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_005678 | 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 1.9 atm at 357 K. What is its pressure at 404 K? | {
"A": "4.15014 atm",
"B": "1.15014 atm",
"C": "5.15014 atm",
"D": "2.15014 atm"
} | D | 2.15014 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.9)(404)/(357)=2.15014 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.15014 atm, not 4.15014 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.15014 atm, not 1.15014 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.... | [
"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_004444 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 4 kg and radius 5 m is acted on by a constant torque of 42 N m about its central axis. Find its angular acceleration. | {
"A": "0.63 rad s⁻²",
"B": "0.84 rad s⁻²",
"C": "1.084 rad s⁻²",
"D": "2.84 rad s⁻²"
} | B | 0.84 rad s⁻² | For a solid disc, I=½MR²=½(4)(5)²=50 kg m². Using τ=Iα, α=42/50=0.84 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.84 rad s⁻², not 0.63 rad s⁻².",
"B": "Correct. The worked calculation gives 0.84 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.84 rad s⁻², not 1.084 rad s⁻².",
"D": "Incorrect. ... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005610 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 20 μF capacitor is charged to a potential difference of 31 V. Calculate the energy stored, expressed in μJ. | {
"A": "7688 μJ",
"B": "9610 μJ",
"C": "19220 μJ",
"D": "14415 μJ"
} | B | 9610 μJ | U=½CV². Since C=20 μF, U in μJ is ½×20×(31)²=9610 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9610 μJ, not 7688 μJ.",
"B": "Correct. The worked calculation gives 9610 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9610 μJ, not 19220 μJ.",
"D": "Incorrect. Substituting the stated v... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009399 | 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_5H_1N_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "10",
"B": "7",
"C": "3.5",
"D": "9"
} | B | 7 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×5+2+3−1−0)/2=7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 10.",
"B": "Correct. The worked calculation gives 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 3.5.",
"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_005771 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3 atm at 380 K. What is its pressure at 569 K? | {
"A": "4.49211 atm",
"B": "8.98421 atm",
"C": "6.49211 atm",
"D": "2.49211 atm"
} | A | 4.49211 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3)(569)/(380)=4.49211 atm. | {
"A": "Correct. The worked calculation gives 4.49211 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.49211 atm, not 8.98421 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.49211 atm, not 6.49211 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_001682 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 79 distinct elements? | {
"A": "1440680596355",
"B": "1080510447266.25",
"C": "1440680596357",
"D": "1440680596353"
} | A | 1440680596355 | Order does not matter, so the count is C(79,10)=79!/[10!(69)!]=1440680596355. | {
"A": "Correct. The worked calculation gives 1440680596355.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1440680596355, not 1080510447266.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1440680596355, not 1440680596357.",
"D": "Inco... | [
"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_005428 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 68 μF capacitor is charged to a potential difference of 23 V. Calculate the energy stored, expressed in μJ. | {
"A": "17986 μJ",
"B": "13489.5 μJ",
"C": "21583.2 μJ",
"D": "17988 μJ"
} | A | 17986 μJ | U=½CV². Since C=68 μF, U in μJ is ½×68×(23)²=17986 μJ. | {
"A": "Correct. The worked calculation gives 17986 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17986 μJ, not 13489.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17986 μJ, not 21583.2 μJ.",
"D": "Incorrect. Substituting the ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004218 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.39. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "28.8 N",
"B": "14.4 N",
"C": "12.4 N",
"D": "10.8 N"
} | B | 14.4 N | Net force=mg(sinθ−μcosθ)=5×10×(0.6−0.39×0.8)=14.4 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14.4 N, not 28.8 N.",
"B": "Correct. The worked calculation gives 14.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14.4 N, not 12.4 N.",
"D": "Incorrect. Substituting the stated values ... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009712 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(CN)_6]^-3, each CN ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "3",
"B": "5",
"C": "1",
"D": "2.25"
} | A | 3 | Let the formal oxidation state of Cu be x. Charge balance gives x+(6)(−1)=-3; hence x=-3+6=+3. | {
"A": "Correct. The worked calculation gives 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001650 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (1x² -6x -4) dx. | {
"A": "-51.2",
"B": "-64",
"C": "-42.66667",
"D": "-85.33333"
} | C | -42.66667 | An antiderivative is (1/3)x³+(-6/2)x²+(-4)x. Evaluating between 0 and 4 gives (1/3)(4)³+(-6/2)(4)²+(-4)(4)=-42.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -42.66667, not -51.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -42.66667, not -64.",
"C": "Correct. The worked calculation gives -42.66667.",
"D": "Incorrect. Substituting the stated va... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005375 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 55 μF capacitor is charged to a potential difference of 16 V. Calculate the energy stored, expressed in μJ. | {
"A": "3520 μJ",
"B": "10560 μJ",
"C": "7040 μJ",
"D": "7039 μJ"
} | C | 7040 μJ | U=½CV². Since C=55 μF, U in μJ is ½×55×(16)²=7040 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7040 μJ, not 3520 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7040 μJ, not 10560 μJ.",
"C": "Correct. The worked calculation gives 7040 μJ.",
"D": "Incorrect. Substituting the stated v... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004231 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 43 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.10. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "223.6 N",
"B": "23.36 N",
"C": "225.6 N",
"D": "335.4 N"
} | A | 223.6 N | Net force=mg(sinθ−μcosθ)=43×10×(0.6−0.10×0.8)=223.6 N. | {
"A": "Correct. The worked calculation gives 223.6 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 223.6 N, not 23.36 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 223.6 N, not 225.6 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005992 | 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 4.5 atm at 288 K. What is its pressure at 482 K? | {
"A": "5.53125 atm",
"B": "8.53125 atm",
"C": "7.53125 atm",
"D": "5.64844 atm"
} | C | 7.53125 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.5)(482)/(288)=7.53125 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.53125 atm, not 5.53125 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.53125 atm, not 8.53125 atm.",
"C": "Correct. The worked calculation gives 7.53125 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_008501 | 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 3 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.4508 K",
"B": "4.4508 K",
"C": "0.4508 K",
"D": "1.14508 K"
} | A | 1.4508 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.52×0.93=1.4508 K. | {
"A": "Correct. The worked calculation gives 1.4508 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4508 K, not 4.4508 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.4508 K, not 0.4508 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_009023 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.05 V, transfers 3 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.0894 V",
"B": "3.0894 V",
"C": "2.0894 V",
"D": "-0.9106 V"
} | A | 1.0894 V | Apply the Nernst equation: E=1.05−(0.0591/3)(-2)=1.0894 V. | {
"A": "Correct. The worked calculation gives 1.0894 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0894 V, not 3.0894 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0894 V, not 2.0894 V.",
"D": "Incorrect. Substituting the stat... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002671 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 3], [2, 7]]. | {
"A": "7.5",
"B": "15",
"C": "14",
"D": "18"
} | B | 15 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(7)−(3)(2)=15. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15, not 7.5.",
"B": "Correct. The worked calculation gives 15.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15, not 14.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001062 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=1x³ -6x² +7x+7. Evaluate f′(-1). | {
"A": "-22",
"B": "33",
"C": "16.5",
"D": "22"
} | D | 22 | Differentiate: f′(x)=3(1)x²+2(-6)x+(7). At x=-1, f′(-1)=3(1)(-1)²+2(-6)(-1)+(7)=22. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22, not -22.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22, not 33.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22, not 16.5.",
"D": "Correct. The ... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007173 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 18 mol of gas at 391 K and 1.81 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "255.25621 L",
"B": "319.07026 L",
"C": "239.30269 L",
"D": "318.07026 L"
} | B | 319.07026 L | PV=nRT, so V=nRT/P=(18)(0.082057)(391)/(1.81)=319.07026 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 319.07026 L, not 255.25621 L.",
"B": "Correct. The worked calculation gives 319.07026 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 319.07026 L, not 239.30269 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003350 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 20 m s⁻¹ at 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "39.39231 m",
"B": "38.39231 m",
"C": "-39.39231 m",
"D": "47.27077 m"
} | A | 39.39231 m | Range R=u²sin(2θ)/g. Substituting u=20, θ=40° and g=10 gives R=(20)²sin(80°)/10=39.39231 m. | {
"A": "Correct. The worked calculation gives 39.39231 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39.39231 m, not 38.39231 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39.39231 m, not -39.39231 m.",
"D": "Incorrect. Substituti... | [
"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_004112 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 19 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.14. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "10.272 N",
"B": "91.72 N",
"C": "139.08 N",
"D": "92.72 N"
} | D | 92.72 N | Net force=mg(sinθ−μcosθ)=19×10×(0.6−0.14×0.8)=92.72 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 92.72 N, not 10.272 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 92.72 N, not 91.72 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 92.72 N, not 139.... | [
"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_007389 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 16 mL of 0.10 M HCl is mixed with 39 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "15.62137",
"B": "12.62137",
"C": "6.31068",
"D": "9.46602"
} | B | 12.62137 | Excess OH⁻ moles=0.10×(39−16)/1000=0.002300 mol. Total volume=0.055 L, so [OH⁻]=0.041818 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.62137. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.62137, not 15.62137.",
"B": "Correct. The worked calculation gives 12.62137.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.62137, not 6.31068.",
"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_006942 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 31 mol H₂ and 7 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "21 mol",
"B": "16 mol",
"C": "17 mol",
"D": "14 mol"
} | D | 14 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 31 mol H₂O; O₂ can produce 14 mol H₂O. The limiting condition is O₂; product=14 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14 mol, not 21 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14 mol, not 16 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14 mol, not 17 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_001678 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 7 elements can be selected from a set of 71 distinct elements? | {
"A": "1063912564",
"B": "1329890705",
"C": "664945352.5",
"D": "132989071.5"
} | B | 1329890705 | Order does not matter, so the count is C(71,7)=71!/[7!(64)!]=1329890705. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1329890705, not 1063912564.",
"B": "Correct. The worked calculation gives 1329890705.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1329890705, not 664945352.5.",
"D": "Incorrect. Substituti... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003197 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-6-13i)/(5+7i). What is Re(z), the real part of z? | {
"A": "-3.63514",
"B": "-1.63514",
"C": "1.36486",
"D": "0.83649"
} | B | -1.63514 | Multiply numerator and denominator by the conjugate (5-7i). Then Re(z)=(ac+bd)/(c²+d²)=((-6)(5)+(-13)(7))/(5²+(7)²)=-1.63514. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.63514, not -3.63514.",
"B": "Correct. The worked calculation gives -1.63514.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.63514, not 1.36486.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009119 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.74 V, transfers 3 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.6218 V",
"B": "0.9327 V",
"C": "0.46635 V",
"D": "3.6218 V"
} | A | 0.6218 V | Apply the Nernst equation: E=0.74−(0.0591/3)(6)=0.6218 V. | {
"A": "Correct. The worked calculation gives 0.6218 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6218 V, not 0.9327 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.6218 V, not 0.46635 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_001868 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 12 elements can be selected from a set of 19 distinct elements? | {
"A": "40310.4",
"B": "37791",
"C": "50388",
"D": "75582"
} | C | 50388 | Order does not matter, so the count is C(19,12)=19!/[12!(7)!]=50388. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 50388, not 40310.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 50388, not 37791.",
"C": "Correct. The worked calculation gives 50388.",
"D": "Incorrect. Substituting the stated values int... | [
"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_006162 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 33 cm in front of a thin convex lens of focal length 11 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.5",
"B": "1.5",
"C": "0.75",
"D": "0.5"
} | D | 0.5 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(33)(11)/(33−11)=16.5 cm. Thus |m|=v/u=16.5/33=0.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5, not -0.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.5, not 1.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5, not 0.75.",
"D": "Correct.... | [
"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_004821 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 2 Ω are connected in series; this combination is connected in parallel with a 3 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "10.8 A",
"B": "13.4 A",
"C": "21.6 A",
"D": "14.4 A"
} | D | 14.4 A | Series branch resistance=13+2=15 Ω. Parallel equivalent R_eq=(15×3)/(15+3)=2.5 Ω. Total current I=V/R_eq=36/2.5=14.4 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14.4 A, not 10.8 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14.4 A, not 13.4 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14.4 A, not 21.6 A.",
... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005217 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +4 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "27.77686 N",
"B": "3.67769 N",
"C": "24.77686 N",
"D": "26.77686 N"
} | D | 26.77686 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(4×10⁻⁶)/(11×10⁻²)²=26.77686 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26.77686 N, not 27.77686 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26.77686 N, not 3.67769 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26.7768... | [
"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_007160 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 9 mol of gas at 398 K and 1.36 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "108.06183 L",
"B": "432.24731 L",
"C": "216.12366 L",
"D": "214.12366 L"
} | C | 216.12366 L | PV=nRT, so V=nRT/P=(9)(0.082057)(398)/(1.36)=216.12366 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 216.12366 L, not 108.06183 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 216.12366 L, not 432.24731 L.",
"C": "Correct. The worked calculation gives 216.12366 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006884 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 1 mol H₂ and 15 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "0.75 mol",
"B": "3 mol",
"C": "4 mol",
"D": "1 mol"
} | D | 1 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 1 mol H₂O; O₂ can produce 30 mol H₂O. The limiting condition is H₂; product=1 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1 mol, not 0.75 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1 mol, not 3 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1 mol, not 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_000595 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -14 and common difference 3. Find the sum of its first 24 terms. | {
"A": "50.2",
"B": "494",
"C": "492",
"D": "246"
} | C | 492 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-14, d=3, n=24: Sₙ=24/2[2(-14)+(24−1)(3)]=492. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 492, not 50.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 492, not 494.",
"C": "Correct. The worked calculation gives 492.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_006594 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 1 kg is attached to an ideal spring of force constant 796 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.14178 s",
"B": "-1.92911 s",
"C": "0.07089 s",
"D": "1.00709 s"
} | C | 0.07089 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(1/796)=0.07089 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.07089 s, not 0.14178 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.07089 s, not -1.92911 s.",
"C": "Correct. The worked calculation gives 0.07089 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008316 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 15 A for 9442 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": "37.27878 g",
"B": "34.94885 g",
"C": "46.59847 g",
"D": "47.59847 g"
} | C | 46.59847 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×15×9442/(2×96500)=46.59847 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 46.59847 g, not 37.27878 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 46.59847 g, not 34.94885 g.",
"C": "Correct. The worked calculation gives 46.59847 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_004184 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 46 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.43. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "118.76 N",
"B": "235.52 N",
"C": "117.76 N",
"D": "141.312 N"
} | C | 117.76 N | Net force=mg(sinθ−μcosθ)=46×10×(0.6−0.43×0.8)=117.76 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 117.76 N, not 118.76 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 117.76 N, not 235.52 N.",
"C": "Correct. The worked calculation gives 117.76 N.",
"D": "Incorrect. Substituting the stat... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000679 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio 5. What is the sum of its first 12 terms? | {
"A": "305175780",
"B": "610351560",
"C": "457763670",
"D": "305175779"
} | A | 305175780 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(5^12−1)/(5−1)=305175780. | {
"A": "Correct. The worked calculation gives 305175780.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 305175780, not 610351560.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 305175780, not 457763670.",
"D": "Incorrect. Substituting the... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007406 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 26 mL of 0.10 M HCl is mixed with 28 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "14.56864",
"B": "2.15686",
"C": "9.56864",
"D": "11.56864"
} | D | 11.56864 | Excess OH⁻ moles=0.10×(28−26)/1000=0.000200 mol. Total volume=0.054 L, so [OH⁻]=0.003704 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=11.56864. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.56864, not 14.56864.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.56864, not 2.15686.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.56864, not 9... | [
"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_001350 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (0x² +1x +5) dx. | {
"A": "10",
"B": "-12",
"C": "12",
"D": "15"
} | C | 12 | An antiderivative is (0/3)x³+(1/2)x²+(5)x. Evaluating between 0 and 2 gives (0/3)(2)³+(1/2)(2)²+(5)(2)=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 -12.",
"C": "Correct. The worked calculation gives 12.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"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_009398 | 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_8H_14N_2X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "0.5",
"B": "1",
"C": "-1",
"D": "0"
} | B | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×8+2+2−14−4)/2=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 -1.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005882 | 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 1.1 atm at 432 K. What is its pressure at 640 K? | {
"A": "1.62963 atm",
"B": "0.81481 atm",
"C": "0.62963 atm",
"D": "-1.37037 atm"
} | A | 1.62963 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.1)(640)/(432)=1.62963 atm. | {
"A": "Correct. The worked calculation gives 1.62963 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.62963 atm, not 0.81481 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.62963 atm, not 0.62963 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_000737 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio 5. What is the sum of its first 12 terms? | {
"A": "292968748.8",
"B": "366210934",
"C": "-366210936",
"D": "366210936"
} | D | 366210936 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(5^12−1)/(5−1)=366210936. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 366210936, not 292968748.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 366210936, not 366210934.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 36621093... | [
"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_001262 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-2x³ +4x² -1x+7. Evaluate f′(-2). | {
"A": "-41",
"B": "-20.5",
"C": "-43",
"D": "-30.75"
} | A | -41 | Differentiate: f′(x)=3(-2)x²+2(4)x+(-1). At x=-2, f′(-2)=3(-2)(-2)²+2(4)(-2)+(-1)=-41. | {
"A": "Correct. The worked calculation gives -41.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -41, not -20.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -41, not -43.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_002566 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, -3], [9, 3]]. | {
"A": "45",
"B": "-45",
"C": "46",
"D": "43"
} | A | 45 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(3)−(-3)(9)=45. | {
"A": "Correct. The worked calculation gives 45.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 45, not -45.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 45, not 46.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008019 | 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 6 A for 17376 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": "4.43018 g",
"B": "34.30184 g",
"C": "35.30184 g",
"D": "36.30184 g"
} | B | 34.30184 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×6×17376/(2×96500)=34.30184 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 34.30184 g, not 4.43018 g.",
"B": "Correct. The worked calculation gives 34.30184 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 34.30184 g, not 35.30184 g.",
"D": "Incorrect. Substituting... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009618 | 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_8H_18. Treat X as the total number of monovalent halogen atoms. | {
"A": "2",
"B": "0",
"C": "1",
"D": "3"
} | B | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×8+2+0−18−0)/2=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 2.",
"B": "Correct. The worked calculation gives 0.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"D": "Incorrect. Substituting the stated values into the governing 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_004850 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 12 Ω are connected in series; this combination is connected in parallel with a 10 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.6 A",
"B": "6.6 A",
"C": "1.36 A",
"D": "2.6 A"
} | A | 3.6 A | Series branch resistance=8+12=20 Ω. Parallel equivalent R_eq=(20×10)/(20+10)=6.66667 Ω. Total current I=V/R_eq=24/6.66667=3.6 A. | {
"A": "Correct. The worked calculation gives 3.6 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.6 A, not 6.6 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.6 A, not 1.36 A.",
"D": "Incorrect. Substituting the stated values into... | [
"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_005019 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +3 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "202.5 N",
"B": "101.25 N",
"C": "100.25 N",
"D": "102.25 N"
} | B | 101.25 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(3×10⁻⁶)/(4×10⁻²)²=101.25 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 101.25 N, not 202.5 N.",
"B": "Correct. The worked calculation gives 101.25 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 101.25 N, not 100.25 N.",
"D": "Incorrect. Substituting the state... | [
"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_000544 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 9 and common difference 15. Find the sum of its first 34 terms. | {
"A": "8719",
"B": "17442",
"C": "8723",
"D": "8721"
} | D | 8721 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=9, d=15, n=34: Sₙ=34/2[2(9)+(34−1)(15)]=8721. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8721, not 8719.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8721, not 17442.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8721, not 8723.",
"D": "Cor... | [
"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_007772 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 56 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "0.32812 mmol L⁻¹",
"B": "3.4375 mmol L⁻¹",
"C": "2.4375 mmol L⁻¹",
"D": "0.4375 mmol L⁻¹"
} | D | 0.4375 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=56/2^7=0.4375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.4375 mmol L⁻¹, not 0.32812 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.4375 mmol L⁻¹, not 3.4375 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing ... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004534 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 3 kg and radius 3 m is acted on by a constant torque of 22 N m about its central axis. Find its angular acceleration. | {
"A": "1.22222 rad s⁻²",
"B": "1.62963 rad s⁻²",
"C": "2.44444 rad s⁻²",
"D": "4.62963 rad s⁻²"
} | B | 1.62963 rad s⁻² | For a solid disc, I=½MR²=½(3)(3)²=13.5 kg m². Using τ=Iα, α=22/13.5=1.62963 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.62963 rad s⁻², not 1.22222 rad s⁻².",
"B": "Correct. The worked calculation gives 1.62963 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.62963 rad s⁻², not 2.44444 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_009990 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(CN)_5]^-3, each CN ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "-2",
"B": "1",
"C": "5",
"D": "2"
} | D | 2 | Let the formal oxidation state of Pt be x. Charge balance gives x+(5)(−1)=-3; hence x=-3+5=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"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 5.",
"D": "Correct. The worked c... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003897 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block initially moves at 10 m s⁻¹. A constant net force does 13 N of work over 19 m in the direction of motion. Find its final kinetic energy. | {
"A": "416.4 J",
"B": "347 J",
"C": "348 J",
"D": "173.5 J"
} | B | 347 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(2)(10)²+(13)(19)=347 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 347 J, not 416.4 J.",
"B": "Correct. The worked calculation gives 347 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 347 J, not 348 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_002768 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-5, -2, -6) and v=(-4, -2, 3), calculate u·v. | {
"A": "3",
"B": "6",
"C": "8",
"D": "1.6"
} | B | 6 | The dot product is the sum of corresponding component products: (-5)(-4)+(-2)(-2)+(-6)(3)=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"B": "Correct. The worked calculation gives 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 8.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_005339 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 49 μF capacitor is charged to a potential difference of 2 V. Calculate the energy stored, expressed in μJ. | {
"A": "73.5 μJ",
"B": "98 μJ",
"C": "97 μJ",
"D": "-98 μJ"
} | B | 98 μJ | U=½CV². Since C=49 μF, U in μJ is ½×49×(2)²=98 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 98 μJ, not 73.5 μJ.",
"B": "Correct. The worked calculation gives 98 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 98 μJ, not 97 μJ.",
"D": "Incorrect. Substituting the stated values int... | [
"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_002045 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 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": "-1.60234",
"B": "0.29825",
"C": "0.39766",
"D": "-2.60234"
} | C | 0.39766 | Favourable pairs = C(5,2)+C(3,2)+C(11,2)=68. Total pairs=C(19,2)=171. Therefore P=68/171=0.39766. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.39766, not -1.60234.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.39766, not 0.29825.",
"C": "Correct. The worked calculation gives 0.39766.",
"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_003420 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 95 m s⁻¹ at 15° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "453.25 m",
"B": "225.625 m",
"C": "338.4375 m",
"D": "451.25 m"
} | D | 451.25 m | Range R=u²sin(2θ)/g. Substituting u=95, θ=15° and g=10 gives R=(95)²sin(30°)/10=451.25 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 451.25 m, not 453.25 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 451.25 m, not 225.625 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 451.25 m, not... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000458 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 21 and common difference 6. Find the sum of its first 18 terms. | {
"A": "1298",
"B": "1296",
"C": "2592",
"D": "1944"
} | B | 1296 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=21, d=6, n=18: Sₙ=18/2[2(21)+(18−1)(6)]=1296. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1296, not 1298.",
"B": "Correct. The worked calculation gives 1296.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1296, not 2592.",
"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_003209 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(2-3i)/(3+3i). What is Re(z), the real part of z? | {
"A": "-1.16667",
"B": "-0.16667",
"C": "0.16667",
"D": "-0.33333"
} | B | -0.16667 | Multiply numerator and denominator by the conjugate (3-3i). Then Re(z)=(ac+bd)/(c²+d²)=((2)(3)+(-3)(3))/(3²+(3)²)=-0.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.16667, not -1.16667.",
"B": "Correct. The worked calculation gives -0.16667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.16667, not 0.16667.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003701 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block initially moves at 3 m s⁻¹. A constant net force does 24 N of work over 20 m in the direction of motion. Find its final kinetic energy. | {
"A": "1014 J",
"B": "253.5 J",
"C": "507 J",
"D": "51.7 J"
} | C | 507 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(6)(3)²+(24)(20)=507 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 507 J, not 1014 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 507 J, not 253.5 J.",
"C": "Correct. The worked calculation gives 507 J.",
"D": "Incorrect. Substituting the stated values in... | [
"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_000956 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio -3. What is the sum of its first 10 terms? | {
"A": "-1475.2",
"B": "-17714.4",
"C": "-14762",
"D": "-22143"
} | C | -14762 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(-3^10−1)/(-3−1)=-14762. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -14762, not -1475.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -14762, not -17714.4.",
"C": "Correct. The worked calculation gives -14762.",
"D": "Incorrect. Substituting the stated valu... | [
"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_000812 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio 5. What is the sum of its first 11 terms? | {
"A": "14648437.2",
"B": "12207031",
"C": "12207032",
"D": "12207033"
} | B | 12207031 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(5^11−1)/(5−1)=12207031. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12207031, not 14648437.2.",
"B": "Correct. The worked calculation gives 12207031.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12207031, not 12207032.",
"D": "Incorrect. Substituting the st... | [
"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_007577 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 49 mL of 0.10 M HCl is mixed with 64 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.12301",
"B": "-12.12301",
"C": "11.12301",
"D": "9.12301"
} | A | 12.12301 | Excess OH⁻ moles=0.10×(64−49)/1000=0.001500 mol. Total volume=0.113 L, so [OH⁻]=0.013274 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.12301. | {
"A": "Correct. The worked calculation gives 12.12301.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.12301, not -12.12301.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.12301, not 11.12301.",
"D": "Incorrect. Substituting the sta... | [
"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_007351 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 92 mL of 0.10 M HCl is mixed with 74 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "3.96484",
"B": "1.47363",
"C": "1.96484",
"D": "3.92967"
} | C | 1.96484 | Excess H⁺ moles=0.10×(92−74)/1000=0.001800 mol. Total volume=0.166 L, so [H⁺]=0.010843 M and pH=−log₁₀[H⁺]=1.96484. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.96484, not 3.96484.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.96484, not 1.47363.",
"C": "Correct. The worked calculation gives 1.96484.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003113 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-11-15i)/(1+9i). What is Re(z), the real part of z? | {
"A": "-1.78049",
"B": "0.82195",
"C": "1.21951",
"D": "0.21951"
} | A | -1.78049 | Multiply numerator and denominator by the conjugate (1-9i). Then Re(z)=(ac+bd)/(c²+d²)=((-11)(1)+(-15)(9))/(1²+(9)²)=-1.78049. | {
"A": "Correct. The worked calculation gives -1.78049.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.78049, not 0.82195.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.78049, not 1.21951.",
"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_002193 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 6 blue and 5 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.35968",
"B": "-1.64032",
"C": "-2.64032",
"D": "0.53953"
} | A | 0.35968 | Favourable pairs = C(12,2)+C(6,2)+C(5,2)=91. Total pairs=C(23,2)=253. Therefore P=91/253=0.35968. | {
"A": "Correct. The worked calculation gives 0.35968.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35968, not -1.64032.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35968, not -2.64032.",
"D": "Incorrect. Substituting the stated ... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009912 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(Cl)_2]^-2, each Cl ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "3",
"B": "-2",
"C": "0",
"D": "-3"
} | C | 0 | Let the formal oxidation state of Pt be x. Charge balance gives x+(2)(−1)=-2; hence x=-2+2=+0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"C": "Correct. The worked calculation gives 0.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002722 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, 4, -6) and v=(-3, 0, -5), calculate u·v. | {
"A": "-27",
"B": "3.7",
"C": "27",
"D": "13.5"
} | C | 27 | The dot product is the sum of corresponding component products: (1)(-3)+(4)(0)+(-6)(-5)=27. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 27, not -27.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 27, not 3.7.",
"C": "Correct. The worked calculation gives 27.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"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_006653 | 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 1124 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.72019 s",
"B": "0.27981 s",
"C": "0.1399 s",
"D": "0.41971 s"
} | B | 0.27981 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(22/1124)=0.27981 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.27981 s, not -1.72019 s.",
"B": "Correct. The worked calculation gives 0.27981 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.27981 s, not 0.1399 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000505 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 10 and common difference 3. Find the sum of its first 20 terms. | {
"A": "772",
"B": "577.5",
"C": "78",
"D": "770"
} | D | 770 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=10, d=3, n=20: Sₙ=20/2[2(10)+(20−1)(3)]=770. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 770, not 772.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 770, not 577.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 770, not 78.",
"D": "Correct. ... | [
"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_006862 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 19 mol H₂ and 34 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "19 mol",
"B": "18 mol",
"C": "2.9 mol",
"D": "28.5 mol"
} | A | 19 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 19 mol H₂O; O₂ can produce 68 mol H₂O. The limiting condition is H₂; product=19 mol. | {
"A": "Correct. The worked calculation gives 19 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19 mol, not 18 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19 mol, not 2.9 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_008629 | 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 1.21 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "3.63 K",
"B": "5.63 K",
"C": "6.63 K",
"D": "5.445 K"
} | A | 3.63 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×1.0×1.21=3.63 K. | {
"A": "Correct. The worked calculation gives 3.63 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.63 K, not 5.63 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.63 K, not 6.63 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_007641 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 87 mL of 0.10 M HCl is mixed with 55 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-1.35286",
"B": "1.23535",
"C": "1.64714",
"D": "2.64714"
} | C | 1.64714 | Excess H⁺ moles=0.10×(87−55)/1000=0.003200 mol. Total volume=0.142 L, so [H⁺]=0.022535 M and pH=−log₁₀[H⁺]=1.64714. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.64714, not -1.35286.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.64714, not 1.23535.",
"C": "Correct. The worked calculation gives 1.64714.",
"D": "Incorrect. Substituting the stated v... | [
"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_004540 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 3 kg and radius 6 m is acted on by a constant torque of 70 N m about its central axis. Find its angular acceleration. | {
"A": "2.59259 rad s⁻²",
"B": "0.97222 rad s⁻²",
"C": "1.2963 rad s⁻²",
"D": "4.2963 rad s⁻²"
} | C | 1.2963 rad s⁻² | For a solid disc, I=½MR²=½(3)(6)²=54 kg m². Using τ=Iα, α=70/54=1.2963 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.2963 rad s⁻², not 2.59259 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.2963 rad s⁻², not 0.97222 rad s⁻².",
"C": "Correct. The worked calculation gives 1.2963 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_008099 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 14 A for 16374 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": "75.42221 g",
"B": "-75.42221 g",
"C": "56.56666 g",
"D": "73.42221 g"
} | A | 75.42221 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×16374/(2×96500)=75.42221 g. | {
"A": "Correct. The worked calculation gives 75.42221 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 75.42221 g, not -75.42221 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 75.42221 g, not 56.56666 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005904 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.5 atm at 245 K. What is its pressure at 394 K? | {
"A": "5.62857 atm",
"B": "11.25714 atm",
"C": "7.62857 atm",
"D": "3.62857 atm"
} | A | 5.62857 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.5)(394)/(245)=5.62857 atm. | {
"A": "Correct. The worked calculation gives 5.62857 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.62857 atm, not 11.25714 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.62857 atm, not 7.62857 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_003635 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 24 m s⁻¹ at 75° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "14.4 m",
"B": "43.2 m",
"C": "27.8 m",
"D": "28.8 m"
} | D | 28.8 m | Range R=u²sin(2θ)/g. Substituting u=24, θ=75° and g=10 gives R=(24)²sin(150°)/10=28.8 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28.8 m, not 14.4 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28.8 m, not 43.2 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28.8 m, not 27.8 m.",
... | [
"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_009530 | 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_13H_16N_3X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "5",
"B": "9",
"C": "6",
"D": "7"
} | D | 7 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×13+2+3−16−1)/2=7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 6.",
"D": "Correct. The worked ca... | [
"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_001145 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=2x³ -2x² -10x+7. Evaluate f′(5). | {
"A": "144",
"B": "240",
"C": "90",
"D": "120"
} | D | 120 | Differentiate: f′(x)=3(2)x²+2(-2)x+(-10). At x=5, f′(5)=3(2)(5)²+2(-2)(5)+(-10)=120. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 120, not 144.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 120, not 240.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 120, not 90.",
"D": "Correct. Th... | [
"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_007561 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 14 mL of 0.10 M HCl is mixed with 74 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "25.66734",
"B": "12.83367",
"C": "-12.83367",
"D": "14.83367"
} | B | 12.83367 | Excess OH⁻ moles=0.10×(74−14)/1000=0.006000 mol. Total volume=0.088 L, so [OH⁻]=0.068182 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.83367. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.83367, not 25.66734.",
"B": "Correct. The worked calculation gives 12.83367.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.83367, not -12.83367.",
"D": "Incorrect. Substituting the sta... | [
"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_008137 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 15 A for 16904 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": "84.42518 g",
"B": "83.42518 g",
"C": "81.42518 g",
"D": "82.42518 g"
} | B | 83.42518 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×15×16904/(2×96500)=83.42518 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 83.42518 g, not 84.42518 g.",
"B": "Correct. The worked calculation gives 83.42518 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 83.42518 g, not 81.42518 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_000435 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 23 and common difference 7. Find the sum of its first 14 terms. | {
"A": "479.5",
"B": "1438.5",
"C": "959",
"D": "96.9"
} | C | 959 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=23, d=7, n=14: Sₙ=14/2[2(23)+(14−1)(7)]=959. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 959, not 479.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 959, not 1438.5.",
"C": "Correct. The worked calculation gives 959.",
"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_008922 | 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 1.67 mol L⁻¹ and initially B is absent. At equilibrium, 57% of A has dissociated at constant volume. Find K_c. | {
"A": "7.57093",
"B": "10.09457",
"C": "8.04728",
"D": "5.04728"
} | D | 5.04728 | Let α=0.57. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.67)(0.57)²/(1−0.57)=5.04728. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.04728, not 7.57093.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.04728, not 10.09457.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.04728, not 8.04... | [
"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_001201 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=3x³ +0x² -6x+7. Evaluate f′(-4). | {
"A": "139",
"B": "140",
"C": "138",
"D": "-138"
} | C | 138 | Differentiate: f′(x)=3(3)x²+2(0)x+(-6). At x=-4, f′(-4)=3(3)(-4)²+2(0)(-4)+(-6)=138. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 138, not 139.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 138, not 140.",
"C": "Correct. The worked calculation gives 138.",
"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_004867 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 3 Ω and 13 Ω are connected in series; this combination is connected in parallel with a 19 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.69079 A",
"B": "0.69079 A",
"C": "1.03618 A",
"D": "1.06908 A"
} | B | 0.69079 A | Series branch resistance=3+13=16 Ω. Parallel equivalent R_eq=(16×19)/(16+19)=8.68571 Ω. Total current I=V/R_eq=6/8.68571=0.69079 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.69079 A, not 1.69079 A.",
"B": "Correct. The worked calculation gives 0.69079 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.69079 A, not 1.03618 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_000507 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -1 and common difference 3. Find the sum of its first 13 terms. | {
"A": "442",
"B": "-221",
"C": "165.75",
"D": "221"
} | D | 221 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-1, d=3, n=13: Sₙ=13/2[2(-1)+(13−1)(3)]=221. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 221, not 442.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 221, not -221.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 221, not 165.75.",
"D": "Correc... | [
"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_000700 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio 5. What is the sum of its first 8 terms? | {
"A": "117187.2",
"B": "97656",
"C": "-97656",
"D": "9766.6"
} | B | 97656 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(5^8−1)/(5−1)=97656. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 97656, not 117187.2.",
"B": "Correct. The worked calculation gives 97656.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 97656, not -97656.",
"D": "Incorrect. Substituting the stated values i... | [
"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_000380 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -18 and common difference 8. Find the sum of its first 20 terms. | {
"A": "1162",
"B": "-1160",
"C": "1740",
"D": "1160"
} | D | 1160 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-18, d=8, n=20: Sₙ=20/2[2(-18)+(20−1)(8)]=1160. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1160, not 1162.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1160, not -1160.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1160, not 1740.",
"D": "Cor... | [
"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_004222 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 24 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.26. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "75.264 N",
"B": "47.04 N",
"C": "188.16 N",
"D": "94.08 N"
} | D | 94.08 N | Net force=mg(sinθ−μcosθ)=24×10×(0.6−0.26×0.8)=94.08 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 94.08 N, not 75.264 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 94.08 N, not 47.04 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 94.08 N, not 188.... | [
"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_009905 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(OH)_3]^-4, each OH ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "0",
"B": "-1",
"C": "-1.5",
"D": "-2"
} | B | -1 | Let the formal oxidation state of Cu be x. Charge balance gives x+(3)(−1)=-4; hence x=-4+3=-1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1, not 0.",
"B": "Correct. The worked calculation gives -1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1, not -1.5.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"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_000251 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 +3x -4=0, let its roots be α and β. What is α²+β²? | {
"A": "0.9949",
"B": "1.32653",
"C": "0.32653",
"D": "1.9898"
} | B | 1.32653 | By Vieta's relations, α+β = -3/7 and αβ = -4/7. Then α²+β²=(α+β)²−2αβ = (-3/7)²−2(-4/7) = 1.32653. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.32653, not 0.9949.",
"B": "Correct. The worked calculation gives 1.32653.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.32653, not 0.32653.",
"D": "Incorrect. Substituting the stated val... | [
"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_005575 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 70 μF capacitor is charged to a potential difference of 11 V. Calculate the energy stored, expressed in μJ. | {
"A": "3388 μJ",
"B": "4235 μJ",
"C": "8470 μJ",
"D": "6352.5 μJ"
} | B | 4235 μJ | U=½CV². Since C=70 μF, U in μJ is ½×70×(11)²=4235 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4235 μJ, not 3388 μJ.",
"B": "Correct. The worked calculation gives 4235 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4235 μJ, not 8470 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008284 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 13 A for 17062 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": "145.95524 g",
"B": "58.3821 g",
"C": "72.97762 g",
"D": "70.97762 g"
} | C | 72.97762 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×17062/(2×96500)=72.97762 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 72.97762 g, not 145.95524 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 72.97762 g, not 58.3821 g.",
"C": "Correct. The worked calculation gives 72.97762 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_009849 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(OH)_6]^-1, each OH ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "2.5",
"B": "6",
"C": "4",
"D": "5"
} | D | 5 | Let the formal oxidation state of Pt be x. Charge balance gives x+(6)(−1)=-1; hence x=-1+6=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 4.",
"D": "Correct. The worked ... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005884 | 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 5 atm at 434 K. What is its pressure at 716 K? | {
"A": "6.18664 atm",
"B": "7.24885 atm",
"C": "11.24885 atm",
"D": "8.24885 atm"
} | D | 8.24885 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(5)(716)/(434)=8.24885 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.24885 atm, not 6.18664 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.24885 atm, not 7.24885 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.... | [
"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_004139 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 24 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.11. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "-122.88 N",
"B": "122.88 N",
"C": "124.88 N",
"D": "184.32 N"
} | B | 122.88 N | Net force=mg(sinθ−μcosθ)=24×10×(0.6−0.11×0.8)=122.88 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 122.88 N, not -122.88 N.",
"B": "Correct. The worked calculation gives 122.88 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 122.88 N, not 124.88 N.",
"D": "Incorrect. Substituting the sta... | [
"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_003652 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 103 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "975.23586 m",
"B": "812.69655 m",
"C": "813.69655 m",
"D": "609.52241 m"
} | B | 812.69655 m | Range R=u²sin(2θ)/g. Substituting u=103, θ=25° and g=10 gives R=(103)²sin(50°)/10=812.69655 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 812.69655 m, not 975.23586 m.",
"B": "Correct. The worked calculation gives 812.69655 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 812.69655 m, not 813.69655 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_000398 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 11 and common difference 8. Find the sum of its first 33 terms. | {
"A": "4587",
"B": "6880.5",
"C": "-4587",
"D": "4589"
} | A | 4587 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=11, d=8, n=33: Sₙ=33/2[2(11)+(33−1)(8)]=4587. | {
"A": "Correct. The worked calculation gives 4587.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4587, not 6880.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4587, not -4587.",
"D": "Incorrect. Substituting the stated values into th... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005462 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 62 μF capacitor is charged to a potential difference of 14 V. Calculate the energy stored, expressed in μJ. | {
"A": "7291.2 μJ",
"B": "6076 μJ",
"C": "9114 μJ",
"D": "4860.8 μJ"
} | B | 6076 μJ | U=½CV². Since C=62 μF, U in μJ is ½×62×(14)²=6076 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6076 μJ, not 7291.2 μJ.",
"B": "Correct. The worked calculation gives 6076 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6076 μJ, not 9114 μJ.",
"D": "Incorrect. Substituting the stated ... | [
"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_004052 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 29 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.27. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "167.04 N",
"B": "89.088 N",
"C": "111.36 N",
"D": "113.36 N"
} | C | 111.36 N | Net force=mg(sinθ−μcosθ)=29×10×(0.6−0.27×0.8)=111.36 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 111.36 N, not 167.04 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 111.36 N, not 89.088 N.",
"C": "Correct. The worked calculation gives 111.36 N.",
"D": "Incorrect. Substituting the stat... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004332 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.11. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "20.48 N",
"B": "-20.48 N",
"C": "16.384 N",
"D": "30.72 N"
} | A | 20.48 N | Net force=mg(sinθ−μcosθ)=4×10×(0.6−0.11×0.8)=20.48 N. | {
"A": "Correct. The worked calculation gives 20.48 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20.48 N, not -20.48 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20.48 N, not 16.384 N.",
"D": "Incorrect. Substituting the stated ... | [
"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 |
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