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_006613 | 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 68 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.24254 s",
"B": "1.24254 s",
"C": "3.24254 s",
"D": "0.12127 s"
} | A | 0.24254 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(1/68)=0.24254 s. | {
"A": "Correct. The worked calculation gives 0.24254 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.24254 s, not 1.24254 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.24254 s, not 3.24254 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_007028 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 8 mol of gas at 533 K and 2.95 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "118.60713 L",
"B": "94.88571 L",
"C": "12.86071 L",
"D": "120.60713 L"
} | A | 118.60713 L | PV=nRT, so V=nRT/P=(8)(0.082057)(533)/(2.95)=118.60713 L. | {
"A": "Correct. The worked calculation gives 118.60713 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 118.60713 L, not 94.88571 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 118.60713 L, not 12.86071 L.",
"D": "Incorrect. Substitu... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003904 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 3 kg block initially moves at 0 m s⁻¹. A constant net force does 25 N of work over 10 m in the direction of motion. Find its final kinetic energy. | {
"A": "200 J",
"B": "-250 J",
"C": "250 J",
"D": "125 J"
} | C | 250 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(3)(0)²+(25)(10)=250 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 250 J, not 200 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 250 J, not -250 J.",
"C": "Correct. The worked calculation gives 250 J.",
"D": "Incorrect. Substituting the stated values into... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002894 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-3, 7, -3) and v=(-7, -2, -6), calculate u·v. | {
"A": "18.75",
"B": "25",
"C": "-25",
"D": "27"
} | B | 25 | The dot product is the sum of corresponding component products: (-3)(-7)+(7)(-2)+(-3)(-6)=25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 25, not 18.75.",
"B": "Correct. The worked calculation gives 25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 25, not -25.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002613 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, -7], [8, -1]]. | {
"A": "41.6",
"B": "52",
"C": "26",
"D": "6.2"
} | B | 52 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(-1)−(-7)(8)=52. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 52, not 41.6.",
"B": "Correct. The worked calculation gives 52.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 52, not 26.",
"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_009259 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.66 V, transfers 1 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.10146 V",
"B": "1.0146 V",
"C": "0.5073 V",
"D": "-1.0146 V"
} | B | 1.0146 V | Apply the Nernst equation: E=0.66−(0.0591/1)(-6)=1.0146 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0146 V, not 1.10146 V.",
"B": "Correct. The worked calculation gives 1.0146 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0146 V, not 0.5073 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_009140 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.76 V, transfers 3 electrons, and has reaction quotient Q=10^2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.07206 V",
"B": "-1.2794 V",
"C": "1.7206 V",
"D": "0.7206 V"
} | D | 0.7206 V | Apply the Nernst equation: E=0.76−(0.0591/3)(2)=0.7206 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7206 V, not 1.07206 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7206 V, not -1.2794 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7206 V, no... | [
"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_003688 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block initially moves at 2 m s⁻¹. A constant net force does 11 N of work over 5 m in the direction of motion. Find its final kinetic energy. | {
"A": "61 J",
"B": "59 J",
"C": "88.5 J",
"D": "6.9 J"
} | B | 59 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(2)(2)²+(11)(5)=59 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 59 J, not 61 J.",
"B": "Correct. The worked calculation gives 59 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 59 J, not 88.5 J.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_008346 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.38 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-1.48 K",
"B": "1.52 K",
"C": "3.52 K",
"D": "-1.52 K"
} | B | 1.52 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×1.0×0.38=1.52 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.52 K, not -1.48 K.",
"B": "Correct. The worked calculation gives 1.52 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.52 K, not 3.52 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000306 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +9x +3=0, let its roots be α and β. What is α²+β²? | {
"A": "4.04",
"B": "1.02",
"C": "2.04",
"D": "-0.96"
} | C | 2.04 | By Vieta's relations, α+β = -9/5 and αβ = 3/5. Then α²+β²=(α+β)²−2αβ = (-9/5)²−2(3/5) = 2.04. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.04, not 4.04.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.04, not 1.02.",
"C": "Correct. The worked calculation gives 2.04.",
"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_009785 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(Cl)_6]^-1, each Cl ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "1.5",
"B": "2",
"C": "3",
"D": "5"
} | D | 5 | Let the formal oxidation state of Ni be x. Charge balance gives x+(6)(−1)=-1; hence x=-1+6=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.",
"D": "Correct. The worked ... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004645 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 1 m is acted on by a constant torque of 93 N m about its central axis. Find its angular acceleration. | {
"A": "74.4 rad s⁻²",
"B": "-93 rad s⁻²",
"C": "139.5 rad s⁻²",
"D": "93 rad s⁻²"
} | D | 93 rad s⁻² | For a solid disc, I=½MR²=½(2)(1)²=1 kg m². Using τ=Iα, α=93/1=93 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 93 rad s⁻², not 74.4 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 93 rad s⁻², not -93 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 93 ... | [
"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_008889 | 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 0.55 mol L⁻¹ and initially B is absent. At equilibrium, 25% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.18333",
"B": "0.1375",
"C": "0.18333",
"D": "0.09167"
} | C | 0.18333 | Let α=0.25. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.55)(0.25)²/(1−0.25)=0.18333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.18333, not -0.18333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.18333, not 0.1375.",
"C": "Correct. The worked calculation gives 0.18333.",
"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_006943 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 6 mol H₂ and 33 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "-6 mol",
"B": "6 mol",
"C": "12 mol",
"D": "7 mol"
} | B | 6 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 6 mol H₂O; O₂ can produce 66 mol H₂O. The limiting condition is H₂; product=6 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not -6 mol.",
"B": "Correct. The worked calculation gives 6 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 12 mol.",
"D": "Incorrect. Substituting the stated values int... | [
"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_000834 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio -2. What is the sum of its first 9 terms? | {
"A": "855",
"B": "1282.5",
"C": "641.25",
"D": "-855"
} | A | 855 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(-2^9−1)/(-2−1)=855. | {
"A": "Correct. The worked calculation gives 855.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 855, not 1282.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 855, not 641.25.",
"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_001882 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 67 distinct elements? | {
"A": "6522361560",
"B": "5217889248",
"C": "6522361558",
"D": "6522361562"
} | A | 6522361560 | Order does not matter, so the count is C(67,8)=67!/[8!(59)!]=6522361560. | {
"A": "Correct. The worked calculation gives 6522361560.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6522361560, not 5217889248.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6522361560, not 6522361558.",
"D": "Incorrect. Substitutin... | [
"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_005623 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 3 μF capacitor is charged to a potential difference of 14 V. Calculate the energy stored, expressed in μJ. | {
"A": "352.8 μJ",
"B": "294 μJ",
"C": "293 μJ",
"D": "147 μJ"
} | B | 294 μJ | U=½CV². Since C=3 μF, U in μJ is ½×3×(14)²=294 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 294 μJ, not 352.8 μJ.",
"B": "Correct. The worked calculation gives 294 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 294 μJ, not 293 μJ.",
"D": "Incorrect. Substituting the stated value... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002553 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, -6], [3, 5]]. | {
"A": "4.3",
"B": "31",
"C": "66",
"D": "33"
} | D | 33 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(5)−(-6)(3)=33. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33, not 4.3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33, not 31.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 33, not 66.",
"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_002468 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, 0], [4, -2]]. | {
"A": "-2",
"B": "-5",
"C": "-4",
"D": "1"
} | A | -2 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(-2)−(0)(4)=-2. | {
"A": "Correct. The worked calculation gives -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2, not -5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2, not -4.",
"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_004987 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 4 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "15.69231 A",
"B": "6.84615 A",
"C": "5.84615 A",
"D": "7.84615 A"
} | D | 7.84615 A | Series branch resistance=9+4=13 Ω. Parallel equivalent R_eq=(13×4)/(13+4)=3.05882 Ω. Total current I=V/R_eq=24/3.05882=7.84615 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.84615 A, not 15.69231 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.84615 A, not 6.84615 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.84615 A... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000252 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 -11x +12=0, let its roots be α and β. What is α²+β²? | {
"A": "-0.63889",
"B": "0.36111",
"C": "0.93611",
"D": "2.36111"
} | A | -0.63889 | By Vieta's relations, α+β = 11/6 and αβ = 12/6. Then α²+β²=(α+β)²−2αβ = (11/6)²−2(12/6) = -0.63889. | {
"A": "Correct. The worked calculation gives -0.63889.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.63889, not 0.36111.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.63889, not 0.93611.",
"D": "Incorrect. Substituting the stated... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005877 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.2 atm at 348 K. What is its pressure at 746 K? | {
"A": "-1.57126 atm",
"B": "1.42874 atm",
"C": "0.85747 atm",
"D": "0.42874 atm"
} | D | 0.42874 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.2)(746)/(348)=0.42874 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.42874 atm, not -1.57126 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.42874 atm, not 1.42874 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0... | [
"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_004169 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.40. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "50.4 N",
"B": "35.6 N",
"C": "40.32 N",
"D": "33.6 N"
} | D | 33.6 N | Net force=mg(sinθ−μcosθ)=12×10×(0.6−0.40×0.8)=33.6 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33.6 N, not 50.4 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33.6 N, not 35.6 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 33.6 N, not 40.32 N.",... | [
"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_002637 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 2], [6, 5]]. | {
"A": "10",
"B": "12",
"C": "8",
"D": "1.8"
} | C | 8 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(5)−(2)(6)=8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 12.",
"C": "Correct. The worked calculation gives 8.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_005176 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +5 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "51.21875 N",
"B": "73.82812 N",
"C": "36.91406 N",
"D": "49.21875 N"
} | D | 49.21875 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(5×10⁻⁶)/(8×10⁻²)²=49.21875 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 49.21875 N, not 51.21875 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 49.21875 N, not 73.82812 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 49.218... | [
"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_007205 | 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 488 K and 2.22 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "272.56632 L",
"B": "135.28316 L",
"C": "270.56632 L",
"D": "216.45306 L"
} | C | 270.56632 L | PV=nRT, so V=nRT/P=(15)(0.082057)(488)/(2.22)=270.56632 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 270.56632 L, not 272.56632 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 270.56632 L, not 135.28316 L.",
"C": "Correct. The worked calculation gives 270.56632 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008488 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.48 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.24 K",
"B": "0.48 K",
"C": "1.048 K",
"D": "-0.52 K"
} | B | 0.48 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×1.0×0.48=0.48 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.48 K, not 0.24 K.",
"B": "Correct. The worked calculation gives 0.48 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.48 K, not 1.048 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003901 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block initially moves at 1 m s⁻¹. A constant net force does 13 N of work over 5 m in the direction of motion. Find its final kinetic energy. | {
"A": "-72.5 J",
"B": "70.5 J",
"C": "145 J",
"D": "72.5 J"
} | D | 72.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(15)(1)²+(13)(5)=72.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 72.5 J, not -72.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 72.5 J, not 70.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 72.5 J, not 145 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_000165 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 -18x -6=0, let its roots be α and β. What is α²+β²? | {
"A": "23.25",
"B": "-23.25",
"C": "21.25",
"D": "18.6"
} | A | 23.25 | By Vieta's relations, α+β = 18/4 and αβ = -6/4. Then α²+β²=(α+β)²−2αβ = (18/4)²−2(-6/4) = 23.25. | {
"A": "Correct. The worked calculation gives 23.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23.25, not -23.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23.25, not 21.25.",
"D": "Incorrect. Substituting the stated values into... | [
"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_006790 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 3 mol H₂ and 17 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "6 mol",
"B": "3 mol",
"C": "2.25 mol",
"D": "1.3 mol"
} | B | 3 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 3 mol H₂O; O₂ can produce 34 mol H₂O. The limiting condition is H₂; product=3 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3 mol, not 6 mol.",
"B": "Correct. The worked calculation gives 3 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3 mol, not 2.25 mol.",
"D": "Incorrect. Substituting the stated values in... | [
"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_009148 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.14 V, transfers 2 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.28775 V",
"B": "0.28775 V",
"C": "1.93162 V",
"D": "-1.28775 V"
} | A | 1.28775 V | Apply the Nernst equation: E=1.14−(0.0591/2)(-5)=1.28775 V. | {
"A": "Correct. The worked calculation gives 1.28775 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.28775 V, not 0.28775 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.28775 V, not 1.93162 V.",
"D": "Incorrect. Substituting the... | [
"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_009919 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(OH)_4]^-2, each OH ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "2",
"B": "1.2",
"C": "-2",
"D": "1.5"
} | A | 2 | Let the formal oxidation state of Pt be x. Charge balance gives x+(4)(−1)=-2; hence x=-2+4=+2. | {
"A": "Correct. The worked calculation gives 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"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_004499 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 6 kg and radius 5 m is acted on by a constant torque of 53 N m about its central axis. Find its angular acceleration. | {
"A": "-2.29333 rad s⁻²",
"B": "0.70667 rad s⁻²",
"C": "1.07067 rad s⁻²",
"D": "1.41333 rad s⁻²"
} | B | 0.70667 rad s⁻² | For a solid disc, I=½MR²=½(6)(5)²=75 kg m². Using τ=Iα, α=53/75=0.70667 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.70667 rad s⁻², not -2.29333 rad s⁻².",
"B": "Correct. The worked calculation gives 0.70667 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.70667 rad s⁻², not 1.07067 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_004340 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 6 kg and radius 5 m is acted on by a constant torque of 13 N m about its central axis. Find its angular acceleration. | {
"A": "0.17333 rad s⁻²",
"B": "0.08667 rad s⁻²",
"C": "1.01733 rad s⁻²",
"D": "3.17333 rad s⁻²"
} | A | 0.17333 rad s⁻² | For a solid disc, I=½MR²=½(6)(5)²=75 kg m². Using τ=Iα, α=13/75=0.17333 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.17333 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.17333 rad s⁻², not 0.08667 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.17333 rad s⁻², not 1.01733 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_007390 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 92 mL of 0.10 M HCl is mixed with 31 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.30458",
"B": "2.30458",
"C": "3.30458",
"D": "0.97843"
} | A | 1.30458 | Excess H⁺ moles=0.10×(92−31)/1000=0.006100 mol. Total volume=0.123 L, so [H⁺]=0.049593 M and pH=−log₁₀[H⁺]=1.30458. | {
"A": "Correct. The worked calculation gives 1.30458.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.30458, not 2.30458.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.30458, not 3.30458.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000289 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 +13x -7=0, let its roots be α and β. What is α²+β²? | {
"A": "91.5",
"B": "183",
"C": "-183",
"D": "137.25"
} | B | 183 | By Vieta's relations, α+β = -13/1 and αβ = -7/1. Then α²+β²=(α+β)²−2αβ = (-13/1)²−2(-7/1) = 183. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 183, not 91.5.",
"B": "Correct. The worked calculation gives 183.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 183, not -183.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_000489 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -19 and common difference 11. Find the sum of its first 24 terms. | {
"A": "2578",
"B": "2581",
"C": "2582",
"D": "2580"
} | D | 2580 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-19, d=11, n=24: Sₙ=24/2[2(-19)+(24−1)(11)]=2580. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2580, not 2578.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2580, not 2581.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2580, not 2582.",
"D": "Corr... | [
"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_005123 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +7 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "787.5 N",
"B": "79.75 N",
"C": "788.5 N",
"D": "785.5 N"
} | A | 787.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(7×10⁻⁶)/(2×10⁻²)²=787.5 N. | {
"A": "Correct. The worked calculation gives 787.5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 787.5 N, not 79.75 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 787.5 N, not 788.5 N.",
"D": "Incorrect. Substituting the stated va... | [
"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_007630 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 63 mL of 0.10 M HCl is mixed with 80 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.07511",
"B": "13.07511",
"C": "24.15023",
"D": "10.07511"
} | A | 12.07511 | Excess OH⁻ moles=0.10×(80−63)/1000=0.001700 mol. Total volume=0.143 L, so [OH⁻]=0.011888 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.07511. | {
"A": "Correct. The worked calculation gives 12.07511.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.07511, not 13.07511.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.07511, not 24.15023.",
"D": "Incorrect. Substituting the stat... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000282 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 +2x -8=0, let its roots be α and β. What is α²+β²? | {
"A": "-2.36735",
"B": "2.36735",
"C": "-0.63265",
"D": "1.36735"
} | B | 2.36735 | By Vieta's relations, α+β = -2/7 and αβ = -8/7. Then α²+β²=(α+β)²−2αβ = (-2/7)²−2(-8/7) = 2.36735. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.36735, not -2.36735.",
"B": "Correct. The worked calculation gives 2.36735.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.36735, not -0.63265.",
"D": "Incorrect. Substituting the stated ... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007116 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 7 mol of gas at 312 K and 2.72 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "49.41521 L",
"B": "65.88694 L",
"C": "52.70956 L",
"D": "64.88694 L"
} | B | 65.88694 L | PV=nRT, so V=nRT/P=(7)(0.082057)(312)/(2.72)=65.88694 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 65.88694 L, not 49.41521 L.",
"B": "Correct. The worked calculation gives 65.88694 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 65.88694 L, not 52.70956 L.",
"D": "Incorrect. Substitutin... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003850 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 10 m s⁻¹. A constant net force does 14 N of work over 17 m in the direction of motion. Find its final kinetic energy. | {
"A": "825.6 J",
"B": "686 J",
"C": "688 J",
"D": "344 J"
} | C | 688 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(10)²+(14)(17)=688 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 688 J, not 825.6 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 688 J, not 686 J.",
"C": "Correct. The worked calculation gives 688 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_003368 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 66 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "452.6888 m",
"B": "375.24067 m",
"C": "377.24067 m",
"D": "282.9305 m"
} | C | 377.24067 m | Range R=u²sin(2θ)/g. Substituting u=66, θ=60° and g=10 gives R=(66)²sin(120°)/10=377.24067 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 377.24067 m, not 452.6888 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 377.24067 m, not 375.24067 m.",
"C": "Correct. The worked calculation gives 377.24067 m.",
"D": "Incorrect. Substit... | [
"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_000705 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio 3. What is the sum of its first 8 terms? | {
"A": "45920",
"B": "22959",
"C": "22960",
"D": "11480"
} | C | 22960 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(3^8−1)/(3−1)=22960. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22960, not 45920.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22960, not 22959.",
"C": "Correct. The worked calculation gives 22960.",
"D": "Incorrect. Substituting the stated values into ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002213 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 11 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": "-0.68736",
"B": "0.31264",
"C": "-0.31264",
"D": "3.31264"
} | B | 0.31264 | Favourable pairs = C(9,2)+C(11,2)+C(10,2)=136. Total pairs=C(30,2)=435. Therefore P=136/435=0.31264. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31264, not -0.68736.",
"B": "Correct. The worked calculation gives 0.31264.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31264, not -0.31264.",
"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_004007 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 28 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.31. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "99.56 N",
"B": "97.56 N",
"C": "73.92 N",
"D": "98.56 N"
} | D | 98.56 N | Net force=mg(sinθ−μcosθ)=28×10×(0.6−0.31×0.8)=98.56 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 98.56 N, not 99.56 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 98.56 N, not 97.56 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 98.56 N, not 73.92... | [
"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_005016 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +6 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "20.25 N",
"B": "16.875 N",
"C": "12.65625 N",
"D": "15.875 N"
} | B | 16.875 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(6×10⁻⁶)/(8×10⁻²)²=16.875 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16.875 N, not 20.25 N.",
"B": "Correct. The worked calculation gives 16.875 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16.875 N, not 12.65625 N.",
"D": "Incorrect. Substituting the sta... | [
"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_001208 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ +9x² -4x+7. Evaluate f′(0). | {
"A": "-3",
"B": "-2",
"C": "-5",
"D": "-4"
} | D | -4 | Differentiate: f′(x)=3(5)x²+2(9)x+(-4). At x=0, f′(0)=3(5)(0)²+2(9)(0)+(-4)=-4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4, not -3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -4, not -2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -4, not -5.",
"D": "Correct. The wor... | [
"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_003718 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 6 m s⁻¹. A constant net force does 14 N of work over 13 m in the direction of motion. Find its final kinetic energy. | {
"A": "360 J",
"B": "364 J",
"C": "-362 J",
"D": "362 J"
} | D | 362 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(6)²+(14)(13)=362 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 362 J, not 360 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 362 J, not 364 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 362 J, not -362 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_002598 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -8], [3, 8]]. | {
"A": "7.4",
"B": "48",
"C": "76.8",
"D": "64"
} | D | 64 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(8)−(-8)(3)=64. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 64, not 7.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 64, not 48.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 64, not 76.8.",
"D": "Correct. The ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006029 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 23 cm in front of a thin convex lens of focal length 9 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.64286",
"B": "1.06429",
"C": "-0.64286",
"D": "1.64286"
} | A | 0.64286 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(23)(9)/(23−9)=14.78571 cm. Thus |m|=v/u=14.78571/23=0.64286. | {
"A": "Correct. The worked calculation gives 0.64286.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.64286, not 1.06429.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.64286, not -0.64286.",
"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_008728 | 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 1.13 mol L⁻¹ and initially B is absent. At equilibrium, 26% of A has dissociated at constant volume. Find K_c. | {
"A": "3.41291",
"B": "-0.58709",
"C": "-2.58709",
"D": "0.41291"
} | D | 0.41291 | Let α=0.26. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.13)(0.26)²/(1−0.26)=0.41291. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.41291, not 3.41291.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.41291, not -0.58709.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.41291, not -2.5... | [
"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_006201 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 66 cm in front of a thin convex lens of focal length 17 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.34694",
"B": "-0.65306",
"C": "3.34694",
"D": "0.52041"
} | A | 0.34694 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(66)(17)/(66−17)=22.89796 cm. Thus |m|=v/u=22.89796/66=0.34694. | {
"A": "Correct. The worked calculation gives 0.34694.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34694, not -0.65306.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34694, not 3.34694.",
"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_002982 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(7, -2, -6) and v=(-7, -3, -2), calculate u·v. | {
"A": "-31",
"B": "-32",
"C": "-23.25",
"D": "-15.5"
} | A | -31 | The dot product is the sum of corresponding component products: (7)(-7)+(-2)(-3)+(-6)(-2)=-31. | {
"A": "Correct. The worked calculation gives -31.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -31, not -32.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -31, not -23.25.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_005537 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 43 μF capacitor is charged to a potential difference of 23 V. Calculate the energy stored, expressed in μJ. | {
"A": "13648.2 μJ",
"B": "11373.5 μJ",
"C": "-11373.5 μJ",
"D": "17060.25 μJ"
} | B | 11373.5 μJ | U=½CV². Since C=43 μF, U in μJ is ½×43×(23)²=11373.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11373.5 μJ, not 13648.2 μJ.",
"B": "Correct. The worked calculation gives 11373.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11373.5 μJ, not -11373.5 μJ.",
"D": "Incorrect. Substituti... | [
"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_003359 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 82 m s⁻¹ at 18° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "296.4201 m",
"B": "395.2268 m",
"C": "40.52268 m",
"D": "592.84021 m"
} | B | 395.2268 m | Range R=u²sin(2θ)/g. Substituting u=82, θ=18° and g=10 gives R=(82)²sin(36°)/10=395.2268 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 395.2268 m, not 296.4201 m.",
"B": "Correct. The worked calculation gives 395.2268 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 395.2268 m, not 40.52268 m.",
"D": "Incorrect. Substitutin... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005565 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 66 μF capacitor is charged to a potential difference of 9 V. Calculate the energy stored, expressed in μJ. | {
"A": "2673 μJ",
"B": "268.3 μJ",
"C": "5346 μJ",
"D": "2672 μJ"
} | A | 2673 μJ | U=½CV². Since C=66 μF, U in μJ is ½×66×(9)²=2673 μJ. | {
"A": "Correct. The worked calculation gives 2673 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2673 μJ, not 268.3 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2673 μJ, not 5346 μJ.",
"D": "Incorrect. Substituting the stated v... | [
"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_008344 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.07 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.21 K",
"B": "-0.79 K",
"C": "-1.79 K",
"D": "0.42 K"
} | A | 0.21 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×1.0×0.07=0.21 K. | {
"A": "Correct. The worked calculation gives 0.21 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.21 K, not -0.79 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.21 K, not -1.79 K.",
"D": "Incorrect. Substituting the stated value... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008149 | 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 12 A for 3946 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": "15.57954 g",
"B": "17.57954 g",
"C": "12.46364 g",
"D": "23.36932 g"
} | A | 15.57954 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×12×3946/(2×96500)=15.57954 g. | {
"A": "Correct. The worked calculation gives 15.57954 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15.57954 g, not 17.57954 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15.57954 g, not 12.46364 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_007587 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 85 mL of 0.10 M HCl is mixed with 97 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "13.81911",
"B": "10.81911",
"C": "11.81911",
"D": "-11.81911"
} | C | 11.81911 | Excess OH⁻ moles=0.10×(97−85)/1000=0.001200 mol. Total volume=0.182 L, so [OH⁻]=0.006593 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=11.81911. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.81911, not 13.81911.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.81911, not 10.81911.",
"C": "Correct. The worked calculation gives 11.81911.",
"D": "Incorrect. Substituting the stat... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009938 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(Cl)_4]^+3, each Cl ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "10",
"B": "7",
"C": "10.5",
"D": "4"
} | B | 7 | Let the formal oxidation state of Co be x. Charge balance gives x+(4)(−1)=+3; hence x=3+4=+7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 10.",
"B": "Correct. The worked calculation gives 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 10.5.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008475 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.67 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.71008 K",
"B": "0.85504 K",
"C": "-1.28992 K",
"D": "3.71008 K"
} | A | 1.71008 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×1.67=1.71008 K. | {
"A": "Correct. The worked calculation gives 1.71008 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.71008 K, not 0.85504 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.71008 K, not -1.28992 K.",
"D": "Incorrect. Substituting th... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000618 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 16 and common difference 2. Find the sum of its first 12 terms. | {
"A": "259.2",
"B": "648",
"C": "324",
"D": "326"
} | C | 324 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=16, d=2, n=12: Sₙ=12/2[2(16)+(12−1)(2)]=324. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 324, not 259.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 324, not 648.",
"C": "Correct. The worked calculation gives 324.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_000342 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -11 and common difference 11. Find the sum of its first 19 terms. | {
"A": "1670",
"B": "1672",
"C": "1254",
"D": "-1672"
} | B | 1672 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-11, d=11, n=19: Sₙ=19/2[2(-11)+(19−1)(11)]=1672. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1672, not 1670.",
"B": "Correct. The worked calculation gives 1672.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1672, not 1254.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004440 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 11 kg and radius 1 m is acted on by a constant torque of 11 N m about its central axis. Find its angular acceleration. | {
"A": "-1 rad s⁻²",
"B": "1.2 rad s⁻²",
"C": "2 rad s⁻²",
"D": "1 rad s⁻²"
} | C | 2 rad s⁻² | For a solid disc, I=½MR²=½(11)(1)²=5.5 kg m². Using τ=Iα, α=11/5.5=2 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2 rad s⁻², not -1 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2 rad s⁻², not 1.2 rad s⁻².",
"C": "Correct. The worked calculation gives 2 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_005394 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 33 μF capacitor is charged to a potential difference of 38 V. Calculate the energy stored, expressed in μJ. | {
"A": "11913 μJ",
"B": "47652 μJ",
"C": "23826 μJ",
"D": "23824 μJ"
} | C | 23826 μJ | U=½CV². Since C=33 μF, U in μJ is ½×33×(38)²=23826 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 23826 μJ, not 11913 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23826 μJ, not 47652 μJ.",
"C": "Correct. The worked calculation gives 23826 μJ.",
"D": "Incorrect. Substituting the stat... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009900 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(Cl)_5]^-4, each Cl ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "0.5",
"B": "2",
"C": "1",
"D": "-1"
} | C | 1 | Let the formal oxidation state of Pt be x. Charge balance gives x+(5)(−1)=-4; hence x=-4+5=+1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"C": "Correct. The worked calculation gives 1.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004962 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 6 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.04412 A",
"B": "2.05882 A",
"C": "4.05882 A",
"D": "2.02941 A"
} | C | 4.05882 A | Series branch resistance=10+7=17 Ω. Parallel equivalent R_eq=(17×6)/(17+6)=4.43478 Ω. Total current I=V/R_eq=18/4.43478=4.05882 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.05882 A, not 3.04412 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.05882 A, not 2.05882 A.",
"C": "Correct. The worked calculation gives 4.05882 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_007871 | 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 54 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "3.375 mmol L⁻¹",
"B": "5.375 mmol L⁻¹",
"C": "2.375 mmol L⁻¹",
"D": "1.6875 mmol L⁻¹"
} | A | 3.375 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=54/2^4=3.375 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 3.375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.375 mmol L⁻¹, not 5.375 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.375 mmol L⁻¹, not 2.375 mmol L⁻¹.",
"D": "In... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003778 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block initially moves at 5 m s⁻¹. A constant net force does 16 N of work over 20 m in the direction of motion. Find its final kinetic energy. | {
"A": "507.5 J",
"B": "253.75 J",
"C": "406 J",
"D": "509.5 J"
} | A | 507.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(15)(5)²+(16)(20)=507.5 J. | {
"A": "Correct. The worked calculation gives 507.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 507.5 J, not 253.75 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 507.5 J, not 406 J.",
"D": "Incorrect. Substituting the stated val... | [
"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_004978 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 9 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "5.44444 A",
"B": "8.88889 A",
"C": "4.44444 A",
"D": "6.66667 A"
} | C | 4.44444 A | Series branch resistance=13+14=27 Ω. Parallel equivalent R_eq=(27×9)/(27+9)=6.75 Ω. Total current I=V/R_eq=30/6.75=4.44444 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.44444 A, not 5.44444 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.44444 A, not 8.88889 A.",
"C": "Correct. The worked calculation gives 4.44444 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_008758 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.37 mol L⁻¹ and initially B is absent. At equilibrium, 23% of A has dissociated at constant volume. Find K_c. | {
"A": "0.05084",
"B": "1.10168",
"C": "0.15252",
"D": "0.10168"
} | D | 0.10168 | Let α=0.23. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.37)(0.23)²/(1−0.23)=0.10168. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.10168, not 0.05084.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.10168, not 1.10168.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.10168, not 0.152... | [
"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_008660 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.19 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "4.21856 K",
"B": "2.21856 K",
"C": "1.82784 K",
"D": "1.21856 K"
} | D | 1.21856 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×1.19=1.21856 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.21856 K, not 4.21856 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.21856 K, not 2.21856 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.21856 K,... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004064 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.34. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "6.56 N",
"B": "4.92 N",
"C": "1.656 N",
"D": "9.56 N"
} | A | 6.56 N | Net force=mg(sinθ−μcosθ)=2×10×(0.6−0.34×0.8)=6.56 N. | {
"A": "Correct. The worked calculation gives 6.56 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.56 N, not 4.92 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.56 N, not 1.656 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_009684 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(Cl)_6]^+1, each Cl ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "5",
"B": "10",
"C": "6",
"D": "7"
} | D | 7 | Let the formal oxidation state of Pt be x. Charge balance gives x+(6)(−1)=+1; hence x=1+6=+7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 6.",
"D": "Correct. The worked c... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005336 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +3 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "116.125 N",
"B": "120.125 N",
"C": "-118.125 N",
"D": "118.125 N"
} | D | 118.125 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(3×10⁻⁶)/(4×10⁻²)²=118.125 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 118.125 N, not 116.125 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 118.125 N, not 120.125 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 118.125 N,... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009097 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.27 V, transfers 1 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "3.6246 V",
"B": "-0.3754 V",
"C": "1.6246 V",
"D": "2.4369 V"
} | C | 1.6246 V | Apply the Nernst equation: E=1.27−(0.0591/1)(-6)=1.6246 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.6246 V, not 3.6246 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.6246 V, not -0.3754 V.",
"C": "Correct. The worked calculation gives 1.6246 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_007381 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 76 mL of 0.10 M HCl is mixed with 45 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-1.40858",
"B": "1.59142",
"C": "-0.40858",
"D": "3.18285"
} | B | 1.59142 | Excess H⁺ moles=0.10×(76−45)/1000=0.003100 mol. Total volume=0.121 L, so [H⁺]=0.025620 M and pH=−log₁₀[H⁺]=1.59142. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.59142, not -1.40858.",
"B": "Correct. The worked calculation gives 1.59142.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.59142, not -0.40858.",
"D": "Incorrect. Substituting the stated ... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005147 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +8 μC and +2 μC are separated by 12 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "10 N",
"B": "20 N",
"C": "8 N",
"D": "5 N"
} | A | 10 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(8×10⁻⁶)(2×10⁻⁶)/(12×10⁻²)²=10 N. | {
"A": "Correct. The worked calculation gives 10 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10 N, not 20 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10 N, not 8 N.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_006965 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 18 mol H₂ and 1 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "2 mol",
"B": "1 mol",
"C": "5 mol",
"D": "4 mol"
} | A | 2 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 18 mol H₂O; O₂ can produce 2 mol H₂O. The limiting condition is O₂; product=2 mol. | {
"A": "Correct. The worked calculation gives 2 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 1 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 5 mol.",
"D": "Incorrect. Substituting the stated values into ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006417 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 13 kg is attached to an ideal spring of force constant 482 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "2.32846 s",
"B": "0.16423 s",
"C": "0.32846 s",
"D": "0.65691 s"
} | C | 0.32846 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(13/482)=0.32846 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32846 s, not 2.32846 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32846 s, not 0.16423 s.",
"C": "Correct. The worked calculation gives 0.32846 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_002152 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 10 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.17368",
"B": "1.03474",
"C": "-0.65263",
"D": "0.34737"
} | D | 0.34737 | Favourable pairs = C(4,2)+C(10,2)+C(6,2)=66. Total pairs=C(20,2)=190. Therefore P=66/190=0.34737. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34737, not 0.17368.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34737, not 1.03474.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34737, not -0.65... | [
"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_004460 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 10 kg and radius 2 m is acted on by a constant torque of 48 N m about its central axis. Find its angular acceleration. | {
"A": "1.4 rad s⁻²",
"B": "1.24 rad s⁻²",
"C": "-2.4 rad s⁻²",
"D": "2.4 rad s⁻²"
} | D | 2.4 rad s⁻² | For a solid disc, I=½MR²=½(10)(2)²=20 kg m². Using τ=Iα, α=48/20=2.4 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.4 rad s⁻², not 1.4 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.4 rad s⁻², not 1.24 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008072 | 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 1 A for 1736 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "-2.42883 g",
"B": "-0.57117 g",
"C": "0.57117 g",
"D": "3.57117 g"
} | C | 0.57117 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×1×1736/(2×96500)=0.57117 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.57117 g, not -2.42883 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.57117 g, not -0.57117 g.",
"C": "Correct. The worked calculation gives 0.57117 g.",
"D": "Incorrect. Substituting t... | [
"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_004826 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 3 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 7 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "-1.45714 A",
"B": "-1.54286 A",
"C": "1.14571 A",
"D": "1.45714 A"
} | D | 1.45714 A | Series branch resistance=3+7=10 Ω. Parallel equivalent R_eq=(10×7)/(10+7)=4.11765 Ω. Total current I=V/R_eq=6/4.11765=1.45714 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.45714 A, not -1.45714 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.45714 A, not -1.54286 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.45714 ... | [
"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_003981 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 3 m s⁻¹. A constant net force does 20 N of work over 15 m in the direction of motion. Find its final kinetic energy. | {
"A": "262.125 J",
"B": "419.4 J",
"C": "349.5 J",
"D": "-349.5 J"
} | C | 349.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(3)²+(20)(15)=349.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 349.5 J, not 262.125 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 349.5 J, not 419.4 J.",
"C": "Correct. The worked calculation gives 349.5 J.",
"D": "Incorrect. Substituting the stated ... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003316 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-7-2i)/(9+2i). What is Re(z), the real part of z? | {
"A": "0.21176",
"B": "0.92118",
"C": "-0.78824",
"D": "-1.57647"
} | C | -0.78824 | Multiply numerator and denominator by the conjugate (9-2i). Then Re(z)=(ac+bd)/(c²+d²)=((-7)(9)+(-2)(2))/(9²+(2)²)=-0.78824. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.78824, not 0.21176.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.78824, not 0.92118.",
"C": "Correct. The worked calculation gives -0.78824.",
"D": "Incorrect. Substituting the stated... | [
"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_007000 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 30 mol H₂ and 26 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "45 mol",
"B": "30 mol",
"C": "29 mol",
"D": "22.5 mol"
} | B | 30 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 30 mol H₂O; O₂ can produce 52 mol H₂O. The limiting condition is H₂; product=30 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 30 mol, not 45 mol.",
"B": "Correct. The worked calculation gives 30 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30 mol, not 29 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_007697 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 37 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "2.625 mmol L⁻¹",
"B": "6.9375 mmol L⁻¹",
"C": "4.625 mmol L⁻¹",
"D": "2.3125 mmol L⁻¹"
} | C | 4.625 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=37/2^3=4.625 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.625 mmol L⁻¹, not 2.625 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.625 mmol L⁻¹, not 6.9375 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 4.625 mmol L⁻¹.",
"D": "I... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001736 | 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 68 distinct elements? | {
"A": "49280065121",
"B": "24640032560",
"C": "49280065120",
"D": "-49280065120"
} | C | 49280065120 | Order does not matter, so the count is C(68,9)=68!/[9!(59)!]=49280065120. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 49280065120, not 49280065121.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 49280065120, not 24640032560.",
"C": "Correct. The worked calculation gives 49280065120.",
"D": "Incorrect. Substi... | [
"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_004065 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 45 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.39. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "97.2 N",
"B": "13.96 N",
"C": "129.6 N",
"D": "128.6 N"
} | C | 129.6 N | Net force=mg(sinθ−μcosθ)=45×10×(0.6−0.39×0.8)=129.6 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 129.6 N, not 97.2 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 129.6 N, not 13.96 N.",
"C": "Correct. The worked calculation gives 129.6 N.",
"D": "Incorrect. Substituting the stated val... | [
"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_004839 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 11 Ω and 10 Ω are connected in series; this combination is connected in parallel with a 2 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "39.42857 A",
"B": "19.71429 A",
"C": "29.57143 A",
"D": "15.77143 A"
} | B | 19.71429 A | Series branch resistance=11+10=21 Ω. Parallel equivalent R_eq=(21×2)/(21+2)=1.82609 Ω. Total current I=V/R_eq=36/1.82609=19.71429 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19.71429 A, not 39.42857 A.",
"B": "Correct. The worked calculation gives 19.71429 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19.71429 A, not 29.57143 A.",
"D": "Incorrect. Substitutin... | [
"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_003679 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 2 m s⁻¹. A constant net force does 7 N of work over 7 m in the direction of motion. Find its final kinetic energy. | {
"A": "69 J",
"B": "138 J",
"C": "82.8 J",
"D": "34.5 J"
} | A | 69 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(2)²+(7)(7)=69 J. | {
"A": "Correct. The worked calculation gives 69 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 69 J, not 138 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 69 J, not 82.8 J.",
"D": "Incorrect. Substituting the stated values into th... | [
"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_007466 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 98 mL of 0.10 M HCl is mixed with 94 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.68124",
"B": "1.68124",
"C": "5.36248",
"D": "3.68124"
} | A | 2.68124 | Excess H⁺ moles=0.10×(98−94)/1000=0.000400 mol. Total volume=0.192 L, so [H⁺]=0.002083 M and pH=−log₁₀[H⁺]=2.68124. | {
"A": "Correct. The worked calculation gives 2.68124.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.68124, not 1.68124.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.68124, not 5.36248.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004553 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 10 kg and radius 6 m is acted on by a constant torque of 8 N m about its central axis. Find its angular acceleration. | {
"A": "3.04444 rad s⁻²",
"B": "-0.04444 rad s⁻²",
"C": "1.00444 rad s⁻²",
"D": "0.04444 rad s⁻²"
} | D | 0.04444 rad s⁻² | For a solid disc, I=½MR²=½(10)(6)²=180 kg m². Using τ=Iα, α=8/180=0.04444 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.04444 rad s⁻², not 3.04444 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.04444 rad s⁻², not -0.04444 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing ... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001894 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 12 elements can be selected from a set of 70 distinct elements? | {
"A": "5319447029260",
"B": "21277788117040",
"C": "10638894058520",
"D": "1063889405853"
} | C | 10638894058520 | Order does not matter, so the count is C(70,12)=70!/[12!(58)!]=10638894058520. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10638894058520, not 5319447029260.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10638894058520, not 21277788117040.",
"C": "Correct. The worked calculation gives 10638894058520.",
"D": "Inc... | [
"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_005843 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.6 atm at 191 K. What is its pressure at 289 K? | {
"A": "1.09079 atm",
"B": "-2.09215 atm",
"C": "0.68089 atm",
"D": "0.90785 atm"
} | D | 0.90785 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.6)(289)/(191)=0.90785 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.90785 atm, not 1.09079 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.90785 atm, not -2.09215 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0... | [
"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_006226 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 66 cm in front of a thin convex lens of focal length 18 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.0375",
"B": "2.375",
"C": "0.75",
"D": "0.375"
} | D | 0.375 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(66)(18)/(66−18)=24.75 cm. Thus |m|=v/u=24.75/66=0.375. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.375, not 1.0375.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.375, not 2.375.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.375, not 0.75.",
"D":... | [
"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_003825 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 3 kg block initially moves at 11 m s⁻¹. A constant net force does 8 N of work over 4 m in the direction of motion. Find its final kinetic energy. | {
"A": "320.25 J",
"B": "170.8 J",
"C": "160.125 J",
"D": "213.5 J"
} | D | 213.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(3)(11)²+(8)(4)=213.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 213.5 J, not 320.25 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 213.5 J, not 170.8 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 213.5 J, not 160.... | [
"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_009388 | 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_0. Treat X as the total number of monovalent halogen atoms. | {
"A": "18",
"B": "36",
"C": "27",
"D": "13.5"
} | A | 18 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×17+2+0−0−0)/2=18. | {
"A": "Correct. The worked calculation gives 18.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18, not 36.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18, not 27.",
"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 |
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