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_003333 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(14-4i)/(5+6i). What is Re(z), the real part of z? | {
"A": "1.13115",
"B": "2.7541",
"C": "-1.2459",
"D": "0.7541"
} | D | 0.7541 | Multiply numerator and denominator by the conjugate (5-6i). Then Re(z)=(ac+bd)/(c²+d²)=((14)(5)+(-4)(6))/(5²+(6)²)=0.7541. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7541, not 1.13115.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7541, not 2.7541.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7541, not -1.2459."... | [
"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_004797 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 12 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 4 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.9375 A",
"B": "7.375 A",
"C": "9.375 A",
"D": "4.6875 A"
} | C | 9.375 A | Series branch resistance=12+4=16 Ω. Parallel equivalent R_eq=(16×4)/(16+4)=3.2 Ω. Total current I=V/R_eq=30/3.2=9.375 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.375 A, not 1.9375 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.375 A, not 7.375 A.",
"C": "Correct. The worked calculation gives 9.375 A.",
"D": "Incorrect. Substituting the stated v... | [
"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_009748 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(OH)_3]^+0, each OH ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "1.3",
"B": "1.5",
"C": "3",
"D": "5"
} | C | 3 | Let the formal oxidation state of Pt be x. Charge balance gives x+(3)(−1)=+0; hence x=0+3=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.5.",
"C": "Correct. The worked calculation gives 3.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_009450 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_17H_8X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "26",
"B": "19.5",
"C": "13",
"D": "16"
} | C | 13 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×17+2+0−8−2)/2=13. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13, not 26.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13, not 19.5.",
"C": "Correct. The worked calculation gives 13.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009374 | 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_17X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "8",
"B": "4",
"C": "7",
"D": "10"
} | C | 7 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×15+2+0−17−1)/2=7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 4.",
"C": "Correct. The worked calculation gives 7.",
"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_003930 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block initially moves at 0 m s⁻¹. A constant net force does 5 N of work over 3 m in the direction of motion. Find its final kinetic energy. | {
"A": "11.25 J",
"B": "16 J",
"C": "15 J",
"D": "2.5 J"
} | C | 15 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(2)(0)²+(5)(3)=15 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15 J, not 11.25 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15 J, not 16 J.",
"C": "Correct. The worked calculation gives 15 J.",
"D": "Incorrect. Substituting the stated values into th... | [
"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_005627 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 17 μF capacitor is charged to a potential difference of 38 V. Calculate the energy stored, expressed in μJ. | {
"A": "12276 μJ",
"B": "12274 μJ",
"C": "12275 μJ",
"D": "9205.5 μJ"
} | B | 12274 μJ | U=½CV². Since C=17 μF, U in μJ is ½×17×(38)²=12274 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12274 μJ, not 12276 μJ.",
"B": "Correct. The worked calculation gives 12274 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12274 μJ, not 12275 μJ.",
"D": "Incorrect. Substituting the stat... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001671 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 6 elements can be selected from a set of 82 distinct elements? | {
"A": "175080906",
"B": "350161812",
"C": "350161811",
"D": "35016182.2"
} | B | 350161812 | Order does not matter, so the count is C(82,6)=82!/[6!(76)!]=350161812. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 350161812, not 175080906.",
"B": "Correct. The worked calculation gives 350161812.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 350161812, not 350161811.",
"D": "Incorrect. Substituting the... | [
"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_008972 | 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 0.94 mol L⁻¹ and initially B is absent. At equilibrium, 26% of A has dissociated at constant volume. Find K_c. | {
"A": "0.34348",
"B": "0.25761",
"C": "-2.65652",
"D": "-0.34348"
} | A | 0.34348 | Let α=0.26. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.94)(0.26)²/(1−0.26)=0.34348. | {
"A": "Correct. The worked calculation gives 0.34348.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34348, not 0.25761.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34348, not -2.65652.",
"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_008953 | 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 1.58 mol L⁻¹ and initially B is absent. At equilibrium, 18% of A has dissociated at constant volume. Find K_c. | {
"A": "0.49943",
"B": "3.24972",
"C": "0.24972",
"D": "-1.75028"
} | C | 0.24972 | Let α=0.18. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.58)(0.18)²/(1−0.18)=0.24972. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.24972, not 0.49943.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.24972, not 3.24972.",
"C": "Correct. The worked calculation gives 0.24972.",
"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_004288 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 44 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.34. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "145.32 N",
"B": "173.184 N",
"C": "144.32 N",
"D": "108.24 N"
} | C | 144.32 N | Net force=mg(sinθ−μcosθ)=44×10×(0.6−0.34×0.8)=144.32 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 144.32 N, not 145.32 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 144.32 N, not 173.184 N.",
"C": "Correct. The worked calculation gives 144.32 N.",
"D": "Incorrect. Substituting the sta... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000757 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio 5. What is the sum of its first 10 terms? | {
"A": "-9765624",
"B": "9765623",
"C": "9765624",
"D": "9765622"
} | C | 9765624 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(5^10−1)/(5−1)=9765624. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9765624, not -9765624.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9765624, not 9765623.",
"C": "Correct. The worked calculation gives 9765624.",
"D": "Incorrect. Substituting the stated v... | [
"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_006121 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 66 cm in front of a thin convex lens of focal length 15 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.29412",
"B": "2.29412",
"C": "1.29412",
"D": "-0.29412"
} | A | 0.29412 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(66)(15)/(66−15)=19.41176 cm. Thus |m|=v/u=19.41176/66=0.29412. | {
"A": "Correct. The worked calculation gives 0.29412.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29412, not 2.29412.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29412, not 1.29412.",
"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_008279 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 14 A for 7281 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": "33.53787 g",
"B": "50.30681 g",
"C": "16.76894 g",
"D": "26.8303 g"
} | A | 33.53787 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×7281/(2×96500)=33.53787 g. | {
"A": "Correct. The worked calculation gives 33.53787 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33.53787 g, not 50.30681 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 33.53787 g, not 16.76894 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_009979 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(CN)_6]^-3, each CN ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "6",
"B": "3",
"C": "2.25",
"D": "-3"
} | B | 3 | Let the formal oxidation state of Cr be x. Charge balance gives x+(6)(−1)=-3; hence x=-3+6=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009000 | 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 0.87 mol L⁻¹ and initially B is absent. At equilibrium, 16% of A has dissociated at constant volume. Find K_c. | {
"A": "0.10606",
"B": "-2.89394",
"C": "-1.89394",
"D": "1.01061"
} | A | 0.10606 | Let α=0.16. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.87)(0.16)²/(1−0.16)=0.10606. | {
"A": "Correct. The worked calculation gives 0.10606.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.10606, not -2.89394.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.10606, not -1.89394.",
"D": "Incorrect. Substituting the stated ... | [
"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_009387 | 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_0X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "9",
"B": "10",
"C": "22",
"D": "11"
} | D | 11 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×12+2+0−0−4)/2=11. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11, not 9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11, not 10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11, not 22.",
"D": "Correct. The work... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009053 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.10 V, transfers 3 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "4.0212 V",
"B": "0.7659 V",
"C": "1.5318 V",
"D": "1.0212 V"
} | D | 1.0212 V | Apply the Nernst equation: E=1.10−(0.0591/3)(4)=1.0212 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0212 V, not 4.0212 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0212 V, not 0.7659 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0212 V, not ... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001930 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 11 elements can be selected from a set of 36 distinct elements? | {
"A": "600805298",
"B": "720966355.2",
"C": "300402648",
"D": "600805296"
} | D | 600805296 | Order does not matter, so the count is C(36,11)=36!/[11!(25)!]=600805296. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 600805296, not 600805298.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 600805296, not 720966355.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 60080529... | [
"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_008277 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 6 A for 28628 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": "28.25717 g",
"B": "56.51434 g",
"C": "45.21147 g",
"D": "84.77151 g"
} | B | 56.51434 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×6×28628/(2×96500)=56.51434 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 56.51434 g, not 28.25717 g.",
"B": "Correct. The worked calculation gives 56.51434 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 56.51434 g, not 45.21147 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_005530 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 25 μF capacitor is charged to a potential difference of 15 V. Calculate the energy stored, expressed in μJ. | {
"A": "2811.5 μJ",
"B": "2810.5 μJ",
"C": "2812.5 μJ",
"D": "2813.5 μJ"
} | C | 2812.5 μJ | U=½CV². Since C=25 μF, U in μJ is ½×25×(15)²=2812.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2812.5 μJ, not 2811.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2812.5 μJ, not 2810.5 μJ.",
"C": "Correct. The worked calculation gives 2812.5 μJ.",
"D": "Incorrect. Substituting the... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008166 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 7 A for 29236 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": "134.66738 g",
"B": "-67.33369 g",
"C": "67.33369 g",
"D": "53.86695 g"
} | C | 67.33369 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×7×29236/(2×96500)=67.33369 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 67.33369 g, not 134.66738 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 67.33369 g, not -67.33369 g.",
"C": "Correct. The worked calculation gives 67.33369 g.",
"D": "Incorrect. Substitut... | [
"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_002154 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 12 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.33333",
"B": "1.33333",
"C": "0.25",
"D": "0.66667"
} | A | 0.33333 | Favourable pairs = C(10,2)+C(12,2)+C(6,2)=126. Total pairs=C(28,2)=378. Therefore P=126/378=0.33333. | {
"A": "Correct. The worked calculation gives 0.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not 1.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not 0.25.",
"D": "Incorrect. Substituting the stated value... | [
"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_007455 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 41 mL of 0.10 M HCl is mixed with 34 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "3.04494",
"B": "2.02996",
"C": "1.52247",
"D": "-0.97004"
} | B | 2.02996 | Excess H⁺ moles=0.10×(41−34)/1000=0.000700 mol. Total volume=0.075 L, so [H⁺]=0.009333 M and pH=−log₁₀[H⁺]=2.02996. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.02996, not 3.04494.",
"B": "Correct. The worked calculation gives 2.02996.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.02996, not 1.52247.",
"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_007618 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 40 mL of 0.10 M HCl is mixed with 88 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.57403",
"B": "9.43052",
"C": "9.57403",
"D": "18.86105"
} | A | 12.57403 | Excess OH⁻ moles=0.10×(88−40)/1000=0.004800 mol. Total volume=0.128 L, so [OH⁻]=0.037500 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.57403. | {
"A": "Correct. The worked calculation gives 12.57403.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.57403, not 9.43052.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.57403, not 9.57403.",
"D": "Incorrect. Substituting the stated... | [
"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_000857 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio -3. What is the sum of its first 10 terms? | {
"A": "-23619.2",
"B": "-29523",
"C": "-29524",
"D": "-29525"
} | C | -29524 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(-3^10−1)/(-3−1)=-29524. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -29524, not -23619.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -29524, not -29523.",
"C": "Correct. The worked calculation gives -29524.",
"D": "Incorrect. Substituting the stated value... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007353 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 99 mL of 0.10 M HCl is mixed with 48 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "3.45975",
"B": "1.45975",
"C": "2.18962",
"D": "-1.45975"
} | B | 1.45975 | Excess H⁺ moles=0.10×(99−48)/1000=0.005100 mol. Total volume=0.147 L, so [H⁺]=0.034694 M and pH=−log₁₀[H⁺]=1.45975. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.45975, not 3.45975.",
"B": "Correct. The worked calculation gives 1.45975.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.45975, not 2.18962.",
"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_003038 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-7+10i)/(9+11i). What is Re(z), the real part of z? | {
"A": "0.46535",
"B": "0.11634",
"C": "0.23267",
"D": "-2.76733"
} | C | 0.23267 | Multiply numerator and denominator by the conjugate (9-11i). Then Re(z)=(ac+bd)/(c²+d²)=((-7)(9)+(10)(11))/(9²+(11)²)=0.23267. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.23267, not 0.46535.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.23267, not 0.11634.",
"C": "Correct. The worked calculation gives 0.23267.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002578 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, 4], [2, 6]]. | {
"A": "-28",
"B": "27",
"C": "28",
"D": "3.8"
} | C | 28 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(6)−(4)(2)=28. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28, not -28.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28, not 27.",
"C": "Correct. The worked calculation gives 28.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008336 | 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 0.72 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": "1.47456 K",
"B": "1.14746 K",
"C": "-1.52544 K",
"D": "3.47456 K"
} | A | 1.47456 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.512×0.72=1.47456 K. | {
"A": "Correct. The worked calculation gives 1.47456 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.47456 K, not 1.14746 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.47456 K, not -1.52544 K.",
"D": "Incorrect. Substituting th... | [
"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_004099 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 18 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.29. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "99.36 N",
"B": "64.24 N",
"C": "79.488 N",
"D": "66.24 N"
} | D | 66.24 N | Net force=mg(sinθ−μcosθ)=18×10×(0.6−0.29×0.8)=66.24 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 66.24 N, not 99.36 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 66.24 N, not 64.24 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 66.24 N, not 79.48... | [
"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_005205 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +4 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "38.73469 N",
"B": "29.38776 N",
"C": "36.73469 N",
"D": "35.73469 N"
} | C | 36.73469 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(4×10⁻⁶)/(7×10⁻²)²=36.73469 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 36.73469 N, not 38.73469 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 36.73469 N, not 29.38776 N.",
"C": "Correct. The worked calculation gives 36.73469 N.",
"D": "Incorrect. Substitutin... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003665 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 80 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "415.69219 m",
"B": "-554.25626 m",
"C": "665.10751 m",
"D": "554.25626 m"
} | D | 554.25626 m | Range R=u²sin(2θ)/g. Substituting u=80, θ=60° and g=10 gives R=(80)²sin(120°)/10=554.25626 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 554.25626 m, not 415.69219 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 554.25626 m, not -554.25626 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5... | [
"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_009656 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_11H_18N_1X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "2",
"B": "1",
"C": "3",
"D": "4"
} | A | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+1−18−3)/2=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 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_006149 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 67 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": "0.675",
"B": "2.675",
"C": "-0.325",
"D": "0.50625"
} | A | 0.675 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(67)(27)/(67−27)=45.225 cm. Thus |m|=v/u=45.225/67=0.675. | {
"A": "Correct. The worked calculation gives 0.675.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.675, not 2.675.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.675, not -0.325.",
"D": "Incorrect. Substituting the stated values into... | [
"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_001485 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (-4x² +2x -4) dx. | {
"A": "276",
"B": "-276",
"C": "-138",
"D": "-274"
} | B | -276 | An antiderivative is (-4/3)x³+(2/2)x²+(-4)x. Evaluating between 0 and 6 gives (-4/3)(6)³+(2/2)(6)²+(-4)(6)=-276. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -276, not 276.",
"B": "Correct. The worked calculation gives -276.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -276, not -138.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_009799 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(OH)_6]^-4, each OH ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "2",
"B": "1",
"C": "3",
"D": "-1"
} | A | 2 | Let the formal oxidation state of Mn be x. Charge balance gives x+(6)(−1)=-4; hence x=-4+6=+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 3.",
"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_008805 | 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 0.09 mol L⁻¹ and initially B is absent. At equilibrium, 42% of A has dissociated at constant volume. Find K_c. | {
"A": "0.10949",
"B": "-0.10949",
"C": "0.05474",
"D": "-1.89051"
} | A | 0.10949 | Let α=0.42. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.09)(0.42)²/(1−0.42)=0.10949. | {
"A": "Correct. The worked calculation gives 0.10949.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.10949, not -0.10949.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.10949, not 0.05474.",
"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_003683 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 13 kg block initially moves at 8 m s⁻¹. A constant net force does 10 N of work over 5 m in the direction of motion. Find its final kinetic energy. | {
"A": "932 J",
"B": "466 J",
"C": "47.6 J",
"D": "-466 J"
} | B | 466 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(13)(8)²+(10)(5)=466 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 466 J, not 932 J.",
"B": "Correct. The worked calculation gives 466 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 466 J, not 47.6 J.",
"D": "Incorrect. Substituting the stated values into... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008602 | 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 0.55 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "2.1 K",
"B": "1.11 K",
"C": "1.1 K",
"D": "-0.9 K"
} | C | 1.1 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×0.55=1.1 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.1 K, not 2.1 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1 K, not 1.11 K.",
"C": "Correct. The worked calculation gives 1.1 K.",
"D": "Incorrect. Substituting the stated values into... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003462 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 78 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "466.06144 m",
"B": "468.06144 m",
"C": "699.09216 m",
"D": "467.06144 m"
} | A | 466.06144 m | Range R=u²sin(2θ)/g. Substituting u=78, θ=25° and g=10 gives R=(78)²sin(50°)/10=466.06144 m. | {
"A": "Correct. The worked calculation gives 466.06144 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 466.06144 m, not 468.06144 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 466.06144 m, not 699.09216 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002845 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(6, 1, -2) and v=(4, 9, 7), calculate u·v. | {
"A": "28.5",
"B": "2.9",
"C": "19",
"D": "-19"
} | C | 19 | The dot product is the sum of corresponding component products: (6)(4)+(1)(9)+(-2)(7)=19. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19, not 28.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19, not 2.9.",
"C": "Correct. The worked calculation gives 19.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006748 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 11 mol H₂ and 4 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "1.8 mol",
"B": "6 mol",
"C": "8 mol",
"D": "5 mol"
} | C | 8 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 11 mol H₂O; O₂ can produce 8 mol H₂O. The limiting condition is O₂; product=8 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8 mol, not 1.8 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8 mol, not 6 mol.",
"C": "Correct. The worked calculation gives 8 mol.",
"D": "Incorrect. Substituting the stated values int... | [
"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_004871 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 11 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 16 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "-4.65 A",
"B": "2.65 A",
"C": "6.975 A",
"D": "4.65 A"
} | D | 4.65 A | Series branch resistance=11+4=15 Ω. Parallel equivalent R_eq=(15×16)/(15+16)=7.74194 Ω. Total current I=V/R_eq=36/7.74194=4.65 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.65 A, not -4.65 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.65 A, not 2.65 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.65 A, not 6.975 A."... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008765 | 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 0.02 mol L⁻¹ and initially B is absent. At equilibrium, 70% of A has dissociated at constant volume. Find K_c. | {
"A": "2.13067",
"B": "0.098",
"C": "0.13067",
"D": "-0.86933"
} | C | 0.13067 | Let α=0.7. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.02)(0.7)²/(1−0.7)=0.13067. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.13067, not 2.13067.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.13067, not 0.098.",
"C": "Correct. The worked calculation gives 0.13067.",
"D": "Incorrect. Substituting the stated valu... | [
"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_000249 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 -8x -6=0, let its roots be α and β. What is α²+β²? | {
"A": "3.77778",
"B": "5.66667",
"C": "2.83333",
"D": "7.55556"
} | A | 3.77778 | By Vieta's relations, α+β = 8/6 and αβ = -6/6. Then α²+β²=(α+β)²−2αβ = (8/6)²−2(-6/6) = 3.77778. | {
"A": "Correct. The worked calculation gives 3.77778.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.77778, not 5.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.77778, not 2.83333.",
"D": "Incorrect. Substituting the stated va... | [
"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_007377 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 82 mL of 0.10 M HCl is mixed with 100 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "5.9976",
"B": "2.19952",
"C": "17.9928",
"D": "11.9952"
} | D | 11.9952 | Excess OH⁻ moles=0.10×(100−82)/1000=0.001800 mol. Total volume=0.182 L, so [OH⁻]=0.009890 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=11.9952. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.9952, not 5.9976.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.9952, not 2.19952.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.9952, not 17.992... | [
"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_008740 | 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 1.48 mol L⁻¹ and initially B is absent. At equilibrium, 78% of A has dissociated at constant volume. Find K_c. | {
"A": "-16.37149",
"B": "17.37149",
"C": "16.37149",
"D": "12.27862"
} | C | 16.37149 | Let α=0.78. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.48)(0.78)²/(1−0.78)=16.37149. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16.37149, not -16.37149.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16.37149, not 17.37149.",
"C": "Correct. The worked calculation gives 16.37149.",
"D": "Incorrect. Substituting the sta... | [
"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_003936 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 4 m s⁻¹. A constant net force does 30 N of work over 8 m in the direction of motion. Find its final kinetic energy. | {
"A": "304 J",
"B": "306 J",
"C": "305 J",
"D": "456 J"
} | A | 304 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(4)²+(30)(8)=304 J. | {
"A": "Correct. The worked calculation gives 304 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 304 J, not 306 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 304 J, not 305 J.",
"D": "Incorrect. Substituting the stated values into ... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004546 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 4 m is acted on by a constant torque of 37 N m about its central axis. Find its angular acceleration. | {
"A": "0.925 rad s⁻²",
"B": "1.3875 rad s⁻²",
"C": "-0.925 rad s⁻²",
"D": "1.925 rad s⁻²"
} | A | 0.925 rad s⁻² | For a solid disc, I=½MR²=½(5)(4)²=40 kg m². Using τ=Iα, α=37/40=0.925 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.925 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.925 rad s⁻², not 1.3875 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.925 rad s⁻², not -0.925 rad s⁻².",
"D": "Incor... | [
"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_005436 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 3 μF capacitor is charged to a potential difference of 36 V. Calculate the energy stored, expressed in μJ. | {
"A": "2916 μJ",
"B": "1458 μJ",
"C": "1942 μJ",
"D": "1944 μJ"
} | D | 1944 μJ | U=½CV². Since C=3 μF, U in μJ is ½×3×(36)²=1944 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1944 μJ, not 2916 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1944 μJ, not 1458 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1944 μJ, not 1942 ... | [
"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_004958 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 5 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "7.85 A",
"B": "11.7 A",
"C": "8.775 A",
"D": "5.85 A"
} | D | 5.85 A | Series branch resistance=4+4=8 Ω. Parallel equivalent R_eq=(8×5)/(8+5)=3.07692 Ω. Total current I=V/R_eq=18/3.07692=5.85 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.85 A, not 7.85 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.85 A, not 11.7 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.85 A, not 8.775 A.",... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001379 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (6x² +7x -5) dx. | {
"A": "0.5",
"B": "0.25",
"C": "2.5",
"D": "1"
} | A | 0.5 | An antiderivative is (6/3)x³+(7/2)x²+(-5)x. Evaluating between 0 and 1 gives (6/3)(1)³+(7/2)(1)²+(-5)(1)=0.5. | {
"A": "Correct. The worked calculation gives 0.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.5, not 0.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5, not 2.5.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005312 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 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": "1.66942 N",
"B": "4.69421 N",
"C": "3.69421 N",
"D": "6.69421 N"
} | D | 6.69421 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(3×10⁻⁶)/(11×10⁻²)²=6.69421 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.69421 N, not 1.66942 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.69421 N, not 4.69421 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.69421 N,... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000884 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio 5. What is the sum of its first 7 terms? | {
"A": "-175779",
"B": "175781",
"C": "175779",
"D": "175778"
} | C | 175779 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(5^7−1)/(5−1)=175779. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 175779, not -175779.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 175779, not 175781.",
"C": "Correct. The worked calculation gives 175779.",
"D": "Incorrect. Substituting the stated values... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009613 | 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_18H_26N_1X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "8",
"B": "6",
"C": "7",
"D": "5"
} | B | 6 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+1−26−1)/2=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 8.",
"B": "Correct. The worked calculation gives 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 7.",
"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_008890 | 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 1.96 mol L⁻¹ and initially B is absent. At equilibrium, 59% of A has dissociated at constant volume. Find K_c. | {
"A": "3.65635",
"B": "6.65635",
"C": "7.65635",
"D": "13.3127"
} | B | 6.65635 | Let α=0.59. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.96)(0.59)²/(1−0.59)=6.65635. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.65635, not 3.65635.",
"B": "Correct. The worked calculation gives 6.65635.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.65635, not 7.65635.",
"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_005630 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 76 μF capacitor is charged to a potential difference of 25 V. Calculate the energy stored, expressed in μJ. | {
"A": "23750 μJ",
"B": "47500 μJ",
"C": "2376 μJ",
"D": "11875 μJ"
} | A | 23750 μJ | U=½CV². Since C=76 μF, U in μJ is ½×76×(25)²=23750 μJ. | {
"A": "Correct. The worked calculation gives 23750 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23750 μJ, not 47500 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23750 μJ, not 2376 μJ.",
"D": "Incorrect. Substituting the state... | [
"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_006471 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 17 kg is attached to an ideal spring of force constant 110 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.17937 s",
"B": "-0.21375 s",
"C": "1.78625 s",
"D": "0.78625 s"
} | D | 0.78625 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(17/110)=0.78625 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.78625 s, not 1.17937 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.78625 s, not -0.21375 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.78625 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_004848 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 8 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.45 A",
"B": "5.175 A",
"C": "2.5875 A",
"D": "2.45 A"
} | A | 3.45 A | Series branch resistance=7+8=15 Ω. Parallel equivalent R_eq=(15×8)/(15+8)=5.21739 Ω. Total current I=V/R_eq=18/5.21739=3.45 A. | {
"A": "Correct. The worked calculation gives 3.45 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.45 A, not 5.175 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.45 A, not 2.5875 A.",
"D": "Incorrect. Substituting the stated valu... | [
"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_001445 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (-2x² +0x +1) dx. | {
"A": "0.25",
"B": "-1.66667",
"C": "-2.66667",
"D": "0.33333"
} | D | 0.33333 | An antiderivative is (-2/3)x³+(0/2)x²+(1)x. Evaluating between 0 and 1 gives (-2/3)(1)³+(0/2)(1)²+(1)(1)=0.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not 0.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not -1.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not -2.6666... | [
"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_004186 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 45 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.27. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "171.8 N",
"B": "172.8 N",
"C": "129.6 N",
"D": "86.4 N"
} | B | 172.8 N | Net force=mg(sinθ−μcosθ)=45×10×(0.6−0.27×0.8)=172.8 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 172.8 N, not 171.8 N.",
"B": "Correct. The worked calculation gives 172.8 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 172.8 N, not 129.6 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006696 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 33 mol H₂ and 13 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "26 mol",
"B": "52 mol",
"C": "39 mol",
"D": "3.6 mol"
} | A | 26 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 33 mol H₂O; O₂ can produce 26 mol H₂O. The limiting condition is O₂; product=26 mol. | {
"A": "Correct. The worked calculation gives 26 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 52 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 39 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006179 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 19 cm in front of a thin convex lens of focal length 9 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.9",
"B": "0.45",
"C": "-1.1",
"D": "0.675"
} | A | 0.9 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(19)(9)/(19−9)=17.1 cm. Thus |m|=v/u=17.1/19=0.9. | {
"A": "Correct. The worked calculation gives 0.9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9, not 0.45.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9, not -1.1.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_003082 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-2+10i)/(11+8i). What is Re(z), the real part of z? | {
"A": "0.31351",
"B": "1.31351",
"C": "0.23514",
"D": "2.31351"
} | A | 0.31351 | Multiply numerator and denominator by the conjugate (11-8i). Then Re(z)=(ac+bd)/(c²+d²)=((-2)(11)+(10)(8))/(11²+(8)²)=0.31351. | {
"A": "Correct. The worked calculation gives 0.31351.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31351, not 1.31351.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31351, not 0.23514.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009254 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.85 V, transfers 3 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-2.1303 V",
"B": "0.8697 V",
"C": "-1.1303 V",
"D": "1.8697 V"
} | B | 0.8697 V | Apply the Nernst equation: E=0.85−(0.0591/3)(-1)=0.8697 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8697 V, not -2.1303 V.",
"B": "Correct. The worked calculation gives 0.8697 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8697 V, not -1.1303 V.",
"D": "Incorrect. Substituting the st... | [
"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_006382 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 4 kg is attached to an ideal spring of force constant 420 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.19518 s",
"B": "1.01952 s",
"C": "3.19518 s",
"D": "0.39036 s"
} | A | 0.19518 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(4/420)=0.19518 s. | {
"A": "Correct. The worked calculation gives 0.19518 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.19518 s, not 1.01952 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.19518 s, not 3.19518 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_005948 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3 atm at 443 K. What is its pressure at 703 K? | {
"A": "4.76072 atm",
"B": "3.57054 atm",
"C": "7.76072 atm",
"D": "1.47607 atm"
} | A | 4.76072 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3)(703)/(443)=4.76072 atm. | {
"A": "Correct. The worked calculation gives 4.76072 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.76072 atm, not 3.57054 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.76072 atm, not 7.76072 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002624 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, -3], [7, 3]]. | {
"A": "45",
"B": "4",
"C": "60",
"D": "30"
} | D | 30 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(3)−(-3)(7)=30. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 30, not 45.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30, not 60.",
"D": "Correct. The work... | [
"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_006143 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 17 cm in front of a thin convex lens of focal length 8 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.88889",
"B": "0.44444",
"C": "1.33333",
"D": "-1.11111"
} | A | 0.88889 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(17)(8)/(17−8)=15.11111 cm. Thus |m|=v/u=15.11111/17=0.88889. | {
"A": "Correct. The worked calculation gives 0.88889.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.88889, not 0.44444.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.88889, not 1.33333.",
"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_007118 | 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 253 K and 1.26 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "-65.9061 L",
"B": "49.42957 L",
"C": "65.9061 L",
"D": "98.85915 L"
} | C | 65.9061 L | PV=nRT, so V=nRT/P=(4)(0.082057)(253)/(1.26)=65.9061 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 65.9061 L, not -65.9061 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 65.9061 L, not 49.42957 L.",
"C": "Correct. The worked calculation gives 65.9061 L.",
"D": "Incorrect. Substituting t... | [
"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_003959 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 1 m s⁻¹. A constant net force does 20 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "111.75 J",
"B": "222.5 J",
"C": "223.5 J",
"D": "224.5 J"
} | C | 223.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(1)²+(20)(11)=223.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 223.5 J, not 111.75 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 223.5 J, not 222.5 J.",
"C": "Correct. The worked calculation gives 223.5 J.",
"D": "Incorrect. Substituting the stated v... | [
"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_000671 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio 3. What is the sum of its first 5 terms? | {
"A": "677.6",
"B": "1694",
"C": "847",
"D": "849"
} | C | 847 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(3^5−1)/(3−1)=847. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 847, not 677.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 847, not 1694.",
"C": "Correct. The worked calculation gives 847.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_004644 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 1 m is acted on by a constant torque of 97 N m about its central axis. Find its angular acceleration. | {
"A": "20.78571 rad s⁻²",
"B": "13.85714 rad s⁻²",
"C": "29.71429 rad s⁻²",
"D": "27.71429 rad s⁻²"
} | D | 27.71429 rad s⁻² | For a solid disc, I=½MR²=½(7)(1)²=3.5 kg m². Using τ=Iα, α=97/3.5=27.71429 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 27.71429 rad s⁻², not 20.78571 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 27.71429 rad s⁻², not 13.85714 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governi... | [
"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_001163 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-1x³ -1x² -9x+7. Evaluate f′(5). | {
"A": "94",
"B": "-95",
"C": "-47",
"D": "-94"
} | D | -94 | Differentiate: f′(x)=3(-1)x²+2(-1)x+(-9). At x=5, f′(5)=3(-1)(5)²+2(-1)(5)+(-9)=-94. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -94, not 94.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -94, not -95.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -94, not -47.",
"D": "Correct. Th... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002642 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -2], [4, 8]]. | {
"A": "57.6",
"B": "-48",
"C": "48",
"D": "96"
} | C | 48 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(8)−(-2)(4)=48. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 48, not 57.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 48, not -48.",
"C": "Correct. The worked calculation gives 48.",
"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_003046 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-7+5i)/(6+2i). What is Re(z), the real part of z? | {
"A": "0.8",
"B": "-1.8",
"C": "-1.2",
"D": "-0.8"
} | D | -0.8 | Multiply numerator and denominator by the conjugate (6-2i). Then Re(z)=(ac+bd)/(c²+d²)=((-7)(6)+(5)(2))/(6²+(2)²)=-0.8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.8, not 0.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.8, not -1.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.8, not -1.2.",
"D": "Corre... | [
"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_003273 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-13-1i)/(5+7i). What is Re(z), the real part of z? | {
"A": "-0.48649",
"B": "1.02703",
"C": "-0.97297",
"D": "0.97297"
} | C | -0.97297 | Multiply numerator and denominator by the conjugate (5-7i). Then Re(z)=(ac+bd)/(c²+d²)=((-13)(5)+(-1)(7))/(5²+(7)²)=-0.97297. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.97297, not -0.48649.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.97297, not 1.02703.",
"C": "Correct. The worked calculation gives -0.97297.",
"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_005760 | 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 426 K. What is its pressure at 484 K? | {
"A": "1.22723 atm",
"B": "0.22723 atm",
"C": "2.22723 atm",
"D": "3.22723 atm"
} | B | 0.22723 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.2)(484)/(426)=0.22723 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.22723 atm, not 1.22723 atm.",
"B": "Correct. The worked calculation gives 0.22723 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.22723 atm, not 2.22723 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005647 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 43 μF capacitor is charged to a potential difference of 5 V. Calculate the energy stored, expressed in μJ. | {
"A": "54.75 μJ",
"B": "536.5 μJ",
"C": "645 μJ",
"D": "537.5 μJ"
} | D | 537.5 μJ | U=½CV². Since C=43 μF, U in μJ is ½×43×(5)²=537.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 537.5 μJ, not 54.75 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 537.5 μJ, not 536.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 537.5 μJ, not ... | [
"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_007108 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 19 mol of gas at 450 K and 0.22 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "2551.22673 L",
"B": "3190.03341 L",
"C": "3189.03341 L",
"D": "4783.55011 L"
} | C | 3189.03341 L | PV=nRT, so V=nRT/P=(19)(0.082057)(450)/(0.22)=3189.03341 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3189.03341 L, not 2551.22673 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3189.03341 L, not 3190.03341 L.",
"C": "Correct. The worked calculation gives 3189.03341 L.",
"D": "Incorrect. S... | [
"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_008495 | 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 1.65 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": "0.8448 K",
"B": "3.3792 K",
"C": "2.6896 K",
"D": "1.6896 K"
} | D | 1.6896 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×1.65=1.6896 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.6896 K, not 0.8448 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.6896 K, not 3.3792 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.6896 K, not ... | [
"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_007806 | 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 27 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "6.75 mmol L⁻¹",
"B": "2.53125 mmol L⁻¹",
"C": "3.375 mmol L⁻¹",
"D": "0.375 mmol L⁻¹"
} | C | 3.375 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=27/2^3=3.375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.375 mmol L⁻¹, not 6.75 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.375 mmol L⁻¹, not 2.53125 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 3.375 mmol L⁻¹.",
"D": "I... | [
"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_005334 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +3 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "182 N",
"B": "180 N",
"C": "181 N",
"D": "216 N"
} | B | 180 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(3×10⁻⁶)/(3×10⁻²)²=180 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 180 N, not 182 N.",
"B": "Correct. The worked calculation gives 180 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 180 N, not 181 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004963 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 3 Ω and 2 Ω are connected in series; this combination is connected in parallel with a 20 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.75 A",
"B": "7.5 A",
"C": "15 A",
"D": "4.5 A"
} | B | 7.5 A | Series branch resistance=3+2=5 Ω. Parallel equivalent R_eq=(5×20)/(5+20)=4 Ω. Total current I=V/R_eq=30/4=7.5 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.5 A, not 1.75 A.",
"B": "Correct. The worked calculation gives 7.5 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.5 A, not 15 A.",
"D": "Incorrect. Substituting the stated values into ... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001085 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-3x³ +5x² +9x+7. Evaluate f′(-2). | {
"A": "47",
"B": "-56.4",
"C": "-47",
"D": "-94"
} | C | -47 | Differentiate: f′(x)=3(-3)x²+2(5)x+(9). At x=-2, f′(-2)=3(-3)(-2)²+2(5)(-2)+(9)=-47. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -47, not 47.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -47, not -56.4.",
"C": "Correct. The worked calculation gives -47.",
"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_007192 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 16 mol of gas at 349 K and 0.83 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "554.05577 L",
"B": "552.05577 L",
"C": "276.02788 L",
"D": "441.64461 L"
} | B | 552.05577 L | PV=nRT, so V=nRT/P=(16)(0.082057)(349)/(0.83)=552.05577 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 552.05577 L, not 554.05577 L.",
"B": "Correct. The worked calculation gives 552.05577 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 552.05577 L, not 276.02788 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_004387 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 4 m is acted on by a constant torque of 96 N m about its central axis. Find its angular acceleration. | {
"A": "6 rad s⁻²",
"B": "4.5 rad s⁻²",
"C": "9 rad s⁻²",
"D": "1.6 rad s⁻²"
} | A | 6 rad s⁻² | For a solid disc, I=½MR²=½(2)(4)²=16 kg m². Using τ=Iα, α=96/16=6 rad s⁻². | {
"A": "Correct. The worked calculation gives 6 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6 rad s⁻², not 4.5 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6 rad s⁻², not 9 rad s⁻².",
"D": "Incorrect. Substituting t... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002520 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, -2], [1, 7]]. | {
"A": "8",
"B": "24",
"C": "16",
"D": "-16"
} | C | 16 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(7)−(-2)(1)=16. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16, not 8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16, not 24.",
"C": "Correct. The worked calculation gives 16.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_006078 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 31 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": "-2.44444",
"B": "-0.55556",
"C": "2.44444",
"D": "3.66667"
} | C | 2.44444 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(31)(22)/(31−22)=75.77778 cm. Thus |m|=v/u=75.77778/31=2.44444. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.44444, not -2.44444.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.44444, not -0.55556.",
"C": "Correct. The worked calculation gives 2.44444.",
"D": "Incorrect. Substituting the stated ... | [
"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_004419 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 6 kg and radius 5 m is acted on by a constant torque of 67 N m about its central axis. Find its angular acceleration. | {
"A": "-0.10667 rad s⁻²",
"B": "0.89333 rad s⁻²",
"C": "-0.89333 rad s⁻²",
"D": "0.67 rad s⁻²"
} | B | 0.89333 rad s⁻² | For a solid disc, I=½MR²=½(6)(5)²=75 kg m². Using τ=Iα, α=67/75=0.89333 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.89333 rad s⁻², not -0.10667 rad s⁻².",
"B": "Correct. The worked calculation gives 0.89333 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.89333 rad s⁻², not -0.89333 rad s⁻².",
"... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003066 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-4+6i)/(12+4i). What is Re(z), the real part of z? | {
"A": "2.85",
"B": "-3.15",
"C": "-0.15",
"D": "0.985"
} | C | -0.15 | Multiply numerator and denominator by the conjugate (12-4i). Then Re(z)=(ac+bd)/(c²+d²)=((-4)(12)+(6)(4))/(12²+(4)²)=-0.15. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.15, not 2.85.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.15, not -3.15.",
"C": "Correct. The worked calculation gives -0.15.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_002043 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 8 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "3.32275",
"B": "0.32275",
"C": "0.24206",
"D": "-2.67725"
} | B | 0.32275 | Favourable pairs = C(8,2)+C(8,2)+C(12,2)=122. Total pairs=C(28,2)=378. Therefore P=122/378=0.32275. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32275, not 3.32275.",
"B": "Correct. The worked calculation gives 0.32275.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32275, not 0.24206.",
"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_007340 | 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 41 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.85415",
"B": "3.42708",
"C": "1.42708",
"D": "0.42708"
} | C | 1.42708 | Excess H⁺ moles=0.10×(90−41)/1000=0.004900 mol. Total volume=0.131 L, so [H⁺]=0.037405 M and pH=−log₁₀[H⁺]=1.42708. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.42708, not 2.85415.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.42708, not 3.42708.",
"C": "Correct. The worked calculation gives 1.42708.",
"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_008037 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 8 A for 12412 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": "32.66993 g",
"B": "30.66993 g",
"C": "39.20391 g",
"D": "26.13594 g"
} | A | 32.66993 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×8×12412/(2×96500)=32.66993 g. | {
"A": "Correct. The worked calculation gives 32.66993 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 32.66993 g, not 30.66993 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 32.66993 g, not 39.20391 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_008227 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 15 A for 29911 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": "147.61776 g",
"B": "149.61776 g",
"C": "145.61776 g",
"D": "177.14131 g"
} | A | 147.61776 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×15×29911/(2×96500)=147.61776 g. | {
"A": "Correct. The worked calculation gives 147.61776 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 147.61776 g, not 149.61776 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 147.61776 g, not 145.61776 g.",
"D": "Incorrect. Substi... | [
"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_006213 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 29 cm in front of a thin convex lens of focal length 13 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.60938",
"B": "0.8125",
"C": "-0.8125",
"D": "-1.1875"
} | B | 0.8125 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(29)(13)/(29−13)=23.5625 cm. Thus |m|=v/u=23.5625/29=0.8125. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8125, not 0.60938.",
"B": "Correct. The worked calculation gives 0.8125.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8125, not -0.8125.",
"D": "Incorrect. Substituting the stated value... | [
"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_003125 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(10+1i)/(10+6i). What is Re(z), the real part of z? | {
"A": "0.77941",
"B": "0.38971",
"C": "-1.22059",
"D": "0.58456"
} | A | 0.77941 | Multiply numerator and denominator by the conjugate (10-6i). Then Re(z)=(ac+bd)/(c²+d²)=((10)(10)+(1)(6))/(10²+(6)²)=0.77941. | {
"A": "Correct. The worked calculation gives 0.77941.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.77941, not 0.38971.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.77941, not -1.22059.",
"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_001283 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ +6x² +10x+7. Evaluate f′(2). | {
"A": "53",
"B": "79.5",
"C": "105",
"D": "106"
} | D | 106 | Differentiate: f′(x)=3(6)x²+2(6)x+(10). At x=2, f′(2)=3(6)(2)²+2(6)(2)+(10)=106. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 106, not 53.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 106, not 79.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 106, not 105.",
"D": "Correct. T... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004502 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 9 kg and radius 6 m is acted on by a constant torque of 78 N m about its central axis. Find its angular acceleration. | {
"A": "3.48148 rad s⁻²",
"B": "-0.48148 rad s⁻²",
"C": "1.48148 rad s⁻²",
"D": "0.48148 rad s⁻²"
} | D | 0.48148 rad s⁻² | For a solid disc, I=½MR²=½(9)(6)²=162 kg m². Using τ=Iα, α=78/162=0.48148 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.48148 rad s⁻², not 3.48148 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.48148 rad s⁻², not -0.48148 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing ... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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