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_008858 | 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 0.66 mol L⁻¹ and initially B is absent. At equilibrium, 77% of A has dissociated at constant volume. Find K_c. | {
"A": "4.80546",
"B": "9.80546",
"C": "6.80546",
"D": "13.61092"
} | C | 6.80546 | Let α=0.77. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.66)(0.77)²/(1−0.77)=6.80546. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.80546, not 4.80546.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.80546, not 9.80546.",
"C": "Correct. The worked calculation gives 6.80546.",
"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_000254 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 +3x +12=0, let its roots be α and β. What is α²+β²? | {
"A": "-3.75",
"B": "-6.75",
"C": "-4.75",
"D": "3.75"
} | A | -3.75 | By Vieta's relations, α+β = -3/6 and αβ = 12/6. Then α²+β²=(α+β)²−2αβ = (-3/6)²−2(12/6) = -3.75. | {
"A": "Correct. The worked calculation gives -3.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -3.75, not -6.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -3.75, not -4.75.",
"D": "Incorrect. Substituting the stated values into ... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009897 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(CN)_5]^-3, each CN ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "2",
"B": "-1",
"C": "1",
"D": "-2"
} | A | 2 | Let the formal oxidation state of Fe be x. Charge balance gives x+(5)(−1)=-3; hence x=-3+5=+2. | {
"A": "Correct. The worked calculation gives 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not -1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 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_008680 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.23 mol L⁻¹ and initially B is absent. At equilibrium, 13% of A has dissociated at constant volume. Find K_c. | {
"A": "0.04779",
"B": "0.09557",
"C": "-0.09557",
"D": "0.19114"
} | B | 0.09557 | Let α=0.13. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.23)(0.13)²/(1−0.13)=0.09557. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.09557, not 0.04779.",
"B": "Correct. The worked calculation gives 0.09557.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.09557, not -0.09557.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002072 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 4 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.78363",
"B": "-1.60819",
"C": "3.39181",
"D": "0.39181"
} | D | 0.39181 | Favourable pairs = C(4,2)+C(4,2)+C(11,2)=67. Total pairs=C(19,2)=171. Therefore P=67/171=0.39181. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.39181, not 0.78363.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.39181, not -1.60819.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.39181, not 3.39... | [
"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_000236 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 +8x +10=0, let its roots be α and β. What is α²+β²? | {
"A": "66",
"B": "43",
"C": "44",
"D": "52.8"
} | C | 44 | By Vieta's relations, α+β = -8/1 and αβ = 10/1. Then α²+β²=(α+β)²−2αβ = (-8/1)²−2(10/1) = 44. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 44, not 66.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 44, not 43.",
"C": "Correct. The worked calculation gives 44.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_004020 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.14. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "14.64 N",
"B": "7.76 N",
"C": "-9.76 N",
"D": "9.76 N"
} | D | 9.76 N | Net force=mg(sinθ−μcosθ)=2×10×(0.6−0.14×0.8)=9.76 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.76 N, not 14.64 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.76 N, not 7.76 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.76 N, not -9.76 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_006469 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 11 kg is attached to an ideal spring of force constant 80 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.25838 s",
"B": "1.07416 s",
"C": "1.11243 s",
"D": "0.74162 s"
} | D | 0.74162 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(11/80)=0.74162 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.74162 s, not -2.25838 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.74162 s, not 1.07416 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.74162 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006872 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 9 mol H₂ and 25 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "6 mol",
"B": "11 mol",
"C": "7 mol",
"D": "9 mol"
} | D | 9 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 9 mol H₂O; O₂ can produce 50 mol H₂O. The limiting condition is H₂; product=9 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9 mol, not 6 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9 mol, not 11 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9 mol, not 7 mol.",
"D"... | [
"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_009338 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_15H_9N_3X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "11",
"B": "8.25",
"C": "2.1",
"D": "10"
} | A | 11 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×15+2+3−9−4)/2=11. | {
"A": "Correct. The worked calculation gives 11.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11, not 8.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11, not 2.1.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_009944 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(CN)_2]^+2, each CN ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "8",
"B": "4",
"C": "2",
"D": "-4"
} | B | 4 | Let the formal oxidation state of Ni 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 8.",
"B": "Correct. The worked calculation gives 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"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_004418 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 2 m is acted on by a constant torque of 99 N m about its central axis. Find its angular acceleration. | {
"A": "-6.1875 rad s⁻²",
"B": "3.1875 rad s⁻²",
"C": "7.1875 rad s⁻²",
"D": "6.1875 rad s⁻²"
} | D | 6.1875 rad s⁻² | For a solid disc, I=½MR²=½(8)(2)²=16 kg m². Using τ=Iα, α=99/16=6.1875 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.1875 rad s⁻², not -6.1875 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.1875 rad s⁻², not 3.1875 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing rela... | [
"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_001662 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (2x² +7x -4) dx. | {
"A": "246",
"B": "295.2",
"C": "-246",
"D": "248"
} | A | 246 | An antiderivative is (2/3)x³+(7/2)x²+(-4)x. Evaluating between 0 and 6 gives (2/3)(6)³+(7/2)(6)²+(-4)(6)=246. | {
"A": "Correct. The worked calculation gives 246.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 246, not 295.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 246, not -246.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008526 | 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 1.02 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "4.04448 K",
"B": "1.04448 K",
"C": "0.52224 K",
"D": "1.56672 K"
} | B | 1.04448 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×1.02=1.04448 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.04448 K, not 4.04448 K.",
"B": "Correct. The worked calculation gives 1.04448 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.04448 K, not 0.52224 K.",
"D": "Incorrect. Substituting the... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000030 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 -10x -7=0, let its roots be α and β. What is α²+β²? | {
"A": "6.8",
"B": "9.8",
"C": "1.68",
"D": "3.4"
} | A | 6.8 | By Vieta's relations, α+β = 10/5 and αβ = -7/5. Then α²+β²=(α+β)²−2αβ = (10/5)²−2(-7/5) = 6.8. | {
"A": "Correct. The worked calculation gives 6.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.8, not 9.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.8, not 1.68.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_008293 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 13 A for 5241 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": "21.41682 g",
"B": "24.41682 g",
"C": "22.41682 g",
"D": "-22.41682 g"
} | C | 22.41682 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×5241/(2×96500)=22.41682 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22.41682 g, not 21.41682 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22.41682 g, not 24.41682 g.",
"C": "Correct. The worked calculation gives 22.41682 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_001728 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 7 elements can be selected from a set of 40 distinct elements? | {
"A": "27965340",
"B": "18643560",
"C": "22372272",
"D": "-18643560"
} | B | 18643560 | Order does not matter, so the count is C(40,7)=40!/[7!(33)!]=18643560. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18643560, not 27965340.",
"B": "Correct. The worked calculation gives 18643560.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18643560, not 22372272.",
"D": "Incorrect. Substituting the stat... | [
"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_006610 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 20 kg is attached to an ideal spring of force constant 843 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.30806 s",
"B": "0.61611 s",
"C": "2.30806 s",
"D": "-0.69194 s"
} | A | 0.30806 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(20/843)=0.30806 s. | {
"A": "Correct. The worked calculation gives 0.30806 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30806 s, not 0.61611 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30806 s, not 2.30806 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005714 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.2 atm at 437 K. What is its pressure at 750 K? | {
"A": "-0.34325 atm",
"B": "0.25744 atm",
"C": "-2.65675 atm",
"D": "0.34325 atm"
} | D | 0.34325 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.2)(750)/(437)=0.34325 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34325 atm, not -0.34325 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34325 atm, not 0.25744 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008663 | 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 1.58 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-1.19104 K",
"B": "0.60672 K",
"C": "-0.80896 K",
"D": "0.80896 K"
} | D | 0.80896 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.512×1.58=0.80896 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.80896 K, not -1.19104 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.80896 K, not 0.60672 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.80896 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_004414 | 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 56 N m about its central axis. Find its angular acceleration. | {
"A": "1.0875 rad s⁻²",
"B": "-0.125 rad s⁻²",
"C": "3.875 rad s⁻²",
"D": "0.875 rad s⁻²"
} | D | 0.875 rad s⁻² | For a solid disc, I=½MR²=½(8)(4)²=64 kg m². Using τ=Iα, α=56/64=0.875 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.875 rad s⁻², not 1.0875 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.875 rad s⁻², not -0.125 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relatio... | [
"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_000957 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio 2. What is the sum of its first 5 terms? | {
"A": "188",
"B": "186",
"C": "185",
"D": "148.8"
} | B | 186 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(2^5−1)/(2−1)=186. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 186, not 188.",
"B": "Correct. The worked calculation gives 186.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 186, not 185.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_005698 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.2 atm at 262 K. What is its pressure at 417 K? | {
"A": "1.90992 atm",
"B": "-1.90992 atm",
"C": "1.43244 atm",
"D": "2.86489 atm"
} | A | 1.90992 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.2)(417)/(262)=1.90992 atm. | {
"A": "Correct. The worked calculation gives 1.90992 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.90992 atm, not -1.90992 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.90992 atm, not 1.43244 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_003428 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 93 m s⁻¹ at 70° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "277.9735 m",
"B": "553.947 m",
"C": "555.947 m",
"D": "1111.89401 m"
} | C | 555.947 m | Range R=u²sin(2θ)/g. Substituting u=93, θ=70° and g=10 gives R=(93)²sin(140°)/10=555.947 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 555.947 m, not 277.9735 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 555.947 m, not 553.947 m.",
"C": "Correct. The worked calculation gives 555.947 m.",
"D": "Incorrect. Substituting th... | [
"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_001090 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ +1x² -3x+7. Evaluate f′(2). | {
"A": "74",
"B": "58.4",
"C": "73",
"D": "109.5"
} | C | 73 | Differentiate: f′(x)=3(6)x²+2(1)x+(-3). At x=2, f′(2)=3(6)(2)²+2(1)(2)+(-3)=73. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 73, not 74.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 73, not 58.4.",
"C": "Correct. The worked calculation gives 73.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004698 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 11 Ω and 3 Ω are connected in series; this combination is connected in parallel with a 14 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.57143 A",
"B": "3.57143 A",
"C": "2.57143 A",
"D": "0.57143 A"
} | C | 2.57143 A | Series branch resistance=11+3=14 Ω. Parallel equivalent R_eq=(14×14)/(14+14)=7 Ω. Total current I=V/R_eq=18/7=2.57143 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.57143 A, not 4.57143 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.57143 A, not 3.57143 A.",
"C": "Correct. The worked calculation gives 2.57143 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_007937 | 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 92 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "46 mmol L⁻¹",
"B": "23 mmol L⁻¹",
"C": "18.4 mmol L⁻¹",
"D": "21 mmol L⁻¹"
} | B | 23 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=92/2^2=23 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 23 mmol L⁻¹, not 46 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 23 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23 mmol L⁻¹, not 18.4 mmol L⁻¹.",
"D": "Incorrect. Subs... | [
"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_002408 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, 2], [2, 4]]. | {
"A": "7",
"B": "3",
"C": "4",
"D": "6"
} | C | 4 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(4)−(2)(2)=4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 3.",
"C": "Correct. The worked calculation gives 4.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_007929 | 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 25 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "0.19531 mmol L⁻¹",
"B": "1.01953 mmol L⁻¹",
"C": "-1.80469 mmol L⁻¹",
"D": "-0.80469 mmol L⁻¹"
} | A | 0.19531 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=25/2^7=0.19531 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 0.19531 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.19531 mmol L⁻¹, not 1.01953 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.19531 mmol L⁻¹, not -1.80469 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_006565 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 13 kg is attached to an ideal spring of force constant 206 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.49758 s",
"B": "0.25121 s",
"C": "-2.49758 s",
"D": "0.50242 s"
} | D | 0.50242 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(13/206)=0.50242 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.50242 s, not -0.49758 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.50242 s, not 0.25121 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.50242 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007347 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 52 mL of 0.10 M HCl is mixed with 86 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "11.3916",
"B": "6.1958",
"C": "2.23916",
"D": "12.3916"
} | D | 12.3916 | Excess OH⁻ moles=0.10×(86−52)/1000=0.003400 mol. Total volume=0.138 L, so [OH⁻]=0.024638 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.3916. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.3916, not 11.3916.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.3916, not 6.1958.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.3916, not 2.2391... | [
"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_001993 | 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 75 distinct elements? | {
"A": "828931106357",
"B": "828931106355",
"C": "621698329766.25",
"D": "663144885084"
} | B | 828931106355 | Order does not matter, so the count is C(75,10)=75!/[10!(65)!]=828931106355. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 828931106355, not 828931106357.",
"B": "Correct. The worked calculation gives 828931106355.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 828931106355, not 621698329766.25.",
"D": "Incorrect... | [
"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_008213 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 12 A for 17168 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": "50.83685 g",
"B": "68.78247 g",
"C": "67.78247 g",
"D": "-67.78247 g"
} | C | 67.78247 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×12×17168/(2×96500)=67.78247 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 67.78247 g, not 50.83685 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 67.78247 g, not 68.78247 g.",
"C": "Correct. The worked calculation gives 67.78247 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_004699 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 9 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.69697 A",
"B": "4.69697 A",
"C": "-4.69697 A",
"D": "9.39394 A"
} | B | 4.69697 A | Series branch resistance=8+14=22 Ω. Parallel equivalent R_eq=(22×9)/(22+9)=6.3871 Ω. Total current I=V/R_eq=30/6.3871=4.69697 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.69697 A, not 2.69697 A.",
"B": "Correct. The worked calculation gives 4.69697 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.69697 A, not -4.69697 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_002320 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 3 blue and 8 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.35263",
"B": "0.52895",
"C": "0.35263",
"D": "-0.35263"
} | C | 0.35263 | Favourable pairs = C(9,2)+C(3,2)+C(8,2)=67. Total pairs=C(20,2)=190. Therefore P=67/190=0.35263. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35263, not 1.35263.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35263, not 0.52895.",
"C": "Correct. The worked calculation gives 0.35263.",
"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_005007 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +6 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "33.75 N",
"B": "50.625 N",
"C": "67.5 N",
"D": "65.5 N"
} | C | 67.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(6×10⁻⁶)/(4×10⁻²)²=67.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 67.5 N, not 33.75 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 67.5 N, not 50.625 N.",
"C": "Correct. The worked calculation gives 67.5 N.",
"D": "Incorrect. Substituting the stated valu... | [
"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_003329 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-10+2i)/(9+4i). What is Re(z), the real part of z? | {
"A": "-1.26804",
"B": "0.84536",
"C": "-0.84536",
"D": "-0.63402"
} | C | -0.84536 | Multiply numerator and denominator by the conjugate (9-4i). Then Re(z)=(ac+bd)/(c²+d²)=((-10)(9)+(2)(4))/(9²+(4)²)=-0.84536. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.84536, not -1.26804.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.84536, not 0.84536.",
"C": "Correct. The worked calculation gives -0.84536.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001236 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=2x³ -10x² +1x+7. Evaluate f′(1). | {
"A": "-19.5",
"B": "13",
"C": "-13",
"D": "-14"
} | C | -13 | Differentiate: f′(x)=3(2)x²+2(-10)x+(1). At x=1, f′(1)=3(2)(1)²+2(-10)(1)+(1)=-13. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -13, not -19.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -13, not 13.",
"C": "Correct. The worked calculation gives -13.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009999 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(CN)_6]^+1, each CN ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "14",
"B": "7",
"C": "4",
"D": "8"
} | B | 7 | Let the formal oxidation state of Cu be x. Charge balance gives x+(6)(−1)=+1; hence x=1+6=+7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 14.",
"B": "Correct. The worked calculation gives 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 4.",
"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_007092 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 4 mol of gas at 198 K and 1.61 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "40.36593 L",
"B": "60.54889 L",
"C": "38.36593 L",
"D": "5.03659 L"
} | A | 40.36593 L | PV=nRT, so V=nRT/P=(4)(0.082057)(198)/(1.61)=40.36593 L. | {
"A": "Correct. The worked calculation gives 40.36593 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 40.36593 L, not 60.54889 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 40.36593 L, not 38.36593 L.",
"D": "Incorrect. Substitutin... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006676 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 21 mol H₂ and 30 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "20 mol",
"B": "25.2 mol",
"C": "21 mol",
"D": "-21 mol"
} | C | 21 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 21 mol H₂O; O₂ can produce 60 mol H₂O. The limiting condition is H₂; product=21 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21 mol, not 20 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21 mol, not 25.2 mol.",
"C": "Correct. The worked calculation gives 21 mol.",
"D": "Incorrect. Substituting the stated value... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002597 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, -2], [3, -5]]. | {
"A": "-11",
"B": "14",
"C": "-14",
"D": "-17"
} | C | -14 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(-5)−(-2)(3)=-14. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -14, not -11.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -14, not 14.",
"C": "Correct. The worked calculation gives -14.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008983 | 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 0.64 mol L⁻¹ and initially B is absent. At equilibrium, 46% of A has dissociated at constant volume. Find K_c. | {
"A": "1.10031",
"B": "-0.99686",
"C": "1.00314",
"D": "1.50471"
} | C | 1.00314 | Let α=0.46. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.64)(0.46)²/(1−0.46)=1.00314. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.00314, not 1.10031.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.00314, not -0.99686.",
"C": "Correct. The worked calculation gives 1.00314.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000819 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio 2. What is the sum of its first 12 terms? | {
"A": "12285",
"B": "24569",
"C": "19656",
"D": "24570"
} | D | 24570 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(2^12−1)/(2−1)=24570. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24570, not 12285.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24570, not 24569.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24570, not 19656.",
"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_003252 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(11+13i)/(6+8i). What is Re(z), the real part of z? | {
"A": "2.7",
"B": "3.4",
"C": "1.7",
"D": "3.7"
} | C | 1.7 | Multiply numerator and denominator by the conjugate (6-8i). Then Re(z)=(ac+bd)/(c²+d²)=((11)(6)+(13)(8))/(6²+(8)²)=1.7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.7, not 2.7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.7, not 3.4.",
"C": "Correct. The worked calculation gives 1.7.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_004152 | 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 0.11. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "221.16 N",
"B": "23.016 N",
"C": "220.16 N",
"D": "222.16 N"
} | C | 220.16 N | Net force=mg(sinθ−μcosθ)=43×10×(0.6−0.11×0.8)=220.16 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 220.16 N, not 221.16 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 220.16 N, not 23.016 N.",
"C": "Correct. The worked calculation gives 220.16 N.",
"D": "Incorrect. Substituting the stat... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004326 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 19 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.26. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "73.48 N",
"B": "89.376 N",
"C": "76.48 N",
"D": "74.48 N"
} | D | 74.48 N | Net force=mg(sinθ−μcosθ)=19×10×(0.6−0.26×0.8)=74.48 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 74.48 N, not 73.48 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 74.48 N, not 89.376 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 74.48 N, not 76.4... | [
"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_001213 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ +5x² +9x+7. Evaluate f′(3). | {
"A": "87",
"B": "130.5",
"C": "174",
"D": "348"
} | C | 174 | Differentiate: f′(x)=3(5)x²+2(5)x+(9). At x=3, f′(3)=3(5)(3)²+2(5)(3)+(9)=174. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 174, not 87.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 174, not 130.5.",
"C": "Correct. The worked calculation gives 174.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004677 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 13 Ω are connected in series; this combination is connected in parallel with a 12 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.2 A",
"B": "6.2 A",
"C": "0.2 A",
"D": "3.2 A"
} | D | 3.2 A | Series branch resistance=7+13=20 Ω. Parallel equivalent R_eq=(20×12)/(20+12)=7.5 Ω. Total current I=V/R_eq=24/7.5=3.2 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.2 A, not 1.2 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.2 A, not 6.2 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.2 A, not 0.2 A.",
"D":... | [
"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_004748 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 15 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 12 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.12069 A",
"B": "2.12069 A",
"C": "4.12069 A",
"D": "1.06034 A"
} | B | 2.12069 A | Series branch resistance=15+14=29 Ω. Parallel equivalent R_eq=(29×12)/(29+12)=8.4878 Ω. Total current I=V/R_eq=18/8.4878=2.12069 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.12069 A, not 1.12069 A.",
"B": "Correct. The worked calculation gives 2.12069 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.12069 A, not 4.12069 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_009355 | 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_12H_19N_1X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "1",
"C": "0",
"D": "4"
} | A | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×12+2+1−19−2)/2=3. | {
"A": "Correct. The worked calculation gives 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 0.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006961 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 27 mol H₂ and 14 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "32.4 mol",
"B": "25 mol",
"C": "27 mol",
"D": "21.6 mol"
} | C | 27 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 27 mol H₂O; O₂ can produce 28 mol H₂O. The limiting condition is H₂; product=27 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 27 mol, not 32.4 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 27 mol, not 25 mol.",
"C": "Correct. The worked calculation gives 27 mol.",
"D": "Incorrect. Substituting the stated value... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003212 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(13+11i)/(2+3i). What is Re(z), the real part of z? | {
"A": "-4.53846",
"B": "4.53846",
"C": "1.45385",
"D": "3.53846"
} | B | 4.53846 | Multiply numerator and denominator by the conjugate (2-3i). Then Re(z)=(ac+bd)/(c²+d²)=((13)(2)+(11)(3))/(2²+(3)²)=4.53846. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.53846, not -4.53846.",
"B": "Correct. The worked calculation gives 4.53846.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.53846, not 1.45385.",
"D": "Incorrect. Substituting the stated v... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001387 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (3x² +8x +0) dx. | {
"A": "94.5",
"B": "65",
"C": "63",
"D": "62"
} | C | 63 | An antiderivative is (3/3)x³+(8/2)x²+(0)x. Evaluating between 0 and 3 gives (3/3)(3)³+(8/2)(3)²+(0)(3)=63. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 63, not 94.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 63, not 65.",
"C": "Correct. The worked calculation gives 63.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004556 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 4 kg and radius 4 m is acted on by a constant torque of 90 N m about its central axis. Find its angular acceleration. | {
"A": "2.8125 rad s⁻²",
"B": "0.8125 rad s⁻²",
"C": "1.8125 rad s⁻²",
"D": "4.21875 rad s⁻²"
} | A | 2.8125 rad s⁻² | For a solid disc, I=½MR²=½(4)(4)²=32 kg m². Using τ=Iα, α=90/32=2.8125 rad s⁻². | {
"A": "Correct. The worked calculation gives 2.8125 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.8125 rad s⁻², not 0.8125 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.8125 rad s⁻², not 1.8125 rad s⁻².",
"D": "In... | [
"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_001465 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (0x² -6x +5) dx. | {
"A": "-2",
"B": "-3",
"C": "-5",
"D": "-4"
} | A | -2 | An antiderivative is (0/3)x³+(-6/2)x²+(5)x. Evaluating between 0 and 2 gives (0/3)(2)³+(-6/2)(2)²+(5)(2)=-2. | {
"A": "Correct. The worked calculation gives -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2, not -3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2, not -5.",
"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_005282 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +3 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "59.5102 N",
"B": "48.59184 N",
"C": "49.59184 N",
"D": "74.38776 N"
} | C | 49.59184 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(3×10⁻⁶)/(7×10⁻²)²=49.59184 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 49.59184 N, not 59.5102 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 49.59184 N, not 48.59184 N.",
"C": "Correct. The worked calculation gives 49.59184 N.",
"D": "Incorrect. Substituting... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009439 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_3H_11N_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "0",
"B": "1",
"C": "2",
"D": "3"
} | A | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×3+2+3−11−0)/2=0. | {
"A": "Correct. The worked calculation gives 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 2.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002913 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-7, -6, 4) and v=(1, -5, 4), calculate u·v. | {
"A": "39",
"B": "46.8",
"C": "38",
"D": "58.5"
} | A | 39 | The dot product is the sum of corresponding component products: (-7)(1)+(-6)(-5)+(4)(4)=39. | {
"A": "Correct. The worked calculation gives 39.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39, not 46.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39, not 38.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008891 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.03 mol L⁻¹ and initially B is absent. At equilibrium, 76% of A has dissociated at constant volume. Find K_c. | {
"A": "6.91547",
"B": "11.91547",
"C": "4.95773",
"D": "9.91547"
} | D | 9.91547 | Let α=0.76. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.03)(0.76)²/(1−0.76)=9.91547. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.91547, not 6.91547.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.91547, not 11.91547.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.91547, not 4.95... | [
"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_008530 | 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 0.17 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.592 K",
"B": "-0.408 K",
"C": "-2.592 K",
"D": "0.408 K"
} | D | 0.408 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.6×0.17=0.408 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.408 K, not -0.592 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.408 K, not -0.408 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.408 K, not -2.... | [
"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_006283 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 101 cm in front of a thin convex lens of focal length 22 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.02785",
"B": "0.27848",
"C": "-0.27848",
"D": "0.55696"
} | B | 0.27848 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(101)(22)/(101−22)=28.12658 cm. Thus |m|=v/u=28.12658/101=0.27848. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.27848, not 1.02785.",
"B": "Correct. The worked calculation gives 0.27848.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.27848, not -0.27848.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002641 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, -8], [7, 0]]. | {
"A": "58",
"B": "56",
"C": "84",
"D": "57"
} | B | 56 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(0)−(-8)(7)=56. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 56, not 58.",
"B": "Correct. The worked calculation gives 56.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 56, not 84.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000581 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -12 and common difference 10. Find the sum of its first 29 terms. | {
"A": "5568",
"B": "7424",
"C": "3711",
"D": "3712"
} | D | 3712 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-12, d=10, n=29: Sₙ=29/2[2(-12)+(29−1)(10)]=3712. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3712, not 5568.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3712, not 7424.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3712, not 3711.",
"D": "Corr... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003294 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(6+0i)/(8+3i). What is Re(z), the real part of z? | {
"A": "0.65753",
"B": "1.06575",
"C": "-0.65753",
"D": "-1.34247"
} | A | 0.65753 | Multiply numerator and denominator by the conjugate (8-3i). Then Re(z)=(ac+bd)/(c²+d²)=((6)(8)+(0)(3))/(8²+(3)²)=0.65753. | {
"A": "Correct. The worked calculation gives 0.65753.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.65753, not 1.06575.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.65753, not -0.65753.",
"D": "Incorrect. Substituting the stated v... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008920 | 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 0.83 mol L⁻¹ and initially B is absent. At equilibrium, 73% of A has dissociated at constant volume. Find K_c. | {
"A": "3.5527",
"B": "-6.5527",
"C": "6.5527",
"D": "13.10539"
} | C | 6.5527 | Let α=0.73. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.83)(0.73)²/(1−0.73)=6.5527. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.5527, not 3.5527.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.5527, not -6.5527.",
"C": "Correct. The worked calculation gives 6.5527.",
"D": "Incorrect. Substituting the stated values... | [
"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_000485 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 24 and common difference 12. Find the sum of its first 8 terms. | {
"A": "422.4",
"B": "53.8",
"C": "528",
"D": "633.6"
} | C | 528 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=24, d=12, n=8: Sₙ=8/2[2(24)+(8−1)(12)]=528. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 528, not 422.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 528, not 53.8.",
"C": "Correct. The worked calculation gives 528.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006703 | 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 20 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "18.5 mol",
"B": "37 mol",
"C": "39 mol",
"D": "4.7 mol"
} | B | 37 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 37 mol H₂O; O₂ can produce 40 mol H₂O. The limiting condition is H₂; product=37 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 37 mol, not 18.5 mol.",
"B": "Correct. The worked calculation gives 37 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 37 mol, not 39 mol.",
"D": "Incorrect. Substituting the stated value... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009062 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.77 V, transfers 3 electrons, and has reaction quotient Q=10^3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.7109 V",
"B": "0.7109 V",
"C": "3.7109 V",
"D": "1.07109 V"
} | B | 0.7109 V | Apply the Nernst equation: E=0.77−(0.0591/3)(3)=0.7109 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7109 V, not -0.7109 V.",
"B": "Correct. The worked calculation gives 0.7109 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7109 V, not 3.7109 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_008473 | 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 0.05 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.0375 K",
"B": "0.05 K",
"C": "1.05 K",
"D": "2.05 K"
} | B | 0.05 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×1.0×0.05=0.05 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.05 K, not 0.0375 K.",
"B": "Correct. The worked calculation gives 0.05 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.05 K, not 1.05 K.",
"D": "Incorrect. Substituting the stated value... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001874 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 75 distinct elements? | {
"A": "12944542.5",
"B": "17259391",
"C": "20711268",
"D": "17259390"
} | D | 17259390 | Order does not matter, so the count is C(75,5)=75!/[5!(70)!]=17259390. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 17259390, not 12944542.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17259390, not 17259391.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17259390, no... | [
"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_004752 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 6 Ω are connected in series; this combination is connected in parallel with a 17 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.88688 A",
"B": "2.88688 A",
"C": "1.48869 A",
"D": "7.33032 A"
} | A | 4.88688 A | Series branch resistance=7+6=13 Ω. Parallel equivalent R_eq=(13×17)/(13+17)=7.36667 Ω. Total current I=V/R_eq=36/7.36667=4.88688 A. | {
"A": "Correct. The worked calculation gives 4.88688 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.88688 A, not 2.88688 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.88688 A, not 1.48869 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_008525 | 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 0.8 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": "1.48 K",
"B": "0.48 K",
"C": "-2.52 K",
"D": "0.24 K"
} | B | 0.48 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.6×0.8=0.48 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.48 K, not 1.48 K.",
"B": "Correct. The worked calculation gives 0.48 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.48 K, not -2.52 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009088 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.57 V, transfers 3 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.6291 V",
"B": "-0.6291 V",
"C": "1.2582 V",
"D": "3.6291 V"
} | A | 0.6291 V | Apply the Nernst equation: E=0.57−(0.0591/3)(-3)=0.6291 V. | {
"A": "Correct. The worked calculation gives 0.6291 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6291 V, not -0.6291 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.6291 V, not 1.2582 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_006005 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 68 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": "-0.34146",
"B": "0.65854",
"C": "0.9878",
"D": "1.06585"
} | B | 0.65854 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(68)(27)/(68−27)=44.78049 cm. Thus |m|=v/u=44.78049/68=0.65854. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.65854, not -0.34146.",
"B": "Correct. The worked calculation gives 0.65854.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.65854, not 0.9878.",
"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_005510 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 74 μF capacitor is charged to a potential difference of 10 V. Calculate the energy stored, expressed in μJ. | {
"A": "3702 μJ",
"B": "5550 μJ",
"C": "3700 μJ",
"D": "371 μJ"
} | C | 3700 μJ | U=½CV². Since C=74 μF, U in μJ is ½×74×(10)²=3700 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3700 μJ, not 3702 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3700 μJ, not 5550 μJ.",
"C": "Correct. The worked calculation gives 3700 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007580 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 90 mL of 0.10 M HCl is mixed with 54 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.16021",
"B": "0.80103",
"C": "1.60206",
"D": "2.60206"
} | C | 1.60206 | Excess H⁺ moles=0.10×(90−54)/1000=0.003600 mol. Total volume=0.144 L, so [H⁺]=0.025000 M and pH=−log₁₀[H⁺]=1.60206. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.60206, not 1.16021.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.60206, not 0.80103.",
"C": "Correct. The worked calculation gives 1.60206.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008508 | 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 0.61 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "3.24928 K",
"B": "1.12493 K",
"C": "0.93696 K",
"D": "1.24928 K"
} | D | 1.24928 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.512×0.61=1.24928 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.24928 K, not 3.24928 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.24928 K, not 1.12493 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.24928 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_006468 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 14 kg is attached to an ideal spring of force constant 589 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.15417 s",
"B": "0.30834 s",
"C": "1.03083 s",
"D": "1.30834 s"
} | B | 0.30834 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(14/589)=0.30834 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30834 s, not 0.15417 s.",
"B": "Correct. The worked calculation gives 0.30834 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30834 s, not 1.03083 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002801 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, 1, -7) and v=(-7, 0, 0), calculate u·v. | {
"A": "-6",
"B": "-7",
"C": "-4",
"D": "0.3"
} | B | -7 | The dot product is the sum of corresponding component products: (1)(-7)+(1)(0)+(-7)(0)=-7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -7, not -6.",
"B": "Correct. The worked calculation gives -7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -7, not -4.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_009375 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_10H_14N_1X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "2",
"B": "4",
"C": "3",
"D": "6"
} | B | 4 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×10+2+1−14−1)/2=4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"B": "Correct. The worked calculation gives 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 3.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009777 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(Cl)_5]^+3, each Cl ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "8",
"B": "4",
"C": "6",
"D": "9"
} | A | 8 | Let the formal oxidation state of Cr be x. Charge balance gives x+(5)(−1)=+3; hence x=3+5=+8. | {
"A": "Correct. The worked calculation gives 8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 6.",
"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_005062 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +3 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "16.875 N",
"B": "32.75 N",
"C": "4.375 N",
"D": "33.75 N"
} | D | 33.75 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(3×10⁻⁶)/(4×10⁻²)²=33.75 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33.75 N, not 16.875 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33.75 N, not 32.75 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 33.75 N, not 4.37... | [
"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_001153 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-2x³ -10x² -5x+7. Evaluate f′(-4). | {
"A": "-1.1",
"B": "-16.8",
"C": "-31.5",
"D": "-21"
} | D | -21 | Differentiate: f′(x)=3(-2)x²+2(-10)x+(-5). At x=-4, f′(-4)=3(-2)(-4)²+2(-10)(-4)+(-5)=-21. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -21, not -1.1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -21, not -16.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -21, not -31.5.",
"D": "Corre... | [
"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_007845 | 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 16 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "1 mmol L⁻¹",
"B": "2 mmol L⁻¹",
"C": "-2 mmol L⁻¹",
"D": "0.5 mmol L⁻¹"
} | A | 1 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=16/2^4=1 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 1 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1 mmol L⁻¹, not 2 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1 mmol L⁻¹, not -2 mmol L⁻¹.",
"D": "Incorrect. Substituti... | [
"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_006576 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 1 kg is attached to an ideal spring of force constant 875 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "3.06761 s",
"B": "0.06761 s",
"C": "1.00676 s",
"D": "0.10142 s"
} | B | 0.06761 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(1/875)=0.06761 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.06761 s, not 3.06761 s.",
"B": "Correct. The worked calculation gives 0.06761 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.06761 s, not 1.00676 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002632 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 0], [8, -4]]. | {
"A": "-6",
"B": "-13",
"C": "-9",
"D": "-12"
} | D | -12 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(-4)−(0)(8)=-12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -12, not -6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -12, not -13.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -12, not -9.",
"D": "Correct. The... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003723 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 5 m s⁻¹. A constant net force does 28 N of work over 9 m in the direction of motion. Find its final kinetic energy. | {
"A": "565.5 J",
"B": "377 J",
"C": "301.6 J",
"D": "38.7 J"
} | B | 377 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(5)²+(28)(9)=377 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 377 J, not 565.5 J.",
"B": "Correct. The worked calculation gives 377 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 377 J, not 301.6 J.",
"D": "Incorrect. Substituting the stated values i... | [
"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_002548 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, -3], [6, 8]]. | {
"A": "82",
"B": "123",
"C": "61.5",
"D": "83"
} | A | 82 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(8)−(-3)(6)=82. | {
"A": "Correct. The worked calculation gives 82.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 82, not 123.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 82, not 61.5.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_005316 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +3 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "4.46281 N",
"B": "2.2314 N",
"C": "3.34711 N",
"D": "1.1157 N"
} | B | 2.2314 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(3×10⁻⁶)/(11×10⁻²)²=2.2314 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.2314 N, not 4.46281 N.",
"B": "Correct. The worked calculation gives 2.2314 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.2314 N, not 3.34711 N.",
"D": "Incorrect. Substituting the st... | [
"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_007318 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 13 mol of gas at 401 K and 2.65 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "121.06504 L",
"B": "161.42005 L",
"C": "193.70406 L",
"D": "129.13604 L"
} | B | 161.42005 L | PV=nRT, so V=nRT/P=(13)(0.082057)(401)/(2.65)=161.42005 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 161.42005 L, not 121.06504 L.",
"B": "Correct. The worked calculation gives 161.42005 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 161.42005 L, not 193.70406 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004559 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 2 m is acted on by a constant torque of 82 N m about its central axis. Find its angular acceleration. | {
"A": "16.4 rad s⁻²",
"B": "3.05 rad s⁻²",
"C": "20.5 rad s⁻²",
"D": "18.5 rad s⁻²"
} | C | 20.5 rad s⁻² | For a solid disc, I=½MR²=½(2)(2)²=4 kg m². Using τ=Iα, α=82/4=20.5 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20.5 rad s⁻², not 16.4 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20.5 rad s⁻², not 3.05 rad s⁻².",
"C": "Correct. The worked calculation gives 20.5 rad s⁻².",
"D": "Incorrect. S... | [
"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_008115 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 1 A for 5978 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": "1.96685 g",
"B": "4.96685 g",
"C": "2.95028 g",
"D": "0.96685 g"
} | A | 1.96685 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×1×5978/(2×96500)=1.96685 g. | {
"A": "Correct. The worked calculation gives 1.96685 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.96685 g, not 4.96685 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.96685 g, not 2.95028 g.",
"D": "Incorrect. Substituting the... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006248 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 44 cm in front of a thin convex lens of focal length 30 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "2.14286",
"B": "4.14286",
"C": "1.07143",
"D": "3.14286"
} | A | 2.14286 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(44)(30)/(44−30)=94.28571 cm. Thus |m|=v/u=94.28571/44=2.14286. | {
"A": "Correct. The worked calculation gives 2.14286.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.14286, not 4.14286.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.14286, not 1.07143.",
"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_007999 | 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 53 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "-3.3125 mmol L⁻¹",
"B": "1.65625 mmol L⁻¹",
"C": "3.3125 mmol L⁻¹",
"D": "6.625 mmol L⁻¹"
} | C | 3.3125 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=53/2^4=3.3125 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.3125 mmol L⁻¹, not -3.3125 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.3125 mmol L⁻¹, not 1.65625 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 3.3125 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_000386 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -4 and common difference 12. Find the sum of its first 26 terms. | {
"A": "2847",
"B": "1898",
"C": "3795",
"D": "3796"
} | D | 3796 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-4, d=12, n=26: Sₙ=26/2[2(-4)+(26−1)(12)]=3796. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3796, not 2847.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3796, not 1898.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3796, not 3795.",
"D": "Corr... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003244 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(6-11i)/(9+4i). What is Re(z), the real part of z? | {
"A": "-0.10309",
"B": "-1.89691",
"C": "-2.89691",
"D": "0.10309"
} | D | 0.10309 | Multiply numerator and denominator by the conjugate (9-4i). Then Re(z)=(ac+bd)/(c²+d²)=((6)(9)+(-11)(4))/(9²+(4)²)=0.10309. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.10309, not -0.10309.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.10309, not -1.89691.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.10309, not -2.... | [
"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_003143 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(4-11i)/(11+5i). What is Re(z), the real part of z? | {
"A": "-0.05651",
"B": "1.92466",
"C": "-0.07534",
"D": "0.07534"
} | C | -0.07534 | Multiply numerator and denominator by the conjugate (11-5i). Then Re(z)=(ac+bd)/(c²+d²)=((4)(11)+(-11)(5))/(11²+(5)²)=-0.07534. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.07534, not -0.05651.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.07534, not 1.92466.",
"C": "Correct. The worked calculation gives -0.07534.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009694 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(CN)_4]^+0, each CN ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "5",
"B": "7",
"C": "1.4",
"D": "4"
} | D | 4 | Let the formal oxidation state of Pt be x. Charge balance gives x+(4)(−1)=+0; hence x=0+4=+4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.4.",
"D": "Correct. The worked ... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000412 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 1 and common difference 14. Find the sum of its first 27 terms. | {
"A": "4939",
"B": "7411.5",
"C": "4943",
"D": "4941"
} | D | 4941 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=1, d=14, n=27: Sₙ=27/2[2(1)+(27−1)(14)]=4941. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4941, not 4939.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4941, not 7411.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4941, not 4943.",
"D": "Co... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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