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_004745 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 15 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 11 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.32253 A",
"B": "3.2253 A",
"C": "1.2253 A",
"D": "5.2253 A"
} | B | 3.2253 A | Series branch resistance=15+8=23 Ω. Parallel equivalent R_eq=(23×11)/(23+11)=7.44118 Ω. Total current I=V/R_eq=24/7.44118=3.2253 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.2253 A, not 1.32253 A.",
"B": "Correct. The worked calculation gives 3.2253 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.2253 A, not 1.2253 A.",
"D": "Incorrect. Substituting the sta... | [
"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_005008 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +6 μC are separated by 12 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "26.25 N",
"B": "31.5 N",
"C": "21 N",
"D": "28.25 N"
} | A | 26.25 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(6×10⁻⁶)/(12×10⁻²)²=26.25 N. | {
"A": "Correct. The worked calculation gives 26.25 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26.25 N, not 31.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26.25 N, not 21 N.",
"D": "Incorrect. Substituting the stated values... | [
"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_002502 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 8], [1, -4]]. | {
"A": "-20",
"B": "-40",
"C": "-18",
"D": "-30"
} | A | -20 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(-4)−(8)(1)=-20. | {
"A": "Correct. The worked calculation gives -20.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -20, not -40.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -20, not -18.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003153 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(9+7i)/(6+9i). What is Re(z), the real part of z? | {
"A": "-1",
"B": "1.1",
"C": "2",
"D": "1"
} | D | 1 | Multiply numerator and denominator by the conjugate (6-9i). Then Re(z)=(ac+bd)/(c²+d²)=((9)(6)+(7)(9))/(6²+(9)²)=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not -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": "Correct. The worked... | [
"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_005020 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +8 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "541 N",
"B": "810 N",
"C": "270 N",
"D": "540 N"
} | D | 540 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(8×10⁻⁶)/(2×10⁻²)²=540 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 540 N, not 541 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 540 N, not 810 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 540 N, not 270 N.",
"D":... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004735 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 12 Ω and 6 Ω are connected in series; this combination is connected in parallel with a 16 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.83333 A",
"B": "1.28333 A",
"C": "4.25 A",
"D": "2.83333 A"
} | D | 2.83333 A | Series branch resistance=12+6=18 Ω. Parallel equivalent R_eq=(18×16)/(18+16)=8.47059 Ω. Total current I=V/R_eq=24/8.47059=2.83333 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.83333 A, not 0.83333 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.83333 A, not 1.28333 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.83333 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_008832 | 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 1.89 mol L⁻¹ and initially B is absent. At equilibrium, 57% of A has dissociated at constant volume. Find K_c. | {
"A": "4.7122",
"B": "4.28415",
"C": "8.56829",
"D": "5.7122"
} | D | 5.7122 | Let α=0.57. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.89)(0.57)²/(1−0.57)=5.7122. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.7122, not 4.7122.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.7122, not 4.28415.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.7122, not 8.56829."... | [
"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_009033 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.87 V, transfers 3 electrons, and has reaction quotient Q=10^1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.8503 V",
"B": "-2.1497 V",
"C": "-1.1497 V",
"D": "-0.8503 V"
} | A | 0.8503 V | Apply the Nernst equation: E=0.87−(0.0591/3)(1)=0.8503 V. | {
"A": "Correct. The worked calculation gives 0.8503 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8503 V, not -2.1497 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8503 V, not -1.1497 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_002663 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, 1], [5, 3]]. | {
"A": "9.5",
"B": "21",
"C": "19",
"D": "15.2"
} | C | 19 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(3)−(1)(5)=19. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19, not 9.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19, not 21.",
"C": "Correct. The worked calculation gives 19.",
"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_000891 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio 2. What is the sum of its first 5 terms? | {
"A": "46.5",
"B": "62",
"C": "49.6",
"D": "-62"
} | B | 62 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(2^5−1)/(2−1)=62. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 62, not 46.5.",
"B": "Correct. The worked calculation gives 62.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 62, not 49.6.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_006318 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 21 cm in front of a thin convex lens of focal length 6 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "3.4",
"B": "0.4",
"C": "-0.4",
"D": "0.3"
} | B | 0.4 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(21)(6)/(21−6)=8.4 cm. Thus |m|=v/u=8.4/21=0.4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.4, not 3.4.",
"B": "Correct. The worked calculation gives 0.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.4, not -0.4.",
"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_000615 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -5 and common difference 2. Find the sum of its first 23 terms. | {
"A": "293.25",
"B": "782",
"C": "391",
"D": "586.5"
} | C | 391 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-5, d=2, n=23: Sₙ=23/2[2(-5)+(23−1)(2)]=391. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 391, not 293.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 391, not 782.",
"C": "Correct. The worked calculation gives 391.",
"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_002469 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, 1], [3, -4]]. | {
"A": "-70",
"B": "-28",
"C": "-2.5",
"D": "-35"
} | D | -35 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(-4)−(1)(3)=-35. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -35, not -70.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -35, not -28.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -35, not -2.5.",
"D": "Correct. ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003616 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 36 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "121.78416 m",
"B": "182.67625 m",
"C": "123.78416 m",
"D": "146.141 m"
} | A | 121.78416 m | Range R=u²sin(2θ)/g. Substituting u=36, θ=55° and g=10 gives R=(36)²sin(110°)/10=121.78416 m. | {
"A": "Correct. The worked calculation gives 121.78416 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 121.78416 m, not 182.67625 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 121.78416 m, not 123.78416 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006466 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 7 kg is attached to an ideal spring of force constant 21 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.1547 s",
"B": "2.3094 s",
"C": "3.1547 s",
"D": "0.1547 s"
} | A | 1.1547 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(7/21)=1.1547 s. | {
"A": "Correct. The worked calculation gives 1.1547 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1547 s, not 2.3094 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1547 s, not 3.1547 s.",
"D": "Incorrect. Substituting the stat... | [
"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_005772 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.5 atm at 214 K. What is its pressure at 679 K? | {
"A": "9.51869 atm",
"B": "-4.75935 atm",
"C": "3.75935 atm",
"D": "4.75935 atm"
} | D | 4.75935 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.5)(679)/(214)=4.75935 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.75935 atm, not 9.51869 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.75935 atm, not -4.75935 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4... | [
"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_005028 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +8 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "20 N",
"B": "-40 N",
"C": "40 N",
"D": "48 N"
} | C | 40 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(8×10⁻⁶)/(6×10⁻²)²=40 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 40 N, not 20 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 40 N, not -40 N.",
"C": "Correct. The worked calculation gives 40 N.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_009642 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_5H_11N_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "1",
"B": "3",
"C": "5",
"D": "2"
} | D | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×5+2+3−11−0)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 5.",
"D": "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_009192 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.16 V, transfers 1 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.2191 V",
"B": "-0.7809 V",
"C": "2.2191 V",
"D": "1.12191 V"
} | A | 1.2191 V | Apply the Nernst equation: E=1.16−(0.0591/1)(-1)=1.2191 V. | {
"A": "Correct. The worked calculation gives 1.2191 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.2191 V, not -0.7809 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2191 V, not 2.2191 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004125 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 34 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.39. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "78.336 N",
"B": "48.96 N",
"C": "-97.92 N",
"D": "97.92 N"
} | D | 97.92 N | Net force=mg(sinθ−μcosθ)=34×10×(0.6−0.39×0.8)=97.92 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 97.92 N, not 78.336 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 97.92 N, not 48.96 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 97.92 N, not -97.... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004334 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 50 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.16. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "236 N",
"B": "24.6 N",
"C": "283.2 N",
"D": "-236 N"
} | A | 236 N | Net force=mg(sinθ−μcosθ)=50×10×(0.6−0.16×0.8)=236 N. | {
"A": "Correct. The worked calculation gives 236 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 236 N, not 24.6 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 236 N, not 283.2 N.",
"D": "Incorrect. Substituting the stated values in... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002146 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 11 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": "1.03126",
"B": "0.31264",
"C": "0.15632",
"D": "-0.31264"
} | B | 0.31264 | Favourable pairs = C(11,2)+C(10,2)+C(9,2)=136. Total pairs=C(30,2)=435. Therefore P=136/435=0.31264. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31264, not 1.03126.",
"B": "Correct. The worked calculation gives 0.31264.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31264, not 0.15632.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009354 | 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_16H_8N_2X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "13",
"B": "6.5",
"C": "11",
"D": "15"
} | A | 13 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×16+2+2−8−2)/2=13. | {
"A": "Correct. The worked calculation gives 13.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13, not 6.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13, not 11.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009241 | 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 1 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.4227 V",
"B": "-1.5773 V",
"C": "1.5773 V",
"D": "2.36595 V"
} | C | 1.5773 V | Apply the Nernst equation: E=1.40−(0.0591/1)(-3)=1.5773 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.5773 V, not -0.4227 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.5773 V, not -1.5773 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_006552 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 18 kg is attached to an ideal spring of force constant 292 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.50344 s",
"B": "1.49656 s",
"C": "0.49656 s",
"D": "1.04966 s"
} | C | 0.49656 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(18/292)=0.49656 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.49656 s, not -2.50344 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.49656 s, not 1.49656 s.",
"C": "Correct. The worked calculation gives 0.49656 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_001112 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ -10x² -10x+7. Evaluate f′(4). | {
"A": "101",
"B": "122.4",
"C": "102",
"D": "153"
} | C | 102 | Differentiate: f′(x)=3(4)x²+2(-10)x+(-10). At x=4, f′(4)=3(4)(4)²+2(-10)(4)+(-10)=102. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 102, not 101.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 102, not 122.4.",
"C": "Correct. The worked calculation gives 102.",
"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_004629 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 10 kg and radius 5 m is acted on by a constant torque of 70 N m about its central axis. Find its angular acceleration. | {
"A": "0.56 rad s⁻²",
"B": "-2.44 rad s⁻²",
"C": "1.12 rad s⁻²",
"D": "0.84 rad s⁻²"
} | A | 0.56 rad s⁻² | For a solid disc, I=½MR²=½(10)(5)²=125 kg m². Using τ=Iα, α=70/125=0.56 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.56 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.56 rad s⁻², not -2.44 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.56 rad s⁻², not 1.12 rad s⁻².",
"D": "Incorrect. ... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007555 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 23 mL of 0.10 M HCl is mixed with 64 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "6.33663",
"B": "12.67326",
"C": "9.67326",
"D": "-12.67326"
} | B | 12.67326 | Excess OH⁻ moles=0.10×(64−23)/1000=0.004100 mol. Total volume=0.087 L, so [OH⁻]=0.047126 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.67326. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.67326, not 6.33663.",
"B": "Correct. The worked calculation gives 12.67326.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.67326, not 9.67326.",
"D": "Incorrect. Substituting the stated... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008191 | 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 9 A for 3083 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": "6.8469 g",
"B": "-9.12919 g",
"C": "9.12919 g",
"D": "11.12919 g"
} | C | 9.12919 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×9×3083/(2×96500)=9.12919 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.12919 g, not 6.8469 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.12919 g, not -9.12919 g.",
"C": "Correct. The worked calculation gives 9.12919 g.",
"D": "Incorrect. Substituting the... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009139 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.68 V, transfers 3 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.7391 V",
"B": "0.36955 V",
"C": "0.7391 V",
"D": "1.4782 V"
} | C | 0.7391 V | Apply the Nernst equation: E=0.68−(0.0591/3)(-3)=0.7391 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7391 V, not 2.7391 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7391 V, not 0.36955 V.",
"C": "Correct. The worked calculation gives 0.7391 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008141 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 4 A for 1982 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": "2.60844 g",
"B": "4.60844 g",
"C": "1.26084 g",
"D": "5.21687 g"
} | A | 2.60844 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×1982/(2×96500)=2.60844 g. | {
"A": "Correct. The worked calculation gives 2.60844 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.60844 g, not 4.60844 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.60844 g, not 1.26084 g.",
"D": "Incorrect. Substituting the... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004181 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 35 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.16. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "82.6 N",
"B": "167.2 N",
"C": "165.2 N",
"D": "198.24 N"
} | C | 165.2 N | Net force=mg(sinθ−μcosθ)=35×10×(0.6−0.16×0.8)=165.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 165.2 N, not 82.6 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 165.2 N, not 167.2 N.",
"C": "Correct. The worked calculation gives 165.2 N.",
"D": "Incorrect. Substituting the stated val... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005688 | 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 3.9 atm at 207 K. What is its pressure at 338 K? | {
"A": "6.36812 atm",
"B": "4.36812 atm",
"C": "5.36812 atm",
"D": "9.36812 atm"
} | A | 6.36812 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.9)(338)/(207)=6.36812 atm. | {
"A": "Correct. The worked calculation gives 6.36812 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.36812 atm, not 4.36812 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.36812 atm, not 5.36812 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_004202 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.33. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "12.6 N",
"B": "8.4 N",
"C": "2.68 N",
"D": "16.8 N"
} | D | 16.8 N | Net force=mg(sinθ−μcosθ)=5×10×(0.6−0.33×0.8)=16.8 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16.8 N, not 12.6 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16.8 N, not 8.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16.8 N, not 2.68 N.",
... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005871 | 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 2.2 atm at 310 K. What is its pressure at 515 K? | {
"A": "1.65484 atm",
"B": "3.65484 atm",
"C": "1.82742 atm",
"D": "2.65484 atm"
} | B | 3.65484 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.2)(515)/(310)=3.65484 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.65484 atm, not 1.65484 atm.",
"B": "Correct. The worked calculation gives 3.65484 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.65484 atm, not 1.82742 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_008544 | 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 0.51 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": "3.02 K",
"B": "1.02 K",
"C": "-1.02 K",
"D": "4.02 K"
} | B | 1.02 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×0.51=1.02 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.02 K, not 3.02 K.",
"B": "Correct. The worked calculation gives 1.02 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.02 K, not -1.02 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_008121 | 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 21000 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": "83.91192 g",
"B": "82.91192 g",
"C": "124.36788 g",
"D": "84.91192 g"
} | B | 82.91192 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×12×21000/(2×96500)=82.91192 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 82.91192 g, not 83.91192 g.",
"B": "Correct. The worked calculation gives 82.91192 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 82.91192 g, not 124.36788 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007475 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 38 mL of 0.10 M HCl is mixed with 45 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "17.88903",
"B": "11.92602",
"C": "23.85204",
"D": "12.92602"
} | B | 11.92602 | Excess OH⁻ moles=0.10×(45−38)/1000=0.000700 mol. Total volume=0.083 L, so [OH⁻]=0.008434 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=11.92602. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.92602, not 17.88903.",
"B": "Correct. The worked calculation gives 11.92602.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.92602, not 23.85204.",
"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_008700 | 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 0.12 mol L⁻¹ and initially B is absent. At equilibrium, 54% of A has dissociated at constant volume. Find K_c. | {
"A": "0.30428",
"B": "0.15214",
"C": "-0.30428",
"D": "-1.69572"
} | A | 0.30428 | Let α=0.54. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.12)(0.54)²/(1−0.54)=0.30428. | {
"A": "Correct. The worked calculation gives 0.30428.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30428, not 0.15214.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30428, not -0.30428.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001234 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ -5x² +11x+7. Evaluate f′(0). | {
"A": "10",
"B": "11",
"C": "8",
"D": "9"
} | B | 11 | Differentiate: f′(x)=3(-4)x²+2(-5)x+(11). At x=0, f′(0)=3(-4)(0)²+2(-5)(0)+(11)=11. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11, not 10.",
"B": "Correct. The worked calculation gives 11.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11, not 8.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_004889 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 9 Ω are connected in series; this combination is connected in parallel with a 18 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.27273 A",
"B": "4.54545 A",
"C": "4.0303 A",
"D": "3.0303 A"
} | D | 3.0303 A | Series branch resistance=13+9=22 Ω. Parallel equivalent R_eq=(22×18)/(22+18)=9.9 Ω. Total current I=V/R_eq=30/9.9=3.0303 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.0303 A, not 2.27273 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.0303 A, not 4.54545 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.0303 A, no... | [
"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_008399 | 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 0.69 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": "3.414 K",
"B": "0.414 K",
"C": "-0.414 K",
"D": "0.621 K"
} | B | 0.414 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.6×0.69=0.414 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.414 K, not 3.414 K.",
"B": "Correct. The worked calculation gives 0.414 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.414 K, not -0.414 K.",
"D": "Incorrect. Substituting the stated v... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009607 | 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_16H_34N_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "-1",
"B": "1",
"C": "-2",
"D": "0.75"
} | B | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×16+2+2−34−0)/2=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not -1.",
"B": "Correct. The worked calculation gives 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... | [
"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_008233 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 1 A for 6501 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": "3.13893 g",
"B": "0.13893 g",
"C": "2.13893 g",
"D": "3.2084 g"
} | C | 2.13893 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×1×6501/(2×96500)=2.13893 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.13893 g, not 3.13893 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.13893 g, not 0.13893 g.",
"C": "Correct. The worked calculation gives 2.13893 g.",
"D": "Incorrect. Substituting the... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004370 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 15 kg and radius 5 m is acted on by a constant torque of 10 N m about its central axis. Find its angular acceleration. | {
"A": "0.10667 rad s⁻²",
"B": "0.05333 rad s⁻²",
"C": "1.05333 rad s⁻²",
"D": "-2.94667 rad s⁻²"
} | B | 0.05333 rad s⁻² | For a solid disc, I=½MR²=½(15)(5)²=187.5 kg m². Using τ=Iα, α=10/187.5=0.05333 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.05333 rad s⁻², not 0.10667 rad s⁻².",
"B": "Correct. The worked calculation gives 0.05333 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.05333 rad s⁻², not 1.05333 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_000960 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 3 and common ratio -3. What is the sum of its first 6 terms? | {
"A": "-53.6",
"B": "-544",
"C": "546",
"D": "-546"
} | D | -546 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=3(-3^6−1)/(-3−1)=-546. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -546, not -53.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -546, not -544.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -546, not 546.",
"D": "Corr... | [
"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_001311 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-3x³ +6x² +7x+7. Evaluate f′(4). | {
"A": "-89",
"B": "-88",
"C": "-7.9",
"D": "-90"
} | A | -89 | Differentiate: f′(x)=3(-3)x²+2(6)x+(7). At x=4, f′(4)=3(-3)(4)²+2(6)(4)+(7)=-89. | {
"A": "Correct. The worked calculation gives -89.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -89, not -88.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -89, not -7.9.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009728 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(OH)_5]^+1, each OH ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "9",
"B": "5",
"C": "6",
"D": "7"
} | C | 6 | Let the formal oxidation state of Pd be x. Charge balance gives x+(5)(−1)=+1; hence x=1+5=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 5.",
"C": "Correct. The worked calculation gives 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_008957 | 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, 22% of A has dissociated at constant volume. Find K_c. | {
"A": "2.29785",
"B": "3.29785",
"C": "0.29785",
"D": "-0.29785"
} | C | 0.29785 | Let α=0.22. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.2)(0.22)²/(1−0.22)=0.29785. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29785, not 2.29785.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29785, not 3.29785.",
"C": "Correct. The worked calculation gives 0.29785.",
"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_004482 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 12 kg and radius 5 m is acted on by a constant torque of 33 N m about its central axis. Find its angular acceleration. | {
"A": "0.11 rad s⁻²",
"B": "-2.78 rad s⁻²",
"C": "3.22 rad s⁻²",
"D": "0.22 rad s⁻²"
} | D | 0.22 rad s⁻² | For a solid disc, I=½MR²=½(12)(5)²=150 kg m². Using τ=Iα, α=33/150=0.22 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.22 rad s⁻², not 0.11 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.22 rad s⁻², not -2.78 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation giv... | [
"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_002662 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, 3], [1, 8]]. | {
"A": "45",
"B": "90",
"C": "67.5",
"D": "44"
} | A | 45 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(8)−(3)(1)=45. | {
"A": "Correct. The worked calculation gives 45.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 45, not 90.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 45, not 67.5.",
"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_002208 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 6 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.47143",
"B": "-2.68571",
"C": "0.15714",
"D": "0.31429"
} | D | 0.31429 | Favourable pairs = C(9,2)+C(6,2)+C(6,2)=66. Total pairs=C(21,2)=210. Therefore P=66/210=0.31429. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31429, not 0.47143.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31429, not -2.68571.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31429, not 0.15... | [
"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_004656 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 14 kg and radius 5 m is acted on by a constant torque of 88 N m about its central axis. Find its angular acceleration. | {
"A": "2.50286 rad s⁻²",
"B": "0.37714 rad s⁻²",
"C": "1.50286 rad s⁻²",
"D": "0.50286 rad s⁻²"
} | D | 0.50286 rad s⁻² | For a solid disc, I=½MR²=½(14)(5)²=175 kg m². Using τ=Iα, α=88/175=0.50286 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.50286 rad s⁻², not 2.50286 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.50286 rad s⁻², not 0.37714 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing r... | [
"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_001280 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=0x³ +10x² +8x+7. Evaluate f′(-4). | {
"A": "-6.2",
"B": "-70",
"C": "-72",
"D": "-73"
} | C | -72 | Differentiate: f′(x)=3(0)x²+2(10)x+(8). At x=-4, f′(-4)=3(0)(-4)²+2(10)(-4)+(8)=-72. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -72, not -6.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -72, not -70.",
"C": "Correct. The worked calculation gives -72.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007013 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 1 mol of gas at 434 K and 1.56 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "3.28287 L",
"B": "22.82868 L",
"C": "11.41434 L",
"D": "34.24302 L"
} | B | 22.82868 L | PV=nRT, so V=nRT/P=(1)(0.082057)(434)/(1.56)=22.82868 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22.82868 L, not 3.28287 L.",
"B": "Correct. The worked calculation gives 22.82868 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22.82868 L, not 11.41434 L.",
"D": "Incorrect. Substituting... | [
"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_007076 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 8 mol of gas at 290 K and 1.59 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "-119.73097 L",
"B": "119.73097 L",
"C": "95.78477 L",
"D": "59.86548 L"
} | B | 119.73097 L | PV=nRT, so V=nRT/P=(8)(0.082057)(290)/(1.59)=119.73097 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 119.73097 L, not -119.73097 L.",
"B": "Correct. The worked calculation gives 119.73097 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 119.73097 L, not 95.78477 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001490 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (6x² -6x +2) dx. | {
"A": "16.5",
"B": "-33",
"C": "33",
"D": "24.75"
} | C | 33 | An antiderivative is (6/3)x³+(-6/2)x²+(2)x. Evaluating between 0 and 3 gives (6/3)(3)³+(-6/2)(3)²+(2)(3)=33. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33, not 16.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33, not -33.",
"C": "Correct. The worked calculation gives 33.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_008558 | 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 0.39 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": "1.78 K",
"B": "0.78 K",
"C": "-1.22 K",
"D": "1.17 K"
} | B | 0.78 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×0.39=0.78 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.78 K, not 1.78 K.",
"B": "Correct. The worked calculation gives 0.78 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.78 K, not -1.22 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_006117 | 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 28 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.06222",
"B": "0.62222",
"C": "-0.62222",
"D": "-0.37778"
} | B | 0.62222 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(73)(28)/(73−28)=45.42222 cm. Thus |m|=v/u=45.42222/73=0.62222. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.62222, not 1.06222.",
"B": "Correct. The worked calculation gives 0.62222.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.62222, not -0.62222.",
"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_009714 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(Cl)_4]^-2, each Cl ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "0",
"B": "4",
"C": "5",
"D": "2"
} | D | 2 | Let the formal oxidation state of Co be x. Charge balance gives x+(4)(−1)=-2; hence x=-2+4=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 5.",
"D": "Correct. The worked ca... | [
"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_002797 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(3, -1, -3) and v=(-7, 7, 6), calculate u·v. | {
"A": "-46",
"B": "-36.8",
"C": "-23",
"D": "-47"
} | A | -46 | The dot product is the sum of corresponding component products: (3)(-7)+(-1)(7)+(-3)(6)=-46. | {
"A": "Correct. The worked calculation gives -46.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -46, not -36.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -46, not -23.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_000294 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 -4x -10=0, let its roots be α and β. What is α²+β²? | {
"A": "4.64",
"B": "2.32",
"C": "1.464",
"D": "7.64"
} | A | 4.64 | By Vieta's relations, α+β = 4/5 and αβ = -10/5. Then α²+β²=(α+β)²−2αβ = (4/5)²−2(-10/5) = 4.64. | {
"A": "Correct. The worked calculation gives 4.64.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.64, not 2.32.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.64, not 1.464.",
"D": "Incorrect. Substituting the stated values into the ... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000114 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 -12x +2=0, let its roots be α and β. What is α²+β²? | {
"A": "4.33333",
"B": "6.33333",
"C": "1.33333",
"D": "3.33333"
} | D | 3.33333 | By Vieta's relations, α+β = 12/6 and αβ = 2/6. Then α²+β²=(α+β)²−2αβ = (12/6)²−2(2/6) = 3.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.33333, not 4.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.33333, not 6.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.33333, not 1.333... | [
"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_003566 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 118 m s⁻¹ at 18° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "820.43219 m",
"B": "1227.64828 m",
"C": "817.43219 m",
"D": "818.43219 m"
} | D | 818.43219 m | Range R=u²sin(2θ)/g. Substituting u=118, θ=18° and g=10 gives R=(118)²sin(36°)/10=818.43219 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 818.43219 m, not 820.43219 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 818.43219 m, not 1227.64828 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8... | [
"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_007701 | 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 64 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "8 mmol L⁻¹",
"B": "16 mmol L⁻¹",
"C": "6 mmol L⁻¹",
"D": "-8 mmol L⁻¹"
} | A | 8 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=64/2^3=8 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 8 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8 mmol L⁻¹, not 16 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8 mmol L⁻¹, not 6 mmol L⁻¹.",
"D": "Incorrect. Substituti... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008412 | 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 0.85 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": "-1.326 K",
"B": "1.1326 K",
"C": "1.326 K",
"D": "0.9945 K"
} | C | 1.326 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.52×0.85=1.326 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.326 K, not -1.326 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.326 K, not 1.1326 K.",
"C": "Correct. The worked calculation gives 1.326 K.",
"D": "Incorrect. Substituting the stated ... | [
"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_005369 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 15 μF capacitor is charged to a potential difference of 24 V. Calculate the energy stored, expressed in μJ. | {
"A": "3240 μJ",
"B": "4320 μJ",
"C": "5184 μJ",
"D": "4319 μJ"
} | B | 4320 μJ | U=½CV². Since C=15 μF, U in μJ is ½×15×(24)²=4320 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4320 μJ, not 3240 μJ.",
"B": "Correct. The worked calculation gives 4320 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4320 μJ, not 5184 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007203 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 7 mol of gas at 639 K and 2.61 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "142.62872 L",
"B": "281.25744 L",
"C": "140.62872 L",
"D": "141.62872 L"
} | C | 140.62872 L | PV=nRT, so V=nRT/P=(7)(0.082057)(639)/(2.61)=140.62872 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 140.62872 L, not 142.62872 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 140.62872 L, not 281.25744 L.",
"C": "Correct. The worked calculation gives 140.62872 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002027 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 11 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": "-0.31281",
"B": "2.31281",
"C": "0.1564",
"D": "0.31281"
} | D | 0.31281 | Favourable pairs = C(9,2)+C(11,2)+C(9,2)=127. Total pairs=C(29,2)=406. Therefore P=127/406=0.31281. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31281, not -0.31281.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31281, not 2.31281.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31281, not 0.15... | [
"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_001355 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (1x² -2x +2) dx. | {
"A": "0.33333",
"B": "4.33333",
"C": "1.33333",
"D": "-1.33333"
} | C | 1.33333 | An antiderivative is (1/3)x³+(-2/2)x²+(2)x. Evaluating between 0 and 1 gives (1/3)(1)³+(-2/2)(1)²+(2)(1)=1.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.33333, not 0.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.33333, not 4.33333.",
"C": "Correct. The worked calculation gives 1.33333.",
"D": "Incorrect. Substituting the stated va... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006350 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 9 kg is attached to an ideal spring of force constant 370 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.62385 s",
"B": "-0.31193 s",
"C": "0.31193 s",
"D": "0.46789 s"
} | C | 0.31193 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(9/370)=0.31193 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31193 s, not 0.62385 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31193 s, not -0.31193 s.",
"C": "Correct. The worked calculation gives 0.31193 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_004959 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 5 Ω and 13 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": "0.93333 A",
"B": "2.93333 A",
"C": "3.93333 A",
"D": "5.86667 A"
} | B | 2.93333 A | Series branch resistance=5+13=18 Ω. Parallel equivalent R_eq=(18×15)/(18+15)=8.18182 Ω. Total current I=V/R_eq=24/8.18182=2.93333 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.93333 A, not 0.93333 A.",
"B": "Correct. The worked calculation gives 2.93333 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.93333 A, not 3.93333 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_003730 | 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 3 m in the direction of motion. Find its final kinetic energy. | {
"A": "36 J",
"B": "28.5 J",
"C": "38 J",
"D": "39 J"
} | C | 38 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(1)²+(12)(3)=38 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 38 J, not 36 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 38 J, not 28.5 J.",
"C": "Correct. The worked calculation gives 38 J.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_007827 | 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 95 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "4.45312 mmol L⁻¹",
"B": "1.96875 mmol L⁻¹",
"C": "5.96875 mmol L⁻¹",
"D": "2.96875 mmol L⁻¹"
} | D | 2.96875 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=95/2^5=2.96875 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.96875 mmol L⁻¹, not 4.45312 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.96875 mmol L⁻¹, not 1.96875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governi... | [
"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_005857 | 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 2.7 atm at 242 K. What is its pressure at 610 K? | {
"A": "5.10434 atm",
"B": "6.80579 atm",
"C": "1.68058 atm",
"D": "3.40289 atm"
} | B | 6.80579 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.7)(610)/(242)=6.80579 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.80579 atm, not 5.10434 atm.",
"B": "Correct. The worked calculation gives 6.80579 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.80579 atm, not 1.68058 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_000627 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 2 and common difference 12. Find the sum of its first 24 terms. | {
"A": "3360",
"B": "3361",
"C": "3359",
"D": "3362"
} | A | 3360 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=2, d=12, n=24: Sₙ=24/2[2(2)+(24−1)(12)]=3360. | {
"A": "Correct. The worked calculation gives 3360.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3360, not 3361.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3360, not 3359.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009324 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.67 V, transfers 1 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.2709 V",
"B": "-2.2709 V",
"C": "0.7291 V",
"D": "3.7291 V"
} | C | 0.7291 V | Apply the Nernst equation: E=0.67−(0.0591/1)(-1)=0.7291 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7291 V, not -1.2709 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7291 V, not -2.2709 V.",
"C": "Correct. The worked calculation gives 0.7291 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_002265 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 11 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": "2.35145",
"B": "0.35145",
"C": "-2.64855",
"D": "1.35145"
} | B | 0.35145 | Favourable pairs = C(11,2)+C(4,2)+C(9,2)=97. Total pairs=C(24,2)=276. Therefore P=97/276=0.35145. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35145, not 2.35145.",
"B": "Correct. The worked calculation gives 0.35145.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35145, not -2.64855.",
"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_003016 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(3-2i)/(11+10i). What is Re(z), the real part of z? | {
"A": "1.05882",
"B": "0.05882",
"C": "3.05882",
"D": "-0.94118"
} | B | 0.05882 | Multiply numerator and denominator by the conjugate (11-10i). Then Re(z)=(ac+bd)/(c²+d²)=((3)(11)+(-2)(10))/(11²+(10)²)=0.05882. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.05882, not 1.05882.",
"B": "Correct. The worked calculation gives 0.05882.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.05882, not 3.05882.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007186 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 2 mol of gas at 498 K and 2.37 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "36.48471 L",
"B": "33.48471 L",
"C": "34.48471 L",
"D": "35.48471 L"
} | C | 34.48471 L | PV=nRT, so V=nRT/P=(2)(0.082057)(498)/(2.37)=34.48471 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 34.48471 L, not 36.48471 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 34.48471 L, not 33.48471 L.",
"C": "Correct. The worked calculation gives 34.48471 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_001768 | 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 83 distinct elements? | {
"A": "-16141841823510",
"B": "19370210188212",
"C": "16141841823510",
"D": "32283683647020"
} | C | 16141841823510 | Order does not matter, so the count is C(83,11)=83!/[11!(72)!]=16141841823510. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16141841823510, not -16141841823510.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16141841823510, not 19370210188212.",
"C": "Correct. The worked calculation gives 16141841823510.",
"D": "I... | [
"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_003260 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-1+7i)/(1+8i). What is Re(z), the real part of z? | {
"A": "-1.15385",
"B": "2.84615",
"C": "1.69231",
"D": "0.84615"
} | D | 0.84615 | Multiply numerator and denominator by the conjugate (1-8i). Then Re(z)=(ac+bd)/(c²+d²)=((-1)(1)+(7)(8))/(1²+(8)²)=0.84615. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.84615, not -1.15385.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.84615, not 2.84615.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.84615, not 1.69... | [
"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_009147 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.28 V, transfers 2 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.4573 V",
"B": "-0.5427 V",
"C": "0.72865 V",
"D": "4.4573 V"
} | A | 1.4573 V | Apply the Nernst equation: E=1.28−(0.0591/2)(-6)=1.4573 V. | {
"A": "Correct. The worked calculation gives 1.4573 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4573 V, not -0.5427 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.4573 V, not 0.72865 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_005182 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +5 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "31.64062 N",
"B": "23.09375 N",
"C": "42.1875 N",
"D": "21.09375 N"
} | D | 21.09375 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(5×10⁻⁶)/(8×10⁻²)²=21.09375 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21.09375 N, not 31.64062 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21.09375 N, not 23.09375 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21.093... | [
"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_009172 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.13 V, transfers 1 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.2482 V",
"B": "-0.7518 V",
"C": "1.8723 V",
"D": "0.93615 V"
} | A | 1.2482 V | Apply the Nernst equation: E=1.13−(0.0591/1)(-2)=1.2482 V. | {
"A": "Correct. The worked calculation gives 1.2482 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.2482 V, not -0.7518 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2482 V, not 1.8723 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004241 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 26 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.31. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "45.76 N",
"B": "91.52 N",
"C": "68.64 N",
"D": "73.216 N"
} | B | 91.52 N | Net force=mg(sinθ−μcosθ)=26×10×(0.6−0.31×0.8)=91.52 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 91.52 N, not 45.76 N.",
"B": "Correct. The worked calculation gives 91.52 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 91.52 N, not 68.64 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002513 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, 3], [4, 8]]. | {
"A": "53",
"B": "78",
"C": "52",
"D": "62.4"
} | C | 52 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(8)−(3)(4)=52. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 52, not 53.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 52, not 78.",
"C": "Correct. The worked calculation gives 52.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004187 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 49 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.21. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "254.016 N",
"B": "105.84 N",
"C": "317.52 N",
"D": "211.68 N"
} | D | 211.68 N | Net force=mg(sinθ−μcosθ)=49×10×(0.6−0.21×0.8)=211.68 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 211.68 N, not 254.016 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 211.68 N, not 105.84 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 211.68 N, not... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001871 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 85 distinct elements? | {
"A": "3129162672638",
"B": "312916267264.60004",
"C": "3129162672636",
"D": "2346872004477"
} | C | 3129162672636 | Order does not matter, so the count is C(85,10)=85!/[10!(75)!]=3129162672636. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3129162672636, not 3129162672638.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3129162672636, not 312916267264.60004.",
"C": "Correct. The worked calculation gives 3129162672636.",
"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_008182 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 2 A for 8842 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "4.36373 g",
"B": "5.81831 g",
"C": "2.90916 g",
"D": "8.72747 g"
} | B | 5.81831 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×2×8842/(2×96500)=5.81831 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.81831 g, not 4.36373 g.",
"B": "Correct. The worked calculation gives 5.81831 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.81831 g, not 2.90916 g.",
"D": "Incorrect. Substituting the... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005302 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +4 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "9.8 N",
"B": "21.6 N",
"C": "10.8 N",
"D": "2.08 N"
} | C | 10.8 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(4×10⁻⁶)/(10×10⁻²)²=10.8 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.8 N, not 9.8 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.8 N, not 21.6 N.",
"C": "Correct. The worked calculation gives 10.8 N.",
"D": "Incorrect. Substituting the stated values i... | [
"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_002530 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, 1], [6, -7]]. | {
"A": "-20.5",
"B": "-41",
"C": "-61.5",
"D": "-43"
} | B | -41 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(-7)−(1)(6)=-41. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -41, not -20.5.",
"B": "Correct. The worked calculation gives -41.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -41, not -61.5.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_003448 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 118 m s⁻¹ at 70° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "-895.01747 m",
"B": "895.01747 m",
"C": "90.50175 m",
"D": "1342.5262 m"
} | B | 895.01747 m | Range R=u²sin(2θ)/g. Substituting u=118, θ=70° and g=10 gives R=(118)²sin(140°)/10=895.01747 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 895.01747 m, not -895.01747 m.",
"B": "Correct. The worked calculation gives 895.01747 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 895.01747 m, not 90.50175 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006496 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 7 kg is attached to an ideal spring of force constant 789 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.18838 s",
"B": "3.18838 s",
"C": "-0.18838 s",
"D": "0.14129 s"
} | A | 0.18838 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(7/789)=0.18838 s. | {
"A": "Correct. The worked calculation gives 0.18838 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.18838 s, not 3.18838 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.18838 s, not -0.18838 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_003008 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-2+7i)/(8+9i). What is Re(z), the real part of z? | {
"A": "1.03241",
"B": "0.32414",
"C": "3.32414",
"D": "0.2431"
} | B | 0.32414 | Multiply numerator and denominator by the conjugate (8-9i). Then Re(z)=(ac+bd)/(c²+d²)=((-2)(8)+(7)(9))/(8²+(9)²)=0.32414. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32414, not 1.03241.",
"B": "Correct. The worked calculation gives 0.32414.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32414, not 3.32414.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006575 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 24 kg is attached to an ideal spring of force constant 1040 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.69618 s",
"B": "1.30382 s",
"C": "0.30382 s",
"D": "0.15191 s"
} | C | 0.30382 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(24/1040)=0.30382 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30382 s, not -1.69618 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30382 s, not 1.30382 s.",
"C": "Correct. The worked calculation gives 0.30382 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_005978 | 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 0.4 atm at 288 K. What is its pressure at 356 K? | {
"A": "-0.49444 atm",
"B": "-0.50556 atm",
"C": "-2.50556 atm",
"D": "0.49444 atm"
} | D | 0.49444 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.4)(356)/(288)=0.49444 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.49444 atm, not -0.49444 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.49444 atm, not -0.50556 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives ... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007393 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 13 mL of 0.10 M HCl is mixed with 17 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "14.12494",
"B": "2.21249",
"C": "11.12494",
"D": "12.12494"
} | D | 12.12494 | Excess OH⁻ moles=0.10×(17−13)/1000=0.000400 mol. Total volume=0.030 L, so [OH⁻]=0.013333 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.12494. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.12494, not 14.12494.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.12494, not 2.21249.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.12494, not 1... | [
"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_008448 | 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 0.41 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.41984 K",
"B": "1.04198 K",
"C": "0.20992 K",
"D": "0.41984 K"
} | D | 0.41984 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×0.41=0.41984 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.41984 K, not -0.41984 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.41984 K, not 1.04198 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.41984 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_004598 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 6 m is acted on by a constant torque of 81 N m about its central axis. Find its angular acceleration. | {
"A": "-2.35714 rad s⁻²",
"B": "3.64286 rad s⁻²",
"C": "-0.35714 rad s⁻²",
"D": "0.64286 rad s⁻²"
} | D | 0.64286 rad s⁻² | For a solid disc, I=½MR²=½(7)(6)²=126 kg m². Using τ=Iα, α=81/126=0.64286 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.64286 rad s⁻², not -2.35714 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.64286 rad s⁻², not 3.64286 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing ... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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