"C": "Correct. The worked calculation gives 3417967.",
"D": "Incorrect. Substituting the state... | [
"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_008954 | 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 1.65 mol L⁻¹ and initially B is absent. At equilibrium, 62% of A has dissociated at constant volume. Find K_c. | {
"A": "9.67642",
"B": "3.33821",
"C": "6.67642",
"D": "13.35284"
} | C | 6.67642 | Let α=0.62. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.65)(0.62)²/(1−0.62)=6.67642. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.67642, not 9.67642.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.67642, not 3.33821.",
"C": "Correct. The worked calculation gives 6.67642.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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