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_009601 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_7H_4N_1X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "-6",
"B": "6",
"C": "1.6",
"D": "5"
} | B | 6 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+1−4−1)/2=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not -6.",
"B": "Correct. The worked calculation gives 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 1.6.",
"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_008955 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.28 mol L⁻¹ and initially B is absent. At equilibrium, 16% of A has dissociated at constant volume. Find K_c. | {
"A": "-1.84396",
"B": "0.11703",
"C": "0.15604",
"D": "3.15604"
} | C | 0.15604 | Let α=0.16. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.28)(0.16)²/(1−0.16)=0.15604. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.15604, not -1.84396.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.15604, not 0.11703.",
"C": "Correct. The worked calculation gives 0.15604.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008471 | 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 1.34 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "2.74432 K",
"B": "5.48864 K",
"C": "1.74432 K",
"D": "4.11648 K"
} | A | 2.74432 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.512×1.34=2.74432 K. | {
"A": "Correct. The worked calculation gives 2.74432 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.74432 K, not 5.48864 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.74432 K, not 1.74432 K.",
"D": "Incorrect. Substituting the... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000791 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio 2. What is the sum of its first 5 terms? | {
"A": "217",
"B": "-217",
"C": "216",
"D": "173.6"
} | A | 217 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(2^5−1)/(2−1)=217. | {
"A": "Correct. The worked calculation gives 217.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 217, not -217.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 217, not 216.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_009621 | 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_16N_3X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "-5",
"B": "1.5",
"C": "5",
"D": "3"
} | C | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+3−16−1)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not -5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 1.5.",
"C": "Correct. The worked calculation gives 5.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005426 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 15 μF capacitor is charged to a potential difference of 39 V. Calculate the energy stored, expressed in μJ. | {
"A": "11407.5 μJ",
"B": "22815 μJ",
"C": "-11407.5 μJ",
"D": "5703.75 μJ"
} | A | 11407.5 μJ | U=½CV². Since C=15 μF, U in μJ is ½×15×(39)²=11407.5 μJ. | {
"A": "Correct. The worked calculation gives 11407.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11407.5 μJ, not 22815 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11407.5 μJ, not -11407.5 μJ.",
"D": "Incorrect. Substituting... | [
"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_003980 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 12 m s⁻¹. A constant net force does 27 N of work over 19 m in the direction of motion. Find its final kinetic energy. | {
"A": "1231 J",
"B": "1232 J",
"C": "1233 J",
"D": "-1233 J"
} | C | 1233 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(12)²+(27)(19)=1233 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1233 J, not 1231 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1233 J, not 1232 J.",
"C": "Correct. The worked calculation gives 1233 J.",
"D": "Incorrect. Substituting the stated values ... | [
"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_008659 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.97 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "2.01728 K",
"B": "4.03456 K",
"C": "1.20173 K",
"D": "5.01728 K"
} | A | 2.01728 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×1.97=2.01728 K. | {
"A": "Correct. The worked calculation gives 2.01728 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.01728 K, not 4.03456 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.01728 K, not 1.20173 K.",
"D": "Incorrect. Substituting the... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009822 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(OH)_4]^+1, each OH ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "1.5",
"B": "-5",
"C": "5",
"D": "4"
} | C | 5 | Let the formal oxidation state of Fe be x. Charge balance gives x+(4)(−1)=+1; hence x=1+4=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not -5.",
"C": "Correct. The worked calculation gives 5.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004472 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 3 kg and radius 1 m is acted on by a constant torque of 94 N m about its central axis. Find its angular acceleration. | {
"A": "31.33333 rad s⁻²",
"B": "7.26667 rad s⁻²",
"C": "125.33333 rad s⁻²",
"D": "62.66667 rad s⁻²"
} | D | 62.66667 rad s⁻² | For a solid disc, I=½MR²=½(3)(1)²=1.5 kg m². Using τ=Iα, α=94/1.5=62.66667 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 62.66667 rad s⁻², not 31.33333 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 62.66667 rad s⁻², not 7.26667 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governin... | [
"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_009832 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(Cl)_5]^+0, each Cl ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "2.5",
"B": "6",
"C": "5",
"D": "1.5"
} | C | 5 | Let the formal oxidation state of Co be x. Charge balance gives x+(5)(−1)=+0; hence x=0+5=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 6.",
"C": "Correct. The worked calculation gives 5.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003402 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 73 m s⁻¹ at 20° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "341.54152 m",
"B": "342.54152 m",
"C": "513.81228 m",
"D": "344.54152 m"
} | B | 342.54152 m | Range R=u²sin(2θ)/g. Substituting u=73, θ=20° and g=10 gives R=(73)²sin(40°)/10=342.54152 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 342.54152 m, not 341.54152 m.",
"B": "Correct. The worked calculation gives 342.54152 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 342.54152 m, not 513.81228 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_003138 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-11+5i)/(12+9i). What is Re(z), the real part of z? | {
"A": "0.61333",
"B": "-0.38667",
"C": "0.38667",
"D": "-0.29"
} | B | -0.38667 | Multiply numerator and denominator by the conjugate (12-9i). Then Re(z)=(ac+bd)/(c²+d²)=((-11)(12)+(5)(9))/(12²+(9)²)=-0.38667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.38667, not 0.61333.",
"B": "Correct. The worked calculation gives -0.38667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.38667, not 0.38667.",
"D": "Incorrect. Substituting the stated... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003085 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(3-7i)/(3+3i). What is Re(z), the real part of z? | {
"A": "-0.5",
"B": "-0.33333",
"C": "-1.66667",
"D": "-0.66667"
} | D | -0.66667 | Multiply numerator and denominator by the conjugate (3-3i). Then Re(z)=(ac+bd)/(c²+d²)=((3)(3)+(-7)(3))/(3²+(3)²)=-0.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.66667, not -0.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.66667, not -0.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.66667, not -1.6... | [
"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_005934 | 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 2.6 atm at 255 K. What is its pressure at 600 K? | {
"A": "9.17647 atm",
"B": "6.11765 atm",
"C": "3.11765 atm",
"D": "12.23529 atm"
} | B | 6.11765 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.6)(600)/(255)=6.11765 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.11765 atm, not 9.17647 atm.",
"B": "Correct. The worked calculation gives 6.11765 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.11765 atm, not 3.11765 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_007295 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 2 mol of gas at 545 K and 2.83 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "31.60499 L",
"B": "37.92599 L",
"C": "25.28399 L",
"D": "30.60499 L"
} | A | 31.60499 L | PV=nRT, so V=nRT/P=(2)(0.082057)(545)/(2.83)=31.60499 L. | {
"A": "Correct. The worked calculation gives 31.60499 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 31.60499 L, not 37.92599 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 31.60499 L, not 25.28399 L.",
"D": "Incorrect. Substitutin... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004031 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.20. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "50.8 N",
"B": "54.8 N",
"C": "63.36 N",
"D": "52.8 N"
} | D | 52.8 N | Net force=mg(sinθ−μcosθ)=12×10×(0.6−0.20×0.8)=52.8 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 52.8 N, not 50.8 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 52.8 N, not 54.8 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 52.8 N, not 63.36 N.",... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001023 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=3x³ +3x² +3x+7. Evaluate f′(5). | {
"A": "258",
"B": "129",
"C": "257",
"D": "516"
} | A | 258 | Differentiate: f′(x)=3(3)x²+2(3)x+(3). At x=5, f′(5)=3(3)(5)²+2(3)(5)+(3)=258. | {
"A": "Correct. The worked calculation gives 258.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 258, not 129.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 258, not 257.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005806 | 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 2.1 atm at 329 K. What is its pressure at 651 K? | {
"A": "8.31064 atm",
"B": "-4.15532 atm",
"C": "3.11649 atm",
"D": "4.15532 atm"
} | D | 4.15532 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.1)(651)/(329)=4.15532 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.15532 atm, not 8.31064 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.15532 atm, not -4.15532 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4... | [
"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_003951 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 7 m s⁻¹. A constant net force does 23 N of work over 4 m in the direction of motion. Find its final kinetic energy. | {
"A": "313.5 J",
"B": "312.5 J",
"C": "375 J",
"D": "468.75 J"
} | B | 312.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(7)²+(23)(4)=312.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 312.5 J, not 313.5 J.",
"B": "Correct. The worked calculation gives 312.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 312.5 J, not 375 J.",
"D": "Incorrect. Substituting the stated valu... | [
"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_009939 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(CN)_5]^-4, each CN ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "0.5",
"B": "1",
"C": "2",
"D": "3"
} | B | 1 | Let the formal oxidation state of Ni be x. Charge balance gives x+(5)(−1)=-4; hence x=-4+5=+1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.5.",
"B": "Correct. The worked calculation gives 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003530 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 84 m s⁻¹ at 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "833.85642 m",
"B": "347.44018 m",
"C": "694.88035 m",
"D": "1042.32053 m"
} | C | 694.88035 m | Range R=u²sin(2θ)/g. Substituting u=84, θ=40° and g=10 gives R=(84)²sin(80°)/10=694.88035 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 694.88035 m, not 833.85642 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 694.88035 m, not 347.44018 m.",
"C": "Correct. The worked calculation gives 694.88035 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_002688 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-5, -3, -4) and v=(-7, -4, 8), calculate u·v. | {
"A": "13",
"B": "7.5",
"C": "12",
"D": "15"
} | D | 15 | The dot product is the sum of corresponding component products: (-5)(-7)+(-3)(-4)+(-4)(8)=15. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15, not 13.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15, not 7.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15, not 12.",
"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_001039 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ +10x² -4x+7. Evaluate f′(4). | {
"A": "-316",
"B": "315",
"C": "237",
"D": "316"
} | D | 316 | Differentiate: f′(x)=3(5)x²+2(10)x+(-4). At x=4, f′(4)=3(5)(4)²+2(10)(4)+(-4)=316. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 316, not -316.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 316, not 315.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 316, not 237.",
"D": "Correct. ... | [
"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_001407 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (5x² +5x +0) dx. | {
"A": "675",
"B": "46",
"C": "450",
"D": "451"
} | C | 450 | An antiderivative is (5/3)x³+(5/2)x²+(0)x. Evaluating between 0 and 6 gives (5/3)(6)³+(5/2)(6)²+(0)(6)=450. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 450, not 675.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 450, not 46.",
"C": "Correct. The worked calculation gives 450.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_007147 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 15 mol of gas at 283 K and 2.51 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "138.77768 L",
"B": "140.77768 L",
"C": "-138.77768 L",
"D": "277.55535 L"
} | A | 138.77768 L | PV=nRT, so V=nRT/P=(15)(0.082057)(283)/(2.51)=138.77768 L. | {
"A": "Correct. The worked calculation gives 138.77768 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 138.77768 L, not 140.77768 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 138.77768 L, not -138.77768 L.",
"D": "Incorrect. Subst... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006977 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 25 mol H₂ and 9 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "2.8 mol",
"B": "27 mol",
"C": "14.4 mol",
"D": "18 mol"
} | D | 18 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 25 mol H₂O; O₂ can produce 18 mol H₂O. The limiting condition is O₂; product=18 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18 mol, not 2.8 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18 mol, not 27 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18 mol, not 14.4 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_001423 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (4x² -8x +1) dx. | {
"A": "72.66667",
"B": "86",
"C": "71.66667",
"D": "57.33333"
} | C | 71.66667 | An antiderivative is (4/3)x³+(-8/2)x²+(1)x. Evaluating between 0 and 5 gives (4/3)(5)³+(-8/2)(5)²+(1)(5)=71.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 71.66667, not 72.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 71.66667, not 86.",
"C": "Correct. The worked calculation gives 71.66667.",
"D": "Incorrect. Substituting the stated val... | [
"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_006256 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 55 cm in front of a thin convex lens of focal length 17 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.44737",
"B": "0.22368",
"C": "0.89474",
"D": "0.44737"
} | D | 0.44737 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(55)(17)/(55−17)=24.60526 cm. Thus |m|=v/u=24.60526/55=0.44737. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.44737, not -0.44737.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.44737, not 0.22368.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.44737, not 0.89... | [
"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_003842 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block initially moves at 4 m s⁻¹. A constant net force does 23 N of work over 12 m in the direction of motion. Find its final kinetic energy. | {
"A": "322 J",
"B": "486 J",
"C": "243 J",
"D": "324 J"
} | D | 324 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(6)(4)²+(23)(12)=324 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 324 J, not 322 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 324 J, not 486 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 324 J, not 243 J.",
"D":... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008570 | 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 1.31 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "2.0436 K",
"B": "1.0436 K",
"C": "5.0436 K",
"D": "3.0654 K"
} | A | 2.0436 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.52×1.31=2.0436 K. | {
"A": "Correct. The worked calculation gives 2.0436 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.0436 K, not 1.0436 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.0436 K, not 5.0436 K.",
"D": "Incorrect. Substituting the stat... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004376 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 1 m is acted on by a constant torque of 6 N m about its central axis. Find its angular acceleration. | {
"A": "7 rad s⁻²",
"B": "6 rad s⁻²",
"C": "4.5 rad s⁻²",
"D": "1.6 rad s⁻²"
} | B | 6 rad s⁻² | For a solid disc, I=½MR²=½(2)(1)²=1 kg m². Using τ=Iα, α=6/1=6 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6 rad s⁻², not 7 rad s⁻².",
"B": "Correct. The worked calculation gives 6 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6 rad s⁻², not 4.5 rad s⁻².",
"D": "Incorrect. Substituting t... | [
"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_005243 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +4 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "272 N",
"B": "270 N",
"C": "540 N",
"D": "-270 N"
} | B | 270 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(4×10⁻⁶)/(2×10⁻²)²=270 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 270 N, not 272 N.",
"B": "Correct. The worked calculation gives 270 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 270 N, not 540 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_009856 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(Cl)_5]^-4, each Cl ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "1.5",
"B": "2",
"C": "1",
"D": "1.1"
} | C | 1 | Let the formal oxidation state of Fe be x. Charge balance gives x+(5)(−1)=-4; hence x=-4+5=+1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"C": "Correct. The worked calculation gives 1.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009742 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(CN)_2]^-4, each CN ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "0",
"B": "-1",
"C": "-4",
"D": "-2"
} | D | -2 | Let the formal oxidation state of Mn be x. Charge balance gives x+(2)(−1)=-4; hence x=-4+2=-2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2, not 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2, not -1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2, not -4.",
"D": "Correct. The work... | [
"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_008486 | 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 1.72 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "3.44 K",
"B": "2.58 K",
"C": "1.344 K",
"D": "-3.44 K"
} | A | 3.44 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×1.72=3.44 K. | {
"A": "Correct. The worked calculation gives 3.44 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.44 K, not 2.58 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.44 K, not 1.344 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008622 | 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 0.95 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.741 K",
"B": "-0.988 K",
"C": "-0.012 K",
"D": "0.988 K"
} | D | 0.988 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×0.95=0.988 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.988 K, not 0.741 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.988 K, not -0.988 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.988 K, not -0.0... | [
"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_005839 | 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 2.2 atm at 333 K. What is its pressure at 699 K? | {
"A": "-4.61802 atm",
"B": "4.61802 atm",
"C": "5.61802 atm",
"D": "3.46351 atm"
} | B | 4.61802 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.2)(699)/(333)=4.61802 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.61802 atm, not -4.61802 atm.",
"B": "Correct. The worked calculation gives 4.61802 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.61802 atm, not 5.61802 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009710 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(Cl)_2]^-3, each Cl ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "1",
"B": "-0.5",
"C": "-0.75",
"D": "-1"
} | D | -1 | Let the formal oxidation state of Ni be x. Charge balance gives x+(2)(−1)=-3; hence x=-3+2=-1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1, not 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1, not -0.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1, not -0.75.",
"D": "Correct. The... | [
"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_003780 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block initially moves at 12 m s⁻¹. A constant net force does 13 N of work over 8 m in the direction of motion. Find its final kinetic energy. | {
"A": "372 J",
"B": "248 J",
"C": "198.4 J",
"D": "124 J"
} | B | 248 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(2)(12)²+(13)(8)=248 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 248 J, not 372 J.",
"B": "Correct. The worked calculation gives 248 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 248 J, not 198.4 J.",
"D": "Incorrect. Substituting the stated values int... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008033 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 2 A for 7048 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "2.6378 g",
"B": "6.6378 g",
"C": "2.3189 g",
"D": "4.6378 g"
} | D | 4.6378 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×2×7048/(2×96500)=4.6378 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.6378 g, not 2.6378 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.6378 g, not 6.6378 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.6378 g, not ... | [
"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_009157 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.30 V, transfers 2 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.11227 V",
"B": "2.1227 V",
"C": "1.1227 V",
"D": "3.1227 V"
} | C | 1.1227 V | Apply the Nernst equation: E=1.30−(0.0591/2)(6)=1.1227 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.1227 V, not 1.11227 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1227 V, not 2.1227 V.",
"C": "Correct. The worked calculation gives 1.1227 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_008572 | 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 1.36 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.39264 K",
"B": "2.39264 K",
"C": "0.69632 K",
"D": "0.39264 K"
} | A | 1.39264 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×1.36=1.39264 K. | {
"A": "Correct. The worked calculation gives 1.39264 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.39264 K, not 2.39264 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.39264 K, not 0.69632 K.",
"D": "Incorrect. Substituting the... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005255 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +2 μC are separated by 5 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "21.6 N",
"B": "86.4 N",
"C": "44.2 N",
"D": "43.2 N"
} | D | 43.2 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(2×10⁻⁶)/(5×10⁻²)²=43.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 43.2 N, not 21.6 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 43.2 N, not 86.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 43.2 N, not 44.2 N.",
... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001250 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=1x³ -4x² +3x+7. Evaluate f′(4). | {
"A": "14.25",
"B": "19",
"C": "2.9",
"D": "9.5"
} | B | 19 | Differentiate: f′(x)=3(1)x²+2(-4)x+(3). At x=4, f′(4)=3(1)(4)²+2(-4)(4)+(3)=19. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19, not 14.25.",
"B": "Correct. The worked calculation gives 19.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19, not 2.9.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_007174 | 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 558 K and 0.64 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "1428.86894 L",
"B": "1430.86894 L",
"C": "715.43447 L",
"D": "1073.1517 L"
} | B | 1430.86894 L | PV=nRT, so V=nRT/P=(20)(0.082057)(558)/(0.64)=1430.86894 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1430.86894 L, not 1428.86894 L.",
"B": "Correct. The worked calculation gives 1430.86894 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1430.86894 L, not 715.43447 L.",
"D": "Incorrect. Su... | [
"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_003048 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(11-1i)/(7+12i). What is Re(z), the real part of z? | {
"A": "1.33679",
"B": "0.33679",
"C": "3.33679",
"D": "-1.66321"
} | B | 0.33679 | Multiply numerator and denominator by the conjugate (7-12i). Then Re(z)=(ac+bd)/(c²+d²)=((11)(7)+(-1)(12))/(7²+(12)²)=0.33679. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33679, not 1.33679.",
"B": "Correct. The worked calculation gives 0.33679.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33679, not 3.33679.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003685 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 7 m s⁻¹. A constant net force does 16 N of work over 8 m in the direction of motion. Find its final kinetic energy. | {
"A": "339 J",
"B": "226 J",
"C": "224 J",
"D": "113 J"
} | B | 226 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(7)²+(16)(8)=226 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 226 J, not 339 J.",
"B": "Correct. The worked calculation gives 226 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 226 J, not 224 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_005234 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +6 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "1080 N",
"B": "810 N",
"C": "405 N",
"D": "540 N"
} | D | 540 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(6×10⁻⁶)/(3×10⁻²)²=540 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 540 N, not 1080 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 540 N, not 810 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 540 N, not 405 N.",
"D"... | [
"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_001571 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (-3x² -8x -1) dx. | {
"A": "-132",
"B": "-198",
"C": "-12.2",
"D": "-130"
} | A | -132 | An antiderivative is (-3/3)x³+(-8/2)x²+(-1)x. Evaluating between 0 and 4 gives (-3/3)(4)³+(-8/2)(4)²+(-1)(4)=-132. | {
"A": "Correct. The worked calculation gives -132.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -132, not -198.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -132, not -12.2.",
"D": "Incorrect. Substituting the stated values into 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_003703 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 3 m s⁻¹. A constant net force does 16 N of work over 13 m in the direction of motion. Find its final kinetic energy. | {
"A": "246.5 J",
"B": "248.5 J",
"C": "186.375 J",
"D": "25.85 J"
} | B | 248.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(3)²+(16)(13)=248.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 248.5 J, not 246.5 J.",
"B": "Correct. The worked calculation gives 248.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 248.5 J, not 186.375 J.",
"D": "Incorrect. Substituting the stated ... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005645 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 54 μF capacitor is charged to a potential difference of 28 V. Calculate the energy stored, expressed in μJ. | {
"A": "21168 μJ",
"B": "42336 μJ",
"C": "21169 μJ",
"D": "21167 μJ"
} | A | 21168 μJ | U=½CV². Since C=54 μF, U in μJ is ½×54×(28)²=21168 μJ. | {
"A": "Correct. The worked calculation gives 21168 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21168 μJ, not 42336 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21168 μJ, not 21169 μJ.",
"D": "Incorrect. Substituting the stat... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008993 | 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 0.61 mol L⁻¹ and initially B is absent. At equilibrium, 16% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.92564",
"B": "-2.92564",
"C": "1.07436",
"D": "0.07436"
} | D | 0.07436 | Let α=0.16. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.61)(0.16)²/(1−0.16)=0.07436. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.07436, not -0.92564.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.07436, not -2.92564.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.07436, not 1.0... | [
"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_003818 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block initially moves at 10 m s⁻¹. A constant net force does 18 N of work over 6 m in the direction of motion. Find its final kinetic energy. | {
"A": "429.6 J",
"B": "358 J",
"C": "356 J",
"D": "268.5 J"
} | B | 358 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(5)(10)²+(18)(6)=358 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 358 J, not 429.6 J.",
"B": "Correct. The worked calculation gives 358 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 358 J, not 356 J.",
"D": "Incorrect. Substituting the stated values int... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007480 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 23 mL of 0.10 M HCl is mixed with 51 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "13.57793",
"B": "12.57793",
"C": "2.25779",
"D": "-12.57793"
} | B | 12.57793 | Excess OH⁻ moles=0.10×(51−23)/1000=0.002800 mol. Total volume=0.074 L, so [OH⁻]=0.037838 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.57793. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.57793, not 13.57793.",
"B": "Correct. The worked calculation gives 12.57793.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.57793, not 2.25779.",
"D": "Incorrect. Substituting the state... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005321 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +4 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "40 N",
"B": "41 N",
"C": "-40 N",
"D": "32 N"
} | A | 40 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(4×10⁻⁶)/(3×10⁻²)²=40 N. | {
"A": "Correct. The worked calculation gives 40 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 40 N, not 41 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 40 N, not -40 N.",
"D": "Incorrect. Substituting the stated values into the ... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009925 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(Cl)_6]^-3, each Cl ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "4.5",
"B": "1.5",
"C": "2.25",
"D": "3"
} | D | 3 | Let the formal oxidation state of Ni be x. Charge balance gives x+(6)(−1)=-3; hence x=-3+6=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"D": "Correct. The wo... | [
"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_009504 | 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_24N_3X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "9",
"C": "1.6",
"D": "6"
} | D | 6 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×17+2+3−24−3)/2=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 1.6.",
"D": "Correct. The worked ... | [
"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_002100 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 11 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.18095",
"B": "0.54286",
"C": "-1.6381",
"D": "0.3619"
} | D | 0.3619 | Favourable pairs = C(6,2)+C(11,2)+C(4,2)=76. Total pairs=C(21,2)=210. Therefore P=76/210=0.3619. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3619, not 0.18095.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3619, not 0.54286.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3619, not -1.6381.... | [
"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_006414 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 22 kg is attached to an ideal spring of force constant 795 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.3327 s",
"B": "0.66541 s",
"C": "-0.6673 s",
"D": "0.3327 s"
} | D | 0.3327 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(22/795)=0.3327 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3327 s, not 1.3327 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3327 s, not 0.66541 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3327 s, not... | [
"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_000267 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 +15x -4=0, let its roots be α and β. What is α²+β²? | {
"A": "-60.25",
"B": "61.25",
"C": "62.25",
"D": "60.25"
} | D | 60.25 | By Vieta's relations, α+β = -15/2 and αβ = -4/2. Then α²+β²=(α+β)²−2αβ = (-15/2)²−2(-4/2) = 60.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 60.25, not -60.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 60.25, not 61.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 60.25, not 62.25.",
"D"... | [
"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_004824 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 17 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.05882 A",
"B": "4.05882 A",
"C": "3.05882 A",
"D": "-0.94118 A"
} | A | 1.05882 A | Series branch resistance=9+8=17 Ω. Parallel equivalent R_eq=(17×17)/(17+17)=8.5 Ω. Total current I=V/R_eq=9/8.5=1.05882 A. | {
"A": "Correct. The worked calculation gives 1.05882 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.05882 A, not 4.05882 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.05882 A, not 3.05882 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002952 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-1, 4, -3) and v=(-7, 7, 7), calculate u·v. | {
"A": "21",
"B": "16",
"C": "11",
"D": "14"
} | D | 14 | The dot product is the sum of corresponding component products: (-1)(-7)+(4)(7)+(-3)(7)=14. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14, not 21.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14, not 16.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14, not 11.",
"D": "Correct. The wor... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008634 | 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 0.93 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.674 K",
"B": "2.116 K",
"C": "0.116 K",
"D": "1.116 K"
} | D | 1.116 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.6×0.93=1.116 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.116 K, not 1.674 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.116 K, not 2.116 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.116 K, not 0.116... | [
"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_009615 | 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_8X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "10",
"B": "1.7",
"C": "7",
"D": "10.5"
} | C | 7 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+0−8−2)/2=7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 1.7.",
"C": "Correct. The worked calculation gives 7.",
"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_006968 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 40 mol H₂ and 16 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "32 mol",
"B": "24 mol",
"C": "-32 mol",
"D": "64 mol"
} | A | 32 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 40 mol H₂O; O₂ can produce 32 mol H₂O. The limiting condition is O₂; product=32 mol. | {
"A": "Correct. The worked calculation gives 32 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 32 mol, not 24 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 32 mol, not -32 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_009329 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.37 V, transfers 1 electrons, and has reaction quotient Q=10^-4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.6064 V",
"B": "0.6064 V",
"C": "-0.3936 V",
"D": "1.6064 V"
} | D | 1.6064 V | Apply the Nernst equation: E=1.37−(0.0591/1)(-4)=1.6064 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.6064 V, not -1.6064 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.6064 V, not 0.6064 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.6064 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_009496 | 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_3H_4N_2X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "5",
"B": "2",
"C": "3",
"D": "-1"
} | B | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×3+2+2−4−2)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 5.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_003173 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-11+1i)/(12+4i). What is Re(z), the real part of z? | {
"A": "-0.8",
"B": "-0.6",
"C": "0.8",
"D": "-3.8"
} | A | -0.8 | Multiply numerator and denominator by the conjugate (12-4i). Then Re(z)=(ac+bd)/(c²+d²)=((-11)(12)+(1)(4))/(12²+(4)²)=-0.8. | {
"A": "Correct. The worked calculation gives -0.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.8, not -0.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.8, not 0.8.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_008269 | 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 1639 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "4.69628 g",
"B": "2.69628 g",
"C": "1.34814 g",
"D": "4.04442 g"
} | B | 2.69628 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×5×1639/(2×96500)=2.69628 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.69628 g, not 4.69628 g.",
"B": "Correct. The worked calculation gives 2.69628 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.69628 g, not 1.34814 g.",
"D": "Incorrect. Substituting the... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009806 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(CN)_4]^-1, each CN ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "3",
"B": "-3",
"C": "1.3",
"D": "1"
} | A | 3 | Let the formal oxidation state of Pt be x. Charge balance gives x+(4)(−1)=-1; hence x=-1+4=+3. | {
"A": "Correct. The worked calculation gives 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not -3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"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_009437 | 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_33N_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "2",
"B": "3",
"C": "1",
"D": "-2"
} | C | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×15+2+3−33−0)/2=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 3.",
"C": "Correct. The worked calculation gives 1.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_002403 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, 8], [9, 4]]. | {
"A": "-5.8",
"B": "-34",
"C": "-68",
"D": "-54.4"
} | C | -68 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(4)−(8)(9)=-68. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -68, not -5.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -68, not -34.",
"C": "Correct. The worked calculation gives -68.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_001840 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 11 elements can be selected from a set of 43 distinct elements? | {
"A": "4314003261.75",
"B": "8628006523.5",
"C": "2876002174.5",
"D": "5752004349"
} | D | 5752004349 | Order does not matter, so the count is C(43,11)=43!/[11!(32)!]=5752004349. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5752004349, not 4314003261.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5752004349, not 8628006523.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5... | [
"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_002336 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 9 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.66333",
"B": "0.33667",
"C": "0.67333",
"D": "1.03367"
} | B | 0.33667 | Favourable pairs = C(5,2)+C(9,2)+C(11,2)=101. Total pairs=C(25,2)=300. Therefore P=101/300=0.33667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33667, not -0.66333.",
"B": "Correct. The worked calculation gives 0.33667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33667, not 0.67333.",
"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_005690 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.4 atm at 270 K. What is its pressure at 444 K? | {
"A": "0.65778 atm",
"B": "0.49333 atm",
"C": "-0.65778 atm",
"D": "1.65778 atm"
} | A | 0.65778 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.4)(444)/(270)=0.65778 atm. | {
"A": "Correct. The worked calculation gives 0.65778 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.65778 atm, not 0.49333 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.65778 atm, not -0.65778 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004481 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 12 kg and radius 6 m is acted on by a constant torque of 45 N m about its central axis. Find its angular acceleration. | {
"A": "0.20833 rad s⁻²",
"B": "1.20833 rad s⁻²",
"C": "3.20833 rad s⁻²",
"D": "-0.79167 rad s⁻²"
} | A | 0.20833 rad s⁻² | For a solid disc, I=½MR²=½(12)(6)²=216 kg m². Using τ=Iα, α=45/216=0.20833 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.20833 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.20833 rad s⁻², not 1.20833 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.20833 rad s⁻², not 3.20833 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_009499 | 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_9H_12N_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "3.75",
"C": "10",
"D": "5"
} | D | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×9+2+2−12−0)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 10.",
"D": "Correct. The worke... | [
"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_007024 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 5 mol of gas at 305 K and 1.82 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "68.75655 L",
"B": "-68.75655 L",
"C": "67.75655 L",
"D": "70.75655 L"
} | A | 68.75655 L | PV=nRT, so V=nRT/P=(5)(0.082057)(305)/(1.82)=68.75655 L. | {
"A": "Correct. The worked calculation gives 68.75655 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 68.75655 L, not -68.75655 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 68.75655 L, not 67.75655 L.",
"D": "Incorrect. Substituti... | [
"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_000763 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio -2. What is the sum of its first 10 terms? | {
"A": "-341",
"B": "-682",
"C": "-343",
"D": "-409.2"
} | A | -341 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(-2^10−1)/(-2−1)=-341. | {
"A": "Correct. The worked calculation gives -341.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -341, not -682.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -341, not -343.",
"D": "Incorrect. Substituting the stated values into the g... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001091 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-3x³ +3x² -7x+7. Evaluate f′(5). | {
"A": "-202",
"B": "-101",
"C": "-204",
"D": "-201"
} | A | -202 | Differentiate: f′(x)=3(-3)x²+2(3)x+(-7). At x=5, f′(5)=3(-3)(5)²+2(3)(5)+(-7)=-202. | {
"A": "Correct. The worked calculation gives -202.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -202, not -101.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -202, not -204.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_009515 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_7H_3N_2X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "-6",
"B": "1.6",
"C": "6",
"D": "3"
} | C | 6 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+2−3−3)/2=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not -6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 1.6.",
"C": "Correct. The worked calculation gives 6.",
"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_001129 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=2x³ +8x² +0x+7. Evaluate f′(2). | {
"A": "56",
"B": "67.2",
"C": "55",
"D": "57"
} | A | 56 | Differentiate: f′(x)=3(2)x²+2(8)x+(0). At x=2, f′(2)=3(2)(2)²+2(8)(2)+(0)=56. | {
"A": "Correct. The worked calculation gives 56.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 56, not 67.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 56, not 55.",
"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_002231 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 11 red, 7 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.32266",
"B": "0.48399",
"C": "-1.67734",
"D": "2.32266"
} | A | 0.32266 | Favourable pairs = C(11,2)+C(7,2)+C(11,2)=131. Total pairs=C(29,2)=406. Therefore P=131/406=0.32266. | {
"A": "Correct. The worked calculation gives 0.32266.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32266, not 0.48399.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32266, not -1.67734.",
"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_002013 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 3 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.38421",
"B": "0.76842",
"C": "0.38421",
"D": "0.19211"
} | C | 0.38421 | Favourable pairs = C(6,2)+C(3,2)+C(11,2)=73. Total pairs=C(20,2)=190. Therefore P=73/190=0.38421. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.38421, not 1.38421.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.38421, not 0.76842.",
"C": "Correct. The worked calculation gives 0.38421.",
"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_009281 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.55 V, transfers 3 electrons, and has reaction quotient Q=10^1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.5303 V",
"B": "3.5303 V",
"C": "0.79545 V",
"D": "1.5303 V"
} | A | 0.5303 V | Apply the Nernst equation: E=0.55−(0.0591/3)(1)=0.5303 V. | {
"A": "Correct. The worked calculation gives 0.5303 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.5303 V, not 3.5303 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5303 V, not 0.79545 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_009078 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.37 V, transfers 2 electrons, and has reaction quotient Q=10^-4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.4882 V",
"B": "2.9764 V",
"C": "1.14882 V",
"D": "4.4882 V"
} | A | 1.4882 V | Apply the Nernst equation: E=1.37−(0.0591/2)(-4)=1.4882 V. | {
"A": "Correct. The worked calculation gives 1.4882 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4882 V, not 2.9764 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.4882 V, not 1.14882 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_008888 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.99 mol L⁻¹ and initially B is absent. At equilibrium, 16% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.24259",
"B": "0.36389",
"C": "-2.75741",
"D": "0.24259"
} | D | 0.24259 | Let α=0.16. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.99)(0.16)²/(1−0.16)=0.24259. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.24259, not -0.24259.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.24259, not 0.36389.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.24259, not -2.7... | [
"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_000392 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -9 and common difference 9. Find the sum of its first 20 terms. | {
"A": "1530",
"B": "1224",
"C": "2295",
"D": "1528"
} | A | 1530 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-9, d=9, n=20: Sₙ=20/2[2(-9)+(20−1)(9)]=1530. | {
"A": "Correct. The worked calculation gives 1530.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1530, not 1224.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1530, not 2295.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008109 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 7 A for 26392 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": "91.17547 g",
"B": "62.78365 g",
"C": "60.78365 g",
"D": "61.78365 g"
} | C | 60.78365 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×7×26392/(2×96500)=60.78365 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 60.78365 g, not 91.17547 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 60.78365 g, not 62.78365 g.",
"C": "Correct. The worked calculation gives 60.78365 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004610 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 6 kg and radius 2 m is acted on by a constant torque of 21 N m about its central axis. Find its angular acceleration. | {
"A": "1.175 rad s⁻²",
"B": "-0.25 rad s⁻²",
"C": "3.75 rad s⁻²",
"D": "1.75 rad s⁻²"
} | D | 1.75 rad s⁻² | For a solid disc, I=½MR²=½(6)(2)²=12 kg m². Using τ=Iα, α=21/12=1.75 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.75 rad s⁻², not 1.175 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.75 rad s⁻², not -0.25 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gi... | [
"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_006792 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 6 mol H₂ and 16 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "3 mol",
"B": "7 mol",
"C": "6 mol",
"D": "9 mol"
} | C | 6 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 6 mol H₂O; O₂ can produce 32 mol H₂O. The limiting condition is H₂; product=6 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 3 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 7 mol.",
"C": "Correct. The worked calculation gives 6 mol.",
"D": "Incorrect. Substituting the stated values into ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009424 | 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_10H_2N_3X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "12",
"B": "14",
"C": "5.5",
"D": "11"
} | D | 11 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×10+2+3−2−1)/2=11. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11, not 12.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11, not 14.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11, not 5.5.",
"D": "Correct. The wo... | [
"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_005247 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +4 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "3.93878 N",
"B": "35.26531 N",
"C": "23.5102 N",
"D": "29.38776 N"
} | D | 29.38776 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(4×10⁻⁶)/(7×10⁻²)²=29.38776 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 29.38776 N, not 3.93878 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 29.38776 N, not 35.26531 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29.3877... | [
"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_005962 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.7 atm at 216 K. What is its pressure at 443 K? | {
"A": "6.48657 atm",
"B": "6.97315 atm",
"C": "3.48657 atm",
"D": "2.48657 atm"
} | C | 3.48657 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.7)(443)/(216)=3.48657 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.48657 atm, not 6.48657 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.48657 atm, not 6.97315 atm.",
"C": "Correct. The worked calculation gives 3.48657 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_009256 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.17 V, transfers 1 electrons, and has reaction quotient Q=10^2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.0518 V",
"B": "1.10518 V",
"C": "1.0518 V",
"D": "0.78885 V"
} | C | 1.0518 V | Apply the Nernst equation: E=1.17−(0.0591/1)(2)=1.0518 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0518 V, not 2.0518 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0518 V, not 1.10518 V.",
"C": "Correct. The worked calculation gives 1.0518 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_006704 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 28 mol H₂ and 27 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "14 mol",
"B": "28 mol",
"C": "56 mol",
"D": "30 mol"
} | B | 28 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 28 mol H₂O; O₂ can produce 54 mol H₂O. The limiting condition is H₂; product=28 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28 mol, not 14 mol.",
"B": "Correct. The worked calculation gives 28 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28 mol, not 56 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_001276 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ -9x² -12x+7. Evaluate f′(1). | {
"A": "-10",
"B": "-9",
"C": "-0.2",
"D": "-12"
} | D | -12 | Differentiate: f′(x)=3(6)x²+2(-9)x+(-12). At x=1, f′(1)=3(6)(1)²+2(-9)(1)+(-12)=-12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -12, not -10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -12, not -9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -12, not -0.2.",
"D": "Correct. T... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003611 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 114 m s⁻¹ at 65° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1194.66163 m",
"B": "-995.55136 m",
"C": "994.55136 m",
"D": "995.55136 m"
} | D | 995.55136 m | Range R=u²sin(2θ)/g. Substituting u=114, θ=65° and g=10 gives R=(114)²sin(130°)/10=995.55136 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 995.55136 m, not 1194.66163 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 995.55136 m, not -995.55136 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives ... | [
"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_009289 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.03 V, transfers 2 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.88225 V",
"B": "-1.11775 V",
"C": "1.88225 V",
"D": "-2.11775 V"
} | A | 0.88225 V | Apply the Nernst equation: E=1.03−(0.0591/2)(5)=0.88225 V. | {
"A": "Correct. The worked calculation gives 0.88225 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.88225 V, not -1.11775 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.88225 V, not 1.88225 V.",
"D": "Incorrect. Substituting th... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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