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_009932 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(OH)_3]^-3, each OH ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "3",
"B": "-2",
"C": "0",
"D": "1"
} | C | 0 | Let the formal oxidation state of Cu be x. Charge balance gives x+(3)(−1)=-3; hence x=-3+3=+0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"C": "Correct. The worked calculation gives 0.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009632 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_7H_6. Treat X as the total number of monovalent halogen atoms. | {
"A": "5",
"B": "6",
"C": "-5",
"D": "2.5"
} | A | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+0−6−0)/2=5. | {
"A": "Correct. The worked calculation gives 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not -5.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005250 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +8 μC and +9 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "-53.55372 N",
"B": "53.55372 N",
"C": "26.77686 N",
"D": "80.33058 N"
} | B | 53.55372 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(8×10⁻⁶)(9×10⁻⁶)/(11×10⁻²)²=53.55372 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 53.55372 N, not -53.55372 N.",
"B": "Correct. The worked calculation gives 53.55372 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 53.55372 N, not 26.77686 N.",
"D": "Incorrect. Substituti... | [
"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_001912 | 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 67 distinct elements? | {
"A": "1285063345178",
"B": "128506334518.60001",
"C": "1285063345174",
"D": "1285063345176"
} | D | 1285063345176 | Order does not matter, so the count is C(67,11)=67!/[11!(56)!]=1285063345176. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1285063345176, not 1285063345178.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1285063345176, not 128506334518.60001.",
"C": "Incorrect. Substituting the stated values into the governing rela... | [
"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_006031 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 30 cm in front of a thin convex lens of focal length 10 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.25",
"B": "0.5",
"C": "2.5",
"D": "0.375"
} | B | 0.5 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(30)(10)/(30−10)=15 cm. Thus |m|=v/u=15/30=0.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5, not 0.25.",
"B": "Correct. The worked calculation gives 0.5.",
"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... | [
"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_000926 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio 5. What is the sum of its first 9 terms? | {
"A": "2441405",
"B": "1220702.5",
"C": "3662107.5",
"D": "244141.5"
} | A | 2441405 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(5^9−1)/(5−1)=2441405. | {
"A": "Correct. The worked calculation gives 2441405.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2441405, not 1220702.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2441405, not 3662107.5.",
"D": "Incorrect. Substituting the state... | [
"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_008335 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 12 A for 27830 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": "111.87803 g",
"B": "131.85364 g",
"C": "109.87803 g",
"D": "107.87803 g"
} | C | 109.87803 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×12×27830/(2×96500)=109.87803 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 109.87803 g, not 111.87803 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 109.87803 g, not 131.85364 g.",
"C": "Correct. The worked calculation gives 109.87803 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_005928 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4 atm at 197 K. What is its pressure at 742 K? | {
"A": "11.29949 atm",
"B": "15.06599 atm",
"C": "22.59898 atm",
"D": "7.53299 atm"
} | B | 15.06599 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4)(742)/(197)=15.06599 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15.06599 atm, not 11.29949 atm.",
"B": "Correct. The worked calculation gives 15.06599 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15.06599 atm, not 22.59898 atm.",
"D": "Incorrect. S... | [
"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_008926 | 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 1.77 mol L⁻¹ and initially B is absent. At equilibrium, 65% of A has dissociated at constant volume. Find K_c. | {
"A": "11.54657",
"B": "5.54657",
"C": "17.09314",
"D": "8.54657"
} | D | 8.54657 | Let α=0.65. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.77)(0.65)²/(1−0.65)=8.54657. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.54657, not 11.54657.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.54657, not 5.54657.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.54657, not 17.0... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001313 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=0x³ -6x² -12x+7. Evaluate f′(-1). | {
"A": "1",
"B": "-3",
"C": "-1",
"D": "0"
} | D | 0 | Differentiate: f′(x)=3(0)x²+2(-6)x+(-12). At x=-1, f′(-1)=3(0)(-1)²+2(-6)(-1)+(-12)=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not -1.",
"D": "Correct. The worked ... | [
"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_002024 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 11 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.31373",
"B": "0.15686",
"C": "-0.31373",
"D": "1.31373"
} | A | 0.31373 | Favourable pairs = C(12,2)+C(11,2)+C(11,2)=176. Total pairs=C(34,2)=561. Therefore P=176/561=0.31373. | {
"A": "Correct. The worked calculation gives 0.31373.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31373, not 0.15686.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31373, not -0.31373.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007930 | 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 40 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "2.625 mmol L⁻¹",
"B": "1.0625 mmol L⁻¹",
"C": "0.625 mmol L⁻¹",
"D": "1.25 mmol L⁻¹"
} | C | 0.625 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=40/2^6=0.625 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.625 mmol L⁻¹, not 2.625 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.625 mmol L⁻¹, not 1.0625 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.625 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_000596 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 23 and common difference 4. Find the sum of its first 15 terms. | {
"A": "765",
"B": "573.75",
"C": "763",
"D": "766"
} | A | 765 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=23, d=4, n=15: Sₙ=15/2[2(23)+(15−1)(4)]=765. | {
"A": "Correct. The worked calculation gives 765.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 765, not 573.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 765, not 763.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008267 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 13 A for 18871 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": "9.07151 g",
"B": "78.71508 g",
"C": "121.07262 g",
"D": "80.71508 g"
} | D | 80.71508 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×18871/(2×96500)=80.71508 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 80.71508 g, not 9.07151 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 80.71508 g, not 78.71508 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 80.7150... | [
"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_003141 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-2-8i)/(5+4i). What is Re(z), the real part of z? | {
"A": "1.97561",
"B": "-1.02439",
"C": "1.02439",
"D": "-2.04878"
} | B | -1.02439 | Multiply numerator and denominator by the conjugate (5-4i). Then Re(z)=(ac+bd)/(c²+d²)=((-2)(5)+(-8)(4))/(5²+(4)²)=-1.02439. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.02439, not 1.97561.",
"B": "Correct. The worked calculation gives -1.02439.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.02439, not 1.02439.",
"D": "Incorrect. Substituting the stated... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007307 | 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 504 K and 0.15 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "2619.25944 L",
"B": "10477.03776 L",
"C": "6286.22266 L",
"D": "5238.51888 L"
} | D | 5238.51888 L | PV=nRT, so V=nRT/P=(19)(0.082057)(504)/(0.15)=5238.51888 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5238.51888 L, not 2619.25944 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5238.51888 L, not 10477.03776 L.",
"C": "Incorrect. Substituting the stated values into the governing relation giv... | [
"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_004809 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 5 Ω are connected in series; this combination is connected in parallel with a 15 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "6.44615 A",
"B": "2.44615 A",
"C": "6.89231 A",
"D": "3.44615 A"
} | D | 3.44615 A | Series branch resistance=8+5=13 Ω. Parallel equivalent R_eq=(13×15)/(13+15)=6.96429 Ω. Total current I=V/R_eq=24/6.96429=3.44615 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.44615 A, not 6.44615 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.44615 A, not 2.44615 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.44615 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_004591 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 9 kg and radius 1 m is acted on by a constant torque of 41 N m about its central axis. Find its angular acceleration. | {
"A": "11.11111 rad s⁻²",
"B": "4.55556 rad s⁻²",
"C": "1.91111 rad s⁻²",
"D": "9.11111 rad s⁻²"
} | D | 9.11111 rad s⁻² | For a solid disc, I=½MR²=½(9)(1)²=4.5 kg m². Using τ=Iα, α=41/4.5=9.11111 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.11111 rad s⁻², not 11.11111 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.11111 rad s⁻², not 4.55556 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing ... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009877 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(CN)_6]^-2, each CN ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "1",
"B": "4",
"C": "6",
"D": "7"
} | B | 4 | Let the formal oxidation state of Mn be x. Charge balance gives x+(6)(−1)=-2; hence x=-2+6=+4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.",
"B": "Correct. The worked calculation gives 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 6.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005526 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 33 μF capacitor is charged to a potential difference of 5 V. Calculate the energy stored, expressed in μJ. | {
"A": "412.5 μJ",
"B": "206.25 μJ",
"C": "495 μJ",
"D": "309.375 μJ"
} | A | 412.5 μJ | U=½CV². Since C=33 μF, U in μJ is ½×33×(5)²=412.5 μJ. | {
"A": "Correct. The worked calculation gives 412.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 412.5 μJ, not 206.25 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 412.5 μJ, not 495 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_006759 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 45 mol H₂ and 26 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "44 mol",
"B": "33.75 mol",
"C": "47 mol",
"D": "45 mol"
} | D | 45 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 45 mol H₂O; O₂ can produce 52 mol H₂O. The limiting condition is H₂; product=45 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45 mol, not 44 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 45 mol, not 33.75 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 45 mol, not 47 mol.... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008724 | 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 0.81 mol L⁻¹ and initially B is absent. At equilibrium, 23% of A has dissociated at constant volume. Find K_c. | {
"A": "0.22259",
"B": "2.22259",
"C": "3.22259",
"D": "0.16694"
} | A | 0.22259 | Let α=0.23. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.81)(0.23)²/(1−0.23)=0.22259. | {
"A": "Correct. The worked calculation gives 0.22259.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.22259, not 2.22259.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.22259, not 3.22259.",
"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_000055 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 -13x -1=0, let its roots be α and β. What is α²+β²? | {
"A": "19.44444",
"B": "38.88889",
"C": "23.33333",
"D": "20.44444"
} | A | 19.44444 | By Vieta's relations, α+β = 13/3 and αβ = -1/3. Then α²+β²=(α+β)²−2αβ = (13/3)²−2(-1/3) = 19.44444. | {
"A": "Correct. The worked calculation gives 19.44444.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19.44444, not 38.88889.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19.44444, not 23.33333.",
"D": "Incorrect. Substituting the stat... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001794 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 57 distinct elements? | {
"A": "1652411475",
"B": "1652411474",
"C": "165241148.5",
"D": "826205737.5"
} | A | 1652411475 | Order does not matter, so the count is C(57,8)=57!/[8!(49)!]=1652411475. | {
"A": "Correct. The worked calculation gives 1652411475.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1652411475, not 1652411474.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1652411475, not 165241148.5.",
"D": "Incorrect. Substituti... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001488 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (1x² +1x -3) dx. | {
"A": "17.33333",
"B": "-17.33333",
"C": "15.33333",
"D": "26"
} | A | 17.33333 | An antiderivative is (1/3)x³+(1/2)x²+(-3)x. Evaluating between 0 and 4 gives (1/3)(4)³+(1/2)(4)²+(-3)(4)=17.33333. | {
"A": "Correct. The worked calculation gives 17.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17.33333, not -17.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17.33333, not 15.33333.",
"D": "Incorrect. Substituting the sta... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001807 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 12 elements can be selected from a set of 82 distinct elements? | {
"A": "66278791487376",
"B": "82848489359220",
"C": "62136367019415",
"D": "82848489359218"
} | B | 82848489359220 | Order does not matter, so the count is C(82,12)=82!/[12!(70)!]=82848489359220. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 82848489359220, not 66278791487376.",
"B": "Correct. The worked calculation gives 82848489359220.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 82848489359220, not 62136367019415.",
"D": "In... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006847 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 40 mol H₂ and 29 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "80 mol",
"B": "32 mol",
"C": "41 mol",
"D": "40 mol"
} | D | 40 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 40 mol H₂O; O₂ can produce 58 mol H₂O. The limiting condition is H₂; product=40 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 40 mol, not 80 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 40 mol, not 32 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 40 mol, not 41 mol.",
... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005734 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.3 atm at 191 K. What is its pressure at 523 K? | {
"A": "0.82147 atm",
"B": "0.41073 atm",
"C": "3.82147 atm",
"D": "-0.17853 atm"
} | A | 0.82147 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.3)(523)/(191)=0.82147 atm. | {
"A": "Correct. The worked calculation gives 0.82147 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.82147 atm, not 0.41073 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.82147 atm, not 3.82147 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_008653 | 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 2 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-1.56 K",
"B": "4.44 K",
"C": "1.144 K",
"D": "1.44 K"
} | D | 1.44 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×0.72=1.44 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.44 K, not -1.56 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.44 K, not 4.44 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.44 K, not 1.144 K."... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004970 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 6 Ω and 13 Ω are connected in series; this combination is connected in parallel with a 18 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.59649 A",
"B": "1.94737 A",
"C": "2.59649 A",
"D": "1.25965 A"
} | C | 2.59649 A | Series branch resistance=6+13=19 Ω. Parallel equivalent R_eq=(19×18)/(19+18)=9.24324 Ω. Total current I=V/R_eq=24/9.24324=2.59649 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.59649 A, not 0.59649 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.59649 A, not 1.94737 A.",
"C": "Correct. The worked calculation gives 2.59649 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003512 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 53 m s⁻¹ at 15° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "139.45 m",
"B": "140.45 m",
"C": "15.045 m",
"D": "141.45 m"
} | B | 140.45 m | Range R=u²sin(2θ)/g. Substituting u=53, θ=15° and g=10 gives R=(53)²sin(30°)/10=140.45 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 140.45 m, not 139.45 m.",
"B": "Correct. The worked calculation gives 140.45 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 140.45 m, not 15.045 m.",
"D": "Incorrect. Substituting the stat... | [
"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_007452 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 43 mL of 0.10 M HCl is mixed with 60 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "18.32642",
"B": "13.21761",
"C": "12.21761",
"D": "-12.21761"
} | C | 12.21761 | Excess OH⁻ moles=0.10×(60−43)/1000=0.001700 mol. Total volume=0.103 L, so [OH⁻]=0.016505 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.21761. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.21761, not 18.32642.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.21761, not 13.21761.",
"C": "Correct. The worked calculation gives 12.21761.",
"D": "Incorrect. Substituting the stat... | [
"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_008510 | 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 1.63 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-1.022 K",
"B": "2.978 K",
"C": "1.978 K",
"D": "0.978 K"
} | D | 0.978 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.6×1.63=0.978 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.978 K, not -1.022 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.978 K, not 2.978 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.978 K, not 1.97... | [
"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_006899 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 21 mol H₂ and 9 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "18 mol",
"B": "2.8 mol",
"C": "19 mol",
"D": "9 mol"
} | A | 18 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 21 mol H₂O; O₂ can produce 18 mol H₂O. The limiting condition is O₂; product=18 mol. | {
"A": "Correct. The worked calculation gives 18 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18 mol, not 2.8 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18 mol, not 19 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_003771 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 1 m s⁻¹. A constant net force does 12 N of work over 2 m in the direction of motion. Find its final kinetic energy. | {
"A": "13 J",
"B": "26 J",
"C": "52 J",
"D": "19.5 J"
} | B | 26 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(1)²+(12)(2)=26 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26 J, not 13 J.",
"B": "Correct. The worked calculation gives 26 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26 J, not 52 J.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_007597 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 59 mL of 0.10 M HCl is mixed with 40 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.71688",
"B": "4.71688",
"C": "-1.71688",
"D": "2.71688"
} | A | 1.71688 | Excess H⁺ moles=0.10×(59−40)/1000=0.001900 mol. Total volume=0.099 L, so [H⁺]=0.019192 M and pH=−log₁₀[H⁺]=1.71688. | {
"A": "Correct. The worked calculation gives 1.71688.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.71688, not 4.71688.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.71688, not -1.71688.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006619 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 21 kg is attached to an ideal spring of force constant 24 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "2.80624 s",
"B": "2.87083 s",
"C": "4.87083 s",
"D": "1.87083 s"
} | D | 1.87083 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(21/24)=1.87083 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.87083 s, not 2.80624 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.87083 s, not 2.87083 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.87083 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_003126 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-10-8i)/(2+1i). What is Re(z), the real part of z? | {
"A": "-5.6",
"B": "-4.6",
"C": "-4.2",
"D": "-3.6"
} | A | -5.6 | Multiply numerator and denominator by the conjugate (2-1i). Then Re(z)=(ac+bd)/(c²+d²)=((-10)(2)+(-8)(1))/(2²+(1)²)=-5.6. | {
"A": "Correct. The worked calculation gives -5.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -5.6, not -4.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -5.6, not -4.2.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_007440 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 25 mL of 0.10 M HCl is mixed with 77 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "13.7074",
"B": "14.7074",
"C": "12.7074",
"D": "9.7074"
} | C | 12.7074 | Excess OH⁻ moles=0.10×(77−25)/1000=0.005200 mol. Total volume=0.102 L, so [OH⁻]=0.050980 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.7074. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.7074, not 13.7074.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.7074, not 14.7074.",
"C": "Correct. The worked calculation gives 12.7074.",
"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_006322 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 86 cm in front of a thin convex lens of focal length 30 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.53571",
"B": "-1.46429",
"C": "3.53571",
"D": "-0.53571"
} | A | 0.53571 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(86)(30)/(86−30)=46.07143 cm. Thus |m|=v/u=46.07143/86=0.53571. | {
"A": "Correct. The worked calculation gives 0.53571.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.53571, not -1.46429.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.53571, not 3.53571.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009386 | 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_18N_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "7.5",
"B": "-10",
"C": "20",
"D": "10"
} | D | 10 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×17+2+2−18−0)/2=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 7.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not -10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 20.",
"D": "Correct. The w... | [
"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_000900 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 3 and common ratio 2. What is the sum of its first 12 terms? | {
"A": "12287",
"B": "9828",
"C": "12285",
"D": "-12285"
} | C | 12285 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=3(2^12−1)/(2−1)=12285. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12285, not 12287.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12285, not 9828.",
"C": "Correct. The worked calculation gives 12285.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_005710 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.1 atm at 215 K. What is its pressure at 580 K? | {
"A": "2.83256 atm",
"B": "6.66512 atm",
"C": "5.66512 atm",
"D": "1.56651 atm"
} | C | 5.66512 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.1)(580)/(215)=5.66512 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.66512 atm, not 2.83256 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.66512 atm, not 6.66512 atm.",
"C": "Correct. The worked calculation gives 5.66512 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_004615 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 6 kg and radius 3 m is acted on by a constant torque of 41 N m about its central axis. Find its angular acceleration. | {
"A": "-1.51852 rad s⁻²",
"B": "4.51852 rad s⁻²",
"C": "1.51852 rad s⁻²",
"D": "-0.48148 rad s⁻²"
} | C | 1.51852 rad s⁻² | For a solid disc, I=½MR²=½(6)(3)²=27 kg m². Using τ=Iα, α=41/27=1.51852 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.51852 rad s⁻², not -1.51852 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.51852 rad s⁻², not 4.51852 rad s⁻².",
"C": "Correct. The worked calculation gives 1.51852 rad s⁻².",
"D... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005819 | 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 3.3 atm at 450 K. What is its pressure at 712 K? | {
"A": "2.22133 atm",
"B": "3.916 atm",
"C": "5.22133 atm",
"D": "10.44267 atm"
} | C | 5.22133 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.3)(712)/(450)=5.22133 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.22133 atm, not 2.22133 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.22133 atm, not 3.916 atm.",
"C": "Correct. The worked calculation gives 5.22133 atm.",
"D": "Incorrect. Substitu... | [
"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_004868 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 6 Ω and 12 Ω are connected in series; this combination is connected in parallel with a 20 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.26667 A",
"B": "1.12667 A",
"C": "3.26667 A",
"D": "2.26667 A"
} | A | 1.26667 A | Series branch resistance=6+12=18 Ω. Parallel equivalent R_eq=(18×20)/(18+20)=9.47368 Ω. Total current I=V/R_eq=12/9.47368=1.26667 A. | {
"A": "Correct. The worked calculation gives 1.26667 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.26667 A, not 1.12667 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.26667 A, not 3.26667 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000667 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -13 and common difference 9. Find the sum of its first 18 terms. | {
"A": "-1143",
"B": "115.3",
"C": "1143",
"D": "857.25"
} | C | 1143 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-13, d=9, n=18: Sₙ=18/2[2(-13)+(18−1)(9)]=1143. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1143, not -1143.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1143, not 115.3.",
"C": "Correct. The worked calculation gives 1143.",
"D": "Incorrect. Substituting the stated values into the... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008425 | 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 1.29 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": "1.58 K",
"B": "3.58 K",
"C": "2.58 K",
"D": "4.58 K"
} | C | 2.58 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×1.29=2.58 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.58 K, not 1.58 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.58 K, not 3.58 K.",
"C": "Correct. The worked calculation gives 2.58 K.",
"D": "Incorrect. Substituting the stated values ... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006271 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 42 cm in front of a thin convex lens of focal length 21 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1",
"B": "1.1",
"C": "2",
"D": "3"
} | A | 1 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(42)(21)/(42−21)=42 cm. Thus |m|=v/u=42/42=1. | {
"A": "Correct. The worked calculation gives 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_003039 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(4-8i)/(2+7i). What is Re(z), the real part of z? | {
"A": "1.09434",
"B": "-1.90566",
"C": "-0.90566",
"D": "0.90943"
} | C | -0.90566 | Multiply numerator and denominator by the conjugate (2-7i). Then Re(z)=(ac+bd)/(c²+d²)=((4)(2)+(-8)(7))/(2²+(7)²)=-0.90566. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.90566, not 1.09434.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.90566, not -1.90566.",
"C": "Correct. The worked calculation gives -0.90566.",
"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_008652 | 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 1.42 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "3.408 K",
"B": "1.704 K",
"C": "1.278 K",
"D": "0.852 K"
} | B | 1.704 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.6×1.42=1.704 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.704 K, not 3.408 K.",
"B": "Correct. The worked calculation gives 1.704 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.704 K, not 1.278 K.",
"D": "Incorrect. Substituting the stated va... | [
"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_008244 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 3 A for 24510 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": "23.19251 g",
"B": "19.35401 g",
"C": "24.19251 g",
"D": "36.28877 g"
} | C | 24.19251 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×3×24510/(2×96500)=24.19251 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24.19251 g, not 23.19251 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24.19251 g, not 19.35401 g.",
"C": "Correct. The worked calculation gives 24.19251 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_002879 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(8, 7, -5) and v=(4, 0, 3), calculate u·v. | {
"A": "8.5",
"B": "17",
"C": "18",
"D": "20.4"
} | B | 17 | The dot product is the sum of corresponding component products: (8)(4)+(7)(0)+(-5)(3)=17. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 17, not 8.5.",
"B": "Correct. The worked calculation gives 17.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17, not 18.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007792 | 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 30 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "4.875 mmol L⁻¹",
"B": "1.875 mmol L⁻¹",
"C": "3.75 mmol L⁻¹",
"D": "-0.125 mmol L⁻¹"
} | B | 1.875 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=30/2^4=1.875 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.875 mmol L⁻¹, not 4.875 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 1.875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.875 mmol L⁻¹, not 3.75 mmol L⁻¹.",
"D": "Inc... | [
"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_007463 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 58 mL of 0.10 M HCl is mixed with 72 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.03218",
"B": "14.03218",
"C": "9.03218",
"D": "6.01609"
} | A | 12.03218 | Excess OH⁻ moles=0.10×(72−58)/1000=0.001400 mol. Total volume=0.130 L, so [OH⁻]=0.010769 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.03218. | {
"A": "Correct. The worked calculation gives 12.03218.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.03218, not 14.03218.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.03218, not 9.03218.",
"D": "Incorrect. Substituting the state... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003888 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 10 m s⁻¹. A constant net force does 17 N of work over 13 m in the direction of motion. Find its final kinetic energy. | {
"A": "620 J",
"B": "621 J",
"C": "745.2 J",
"D": "496.8 J"
} | B | 621 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(10)²+(17)(13)=621 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 621 J, not 620 J.",
"B": "Correct. The worked calculation gives 621 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 621 J, not 745.2 J.",
"D": "Incorrect. Substituting the stated values int... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001514 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (5x² +4x +1) dx. | {
"A": "171.2",
"B": "140.66667",
"C": "142.66667",
"D": "-142.66667"
} | C | 142.66667 | An antiderivative is (5/3)x³+(4/2)x²+(1)x. Evaluating between 0 and 4 gives (5/3)(4)³+(4/2)(4)²+(1)(4)=142.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 142.66667, not 171.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 142.66667, not 140.66667.",
"C": "Correct. The worked calculation gives 142.66667.",
"D": "Incorrect. Substituting the sta... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000740 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 12 and common ratio 4. What is the sum of its first 11 terms? | {
"A": "-16777212",
"B": "12582909",
"C": "25165818",
"D": "16777212"
} | D | 16777212 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=12(4^11−1)/(4−1)=16777212. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16777212, not -16777212.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16777212, not 12582909.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16777212, not... | [
"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_001160 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ +7x² +11x+7. Evaluate f′(-3). | {
"A": "61.6",
"B": "78",
"C": "77",
"D": "57.75"
} | C | 77 | Differentiate: f′(x)=3(4)x²+2(7)x+(11). At x=-3, f′(-3)=3(4)(-3)²+2(7)(-3)+(11)=77. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 77, not 61.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 77, not 78.",
"C": "Correct. The worked calculation gives 77.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000038 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 +5x -7=0, let its roots be α and β. What is α²+β²? | {
"A": "7.0625",
"B": "3.79688",
"C": "5.0625",
"D": "-5.0625"
} | C | 5.0625 | By Vieta's relations, α+β = -5/4 and αβ = -7/4. Then α²+β²=(α+β)²−2αβ = (-5/4)²−2(-7/4) = 5.0625. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.0625, not 7.0625.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.0625, not 3.79688.",
"C": "Correct. The worked calculation gives 5.0625.",
"D": "Incorrect. Substituting the stated values... | [
"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_001306 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-2x³ -4x² +12x+7. Evaluate f′(2). | {
"A": "-30",
"B": "-28",
"C": "-22.4",
"D": "-33.6"
} | B | -28 | Differentiate: f′(x)=3(-2)x²+2(-4)x+(12). At x=2, f′(2)=3(-2)(2)²+2(-4)(2)+(12)=-28. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -28, not -30.",
"B": "Correct. The worked calculation gives -28.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -28, not -22.4.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009122 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.40 V, transfers 2 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.4227 V",
"B": "-0.4227 V",
"C": "1.5773 V",
"D": "4.5773 V"
} | C | 1.5773 V | Apply the Nernst equation: E=1.40−(0.0591/2)(-6)=1.5773 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.5773 V, not -1.4227 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.5773 V, not -0.4227 V.",
"C": "Correct. The worked calculation gives 1.5773 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_000107 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 +14x -3=0, let its roots be α and β. What is α²+β²? | {
"A": "13.75",
"B": "27.5",
"C": "11.75",
"D": "16.75"
} | A | 13.75 | By Vieta's relations, α+β = -14/4 and αβ = -3/4. Then α²+β²=(α+β)²−2αβ = (-14/4)²−2(-3/4) = 13.75. | {
"A": "Correct. The worked calculation gives 13.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13.75, not 27.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13.75, not 11.75.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_009551 | 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_30N_1X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "6",
"B": "2",
"C": "3",
"D": "4"
} | D | 4 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+1−30−1)/2=4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 3.",
"D": "Correct. The worked ca... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008535 | 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 1.06 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.6536 K",
"B": "3.6536 K",
"C": "1.2402 K",
"D": "2.6536 K"
} | A | 1.6536 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.52×1.06=1.6536 K. | {
"A": "Correct. The worked calculation gives 1.6536 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.6536 K, not 3.6536 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.6536 K, not 1.2402 K.",
"D": "Incorrect. Substituting the stat... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006504 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 12 kg is attached to an ideal spring of force constant 269 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.42242 s",
"B": "0.84484 s",
"C": "-2.57758 s",
"D": "-0.57758 s"
} | A | 0.42242 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(12/269)=0.42242 s. | {
"A": "Correct. The worked calculation gives 0.42242 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.42242 s, not 0.84484 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.42242 s, not -2.57758 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006347 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 22 kg is attached to an ideal spring of force constant 46 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.38313 s",
"B": "1.13831 s",
"C": "-0.61687 s",
"D": "2.38313 s"
} | A | 1.38313 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(22/46)=1.38313 s. | {
"A": "Correct. The worked calculation gives 1.38313 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.38313 s, not 1.13831 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.38313 s, not -0.61687 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005371 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 18 μF capacitor is charged to a potential difference of 25 V. Calculate the energy stored, expressed in μJ. | {
"A": "5626 μJ",
"B": "4218.75 μJ",
"C": "5623 μJ",
"D": "5625 μJ"
} | D | 5625 μJ | U=½CV². Since C=18 μF, U in μJ is ½×18×(25)²=5625 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5625 μJ, not 5626 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5625 μJ, not 4218.75 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5625 μJ, not 56... | [
"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_002168 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 4 blue and 9 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.35294",
"B": "-2.64706",
"C": "0.35294",
"D": "1.35294"
} | C | 0.35294 | Favourable pairs = C(4,2)+C(4,2)+C(9,2)=48. Total pairs=C(17,2)=136. Therefore P=48/136=0.35294. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35294, not -0.35294.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35294, not -2.64706.",
"C": "Correct. The worked calculation gives 0.35294.",
"D": "Incorrect. Substituting the stated ... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003208 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(3-4i)/(12+6i). What is Re(z), the real part of z? | {
"A": "0.06667",
"B": "0.05",
"C": "-2.93333",
"D": "2.06667"
} | A | 0.06667 | Multiply numerator and denominator by the conjugate (12-6i). Then Re(z)=(ac+bd)/(c²+d²)=((3)(12)+(-4)(6))/(12²+(6)²)=0.06667. | {
"A": "Correct. The worked calculation gives 0.06667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.06667, not 0.05.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.06667, not -2.93333.",
"D": "Incorrect. Substituting the stated valu... | [
"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_002511 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, -3], [1, -6]]. | {
"A": "-3",
"B": "-5",
"C": "-4.5",
"D": "-2"
} | A | -3 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(-6)−(-3)(1)=-3. | {
"A": "Correct. The worked calculation gives -3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -3, not -5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -3, not -4.5.",
"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_005829 | 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 3.7 atm at 389 K. What is its pressure at 594 K? | {
"A": "1.56499 atm",
"B": "4.2374 atm",
"C": "4.64987 atm",
"D": "5.64987 atm"
} | D | 5.64987 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.7)(594)/(389)=5.64987 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.64987 atm, not 1.56499 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.64987 atm, not 4.2374 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.6... | [
"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_006257 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 73 cm in front of a thin convex lens of focal length 18 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.67273",
"B": "-1.67273",
"C": "0.32727",
"D": "-2.67273"
} | C | 0.32727 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(73)(18)/(73−18)=23.89091 cm. Thus |m|=v/u=23.89091/73=0.32727. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32727, not -0.67273.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32727, not -1.67273.",
"C": "Correct. The worked calculation gives 0.32727.",
"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_005285 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +1 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "41.375 N",
"B": "39.375 N",
"C": "47.25 N",
"D": "4.9375 N"
} | B | 39.375 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(1×10⁻⁶)/(4×10⁻²)²=39.375 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 39.375 N, not 41.375 N.",
"B": "Correct. The worked calculation gives 39.375 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39.375 N, not 47.25 N.",
"D": "Incorrect. Substituting the state... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000848 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 5. What is the sum of its first 9 terms? | {
"A": "4882809",
"B": "4882810",
"C": "-4882810",
"D": "4882812"
} | B | 4882810 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(5^9−1)/(5−1)=4882810. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4882810, not 4882809.",
"B": "Correct. The worked calculation gives 4882810.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4882810, not -4882810.",
"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_001555 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (3x² +1x +2) dx. | {
"A": "246",
"B": "25.6",
"C": "295.2",
"D": "492"
} | A | 246 | An antiderivative is (3/3)x³+(1/2)x²+(2)x. Evaluating between 0 and 6 gives (3/3)(6)³+(1/2)(6)²+(2)(6)=246. | {
"A": "Correct. The worked calculation gives 246.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 246, not 25.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 246, not 295.2.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006154 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 136 cm in front of a thin convex lens of focal length 29 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-1.72897",
"B": "-0.27103",
"C": "0.27103",
"D": "3.27103"
} | C | 0.27103 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(136)(29)/(136−29)=36.85981 cm. Thus |m|=v/u=36.85981/136=0.27103. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.27103, not -1.72897.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.27103, not -0.27103.",
"C": "Correct. The worked calculation gives 0.27103.",
"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_003837 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block initially moves at 6 m s⁻¹. A constant net force does 12 N of work over 4 m in the direction of motion. Find its final kinetic energy. | {
"A": "139 J",
"B": "137 J",
"C": "165.6 J",
"D": "138 J"
} | D | 138 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(5)(6)²+(12)(4)=138 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 138 J, not 139 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 138 J, not 137 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 138 J, not 165.6 J.",
"D... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000499 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 8 and common difference 15. Find the sum of its first 8 terms. | {
"A": "387.2",
"B": "484",
"C": "486",
"D": "483"
} | B | 484 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=8, d=15, n=8: Sₙ=8/2[2(8)+(8−1)(15)]=484. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 484, not 387.2.",
"B": "Correct. The worked calculation gives 484.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 484, not 486.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007502 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 26 mL of 0.10 M HCl is mixed with 35 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "18.25337",
"B": "12.16891",
"C": "15.16891",
"D": "11.16891"
} | B | 12.16891 | Excess OH⁻ moles=0.10×(35−26)/1000=0.000900 mol. Total volume=0.061 L, so [OH⁻]=0.014754 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.16891. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.16891, not 18.25337.",
"B": "Correct. The worked calculation gives 12.16891.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.16891, not 15.16891.",
"D": "Incorrect. Substituting the stat... | [
"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_002776 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-1, 3, 5) and v=(-2, -1, -5), calculate u·v. | {
"A": "-1.6",
"B": "-26",
"C": "-20.8",
"D": "-19.5"
} | B | -26 | The dot product is the sum of corresponding component products: (-1)(-2)+(3)(-1)+(5)(-5)=-26. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -26, not -1.6.",
"B": "Correct. The worked calculation gives -26.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -26, not -20.8.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_001987 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 9 elements can be selected from a set of 56 distinct elements? | {
"A": "15151936800",
"B": "6060774720",
"C": "757596841",
"D": "7575968400"
} | D | 7575968400 | Order does not matter, so the count is C(56,9)=56!/[9!(47)!]=7575968400. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7575968400, not 15151936800.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7575968400, not 6060774720.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 75759... | [
"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_002529 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, 2], [2, 7]]. | {
"A": "37",
"B": "4.8",
"C": "36",
"D": "38"
} | D | 38 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(7)−(2)(2)=38. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 38, not 37.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 38, not 4.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 38, not 36.",
"D": "Correct. The wo... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008092 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 12 A for 12479 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": "5.92694 g",
"B": "50.26942 g",
"C": "36.95206 g",
"D": "49.26942 g"
} | D | 49.26942 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×12×12479/(2×96500)=49.26942 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 49.26942 g, not 5.92694 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 49.26942 g, not 50.26942 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 49.2694... | [
"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_002659 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, 8], [7, 6]]. | {
"A": "-44",
"B": "44",
"C": "-46",
"D": "-22"
} | A | -44 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(6)−(8)(7)=-44. | {
"A": "Correct. The worked calculation gives -44.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -44, not 44.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -44, not -46.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007574 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 39 mL of 0.10 M HCl is mixed with 67 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.42185",
"B": "14.42185",
"C": "10.42185",
"D": "13.42185"
} | A | 12.42185 | Excess OH⁻ moles=0.10×(67−39)/1000=0.002800 mol. Total volume=0.106 L, so [OH⁻]=0.026415 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.42185. | {
"A": "Correct. The worked calculation gives 12.42185.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.42185, not 14.42185.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.42185, not 10.42185.",
"D": "Incorrect. Substituting the stat... | [
"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_000591 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 6 and common difference 15. Find the sum of its first 35 terms. | {
"A": "6851.25",
"B": "4567.5",
"C": "9135",
"D": "9136"
} | C | 9135 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=6, d=15, n=35: Sₙ=35/2[2(6)+(35−1)(15)]=9135. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9135, not 6851.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9135, not 4567.5.",
"C": "Correct. The worked calculation gives 9135.",
"D": "Incorrect. Substituting the stated values into ... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005448 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 71 μF capacitor is charged to a potential difference of 22 V. Calculate the energy stored, expressed in μJ. | {
"A": "25773 μJ",
"B": "13745.6 μJ",
"C": "17182 μJ",
"D": "17180 μJ"
} | C | 17182 μJ | U=½CV². Since C=71 μF, U in μJ is ½×71×(22)²=17182 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 17182 μJ, not 25773 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17182 μJ, not 13745.6 μJ.",
"C": "Correct. The worked calculation gives 17182 μJ.",
"D": "Incorrect. Substituting the st... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005108 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +5 μC are separated by 12 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "28.125 N",
"B": "22.5 N",
"C": "56.25 N",
"D": "33.75 N"
} | A | 28.125 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(5×10⁻⁶)/(12×10⁻²)²=28.125 N. | {
"A": "Correct. The worked calculation gives 28.125 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28.125 N, not 22.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28.125 N, not 56.25 N.",
"D": "Incorrect. Substituting the stated ... | [
"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_007330 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 3 mol of gas at 597 K and 2 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "88.17845 L",
"B": "36.74102 L",
"C": "73.48204 L",
"D": "74.48204 L"
} | C | 73.48204 L | PV=nRT, so V=nRT/P=(3)(0.082057)(597)/(2)=73.48204 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 73.48204 L, not 88.17845 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 73.48204 L, not 36.74102 L.",
"C": "Correct. The worked calculation gives 73.48204 L.",
"D": "Incorrect. Substitutin... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006981 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 13 mol H₂ and 11 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "6.5 mol",
"B": "11 mol",
"C": "13 mol",
"D": "15 mol"
} | C | 13 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 13 mol H₂O; O₂ can produce 22 mol H₂O. The limiting condition is H₂; product=13 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13 mol, not 6.5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13 mol, not 11 mol.",
"C": "Correct. The worked calculation gives 13 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_007900 | 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 99 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "14.375 mmol L⁻¹",
"B": "11.375 mmol L⁻¹",
"C": "12.375 mmol L⁻¹",
"D": "6.1875 mmol L⁻¹"
} | C | 12.375 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=99/2^3=12.375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.375 mmol L⁻¹, not 14.375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.375 mmol L⁻¹, not 11.375 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 12.375 mmol L⁻¹.",
"D"... | [
"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_003091 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-9-7i)/(7+7i). What is Re(z), the real part of z? | {
"A": "-4.14286",
"B": "-1.14286",
"C": "-2.14286",
"D": "-0.85714"
} | B | -1.14286 | Multiply numerator and denominator by the conjugate (7-7i). Then Re(z)=(ac+bd)/(c²+d²)=((-9)(7)+(-7)(7))/(7²+(7)²)=-1.14286. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.14286, not -4.14286.",
"B": "Correct. The worked calculation gives -1.14286.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.14286, not -2.14286.",
"D": "Incorrect. Substituting the stat... | [
"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_008844 | 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 1.2 mol L⁻¹ and initially B is absent. At equilibrium, 57% of A has dissociated at constant volume. Find K_c. | {
"A": "4.62679",
"B": "1.62679",
"C": "1.36268",
"D": "3.62679"
} | D | 3.62679 | Let α=0.57. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.2)(0.57)²/(1−0.57)=3.62679. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.62679, not 4.62679.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.62679, not 1.62679.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.62679, not 1.362... | [
"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_002229 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 10 blue and 9 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.48",
"B": "0.32",
"C": "-0.32",
"D": "1.32"
} | B | 0.32 | Favourable pairs = C(6,2)+C(10,2)+C(9,2)=96. Total pairs=C(25,2)=300. Therefore P=96/300=0.32. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32, not 0.48.",
"B": "Correct. The worked calculation gives 0.32.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32, not -0.32.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_008388 | 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 1.17 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "2.34 K",
"B": "1.17 K",
"C": "-1.17 K",
"D": "-0.83 K"
} | B | 1.17 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×1.0×1.17=1.17 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.17 K, not 2.34 K.",
"B": "Correct. The worked calculation gives 1.17 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.17 K, not -1.17 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005445 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 48 μF capacitor is charged to a potential difference of 12 V. Calculate the energy stored, expressed in μJ. | {
"A": "3454 μJ",
"B": "3457 μJ",
"C": "1728 μJ",
"D": "3456 μJ"
} | D | 3456 μJ | U=½CV². Since C=48 μF, U in μJ is ½×48×(12)²=3456 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3456 μJ, not 3454 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3456 μJ, not 3457 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3456 μJ, not 1728 ... | [
"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_008900 | 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 0.9 mol L⁻¹ and initially B is absent. At equilibrium, 10% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.96",
"B": "0.04",
"C": "0.06",
"D": "0.08"
} | B | 0.04 | Let α=0.1. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.9)(0.1)²/(1−0.1)=0.04. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.04, not -0.96.",
"B": "Correct. The worked calculation gives 0.04.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.04, not 0.06.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_006055 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 106 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": "0.34177",
"B": "0.17089",
"C": "-1.65823",
"D": "-0.65823"
} | A | 0.34177 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(106)(27)/(106−27)=36.22785 cm. Thus |m|=v/u=36.22785/106=0.34177. | {
"A": "Correct. The worked calculation gives 0.34177.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34177, not 0.17089.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34177, not -1.65823.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001428 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (1x² -3x -3) dx. | {
"A": "-16.5",
"B": "-6.75",
"C": "-10.5",
"D": "-13.5"
} | D | -13.5 | An antiderivative is (1/3)x³+(-3/2)x²+(-3)x. Evaluating between 0 and 3 gives (1/3)(3)³+(-3/2)(3)²+(-3)(3)=-13.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -13.5, not -16.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -13.5, not -6.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -13.5, not -10.5.",
"D":... | [
"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 |
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