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_005355 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 10 μF capacitor is charged to a potential difference of 2 V. Calculate the energy stored, expressed in μJ. | {
"A": "18 μJ",
"B": "20 μJ",
"C": "3 μJ",
"D": "10 μJ"
} | B | 20 μJ | U=½CV². Since C=10 μF, U in μJ is ½×10×(2)²=20 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20 μJ, not 18 μJ.",
"B": "Correct. The worked calculation gives 20 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20 μJ, not 3 μJ.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_009481 | 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_4H_0N_3X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "10",
"B": "2",
"C": "7",
"D": "5"
} | D | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×4+2+3−0−3)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.",
"D": "Correct. The worked c... | [
"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_006780 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 20 mol H₂ and 13 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "19 mol",
"B": "30 mol",
"C": "20 mol",
"D": "10 mol"
} | C | 20 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 20 mol H₂O; O₂ can produce 26 mol H₂O. The limiting condition is H₂; product=20 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20 mol, not 19 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20 mol, not 30 mol.",
"C": "Correct. The worked calculation gives 20 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_004874 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 3 Ω and 15 Ω are connected in series; this combination is connected in parallel with a 20 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.75 A",
"B": "-3.16667 A",
"C": "6.16667 A",
"D": "3.16667 A"
} | D | 3.16667 A | Series branch resistance=3+15=18 Ω. Parallel equivalent R_eq=(18×20)/(18+20)=9.47368 Ω. Total current I=V/R_eq=30/9.47368=3.16667 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.16667 A, not 4.75 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.16667 A, not -3.16667 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.16667 A, n... | [
"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_009983 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(CN)_6]^-3, each CN ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "1",
"B": "1.3",
"C": "3",
"D": "6"
} | C | 3 | Let the formal oxidation state of Co be x. Charge balance gives x+(6)(−1)=-3; hence x=-3+6=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"C": "Correct. The worked calculation gives 3.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002999 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, -2, 0) and v=(1, 7, -5), calculate u·v. | {
"A": "-11",
"B": "-13",
"C": "13",
"D": "-15"
} | B | -13 | The dot product is the sum of corresponding component products: (1)(1)+(-2)(7)+(0)(-5)=-13. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -13, not -11.",
"B": "Correct. The worked calculation gives -13.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -13, not 13.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005024 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +6 μC are separated by 5 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "155.52 N",
"B": "194.4 N",
"C": "195.4 N",
"D": "196.4 N"
} | B | 194.4 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(6×10⁻⁶)/(5×10⁻²)²=194.4 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 194.4 N, not 155.52 N.",
"B": "Correct. The worked calculation gives 194.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 194.4 N, not 195.4 N.",
"D": "Incorrect. Substituting the stated v... | [
"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_000260 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 -2x -11=0, let its roots be α and β. What is α²+β²? | {
"A": "2.75",
"B": "5.75",
"C": "-5.75",
"D": "3.75"
} | B | 5.75 | By Vieta's relations, α+β = 2/4 and αβ = -11/4. Then α²+β²=(α+β)²−2αβ = (2/4)²−2(-11/4) = 5.75. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.75, not 2.75.",
"B": "Correct. The worked calculation gives 5.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.75, not -5.75.",
"D": "Incorrect. Substituting the stated values into the ... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008690 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.63 mol L⁻¹ and initially B is absent. At equilibrium, 39% of A has dissociated at constant volume. Find K_c. | {
"A": "0.94252",
"B": "0.62835",
"C": "2.62835",
"D": "-0.37165"
} | B | 0.62835 | Let α=0.39. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.63)(0.39)²/(1−0.39)=0.62835. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.62835, not 0.94252.",
"B": "Correct. The worked calculation gives 0.62835.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.62835, not 2.62835.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004497 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 15 kg and radius 5 m is acted on by a constant torque of 5 N m about its central axis. Find its angular acceleration. | {
"A": "0.04 rad s⁻²",
"B": "0.02667 rad s⁻²",
"C": "1.02667 rad s⁻²",
"D": "-0.97333 rad s⁻²"
} | B | 0.02667 rad s⁻² | For a solid disc, I=½MR²=½(15)(5)²=187.5 kg m². Using τ=Iα, α=5/187.5=0.02667 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.02667 rad s⁻², not 0.04 rad s⁻².",
"B": "Correct. The worked calculation gives 0.02667 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.02667 rad s⁻², not 1.02667 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_008642 | 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 0.43 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "2.258 K",
"B": "-1.742 K",
"C": "0.258 K",
"D": "0.1935 K"
} | C | 0.258 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.6×0.43=0.258 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.258 K, not 2.258 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.258 K, not -1.742 K.",
"C": "Correct. The worked calculation gives 0.258 K.",
"D": "Incorrect. Substituting the stated v... | [
"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_003847 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 1 m s⁻¹. A constant net force does 13 N of work over 14 m in the direction of motion. Find its final kinetic energy. | {
"A": "225 J",
"B": "140.625 J",
"C": "187.5 J",
"D": "150 J"
} | C | 187.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(1)²+(13)(14)=187.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 187.5 J, not 225 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 187.5 J, not 140.625 J.",
"C": "Correct. The worked calculation gives 187.5 J.",
"D": "Incorrect. Substituting the stated va... | [
"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_005430 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 36 μF capacitor is charged to a potential difference of 7 V. Calculate the energy stored, expressed in μJ. | {
"A": "884 μJ",
"B": "-882 μJ",
"C": "1058.4 μJ",
"D": "882 μJ"
} | D | 882 μJ | U=½CV². Since C=36 μF, U in μJ is ½×36×(7)²=882 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 882 μJ, not 884 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 882 μJ, not -882 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 882 μJ, not 1058.4 μJ... | [
"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_003167 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(6+3i)/(12+7i). What is Re(z), the real part of z? | {
"A": "-1.51813",
"B": "0.24093",
"C": "0.3614",
"D": "0.48187"
} | D | 0.48187 | Multiply numerator and denominator by the conjugate (12-7i). Then Re(z)=(ac+bd)/(c²+d²)=((6)(12)+(3)(7))/(12²+(7)²)=0.48187. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.48187, not -1.51813.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.48187, not 0.24093.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.48187, not 0.36... | [
"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_000939 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 12 and common ratio 3. What is the sum of its first 12 terms? | {
"A": "3188640",
"B": "6377280",
"C": "318865",
"D": "2550912"
} | A | 3188640 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=12(3^12−1)/(3−1)=3188640. | {
"A": "Correct. The worked calculation gives 3188640.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3188640, not 6377280.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3188640, not 318865.",
"D": "Incorrect. Substituting the stated val... | [
"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_005703 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.5 atm at 192 K. What is its pressure at 221 K? | {
"A": "-1.42448 atm",
"B": "0.57552 atm",
"C": "1.15104 atm",
"D": "3.57552 atm"
} | B | 0.57552 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.5)(221)/(192)=0.57552 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.57552 atm, not -1.42448 atm.",
"B": "Correct. The worked calculation gives 0.57552 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.57552 atm, not 1.15104 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_000798 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio 3. What is the sum of its first 8 terms? | {
"A": "16398",
"B": "8200",
"C": "16402",
"D": "16400"
} | D | 16400 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(3^8−1)/(3−1)=16400. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16400, not 16398.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16400, not 8200.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16400, not 16402.",
"D": ... | [
"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_000153 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 -10x -5=0, let its roots be α and β. What is α²+β²? | {
"A": "7",
"B": "3",
"C": "4",
"D": "6"
} | D | 6 | By Vieta's relations, α+β = 10/5 and αβ = -5/5. Then α²+β²=(α+β)²−2αβ = (10/5)²−2(-5/5) = 6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.",
"D": "Correct. The worked ca... | [
"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_009913 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(CN)_5]^+3, each CN ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "11",
"B": "6",
"C": "9",
"D": "8"
} | D | 8 | Let the formal oxidation state of Co be x. Charge balance gives x+(5)(−1)=+3; hence x=3+5=+8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 11.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 9.",
"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_004175 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.38. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "22.2 N",
"B": "43.4 N",
"C": "44.4 N",
"D": "53.28 N"
} | C | 44.4 N | Net force=mg(sinθ−μcosθ)=15×10×(0.6−0.38×0.8)=44.4 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 44.4 N, not 22.2 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 44.4 N, not 43.4 N.",
"C": "Correct. The worked calculation gives 44.4 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_000726 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio 2. What is the sum of its first 10 terms? | {
"A": "6905.25",
"B": "4603.5",
"C": "9206",
"D": "9207"
} | D | 9207 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(2^10−1)/(2−1)=9207. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9207, not 6905.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9207, not 4603.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9207, not 9206.",
"D": ... | [
"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_001900 | 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 43 distinct elements? | {
"A": "3834669566",
"B": "1917334783",
"C": "1917334785",
"D": "1917334782"
} | B | 1917334783 | Order does not matter, so the count is C(43,10)=43!/[10!(33)!]=1917334783. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1917334783, not 3834669566.",
"B": "Correct. The worked calculation gives 1917334783.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1917334783, not 1917334785.",
"D": "Incorrect. Substitutin... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004049 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 16 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.40. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "35.84 N",
"B": "46.8 N",
"C": "44.8 N",
"D": "67.2 N"
} | C | 44.8 N | Net force=mg(sinθ−μcosθ)=16×10×(0.6−0.40×0.8)=44.8 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 44.8 N, not 35.84 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 44.8 N, not 46.8 N.",
"C": "Correct. The worked calculation gives 44.8 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_003833 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 7 m s⁻¹. A constant net force does 9 N of work over 8 m in the direction of motion. Find its final kinetic energy. | {
"A": "-170 J",
"B": "172 J",
"C": "168 J",
"D": "170 J"
} | D | 170 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(7)²+(9)(8)=170 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 170 J, not -170 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 170 J, not 172 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 170 J, not 168 J.",
"D"... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009261 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.46 V, transfers 2 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.5191 V",
"B": "3.0382 V",
"C": "1.15191 V",
"D": "0.75955 V"
} | A | 1.5191 V | Apply the Nernst equation: E=1.46−(0.0591/2)(-2)=1.5191 V. | {
"A": "Correct. The worked calculation gives 1.5191 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.5191 V, not 3.0382 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.5191 V, not 1.15191 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_006123 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 82 cm in front of a thin convex lens of focal length 27 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.49091",
"B": "2.49091",
"C": "0.36818",
"D": "3.49091"
} | A | 0.49091 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(82)(27)/(82−27)=40.25455 cm. Thus |m|=v/u=40.25455/82=0.49091. | {
"A": "Correct. The worked calculation gives 0.49091.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.49091, not 2.49091.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.49091, not 0.36818.",
"D": "Incorrect. Substituting the stated va... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003317 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-8-5i)/(3+4i). What is Re(z), the real part of z? | {
"A": "-4.76",
"B": "1.76",
"C": "-1.32",
"D": "-1.76"
} | D | -1.76 | Multiply numerator and denominator by the conjugate (3-4i). Then Re(z)=(ac+bd)/(c²+d²)=((-8)(3)+(-5)(4))/(3²+(4)²)=-1.76. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.76, not -4.76.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.76, not 1.76.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.76, not -1.32.",
"D": ... | [
"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_000681 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 3. What is the sum of its first 12 terms? | {
"A": "2657199",
"B": "2657200",
"C": "3985800",
"D": "2657202"
} | B | 2657200 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(3^12−1)/(3−1)=2657200. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2657200, not 2657199.",
"B": "Correct. The worked calculation gives 2657200.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2657200, not 3985800.",
"D": "Incorrect. Substituting the stated va... | [
"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_008055 | 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 8 A for 20482 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": "53.91117 g",
"B": "64.69341 g",
"C": "6.39112 g",
"D": "26.95559 g"
} | A | 53.91117 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×8×20482/(2×96500)=53.91117 g. | {
"A": "Correct. The worked calculation gives 53.91117 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 53.91117 g, not 64.69341 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 53.91117 g, not 6.39112 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_004283 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 32 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": "184.32 N",
"B": "91.16 N",
"C": "92.16 N",
"D": "69.12 N"
} | C | 92.16 N | Net force=mg(sinθ−μcosθ)=32×10×(0.6−0.39×0.8)=92.16 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 92.16 N, not 184.32 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 92.16 N, not 91.16 N.",
"C": "Correct. The worked calculation gives 92.16 N.",
"D": "Incorrect. Substituting the stated v... | [
"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_005724 | 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 3.1 atm at 262 K. What is its pressure at 580 K? | {
"A": "8.8626 atm",
"B": "4.8626 atm",
"C": "6.8626 atm",
"D": "13.72519 atm"
} | C | 6.8626 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.1)(580)/(262)=6.8626 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.8626 atm, not 8.8626 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.8626 atm, not 4.8626 atm.",
"C": "Correct. The worked calculation gives 6.8626 atm.",
"D": "Incorrect. Substitutin... | [
"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_001024 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ -4x² +4x+7. Evaluate f′(5). | {
"A": "-409",
"B": "-411",
"C": "-493.2",
"D": "-328.8"
} | B | -411 | Differentiate: f′(x)=3(-5)x²+2(-4)x+(4). At x=5, f′(5)=3(-5)(5)²+2(-4)(5)+(4)=-411. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -411, not -409.",
"B": "Correct. The worked calculation gives -411.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -411, not -493.2.",
"D": "Incorrect. Substituting the stated values into 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_005892 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.1 atm at 304 K. What is its pressure at 375 K? | {
"A": "-0.87664 atm",
"B": "-1.87664 atm",
"C": "0.24671 atm",
"D": "0.12336 atm"
} | D | 0.12336 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.1)(375)/(304)=0.12336 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.12336 atm, not -0.87664 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.12336 atm, not -1.87664 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives ... | [
"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_004067 | 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 0.31. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "16.136 N",
"B": "181.632 N",
"C": "151.36 N",
"D": "75.68 N"
} | C | 151.36 N | Net force=mg(sinθ−μcosθ)=43×10×(0.6−0.31×0.8)=151.36 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 151.36 N, not 16.136 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 151.36 N, not 181.632 N.",
"C": "Correct. The worked calculation gives 151.36 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_004633 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 10 kg and radius 6 m is acted on by a constant torque of 63 N m about its central axis. Find its angular acceleration. | {
"A": "0.35 rad s⁻²",
"B": "0.7 rad s⁻²",
"C": "2.35 rad s⁻²",
"D": "-0.65 rad s⁻²"
} | A | 0.35 rad s⁻² | For a solid disc, I=½MR²=½(10)(6)²=180 kg m². Using τ=Iα, α=63/180=0.35 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.35 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35 rad s⁻², not 0.7 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35 rad s⁻², not 2.35 rad s⁻².",
"D": "Incorrect. Su... | [
"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_008528 | 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 1.14 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.42 K",
"B": "-3.42 K",
"C": "6.84 K",
"D": "3.42 K"
} | D | 3.42 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×1.0×1.14=3.42 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.42 K, not 0.42 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.42 K, not -3.42 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.42 K, not 6.84 K.",... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003001 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, 9, -7) and v=(7, -7, 4), calculate u·v. | {
"A": "-84",
"B": "-86",
"C": "-82",
"D": "84"
} | A | -84 | The dot product is the sum of corresponding component products: (1)(7)+(9)(-7)+(-7)(4)=-84. | {
"A": "Correct. The worked calculation gives -84.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -84, not -86.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -84, not -82.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_001929 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 6 elements can be selected from a set of 49 distinct elements? | {
"A": "-13983816",
"B": "13983816",
"C": "13983818",
"D": "13983814"
} | B | 13983816 | Order does not matter, so the count is C(49,6)=49!/[6!(43)!]=13983816. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13983816, not -13983816.",
"B": "Correct. The worked calculation gives 13983816.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13983816, not 13983818.",
"D": "Incorrect. Substituting the sta... | [
"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_005017 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +7 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "2.75 N",
"B": "18.5 N",
"C": "14 N",
"D": "17.5 N"
} | D | 17.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(7×10⁻⁶)/(6×10⁻²)²=17.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 17.5 N, not 2.75 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17.5 N, not 18.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17.5 N, not 14 N.",
... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004489 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 3 m is acted on by a constant torque of 16 N m about its central axis. Find its angular acceleration. | {
"A": "3.44444 rad s⁻²",
"B": "-1.55556 rad s⁻²",
"C": "0.66667 rad s⁻²",
"D": "0.44444 rad s⁻²"
} | D | 0.44444 rad s⁻² | For a solid disc, I=½MR²=½(8)(3)²=36 kg m². Using τ=Iα, α=16/36=0.44444 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.44444 rad s⁻², not 3.44444 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.44444 rad s⁻², not -1.55556 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing ... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000727 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio 5. What is the sum of its first 6 terms? | {
"A": "31248",
"B": "62496",
"C": "31249",
"D": "15624"
} | A | 31248 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(5^6−1)/(5−1)=31248. | {
"A": "Correct. The worked calculation gives 31248.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 31248, not 62496.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 31248, not 31249.",
"D": "Incorrect. Substituting the stated values into ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003823 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 3 m s⁻¹. A constant net force does 21 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "133.5 J",
"B": "200.25 J",
"C": "267 J",
"D": "268 J"
} | C | 267 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(3)²+(21)(11)=267 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 267 J, not 133.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 267 J, not 200.25 J.",
"C": "Correct. The worked calculation gives 267 J.",
"D": "Incorrect. Substituting the stated values ... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007644 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 42 mL of 0.10 M HCl is mixed with 81 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.25012",
"B": "18.75174",
"C": "12.50116",
"D": "25.00232"
} | C | 12.50116 | Excess OH⁻ moles=0.10×(81−42)/1000=0.003900 mol. Total volume=0.123 L, so [OH⁻]=0.031707 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.50116. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.50116, not 2.25012.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.50116, not 18.75174.",
"C": "Correct. The worked calculation gives 12.50116.",
"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_000759 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio 3. What is the sum of its first 5 terms? | {
"A": "966",
"B": "1452",
"C": "968",
"D": "484"
} | C | 968 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(3^5−1)/(3−1)=968. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 968, not 966.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 968, not 1452.",
"C": "Correct. The worked calculation gives 968.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008208 | 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 4 A for 27145 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": "35.72451 g",
"B": "-35.72451 g",
"C": "71.44902 g",
"D": "34.72451 g"
} | A | 35.72451 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×27145/(2×96500)=35.72451 g. | {
"A": "Correct. The worked calculation gives 35.72451 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 35.72451 g, not -35.72451 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 35.72451 g, not 71.44902 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_002588 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, 5], [9, 3]]. | {
"A": "-42",
"B": "-44",
"C": "-41",
"D": "42"
} | A | -42 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(3)−(5)(9)=-42. | {
"A": "Correct. The worked calculation gives -42.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -42, not -44.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -42, not -41.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_002670 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, 5], [8, -8]]. | {
"A": "-55",
"B": "-54",
"C": "-4.6",
"D": "-56"
} | D | -56 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(-8)−(5)(8)=-56. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -56, not -55.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -56, not -54.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -56, not -4.6.",
"D": "Correct. ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008350 | 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 0.6 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "5.4 K",
"B": "1.24 K",
"C": "4.8 K",
"D": "2.4 K"
} | D | 2.4 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×1.0×0.6=2.4 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.4 K, not 5.4 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.4 K, not 1.24 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.4 K, not 4.8 K.",
"D"... | [
"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_004912 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 11 Ω and 5 Ω are connected in series; this combination is connected in parallel with a 9 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.08333 A",
"B": "3.125 A",
"C": "-2.08333 A",
"D": "1.08333 A"
} | A | 2.08333 A | Series branch resistance=11+5=16 Ω. Parallel equivalent R_eq=(16×9)/(16+9)=5.76 Ω. Total current I=V/R_eq=12/5.76=2.08333 A. | {
"A": "Correct. The worked calculation gives 2.08333 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.08333 A, not 3.125 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.08333 A, not -2.08333 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_009745 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(OH)_3]^-3, each OH ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "0",
"B": "-3",
"C": "1",
"D": "-1"
} | A | 0 | Let the formal oxidation state of Co be x. Charge balance gives x+(3)(−1)=-3; hence x=-3+3=+0. | {
"A": "Correct. The worked calculation gives 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"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_002987 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, 2, 6) and v=(-1, 5, 2), calculate u·v. | {
"A": "18",
"B": "14.4",
"C": "-18",
"D": "16"
} | A | 18 | The dot product is the sum of corresponding component products: (4)(-1)+(2)(5)+(6)(2)=18. | {
"A": "Correct. The worked calculation gives 18.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18, not 14.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18, not -18.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007878 | 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 55 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "1.28906 mmol L⁻¹",
"B": "1.71875 mmol L⁻¹",
"C": "3.71875 mmol L⁻¹",
"D": "2.71875 mmol L⁻¹"
} | B | 1.71875 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=55/2^5=1.71875 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.71875 mmol L⁻¹, not 1.28906 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 1.71875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.71875 mmol L⁻¹, not 3.71875 mmol L⁻¹.",
... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005117 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +8 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "112 N",
"B": "210 N",
"C": "280 N",
"D": "140 N"
} | D | 140 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(8×10⁻⁶)/(6×10⁻²)²=140 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 140 N, not 112 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 140 N, not 210 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 140 N, not 280 N.",
"D":... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009155 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.88 V, transfers 3 electrons, and has reaction quotient Q=10^2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.6812 V",
"B": "0.4203 V",
"C": "-0.1594 V",
"D": "0.8406 V"
} | D | 0.8406 V | Apply the Nernst equation: E=0.88−(0.0591/3)(2)=0.8406 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8406 V, not 1.6812 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8406 V, not 0.4203 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8406 V, not ... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001612 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (6x² +8x -5) dx. | {
"A": "172",
"B": "171",
"C": "18.2",
"D": "137.6"
} | A | 172 | An antiderivative is (6/3)x³+(8/2)x²+(-5)x. Evaluating between 0 and 4 gives (6/3)(4)³+(8/2)(4)²+(-5)(4)=172. | {
"A": "Correct. The worked calculation gives 172.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 172, not 171.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 172, not 18.2.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_006710 | 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 15 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "28 mol",
"B": "45 mol",
"C": "-30 mol",
"D": "30 mol"
} | D | 30 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 31 mol H₂O; O₂ can produce 30 mol H₂O. The limiting condition is O₂; product=30 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 30 mol, not 28 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30 mol, not 45 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30 mol, not -30 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_006705 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 47 mol H₂ and 19 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "4.8 mol",
"B": "38 mol",
"C": "28.5 mol",
"D": "-38 mol"
} | B | 38 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 47 mol H₂O; O₂ can produce 38 mol H₂O. The limiting condition is O₂; product=38 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 38 mol, not 4.8 mol.",
"B": "Correct. The worked calculation gives 38 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 38 mol, not 28.5 mol.",
"D": "Incorrect. Substituting the stated valu... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001641 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (-4x² -6x +0) dx. | {
"A": "-20.66667",
"B": "-22.66667",
"C": "-27.2",
"D": "-34"
} | B | -22.66667 | An antiderivative is (-4/3)x³+(-6/2)x²+(0)x. Evaluating between 0 and 2 gives (-4/3)(2)³+(-6/2)(2)²+(0)(2)=-22.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -22.66667, not -20.66667.",
"B": "Correct. The worked calculation gives -22.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -22.66667, not -27.2.",
"D": "Incorrect. Substituting the sta... | [
"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_008107 | 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 3 A for 1456 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": "4.43714 g",
"B": "-1.56286 g",
"C": "1.43714 g",
"D": "1.14371 g"
} | C | 1.43714 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×3×1456/(2×96500)=1.43714 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.43714 g, not 4.43714 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.43714 g, not -1.56286 g.",
"C": "Correct. The worked calculation gives 1.43714 g.",
"D": "Incorrect. Substituting th... | [
"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_006932 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 37 mol H₂ and 22 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "38 mol",
"B": "35 mol",
"C": "37 mol",
"D": "4.7 mol"
} | C | 37 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 37 mol H₂O; O₂ can produce 44 mol H₂O. The limiting condition is H₂; product=37 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 37 mol, not 38 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 37 mol, not 35 mol.",
"C": "Correct. The worked calculation gives 37 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_005370 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 58 μF capacitor is charged to a potential difference of 19 V. Calculate the energy stored, expressed in μJ. | {
"A": "10469 μJ",
"B": "12562.8 μJ",
"C": "10468 μJ",
"D": "7851.75 μJ"
} | A | 10469 μJ | U=½CV². Since C=58 μF, U in μJ is ½×58×(19)²=10469 μJ. | {
"A": "Correct. The worked calculation gives 10469 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10469 μJ, not 12562.8 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10469 μJ, not 10468 μJ.",
"D": "Incorrect. Substituting the st... | [
"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_001178 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ +8x² -12x+7. Evaluate f′(-4). | {
"A": "212",
"B": "318",
"C": "214",
"D": "169.6"
} | A | 212 | Differentiate: f′(x)=3(6)x²+2(8)x+(-12). At x=-4, f′(-4)=3(6)(-4)²+2(8)(-4)+(-12)=212. | {
"A": "Correct. The worked calculation gives 212.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 212, not 318.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 212, not 214.",
"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_004045 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 20 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.31. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "35.2 N",
"B": "-70.4 N",
"C": "70.4 N",
"D": "105.6 N"
} | C | 70.4 N | Net force=mg(sinθ−μcosθ)=20×10×(0.6−0.31×0.8)=70.4 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 70.4 N, not 35.2 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 70.4 N, not -70.4 N.",
"C": "Correct. The worked calculation gives 70.4 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_009520 | 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_4H_0X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "-3",
"B": "6",
"C": "3",
"D": "4.5"
} | C | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×4+2+0−0−4)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not -3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"C": "Correct. The worked calculation gives 3.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_000035 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 -2x +7=0, let its roots be α and β. What is α²+β²? | {
"A": "-3.16667",
"B": "-6.22222",
"C": "-4.22222",
"D": "-8.44444"
} | C | -4.22222 | By Vieta's relations, α+β = 2/3 and αβ = 7/3. Then α²+β²=(α+β)²−2αβ = (2/3)²−2(7/3) = -4.22222. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4.22222, not -3.16667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -4.22222, not -6.22222.",
"C": "Correct. The worked calculation gives -4.22222.",
"D": "Incorrect. Substituting the stat... | [
"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_006084 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 61 cm in front of a thin convex lens of focal length 17 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.38636",
"B": "0.38636",
"C": "0.19318",
"D": "2.38636"
} | B | 0.38636 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(61)(17)/(61−17)=23.56818 cm. Thus |m|=v/u=23.56818/61=0.38636. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.38636, not 1.38636.",
"B": "Correct. The worked calculation gives 0.38636.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.38636, not 0.19318.",
"D": "Incorrect. Substituting the stated va... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005911 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.3 atm at 312 K. What is its pressure at 575 K? | {
"A": "1.55288 atm",
"B": "0.55288 atm",
"C": "-0.55288 atm",
"D": "0.41466 atm"
} | B | 0.55288 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.3)(575)/(312)=0.55288 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.55288 atm, not 1.55288 atm.",
"B": "Correct. The worked calculation gives 0.55288 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.55288 atm, not -0.55288 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_004257 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 40 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": "104.4 N",
"B": "51.2 N",
"C": "76.8 N",
"D": "102.4 N"
} | D | 102.4 N | Net force=mg(sinθ−μcosθ)=40×10×(0.6−0.43×0.8)=102.4 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 102.4 N, not 104.4 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 102.4 N, not 51.2 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 102.4 N, not 76.8 N... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009082 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.13 V, transfers 2 electrons, and has reaction quotient Q=10^3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.10414 V",
"B": "3.04135 V",
"C": "-0.95865 V",
"D": "1.04135 V"
} | D | 1.04135 V | Apply the Nernst equation: E=1.13−(0.0591/2)(3)=1.04135 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.04135 V, not 1.10414 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.04135 V, not 3.04135 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.04135 V,... | [
"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_002264 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 5 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.35968",
"B": "1.03597",
"C": "1.35968",
"D": "0.26976"
} | A | 0.35968 | Favourable pairs = C(12,2)+C(5,2)+C(6,2)=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 1.03597.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35968, not 1.35968.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008838 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.33 mol L⁻¹ and initially B is absent. At equilibrium, 57% of A has dissociated at constant volume. Find K_c. | {
"A": "1.49605",
"B": "-2.00263",
"C": "-0.99737",
"D": "0.99737"
} | D | 0.99737 | Let α=0.57. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.33)(0.57)²/(1−0.57)=0.99737. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.99737, not 1.49605.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.99737, not -2.00263.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.99737, not -0.9... | [
"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_002464 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -5], [5, 2]]. | {
"A": "17.5",
"B": "70",
"C": "33",
"D": "35"
} | D | 35 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(2)−(-5)(5)=35. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 35, not 17.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 35, not 70.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 35, not 33.",
"D": "Correct. The w... | [
"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_004659 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 4 m is acted on by a constant torque of 43 N m about its central axis. Find its angular acceleration. | {
"A": "0.67188 rad s⁻²",
"B": "-2.32812 rad s⁻²",
"C": "1.06719 rad s⁻²",
"D": "1.34375 rad s⁻²"
} | A | 0.67188 rad s⁻² | For a solid disc, I=½MR²=½(8)(4)²=64 kg m². Using τ=Iα, α=43/64=0.67188 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.67188 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.67188 rad s⁻², not -2.32812 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.67188 rad s⁻², not 1.06719 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_002008 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 7 blue and 5 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.35145",
"B": "3.35145",
"C": "0.35145",
"D": "-2.64855"
} | C | 0.35145 | Favourable pairs = C(12,2)+C(7,2)+C(5,2)=97. Total pairs=C(24,2)=276. Therefore P=97/276=0.35145. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35145, not 1.35145.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35145, not 3.35145.",
"C": "Correct. The worked calculation gives 0.35145.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002483 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, 0], [3, -8]]. | {
"A": "-50",
"B": "-57.6",
"C": "-48",
"D": "-46"
} | C | -48 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(-8)−(0)(3)=-48. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -48, not -50.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -48, not -57.6.",
"C": "Correct. The worked calculation gives -48.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_004292 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 47 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.37. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "285.76 N",
"B": "114.304 N",
"C": "-142.88 N",
"D": "142.88 N"
} | D | 142.88 N | Net force=mg(sinθ−μcosθ)=47×10×(0.6−0.37×0.8)=142.88 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 142.88 N, not 285.76 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 142.88 N, not 114.304 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 142.88 N, not... | [
"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_000806 | 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 7 terms? | {
"A": "117187",
"B": "117186",
"C": "117188",
"D": "11719.6"
} | B | 117186 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(5^7−1)/(5−1)=117186. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 117186, not 117187.",
"B": "Correct. The worked calculation gives 117186.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 117186, not 117188.",
"D": "Incorrect. Substituting the stated values ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003645 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 66 m s⁻¹ at 15° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "108.9 m",
"B": "217.8 m",
"C": "218.8 m",
"D": "215.8 m"
} | B | 217.8 m | Range R=u²sin(2θ)/g. Substituting u=66, θ=15° and g=10 gives R=(66)²sin(30°)/10=217.8 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 217.8 m, not 108.9 m.",
"B": "Correct. The worked calculation gives 217.8 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 217.8 m, not 218.8 m.",
"D": "Incorrect. Substituting the stated va... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003297 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(7+9i)/(6+12i). What is Re(z), the real part of z? | {
"A": "-1.16667",
"B": "0.83333",
"C": "-0.16667",
"D": "2.83333"
} | B | 0.83333 | Multiply numerator and denominator by the conjugate (6-12i). Then Re(z)=(ac+bd)/(c²+d²)=((7)(6)+(9)(12))/(6²+(12)²)=0.83333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.83333, not -1.16667.",
"B": "Correct. The worked calculation gives 0.83333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.83333, not -0.16667.",
"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_008035 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 2 A for 20761 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": "14.66138 g",
"B": "13.66138 g",
"C": "2.36614 g",
"D": "10.24604 g"
} | B | 13.66138 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×2×20761/(2×96500)=13.66138 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13.66138 g, not 14.66138 g.",
"B": "Correct. The worked calculation gives 13.66138 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13.66138 g, not 2.36614 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_001697 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 3 elements can be selected from a set of 55 distinct elements? | {
"A": "19676.25",
"B": "26235",
"C": "26234",
"D": "52470"
} | B | 26235 | Order does not matter, so the count is C(55,3)=55!/[3!(52)!]=26235. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26235, not 19676.25.",
"B": "Correct. The worked calculation gives 26235.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26235, not 26234.",
"D": "Incorrect. Substituting the stated values in... | [
"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_005982 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.6 atm at 298 K. What is its pressure at 757 K? | {
"A": "1.52416 atm",
"B": "-1.52416 atm",
"C": "1.15242 atm",
"D": "0.52416 atm"
} | A | 1.52416 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.6)(757)/(298)=1.52416 atm. | {
"A": "Correct. The worked calculation gives 1.52416 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.52416 atm, not -1.52416 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.52416 atm, not 1.15242 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_007935 | 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 38 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "19 mmol L⁻¹",
"B": "38 mmol L⁻¹",
"C": "18 mmol L⁻¹",
"D": "17 mmol L⁻¹"
} | A | 19 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=38/2^1=19 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 19 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19 mmol L⁻¹, not 38 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19 mmol L⁻¹, not 18 mmol L⁻¹.",
"D": "Incorrect. Substi... | [
"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_002623 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -1], [7, 2]]. | {
"A": "8.5",
"B": "18",
"C": "16",
"D": "17"
} | D | 17 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(2)−(-1)(7)=17. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 17, not 8.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17, not 18.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17, not 16.",
"D": "Correct. The wo... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009819 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(CN)_2]^+2, each CN ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "1",
"B": "2",
"C": "4",
"D": "5"
} | C | 4 | Let the formal oxidation state of Cu be x. Charge balance gives x+(2)(−1)=+2; hence x=2+2=+4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"C": "Correct. The worked calculation gives 4.",
"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_005084 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +5 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "52 N",
"B": "6 N",
"C": "51 N",
"D": "50 N"
} | D | 50 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(5×10⁻⁶)/(3×10⁻²)²=50 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 50 N, not 52 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 50 N, not 6 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 50 N, not 51 N.",
"D": "Corre... | [
"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_002225 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 11 red, 8 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.03723",
"B": "0.37229",
"C": "-0.62771",
"D": "0.55844"
} | B | 0.37229 | Favourable pairs = C(11,2)+C(8,2)+C(3,2)=86. Total pairs=C(22,2)=231. Therefore P=86/231=0.37229. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.37229, not 1.03723.",
"B": "Correct. The worked calculation gives 0.37229.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.37229, not -0.62771.",
"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_008759 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.56 mol L⁻¹ and initially B is absent. At equilibrium, 59% of A has dissociated at constant volume. Find K_c. | {
"A": "4.90181",
"B": "1.90181",
"C": "0.95091",
"D": "1.19018"
} | B | 1.90181 | Let α=0.59. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.56)(0.59)²/(1−0.59)=1.90181. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.90181, not 4.90181.",
"B": "Correct. The worked calculation gives 1.90181.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.90181, not 0.95091.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008255 | 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 10 A for 19417 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": "63.88495 g",
"B": "95.82742 g",
"C": "47.91371 g",
"D": "62.88495 g"
} | A | 63.88495 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×10×19417/(2×96500)=63.88495 g. | {
"A": "Correct. The worked calculation gives 63.88495 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 63.88495 g, not 95.82742 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 63.88495 g, not 47.91371 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_002656 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, -8], [7, 7]]. | {
"A": "76",
"B": "8.7",
"C": "78",
"D": "77"
} | D | 77 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(7)−(-8)(7)=77. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 77, not 76.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 77, not 8.7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 77, not 78.",
"D": "Correct. The wo... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004494 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 5 m is acted on by a constant torque of 50 N m about its central axis. Find its angular acceleration. | {
"A": "1 rad s⁻²",
"B": "0.5 rad s⁻²",
"C": "0.25 rad s⁻²",
"D": "2.5 rad s⁻²"
} | B | 0.5 rad s⁻² | For a solid disc, I=½MR²=½(8)(5)²=100 kg m². Using τ=Iα, α=50/100=0.5 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5 rad s⁻², not 1 rad s⁻².",
"B": "Correct. The worked calculation gives 0.5 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5 rad s⁻², not 0.25 rad s⁻².",
"D": "Incorrect. Substit... | [
"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_005529 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 1 μF capacitor is charged to a potential difference of 23 V. Calculate the energy stored, expressed in μJ. | {
"A": "265.5 μJ",
"B": "132.25 μJ",
"C": "264.5 μJ",
"D": "27.45 μJ"
} | C | 264.5 μJ | U=½CV². Since C=1 μF, U in μJ is ½×1×(23)²=264.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 264.5 μJ, not 265.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 264.5 μJ, not 132.25 μJ.",
"C": "Correct. The worked calculation gives 264.5 μJ.",
"D": "Incorrect. Substituting the sta... | [
"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_004844 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 11 Ω are connected in series; this combination is connected in parallel with a 5 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "9 A",
"B": "4 A",
"C": "6 A",
"D": "8 A"
} | D | 8 A | Series branch resistance=4+11=15 Ω. Parallel equivalent R_eq=(15×5)/(15+5)=3.75 Ω. Total current I=V/R_eq=30/3.75=8 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8 A, not 9 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8 A, not 4 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8 A, not 6 A.",
"D": "Correct. T... | [
"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_002951 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, 3, 5) and v=(-1, 6, -5), calculate u·v. | {
"A": "-22",
"B": "11",
"C": "-11",
"D": "-14"
} | C | -11 | The dot product is the sum of corresponding component products: (4)(-1)+(3)(6)+(5)(-5)=-11. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -11, not -22.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -11, not 11.",
"C": "Correct. The worked calculation gives -11.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004910 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 20 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.63333 A",
"B": "1.26667 A",
"C": "-0.36667 A",
"D": "1.63333 A"
} | A | 0.63333 A | Series branch resistance=4+14=18 Ω. Parallel equivalent R_eq=(18×20)/(18+20)=9.47368 Ω. Total current I=V/R_eq=6/9.47368=0.63333 A. | {
"A": "Correct. The worked calculation gives 0.63333 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.63333 A, not 1.26667 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.63333 A, not -0.36667 A.",
"D": "Incorrect. Substituting th... | [
"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_001470 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (3x² +7x -1) dx. | {
"A": "18",
"B": "20",
"C": "15",
"D": "3"
} | B | 20 | An antiderivative is (3/3)x³+(7/2)x²+(-1)x. Evaluating between 0 and 2 gives (3/3)(2)³+(7/2)(2)²+(-1)(2)=20. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20, not 18.",
"B": "Correct. The worked calculation gives 20.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20, not 15.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_000847 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio -3. What is the sum of its first 8 terms? | {
"A": "-13120",
"B": "-13118",
"C": "-26240",
"D": "-1311"
} | A | -13120 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(-3^8−1)/(-3−1)=-13120. | {
"A": "Correct. The worked calculation gives -13120.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -13120, not -13118.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -13120, not -26240.",
"D": "Incorrect. Substituting the stated values ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000996 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio 4. What is the sum of its first 8 terms? | {
"A": "163837.5",
"B": "218450",
"C": "109225",
"D": "87380"
} | C | 109225 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(4^8−1)/(4−1)=109225. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 109225, not 163837.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 109225, not 218450.",
"C": "Correct. The worked calculation gives 109225.",
"D": "Incorrect. Substituting the stated value... | [
"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_001047 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ +6x² +5x+7. Evaluate f′(-1). | {
"A": "8",
"B": "5",
"C": "6",
"D": "10"
} | A | 8 | Differentiate: f′(x)=3(5)x²+2(6)x+(5). At x=-1, f′(-1)=3(5)(-1)²+2(6)(-1)+(5)=8. | {
"A": "Correct. The worked calculation gives 8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 6.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_003831 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 13 kg block initially moves at 4 m s⁻¹. A constant net force does 21 N of work over 6 m in the direction of motion. Find its final kinetic energy. | {
"A": "232 J",
"B": "228 J",
"C": "230 J",
"D": "345 J"
} | C | 230 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(13)(4)²+(21)(6)=230 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 230 J, not 232 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 230 J, not 228 J.",
"C": "Correct. The worked calculation gives 230 J.",
"D": "Incorrect. Substituting the stated values into ... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.