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_002246 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 9 blue and 10 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.65613",
"B": "0.34387",
"C": "0.17194",
"D": "2.34387"
} | B | 0.34387 | Favourable pairs = C(4,2)+C(9,2)+C(10,2)=87. Total pairs=C(23,2)=253. Therefore P=87/253=0.34387. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34387, not -0.65613.",
"B": "Correct. The worked calculation gives 0.34387.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34387, not 0.17194.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004665 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 13 kg and radius 1 m is acted on by a constant torque of 66 N m about its central axis. Find its angular acceleration. | {
"A": "7.15385 rad s⁻²",
"B": "11.15385 rad s⁻²",
"C": "10.15385 rad s⁻²",
"D": "7.61538 rad s⁻²"
} | C | 10.15385 rad s⁻² | For a solid disc, I=½MR²=½(13)(1)²=6.5 kg m². Using τ=Iα, α=66/6.5=10.15385 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.15385 rad s⁻², not 7.15385 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.15385 rad s⁻², not 11.15385 rad s⁻².",
"C": "Correct. The worked calculation gives 10.15385 rad s⁻².",
... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008178 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 5 A for 12203 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": "24.08986 g",
"B": "10.03744 g",
"C": "40.14977 g",
"D": "20.07488 g"
} | D | 20.07488 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×5×12203/(2×96500)=20.07488 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20.07488 g, not 24.08986 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20.07488 g, not 10.03744 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20.074... | [
"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_009404 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_15H_12N_3X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "-11",
"B": "11",
"C": "2.1",
"D": "16.5"
} | B | 11 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×15+2+3−12−1)/2=11. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11, not -11.",
"B": "Correct. The worked calculation gives 11.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11, not 2.1.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001131 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-3x³ -6x² +6x+7. Evaluate f′(4). | {
"A": "-223.2",
"B": "-17.6",
"C": "-187",
"D": "-186"
} | D | -186 | Differentiate: f′(x)=3(-3)x²+2(-6)x+(6). At x=4, f′(4)=3(-3)(4)²+2(-6)(4)+(6)=-186. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -186, not -223.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -186, not -17.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -186, not -187.",
"D": "C... | [
"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_008454 | 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 0.37 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-1.334 K",
"B": "0.666 K",
"C": "-0.334 K",
"D": "1.332 K"
} | B | 0.666 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.6×0.37=0.666 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.666 K, not -1.334 K.",
"B": "Correct. The worked calculation gives 0.666 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.666 K, not -0.334 K.",
"D": "Incorrect. Substituting the stated ... | [
"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_008943 | 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 0.74 mol L⁻¹ and initially B is absent. At equilibrium, 17% of A has dissociated at constant volume. Find K_c. | {
"A": "0.1546",
"B": "-0.89693",
"C": "2.10307",
"D": "0.10307"
} | D | 0.10307 | Let α=0.17. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.74)(0.17)²/(1−0.17)=0.10307. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.10307, not 0.1546.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.10307, not -0.89693.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.10307, not 2.103... | [
"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_006041 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 70 cm in front of a thin convex lens of focal length 14 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.125",
"B": "-0.25",
"C": "0.25",
"D": "0.5"
} | C | 0.25 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(70)(14)/(70−14)=17.5 cm. Thus |m|=v/u=17.5/70=0.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25, not 0.125.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25, not -0.25.",
"C": "Correct. The worked calculation gives 0.25.",
"D": "Incorrect. Substituting the stated values into the... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009904 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(OH)_6]^+2, each OH ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "9",
"B": "5",
"C": "4",
"D": "8"
} | D | 8 | Let the formal oxidation state of Ni be x. Charge balance gives x+(6)(−1)=+2; hence x=2+6=+8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 4.",
"D": "Correct. The worked ca... | [
"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_003514 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 35 m s⁻¹ at 20° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "78.74148 m",
"B": "39.37074 m",
"C": "77.74148 m",
"D": "118.11222 m"
} | A | 78.74148 m | Range R=u²sin(2θ)/g. Substituting u=35, θ=20° and g=10 gives R=(35)²sin(40°)/10=78.74148 m. | {
"A": "Correct. The worked calculation gives 78.74148 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 78.74148 m, not 39.37074 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 78.74148 m, not 77.74148 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_004572 | 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 77 N m about its central axis. Find its angular acceleration. | {
"A": "0.85556 rad s⁻²",
"B": "0.42778 rad s⁻²",
"C": "1.42778 rad s⁻²",
"D": "-1.57222 rad s⁻²"
} | B | 0.42778 rad s⁻² | For a solid disc, I=½MR²=½(10)(6)²=180 kg m². Using τ=Iα, α=77/180=0.42778 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.42778 rad s⁻², not 0.85556 rad s⁻².",
"B": "Correct. The worked calculation gives 0.42778 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.42778 rad s⁻², not 1.42778 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_008046 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 15 A for 12222 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "72.3821 g",
"B": "60.31842 g",
"C": "45.23881 g",
"D": "59.31842 g"
} | B | 60.31842 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×15×12222/(2×96500)=60.31842 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 60.31842 g, not 72.3821 g.",
"B": "Correct. The worked calculation gives 60.31842 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 60.31842 g, not 45.23881 g.",
"D": "Incorrect. Substituting... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000550 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -20 and common difference 6. Find the sum of its first 14 terms. | {
"A": "399",
"B": "266",
"C": "319.2",
"D": "212.8"
} | B | 266 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-20, d=6, n=14: Sₙ=14/2[2(-20)+(14−1)(6)]=266. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 266, not 399.",
"B": "Correct. The worked calculation gives 266.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 266, not 319.2.",
"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_005831 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.7 atm at 228 K. What is its pressure at 476 K? | {
"A": "5.63684 atm",
"B": "4.22763 atm",
"C": "8.45526 atm",
"D": "2.63684 atm"
} | A | 5.63684 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.7)(476)/(228)=5.63684 atm. | {
"A": "Correct. The worked calculation gives 5.63684 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.63684 atm, not 4.22763 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.63684 atm, not 8.45526 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000782 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio 4. What is the sum of its first 12 terms? | {
"A": "5592405",
"B": "8388607.5",
"C": "-5592405",
"D": "6710886"
} | A | 5592405 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(4^12−1)/(4−1)=5592405. | {
"A": "Correct. The worked calculation gives 5592405.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5592405, not 8388607.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5592405, not -5592405.",
"D": "Incorrect. Substituting the stated... | [
"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_003632 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 104 m s⁻¹ at 15° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "542.8 m",
"B": "540.8 m",
"C": "541.8 m",
"D": "648.96 m"
} | B | 540.8 m | Range R=u²sin(2θ)/g. Substituting u=104, θ=15° and g=10 gives R=(104)²sin(30°)/10=540.8 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 540.8 m, not 542.8 m.",
"B": "Correct. The worked calculation gives 540.8 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 540.8 m, not 541.8 m.",
"D": "Incorrect. Substituting the stated va... | [
"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_009002 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.21 V, transfers 2 electrons, and has reaction quotient Q=10^0. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.21 V",
"B": "-1.21 V",
"C": "1.815 V",
"D": "0.21 V"
} | A | 1.21 V | Apply the Nernst equation: E=1.21−(0.0591/2)(0)=1.21 V. | {
"A": "Correct. The worked calculation gives 1.21 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.21 V, not -1.21 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.21 V, not 1.815 V.",
"D": "Incorrect. Substituting the stated value... | [
"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_004155 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 44 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.36. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "138.28 N",
"B": "205.92 N",
"C": "137.28 N",
"D": "139.28 N"
} | C | 137.28 N | Net force=mg(sinθ−μcosθ)=44×10×(0.6−0.36×0.8)=137.28 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 137.28 N, not 138.28 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 137.28 N, not 205.92 N.",
"C": "Correct. The worked calculation gives 137.28 N.",
"D": "Incorrect. Substituting the stat... | [
"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_003828 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 2 m s⁻¹. A constant net force does 23 N of work over 18 m in the direction of motion. Find its final kinetic energy. | {
"A": "-438 J",
"B": "350.4 J",
"C": "657 J",
"D": "438 J"
} | D | 438 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(2)²+(23)(18)=438 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 438 J, not -438 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 438 J, not 350.4 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 438 J, not 657 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_009568 | 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_11H_4N_1X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "18",
"B": "12",
"C": "13.5",
"D": "9"
} | D | 9 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+1−4−3)/2=9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9, not 18.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9, not 12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9, not 13.5.",
"D": "Correct. The work... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002166 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 8 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": "0.23413",
"B": "0.31217",
"C": "0.15608",
"D": "1.03122"
} | B | 0.31217 | Favourable pairs = C(10,2)+C(8,2)+C(10,2)=118. Total pairs=C(28,2)=378. Therefore P=118/378=0.31217. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31217, not 0.23413.",
"B": "Correct. The worked calculation gives 0.31217.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31217, not 0.15608.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004734 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 5 Ω and 13 Ω are connected in series; this combination is connected in parallel with a 2 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "13.33333 A",
"B": "20 A",
"C": "26.66667 A",
"D": "-13.33333 A"
} | A | 13.33333 A | Series branch resistance=5+13=18 Ω. Parallel equivalent R_eq=(18×2)/(18+2)=1.8 Ω. Total current I=V/R_eq=24/1.8=13.33333 A. | {
"A": "Correct. The worked calculation gives 13.33333 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13.33333 A, not 20 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13.33333 A, not 26.66667 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_003093 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(13-2i)/(8+8i). What is Re(z), the real part of z? | {
"A": "-2.3125",
"B": "1.6875",
"C": "0.6875",
"D": "2.6875"
} | C | 0.6875 | Multiply numerator and denominator by the conjugate (8-8i). Then Re(z)=(ac+bd)/(c²+d²)=((13)(8)+(-2)(8))/(8²+(8)²)=0.6875. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6875, not -2.3125.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6875, not 1.6875.",
"C": "Correct. The worked calculation gives 0.6875.",
"D": "Incorrect. Substituting the stated values... | [
"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_003184 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-6+14i)/(11+4i). What is Re(z), the real part of z? | {
"A": "-0.07299",
"B": "-2.07299",
"C": "0.07299",
"D": "-0.05474"
} | A | -0.07299 | Multiply numerator and denominator by the conjugate (11-4i). Then Re(z)=(ac+bd)/(c²+d²)=((-6)(11)+(14)(4))/(11²+(4)²)=-0.07299. | {
"A": "Correct. The worked calculation gives -0.07299.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.07299, not -2.07299.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.07299, not 0.07299.",
"D": "Incorrect. Substituting the state... | [
"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_003947 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 7 m s⁻¹. A constant net force does 9 N of work over 18 m in the direction of motion. Find its final kinetic energy. | {
"A": "406 J",
"B": "405 J",
"C": "407 J",
"D": "325.6 J"
} | C | 407 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(7)²+(9)(18)=407 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 407 J, not 406 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 407 J, not 405 J.",
"C": "Correct. The worked calculation gives 407 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_009223 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.86 V, transfers 1 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.2527 V",
"B": "-1.4946 V",
"C": "0.5054 V",
"D": "-0.5054 V"
} | C | 0.5054 V | Apply the Nernst equation: E=0.86−(0.0591/1)(6)=0.5054 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5054 V, not 0.2527 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.5054 V, not -1.4946 V.",
"C": "Correct. The worked calculation gives 0.5054 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_001329 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=7x³ +0x² -4x+7. Evaluate f′(-2). | {
"A": "60",
"B": "80",
"C": "160",
"D": "-80"
} | B | 80 | Differentiate: f′(x)=3(7)x²+2(0)x+(-4). At x=-2, f′(-2)=3(7)(-2)²+2(0)(-2)+(-4)=80. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 80, not 60.",
"B": "Correct. The worked calculation gives 80.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 80, not 160.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001161 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=7x³ +8x² -5x+7. Evaluate f′(-4). | {
"A": "133.5",
"B": "320.4",
"C": "267",
"D": "268"
} | C | 267 | Differentiate: f′(x)=3(7)x²+2(8)x+(-5). At x=-4, f′(-4)=3(7)(-4)²+2(8)(-4)+(-5)=267. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 267, not 133.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 267, not 320.4.",
"C": "Correct. The worked calculation gives 267.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_005231 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +5 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "57.10204 N",
"B": "55.10204 N",
"C": "66.12245 N",
"D": "54.10204 N"
} | B | 55.10204 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(5×10⁻⁶)/(7×10⁻²)²=55.10204 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 55.10204 N, not 57.10204 N.",
"B": "Correct. The worked calculation gives 55.10204 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 55.10204 N, not 66.12245 N.",
"D": "Incorrect. Substitutin... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009018 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.95 V, transfers 2 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.7727 V",
"B": "-0.7727 V",
"C": "1.5454 V",
"D": "0.7727 V"
} | D | 0.7727 V | Apply the Nernst equation: E=0.95−(0.0591/2)(6)=0.7727 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7727 V, not 1.7727 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7727 V, not -0.7727 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7727 V, not... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001230 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ +5x² -6x+7. Evaluate f′(-3). | {
"A": "125",
"B": "126",
"C": "94.5",
"D": "189"
} | B | 126 | Differentiate: f′(x)=3(6)x²+2(5)x+(-6). At x=-3, f′(-3)=3(6)(-3)²+2(5)(-3)+(-6)=126. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 126, not 125.",
"B": "Correct. The worked calculation gives 126.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 126, not 94.5.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000403 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 17 and common difference 7. Find the sum of its first 33 terms. | {
"A": "4257",
"B": "4255",
"C": "3192.75",
"D": "3405.6"
} | A | 4257 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=17, d=7, n=33: Sₙ=33/2[2(17)+(33−1)(7)]=4257. | {
"A": "Correct. The worked calculation gives 4257.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4257, not 4255.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4257, not 3192.75.",
"D": "Incorrect. Substituting the stated values into th... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009955 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(OH)_6]^+3, each OH ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "10",
"B": "9",
"C": "8",
"D": "18"
} | B | 9 | Let the formal oxidation state of Pt be x. Charge balance gives x+(6)(−1)=+3; hence x=3+6=+9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9, not 10.",
"B": "Correct. The worked calculation gives 9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9, not 8.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_001120 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ -9x² +8x+7. Evaluate f′(-4). | {
"A": "-224",
"B": "112",
"C": "-112",
"D": "-114"
} | C | -112 | Differentiate: f′(x)=3(-4)x²+2(-9)x+(8). At x=-4, f′(-4)=3(-4)(-4)²+2(-9)(-4)+(8)=-112. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -112, not -224.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -112, not 112.",
"C": "Correct. The worked calculation gives -112.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_009222 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.79 V, transfers 2 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.9673 V",
"B": "0.9673 V",
"C": "1.45095 V",
"D": "-0.0327 V"
} | B | 0.9673 V | Apply the Nernst equation: E=0.79−(0.0591/2)(-6)=0.9673 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9673 V, not 2.9673 V.",
"B": "Correct. The worked calculation gives 0.9673 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9673 V, not 1.45095 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_001299 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=3x³ +5x² +6x+7. Evaluate f′(0). | {
"A": "4",
"B": "7",
"C": "8",
"D": "6"
} | D | 6 | Differentiate: f′(x)=3(3)x²+2(5)x+(6). At x=0, f′(0)=3(3)(0)²+2(5)(0)+(6)=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 8.",
"D": "Correct. The worked ca... | [
"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_002003 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 83 distinct elements? | {
"A": "58068792",
"B": "29034394",
"C": "21775797",
"D": "29034396"
} | D | 29034396 | Order does not matter, so the count is C(83,5)=83!/[5!(78)!]=29034396. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 29034396, not 58068792.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 29034396, not 29034394.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29034396, not ... | [
"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_005092 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +2 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "4.34694 N",
"B": "14.69388 N",
"C": "7.34694 N",
"D": "8.34694 N"
} | C | 7.34694 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(2×10⁻⁶)/(7×10⁻²)²=7.34694 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.34694 N, not 4.34694 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.34694 N, not 14.69388 N.",
"C": "Correct. The worked calculation gives 7.34694 N.",
"D": "Incorrect. Substituting th... | [
"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_005251 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +7 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "12.85714 N",
"B": "6.42857 N",
"C": "9.85714 N",
"D": "11.85714 N"
} | A | 12.85714 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(7×10⁻⁶)/(7×10⁻²)²=12.85714 N. | {
"A": "Correct. The worked calculation gives 12.85714 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.85714 N, not 6.42857 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.85714 N, not 9.85714 N.",
"D": "Incorrect. Substituting ... | [
"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_006135 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 74 cm in front of a thin convex lens of focal length 15 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-1.74576",
"B": "0.25424",
"C": "0.12712",
"D": "1.02542"
} | B | 0.25424 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(74)(15)/(74−15)=18.81356 cm. Thus |m|=v/u=18.81356/74=0.25424. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25424, not -1.74576.",
"B": "Correct. The worked calculation gives 0.25424.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25424, not 0.12712.",
"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_000290 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +7x -3=0, let its roots be α and β. What is α²+β²? | {
"A": "-3.16",
"B": "3.16",
"C": "6.32",
"D": "1.58"
} | B | 3.16 | By Vieta's relations, α+β = -7/5 and αβ = -3/5. Then α²+β²=(α+β)²−2αβ = (-7/5)²−2(-3/5) = 3.16. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.16, not -3.16.",
"B": "Correct. The worked calculation gives 3.16.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.16, not 6.32.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_000676 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio 3. What is the sum of its first 8 terms? | {
"A": "4920",
"B": "6561",
"C": "657",
"D": "6560"
} | D | 6560 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(3^8−1)/(3−1)=6560. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6560, not 4920.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6560, not 6561.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6560, not 657.",
"D": "Corre... | [
"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_006087 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 122 cm in front of a thin convex lens of focal length 27 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.28421",
"B": "1.28421",
"C": "1.02842",
"D": "0.56842"
} | A | 0.28421 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(122)(27)/(122−27)=34.67368 cm. Thus |m|=v/u=34.67368/122=0.28421. | {
"A": "Correct. The worked calculation gives 0.28421.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.28421, not 1.28421.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.28421, not 1.02842.",
"D": "Incorrect. Substituting the stated va... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001597 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (-2x² -8x -5) dx. | {
"A": "-639.33333",
"B": "-637.33333",
"C": "-764.8",
"D": "-478"
} | B | -637.33333 | An antiderivative is (-2/3)x³+(-8/2)x²+(-5)x. Evaluating between 0 and 8 gives (-2/3)(8)³+(-8/2)(8)²+(-5)(8)=-637.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -637.33333, not -639.33333.",
"B": "Correct. The worked calculation gives -637.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -637.33333, not -764.8.",
"D": "Incorrect. Substituting th... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009206 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.40 V, transfers 1 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.17546 V",
"B": "3.7546 V",
"C": "1.7546 V",
"D": "4.7546 V"
} | C | 1.7546 V | Apply the Nernst equation: E=1.40−(0.0591/1)(-6)=1.7546 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.7546 V, not 1.17546 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.7546 V, not 3.7546 V.",
"C": "Correct. The worked calculation gives 1.7546 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_003658 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 80 m s⁻¹ at 18° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "282.13692 m",
"B": "374.18256 m",
"C": "-376.18256 m",
"D": "376.18256 m"
} | D | 376.18256 m | Range R=u²sin(2θ)/g. Substituting u=80, θ=18° and g=10 gives R=(80)²sin(36°)/10=376.18256 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 376.18256 m, not 282.13692 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 376.18256 m, not 374.18256 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 37... | [
"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_006861 | 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 33 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "17 mol",
"B": "18 mol",
"C": "21.6 mol",
"D": "13.5 mol"
} | B | 18 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 18 mol H₂O; O₂ can produce 66 mol H₂O. The limiting condition is H₂; product=18 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18 mol, not 17 mol.",
"B": "Correct. The worked calculation gives 18 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18 mol, not 21.6 mol.",
"D": "Incorrect. Substituting the stated value... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009466 | 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_11H_15N_2X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "1.5",
"B": "5",
"C": "3.75",
"D": "3"
} | B | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+2−15−1)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 1.5.",
"B": "Correct. The worked calculation gives 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.75.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001788 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 6 elements can be selected from a set of 26 distinct elements? | {
"A": "230229",
"B": "230231",
"C": "230230",
"D": "172672.5"
} | C | 230230 | Order does not matter, so the count is C(26,6)=26!/[6!(20)!]=230230. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 230230, not 230229.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 230230, not 230231.",
"C": "Correct. The worked calculation gives 230230.",
"D": "Incorrect. Substituting the stated values ... | [
"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_007743 | 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 71 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "28.4 mmol L⁻¹",
"B": "35.5 mmol L⁻¹",
"C": "42.6 mmol L⁻¹",
"D": "36.5 mmol L⁻¹"
} | B | 35.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=71/2^1=35.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 35.5 mmol L⁻¹, not 28.4 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 35.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 35.5 mmol L⁻¹, not 42.6 mmol L⁻¹.",
"D": "Incorre... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006693 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 29 mol H₂ and 25 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "29 mol",
"B": "23.2 mol",
"C": "-29 mol",
"D": "58 mol"
} | A | 29 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 29 mol H₂O; O₂ can produce 50 mol H₂O. The limiting condition is H₂; product=29 mol. | {
"A": "Correct. The worked calculation gives 29 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 29 mol, not 23.2 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29 mol, not -29 mol.",
"D": "Incorrect. Substituting the stated valu... | [
"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_007213 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 4 mol of gas at 616 K and 0.08 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "2527.3556 L",
"B": "-2527.3556 L",
"C": "2021.88448 L",
"D": "5054.7112 L"
} | A | 2527.3556 L | PV=nRT, so V=nRT/P=(4)(0.082057)(616)/(0.08)=2527.3556 L. | {
"A": "Correct. The worked calculation gives 2527.3556 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2527.3556 L, not -2527.3556 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2527.3556 L, not 2021.88448 L.",
"D": "Incorrect. Subs... | [
"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_004352 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 4 m is acted on by a constant torque of 97 N m about its central axis. Find its angular acceleration. | {
"A": "1.73214 rad s⁻²",
"B": "0.73214 rad s⁻²",
"C": "1.29911 rad s⁻²",
"D": "0.86607 rad s⁻²"
} | A | 1.73214 rad s⁻² | For a solid disc, I=½MR²=½(7)(4)²=56 kg m². Using τ=Iα, α=97/56=1.73214 rad s⁻². | {
"A": "Correct. The worked calculation gives 1.73214 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.73214 rad s⁻², not 0.73214 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.73214 rad s⁻², not 1.29911 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_002270 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 9 blue and 5 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.03446",
"B": "0.34462",
"C": "2.34462",
"D": "-0.34462"
} | B | 0.34462 | Favourable pairs = C(12,2)+C(9,2)+C(5,2)=112. Total pairs=C(26,2)=325. Therefore P=112/325=0.34462. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34462, not 1.03446.",
"B": "Correct. The worked calculation gives 0.34462.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34462, not 2.34462.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001802 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 3 elements can be selected from a set of 49 distinct elements? | {
"A": "18425",
"B": "-18424",
"C": "18424",
"D": "1843.4"
} | C | 18424 | Order does not matter, so the count is C(49,3)=49!/[3!(46)!]=18424. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18424, not 18425.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18424, not -18424.",
"C": "Correct. The worked calculation gives 18424.",
"D": "Incorrect. Substituting the stated values into... | [
"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_003720 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 7 m s⁻¹. A constant net force does 21 N of work over 5 m in the direction of motion. Find its final kinetic energy. | {
"A": "375.5 J",
"B": "449.4 J",
"C": "561.75 J",
"D": "374.5 J"
} | D | 374.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(7)²+(21)(5)=374.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 374.5 J, not 375.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 374.5 J, not 449.4 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 374.5 J, not 561.7... | [
"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_007945 | 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 15 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "3.75 mmol L⁻¹",
"B": "2.75 mmol L⁻¹",
"C": "2.8125 mmol L⁻¹",
"D": "0.75 mmol L⁻¹"
} | A | 3.75 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=15/2^2=3.75 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 3.75 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.75 mmol L⁻¹, not 2.75 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.75 mmol L⁻¹, not 2.8125 mmol L⁻¹.",
"D": "Incor... | [
"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_003927 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 4 m s⁻¹. A constant net force does 26 N of work over 2 m in the direction of motion. Find its final kinetic energy. | {
"A": "132 J",
"B": "66 J",
"C": "133 J",
"D": "99 J"
} | A | 132 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(4)²+(26)(2)=132 J. | {
"A": "Correct. The worked calculation gives 132 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 132 J, not 66 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 132 J, not 133 J.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_007050 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 9 mol of gas at 486 K and 1.13 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "319.62595 L",
"B": "381.15113 L",
"C": "476.43892 L",
"D": "317.62595 L"
} | D | 317.62595 L | PV=nRT, so V=nRT/P=(9)(0.082057)(486)/(1.13)=317.62595 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 317.62595 L, not 319.62595 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 317.62595 L, not 381.15113 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 31... | [
"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_003356 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 106 m s⁻¹ at 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "2213.05998 m",
"B": "1106.52999 m",
"C": "1105.52999 m",
"D": "1659.79499 m"
} | B | 1106.52999 m | Range R=u²sin(2θ)/g. Substituting u=106, θ=40° and g=10 gives R=(106)²sin(80°)/10=1106.52999 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1106.52999 m, not 2213.05998 m.",
"B": "Correct. The worked calculation gives 1106.52999 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1106.52999 m, not 1105.52999 m.",
"D": "Incorrect. S... | [
"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_003597 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 33 m s⁻¹ at 75° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "108.9 m",
"B": "-54.45 m",
"C": "52.45 m",
"D": "54.45 m"
} | D | 54.45 m | Range R=u²sin(2θ)/g. Substituting u=33, θ=75° and g=10 gives R=(33)²sin(150°)/10=54.45 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 54.45 m, not 108.9 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 54.45 m, not -54.45 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 54.45 m, not 52.4... | [
"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_008749 | 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 0.28 mol L⁻¹ and initially B is absent. At equilibrium, 19% of A has dissociated at constant volume. Find K_c. | {
"A": "2.04992",
"B": "0.03744",
"C": "0.02496",
"D": "0.04992"
} | D | 0.04992 | Let α=0.19. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.28)(0.19)²/(1−0.19)=0.04992. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.04992, not 2.04992.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.04992, not 0.03744.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.04992, not 0.024... | [
"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_006860 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 8 mol H₂ and 35 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "10 mol",
"B": "16 mol",
"C": "1.8 mol",
"D": "8 mol"
} | D | 8 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 8 mol H₂O; O₂ can produce 70 mol H₂O. The limiting condition is H₂; product=8 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8 mol, not 10 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8 mol, not 16 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8 mol, not 1.8 mol.",
... | [
"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_001151 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=0x³ +7x² +11x+7. Evaluate f′(2). | {
"A": "-39",
"B": "31.2",
"C": "38",
"D": "39"
} | D | 39 | Differentiate: f′(x)=3(0)x²+2(7)x+(11). At x=2, f′(2)=3(0)(2)²+2(7)(2)+(11)=39. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 39, not -39.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39, not 31.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39, not 38.",
"D": "Correct. The ... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004433 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 13 kg and radius 4 m is acted on by a constant torque of 81 N m about its central axis. Find its angular acceleration. | {
"A": "-0.22115 rad s⁻²",
"B": "0.58413 rad s⁻²",
"C": "0.77885 rad s⁻²",
"D": "2.77885 rad s⁻²"
} | C | 0.77885 rad s⁻² | For a solid disc, I=½MR²=½(13)(4)²=104 kg m². Using τ=Iα, α=81/104=0.77885 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.77885 rad s⁻², not -0.22115 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.77885 rad s⁻², not 0.58413 rad s⁻².",
"C": "Correct. The worked calculation gives 0.77885 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_003192 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(9+15i)/(6+5i). What is Re(z), the real part of z? | {
"A": "1.05738",
"B": "3.11475",
"C": "1.58607",
"D": "2.11475"
} | D | 2.11475 | Multiply numerator and denominator by the conjugate (6-5i). Then Re(z)=(ac+bd)/(c²+d²)=((9)(6)+(15)(5))/(6²+(5)²)=2.11475. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.11475, not 1.05738.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.11475, not 3.11475.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.11475, not 1.586... | [
"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_006214 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 137 cm in front of a thin convex lens of focal length 29 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.26852",
"B": "1.26852",
"C": "0.13426",
"D": "1.02685"
} | A | 0.26852 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(137)(29)/(137−29)=36.78704 cm. Thus |m|=v/u=36.78704/137=0.26852. | {
"A": "Correct. The worked calculation gives 0.26852.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.26852, not 1.26852.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.26852, not 0.13426.",
"D": "Incorrect. Substituting the stated va... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001463 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (-2x² +5x -2) dx. | {
"A": "-119.16667",
"B": "-11.01667",
"C": "-118.16667",
"D": "-120.16667"
} | D | -120.16667 | An antiderivative is (-2/3)x³+(5/2)x²+(-2)x. Evaluating between 0 and 7 gives (-2/3)(7)³+(5/2)(7)²+(-2)(7)=-120.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -120.16667, not -119.16667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -120.16667, not -11.01667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -120.16... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008445 | 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 1.1 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": "3.3 K",
"B": "4.3 K",
"C": "1.3 K",
"D": "5.3 K"
} | A | 3.3 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×1.0×1.1=3.3 K. | {
"A": "Correct. The worked calculation gives 3.3 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.3 K, not 4.3 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.3 K, not 1.3 K.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_003289 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(11+5i)/(5+11i). What is Re(z), the real part of z? | {
"A": "1.07534",
"B": "-0.75342",
"C": "0.75342",
"D": "3.75342"
} | C | 0.75342 | Multiply numerator and denominator by the conjugate (5-11i). Then Re(z)=(ac+bd)/(c²+d²)=((11)(5)+(5)(11))/(5²+(11)²)=0.75342. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.75342, not 1.07534.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.75342, not -0.75342.",
"C": "Correct. The worked calculation gives 0.75342.",
"D": "Incorrect. Substituting the stated v... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006215 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 125 cm in front of a thin convex lens of focal length 27 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-1.72449",
"B": "0.13776",
"C": "0.27551",
"D": "1.27551"
} | C | 0.27551 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(125)(27)/(125−27)=34.43878 cm. Thus |m|=v/u=34.43878/125=0.27551. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.27551, not -1.72449.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.27551, not 0.13776.",
"C": "Correct. The worked calculation gives 0.27551.",
"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_006505 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 15 kg is attached to an ideal spring of force constant 864 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.26352 s",
"B": "0.13176 s",
"C": "0.52705 s",
"D": "0.39528 s"
} | A | 0.26352 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(15/864)=0.26352 s. | {
"A": "Correct. The worked calculation gives 0.26352 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.26352 s, not 0.13176 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.26352 s, not 0.52705 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_005531 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 55 μF capacitor is charged to a potential difference of 12 V. Calculate the energy stored, expressed in μJ. | {
"A": "3960 μJ",
"B": "3958 μJ",
"C": "397 μJ",
"D": "7920 μJ"
} | A | 3960 μJ | U=½CV². Since C=55 μF, U in μJ is ½×55×(12)²=3960 μJ. | {
"A": "Correct. The worked calculation gives 3960 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3960 μJ, not 3958 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3960 μJ, not 397 μJ.",
"D": "Incorrect. Substituting the stated val... | [
"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_005392 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 31 μF capacitor is charged to a potential difference of 37 V. Calculate the energy stored, expressed in μJ. | {
"A": "21219.5 μJ",
"B": "-21219.5 μJ",
"C": "21220.5 μJ",
"D": "42439 μJ"
} | A | 21219.5 μJ | U=½CV². Since C=31 μF, U in μJ is ½×31×(37)²=21219.5 μJ. | {
"A": "Correct. The worked calculation gives 21219.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21219.5 μJ, not -21219.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21219.5 μJ, not 21220.5 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_009340 | 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_32X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "0.75",
"B": "0",
"C": "1",
"D": "-1"
} | C | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×17+2+0−32−2)/2=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.",
"C": "Correct. The worked calculation gives 1.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009593 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_15H_6N_1X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "13",
"B": "10",
"C": "12",
"D": "6.5"
} | A | 13 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×15+2+1−6−1)/2=13. | {
"A": "Correct. The worked calculation gives 13.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13, not 10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13, not 12.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004427 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 5 m is acted on by a constant torque of 32 N m about its central axis. Find its angular acceleration. | {
"A": "0.64 rad s⁻²",
"B": "0.32 rad s⁻²",
"C": "-2.68 rad s⁻²",
"D": "1.032 rad s⁻²"
} | B | 0.32 rad s⁻² | For a solid disc, I=½MR²=½(8)(5)²=100 kg m². Using τ=Iα, α=32/100=0.32 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32 rad s⁻², not 0.64 rad s⁻².",
"B": "Correct. The worked calculation gives 0.32 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32 rad s⁻², not -2.68 rad s⁻².",
"D": "Incorrect. ... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002134 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 12 blue and 7 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "2.32764",
"B": "-0.32764",
"C": "0.32764",
"D": "0.65527"
} | C | 0.32764 | Favourable pairs = C(8,2)+C(12,2)+C(7,2)=115. Total pairs=C(27,2)=351. Therefore P=115/351=0.32764. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32764, not 2.32764.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32764, not -0.32764.",
"C": "Correct. The worked calculation gives 0.32764.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005495 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 25 μF capacitor is charged to a potential difference of 25 V. Calculate the energy stored, expressed in μJ. | {
"A": "7813.5 μJ",
"B": "7812.5 μJ",
"C": "7810.5 μJ",
"D": "7811.5 μJ"
} | B | 7812.5 μJ | U=½CV². Since C=25 μF, U in μJ is ½×25×(25)²=7812.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7812.5 μJ, not 7813.5 μJ.",
"B": "Correct. The worked calculation gives 7812.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7812.5 μJ, not 7810.5 μJ.",
"D": "Incorrect. Substituting the... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003337 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(1+13i)/(8+9i). What is Re(z), the real part of z? | {
"A": "1.86207",
"B": "3.86207",
"C": "-1.13793",
"D": "0.86207"
} | D | 0.86207 | Multiply numerator and denominator by the conjugate (8-9i). Then Re(z)=(ac+bd)/(c²+d²)=((1)(8)+(13)(9))/(8²+(9)²)=0.86207. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.86207, not 1.86207.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.86207, not 3.86207.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.86207, not -1.13... | [
"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_009879 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(CN)_2]^+0, each CN ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "-2",
"B": "2",
"C": "1.2",
"D": "0"
} | B | 2 | Let the formal oxidation state of Pd be x. Charge balance gives x+(2)(−1)=+0; hence x=0+2=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.2.",
"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_004994 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 10 Ω are connected in series; this combination is connected in parallel with a 4 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "9.33333 A",
"B": "8.33333 A",
"C": "-7.33333 A",
"D": "7.33333 A"
} | D | 7.33333 A | Series branch resistance=8+10=18 Ω. Parallel equivalent R_eq=(18×4)/(18+4)=3.27273 Ω. Total current I=V/R_eq=24/3.27273=7.33333 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.33333 A, not 9.33333 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.33333 A, not 8.33333 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.33333 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_003366 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 43 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "347.49833 m",
"B": "175.74917 m",
"C": "173.74917 m",
"D": "18.37492 m"
} | C | 173.74917 m | Range R=u²sin(2θ)/g. Substituting u=43, θ=55° and g=10 gives R=(43)²sin(110°)/10=173.74917 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 173.74917 m, not 347.49833 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 173.74917 m, not 175.74917 m.",
"C": "Correct. The worked calculation gives 173.74917 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008537 | 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 0.75 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": "-0.75 K",
"B": "-2.25 K",
"C": "2.25 K",
"D": "1.6875 K"
} | C | 2.25 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×1.0×0.75=2.25 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.25 K, not -0.75 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.25 K, not -2.25 K.",
"C": "Correct. The worked calculation gives 2.25 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_001515 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (-4x² +0x -3) dx. | {
"A": "-47",
"B": "-33.75",
"C": "-45",
"D": "-44"
} | C | -45 | An antiderivative is (-4/3)x³+(0/2)x²+(-3)x. Evaluating between 0 and 3 gives (-4/3)(3)³+(0/2)(3)²+(-3)(3)=-45. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -45, not -47.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -45, not -33.75.",
"C": "Correct. The worked calculation gives -45.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001765 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 20 distinct elements? | {
"A": "15504",
"B": "7752",
"C": "31008",
"D": "11628"
} | A | 15504 | Order does not matter, so the count is C(20,5)=20!/[5!(15)!]=15504. | {
"A": "Correct. The worked calculation gives 15504.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15504, not 7752.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15504, not 31008.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_002988 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(7, 4, -3) and v=(3, -5, -3), calculate u·v. | {
"A": "13",
"B": "7.5",
"C": "11",
"D": "10"
} | D | 10 | The dot product is the sum of corresponding component products: (7)(3)+(4)(-5)+(-3)(-3)=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 13.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 7.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 11.",
"D": "Correct. The wo... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007196 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 11 mol of gas at 282 K and 0.75 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "337.38775 L",
"B": "509.08163 L",
"C": "339.38775 L",
"D": "340.38775 L"
} | C | 339.38775 L | PV=nRT, so V=nRT/P=(11)(0.082057)(282)/(0.75)=339.38775 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 339.38775 L, not 337.38775 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 339.38775 L, not 509.08163 L.",
"C": "Correct. The worked calculation gives 339.38775 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_007059 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 12 mol of gas at 298 K and 2.24 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "130.99814 L",
"B": "104.79851 L",
"C": "98.2486 L",
"D": "196.49721 L"
} | A | 130.99814 L | PV=nRT, so V=nRT/P=(12)(0.082057)(298)/(2.24)=130.99814 L. | {
"A": "Correct. The worked calculation gives 130.99814 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 130.99814 L, not 104.79851 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 130.99814 L, not 98.2486 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_009131 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.07 V, transfers 1 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.1882 V",
"B": "1.11882 V",
"C": "1.1882 V",
"D": "-1.1882 V"
} | C | 1.1882 V | Apply the Nernst equation: E=1.07−(0.0591/1)(-2)=1.1882 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.1882 V, not 2.1882 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1882 V, not 1.11882 V.",
"C": "Correct. The worked calculation gives 1.1882 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_006225 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 43 cm in front of a thin convex lens of focal length 21 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.04545",
"B": "1.09545",
"C": "0.71591",
"D": "0.95455"
} | D | 0.95455 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(43)(21)/(43−21)=41.04545 cm. Thus |m|=v/u=41.04545/43=0.95455. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.95455, not -0.04545.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.95455, not 1.09545.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.95455, not 0.71... | [
"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_004713 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 2 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 17 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.42941 A",
"B": "3.95294 A",
"C": "1.95294 A",
"D": "0.95294 A"
} | D | 0.95294 A | Series branch resistance=2+8=10 Ω. Parallel equivalent R_eq=(10×17)/(10+17)=6.2963 Ω. Total current I=V/R_eq=6/6.2963=0.95294 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.95294 A, not 1.42941 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.95294 A, not 3.95294 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.95294 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_007053 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 20 mol of gas at 589 K and 0.08 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "12081.89325 L",
"B": "-12082.89325 L",
"C": "12082.89325 L",
"D": "12084.89325 L"
} | C | 12082.89325 L | PV=nRT, so V=nRT/P=(20)(0.082057)(589)/(0.08)=12082.89325 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12082.89325 L, not 12081.89325 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12082.89325 L, not -12082.89325 L.",
"C": "Correct. The worked calculation gives 12082.89325 L.",
"D": "Incorr... | [
"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_002604 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, 3], [5, -5]]. | {
"A": "-25",
"B": "-30",
"C": "25",
"D": "-1.5"
} | A | -25 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(-5)−(3)(5)=-25. | {
"A": "Correct. The worked calculation gives -25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -25, not -30.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -25, not 25.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_001375 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (5x² -8x +2) dx. | {
"A": "613.33333",
"B": "614.33333",
"C": "615.33333",
"D": "920"
} | A | 613.33333 | An antiderivative is (5/3)x³+(-8/2)x²+(2)x. Evaluating between 0 and 8 gives (5/3)(8)³+(-8/2)(8)²+(2)(8)=613.33333. | {
"A": "Correct. The worked calculation gives 613.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 613.33333, not 614.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 613.33333, not 615.33333.",
"D": "Incorrect. Substituting the... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006747 | 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 6 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "14 mol",
"B": "-12 mol",
"C": "15 mol",
"D": "12 mol"
} | D | 12 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 30 mol H₂O; O₂ can produce 12 mol H₂O. The limiting condition is O₂; product=12 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 14 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not -12 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 15 mol.",... | [
"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_000858 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio 2. What is the sum of its first 10 terms? | {
"A": "3069",
"B": "-2046",
"C": "2046",
"D": "2455.2"
} | C | 2046 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(2^10−1)/(2−1)=2046. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2046, not 3069.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2046, not -2046.",
"C": "Correct. The worked calculation gives 2046.",
"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_008132 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 14 A for 22531 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": "83.02615 g",
"B": "102.78269 g",
"C": "103.78269 g",
"D": "207.56538 g"
} | C | 103.78269 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×22531/(2×96500)=103.78269 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 103.78269 g, not 83.02615 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 103.78269 g, not 102.78269 g.",
"C": "Correct. The worked calculation gives 103.78269 g.",
"D": "Incorrect. Substit... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006796 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 37 mol H₂ and 6 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "18 mol",
"B": "13 mol",
"C": "12 mol",
"D": "9 mol"
} | C | 12 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 37 mol H₂O; O₂ can produce 12 mol H₂O. The limiting condition is O₂; product=12 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 18 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 13 mol.",
"C": "Correct. The worked calculation gives 12 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003194 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-13+10i)/(7+3i). What is Re(z), the real part of z? | {
"A": "-1.05172",
"B": "-0.52586",
"C": "1.05172",
"D": "-0.78879"
} | A | -1.05172 | Multiply numerator and denominator by the conjugate (7-3i). Then Re(z)=(ac+bd)/(c²+d²)=((-13)(7)+(10)(3))/(7²+(3)²)=-1.05172. | {
"A": "Correct. The worked calculation gives -1.05172.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.05172, not -0.52586.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.05172, not 1.05172.",
"D": "Incorrect. Substituting the state... | [
"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 |
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