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_003298 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(13+8i)/(4+11i). What is Re(z), the real part of z? | {
"A": "1.53285",
"B": "0.76642",
"C": "1.0219",
"D": "-0.9781"
} | C | 1.0219 | Multiply numerator and denominator by the conjugate (4-11i). Then Re(z)=(ac+bd)/(c²+d²)=((13)(4)+(8)(11))/(4²+(11)²)=1.0219. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0219, not 1.53285.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0219, not 0.76642.",
"C": "Correct. The worked calculation gives 1.0219.",
"D": "Incorrect. Substituting the stated value... | [
"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_004772 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 3 Ω are connected in series; this combination is connected in parallel with a 7 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "5.82857 A",
"B": "-2.91429 A",
"C": "2.91429 A",
"D": "2.18571 A"
} | C | 2.91429 A | Series branch resistance=7+3=10 Ω. Parallel equivalent R_eq=(10×7)/(10+7)=4.11765 Ω. Total current I=V/R_eq=12/4.11765=2.91429 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.91429 A, not 5.82857 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.91429 A, not -2.91429 A.",
"C": "Correct. The worked calculation gives 2.91429 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009887 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(CN)_4]^-3, each CN ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "1",
"B": "0.5",
"C": "-2",
"D": "4"
} | A | 1 | Let the formal oxidation state of Co be x. Charge balance gives x+(4)(−1)=-3; hence x=-3+4=+1. | {
"A": "Correct. The worked calculation gives 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not -2.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004294 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 40 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.37. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "121.6 N",
"B": "13.16 N",
"C": "123.6 N",
"D": "122.6 N"
} | A | 121.6 N | Net force=mg(sinθ−μcosθ)=40×10×(0.6−0.37×0.8)=121.6 N. | {
"A": "Correct. The worked calculation gives 121.6 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 121.6 N, not 13.16 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 121.6 N, not 123.6 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001972 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 7 elements can be selected from a set of 17 distinct elements? | {
"A": "19450",
"B": "38896",
"C": "9724",
"D": "19448"
} | D | 19448 | Order does not matter, so the count is C(17,7)=17!/[7!(10)!]=19448. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19448, not 19450.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19448, not 38896.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19448, not 9724.",
"D": ... | [
"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_002877 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-6, 6, -1) and v=(-3, -3, -5), calculate u·v. | {
"A": "2.5",
"B": "2",
"C": "5",
"D": "3.75"
} | C | 5 | The dot product is the sum of corresponding component products: (-6)(-3)+(6)(-3)+(-1)(-5)=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.",
"C": "Correct. The worked calculation gives 5.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_002825 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-5, -6, 5) and v=(-6, -4, 1), calculate u·v. | {
"A": "59",
"B": "57",
"C": "70.8",
"D": "44.25"
} | A | 59 | The dot product is the sum of corresponding component products: (-5)(-6)+(-6)(-4)+(5)(1)=59. | {
"A": "Correct. The worked calculation gives 59.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 59, not 57.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 59, not 70.8.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000300 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 -13x -1=0, let its roots be α and β. What is α²+β²? | {
"A": "14.0625",
"B": "11.0625",
"C": "9.0625",
"D": "8.0625"
} | B | 11.0625 | By Vieta's relations, α+β = 13/4 and αβ = -1/4. Then α²+β²=(α+β)²−2αβ = (13/4)²−2(-1/4) = 11.0625. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.0625, not 14.0625.",
"B": "Correct. The worked calculation gives 11.0625.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.0625, not 9.0625.",
"D": "Incorrect. Substituting the stated val... | [
"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_008581 | 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 0.95 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "6.8 K",
"B": "3.8 K",
"C": "7.6 K",
"D": "4.8 K"
} | B | 3.8 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×1.0×0.95=3.8 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.8 K, not 6.8 K.",
"B": "Correct. The worked calculation gives 3.8 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.8 K, not 7.6 K.",
"D": "Incorrect. Substituting the stated values into ... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006268 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 62 cm in front of a thin convex lens of focal length 30 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.46875",
"B": "-2.0625",
"C": "0.9375",
"D": "1.40625"
} | C | 0.9375 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(62)(30)/(62−30)=58.125 cm. Thus |m|=v/u=58.125/62=0.9375. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9375, not 0.46875.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9375, not -2.0625.",
"C": "Correct. The worked calculation gives 0.9375.",
"D": "Incorrect. Substituting the stated value... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006645 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 5 kg is attached to an ideal spring of force constant 42 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.0351 s",
"B": "0.69007 s",
"C": "1.06901 s",
"D": "1.69007 s"
} | B | 0.69007 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(5/42)=0.69007 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.69007 s, not 1.0351 s.",
"B": "Correct. The worked calculation gives 0.69007 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.69007 s, not 1.06901 s.",
"D": "Incorrect. Substituting the ... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007126 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 16 mol of gas at 370 K and 2.34 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "207.5972 L",
"B": "205.5972 L",
"C": "103.7986 L",
"D": "208.5972 L"
} | A | 207.5972 L | PV=nRT, so V=nRT/P=(16)(0.082057)(370)/(2.34)=207.5972 L. | {
"A": "Correct. The worked calculation gives 207.5972 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 207.5972 L, not 205.5972 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 207.5972 L, not 103.7986 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_007790 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 16 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "-0.5 mmol L⁻¹",
"B": "0.5 mmol L⁻¹",
"C": "1.05 mmol L⁻¹",
"D": "0.375 mmol L⁻¹"
} | B | 0.5 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=16/2^5=0.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5 mmol L⁻¹, not -0.5 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5 mmol L⁻¹, not 1.05 mmol L⁻¹.",
"D": "Incorrect.... | [
"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_002463 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, -7], [5, 3]]. | {
"A": "52",
"B": "53",
"C": "63.6",
"D": "26.5"
} | B | 53 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(3)−(-7)(5)=53. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 53, not 52.",
"B": "Correct. The worked calculation gives 53.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 53, not 63.6.",
"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_008416 | 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 0.77 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.4004 K",
"B": "0.8008 K",
"C": "2.4004 K",
"D": "3.4004 K"
} | A | 0.4004 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.52×0.77=0.4004 K. | {
"A": "Correct. The worked calculation gives 0.4004 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.4004 K, not 0.8008 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.4004 K, not 2.4004 K.",
"D": "Incorrect. Substituting the stat... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008691 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.02 mol L⁻¹ and initially B is absent. At equilibrium, 24% of A has dissociated at constant volume. Find K_c. | {
"A": "0.00606",
"B": "1.00606",
"C": "3.00606",
"D": "-1.99394"
} | A | 0.00606 | Let α=0.24. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.02)(0.24)²/(1−0.24)=0.00606. | {
"A": "Correct. The worked calculation gives 0.00606.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.00606, not 1.00606.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.00606, not 3.00606.",
"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_008398 | 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 0.57 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.026 K",
"B": "1.368 K",
"C": "2.736 K",
"D": "-0.632 K"
} | B | 1.368 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.6×0.57=1.368 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.368 K, not 1.026 K.",
"B": "Correct. The worked calculation gives 1.368 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.368 K, not 2.736 K.",
"D": "Incorrect. Substituting the stated va... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007666 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 89 mL of 0.10 M HCl is mixed with 75 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.06872",
"B": "-0.93128",
"C": "-2.06872",
"D": "4.06872"
} | A | 2.06872 | Excess H⁺ moles=0.10×(89−75)/1000=0.001400 mol. Total volume=0.164 L, so [H⁺]=0.008537 M and pH=−log₁₀[H⁺]=2.06872. | {
"A": "Correct. The worked calculation gives 2.06872.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.06872, not -0.93128.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.06872, not -2.06872.",
"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_007991 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 27 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "0.10547 mmol L⁻¹",
"B": "2.21094 mmol L⁻¹",
"C": "0.21094 mmol L⁻¹",
"D": "-0.78906 mmol L⁻¹"
} | C | 0.21094 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=27/2^7=0.21094 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.21094 mmol L⁻¹, not 0.10547 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.21094 mmol L⁻¹, not 2.21094 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.21094 mmol L⁻¹.",
... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007100 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 6 mol of gas at 424 K and 1.85 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "56.41973 L",
"B": "12.28395 L",
"C": "112.83946 L",
"D": "110.83946 L"
} | C | 112.83946 L | PV=nRT, so V=nRT/P=(6)(0.082057)(424)/(1.85)=112.83946 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 112.83946 L, not 56.41973 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 112.83946 L, not 12.28395 L.",
"C": "Correct. The worked calculation gives 112.83946 L.",
"D": "Incorrect. Substitu... | [
"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_006843 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 9 mol H₂ and 20 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "13.5 mol",
"B": "9 mol",
"C": "8 mol",
"D": "1.9 mol"
} | B | 9 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 9 mol H₂O; O₂ can produce 40 mol H₂O. The limiting condition is H₂; product=9 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9 mol, not 13.5 mol.",
"B": "Correct. The worked calculation gives 9 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9 mol, not 8 mol.",
"D": "Incorrect. Substituting the stated values in... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000810 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio 3. What is the sum of its first 9 terms? | {
"A": "-19682",
"B": "39364",
"C": "19684",
"D": "19682"
} | D | 19682 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(3^9−1)/(3−1)=19682. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19682, not -19682.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19682, not 39364.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19682, not 19684.",
"D"... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000063 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 +3x +12=0, let its roots be α and β. What is α²+β²? | {
"A": "-7.3125",
"B": "-19.5",
"C": "-9.75",
"D": "-12.75"
} | C | -9.75 | By Vieta's relations, α+β = -3/2 and αβ = 12/2. Then α²+β²=(α+β)²−2αβ = (-3/2)²−2(12/2) = -9.75. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -9.75, not -7.3125.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -9.75, not -19.5.",
"C": "Correct. The worked calculation gives -9.75.",
"D": "Incorrect. Substituting the stated values int... | [
"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_003170 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(6+8i)/(6+11i). What is Re(z), the real part of z? | {
"A": "1.57962",
"B": "1.18471",
"C": "2.78981",
"D": "0.78981"
} | D | 0.78981 | Multiply numerator and denominator by the conjugate (6-11i). Then Re(z)=(ac+bd)/(c²+d²)=((6)(6)+(8)(11))/(6²+(11)²)=0.78981. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.78981, not 1.57962.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.78981, not 1.18471.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.78981, not 2.789... | [
"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_002411 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, -6], [5, -4]]. | {
"A": "-18",
"B": "18",
"C": "36",
"D": "2.8"
} | B | 18 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(-4)−(-6)(5)=18. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18, not -18.",
"B": "Correct. The worked calculation gives 18.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18, not 36.",
"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_000379 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -9 and common difference 3. Find the sum of its first 32 terms. | {
"A": "600",
"B": "1198",
"C": "1200",
"D": "1202"
} | C | 1200 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-9, d=3, n=32: Sₙ=32/2[2(-9)+(32−1)(3)]=1200. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1200, not 600.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1200, not 1198.",
"C": "Correct. The worked calculation gives 1200.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_003507 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 41 m s⁻¹ at 70° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "107.0526 m",
"B": "108.0526 m",
"C": "54.0263 m",
"D": "11.80526 m"
} | B | 108.0526 m | Range R=u²sin(2θ)/g. Substituting u=41, θ=70° and g=10 gives R=(41)²sin(140°)/10=108.0526 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 108.0526 m, not 107.0526 m.",
"B": "Correct. The worked calculation gives 108.0526 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 108.0526 m, not 54.0263 m.",
"D": "Incorrect. Substituting... | [
"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_005202 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +5 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "16.66667 N",
"B": "14.66667 N",
"C": "12.5 N",
"D": "17.66667 N"
} | A | 16.66667 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(5×10⁻⁶)/(9×10⁻²)²=16.66667 N. | {
"A": "Correct. The worked calculation gives 16.66667 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16.66667 N, not 14.66667 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16.66667 N, not 12.5 N.",
"D": "Incorrect. Substituting th... | [
"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_006452 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 5 kg is attached to an ideal spring of force constant 393 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.02256 s",
"B": "0.22559 s",
"C": "-0.77441 s",
"D": "-1.77441 s"
} | B | 0.22559 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(5/393)=0.22559 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.22559 s, not 1.02256 s.",
"B": "Correct. The worked calculation gives 0.22559 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.22559 s, not -0.77441 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_005088 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +5 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "112.5 N",
"B": "168.75 N",
"C": "111.5 N",
"D": "56.25 N"
} | A | 112.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(5×10⁻⁶)/(6×10⁻²)²=112.5 N. | {
"A": "Correct. The worked calculation gives 112.5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 112.5 N, not 168.75 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 112.5 N, not 111.5 N.",
"D": "Incorrect. Substituting the stated v... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004271 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 16 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.28. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "45.12 N",
"B": "58.16 N",
"C": "48.128 N",
"D": "60.16 N"
} | D | 60.16 N | Net force=mg(sinθ−μcosθ)=16×10×(0.6−0.28×0.8)=60.16 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 60.16 N, not 45.12 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 60.16 N, not 58.16 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 60.16 N, not 48.12... | [
"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_005085 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +4 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "50.625 N",
"B": "-50.625 N",
"C": "37.96875 N",
"D": "51.625 N"
} | A | 50.625 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(4×10⁻⁶)/(8×10⁻²)²=50.625 N. | {
"A": "Correct. The worked calculation gives 50.625 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 50.625 N, not -50.625 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 50.625 N, not 37.96875 N.",
"D": "Incorrect. Substituting the s... | [
"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_006528 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 15 kg is attached to an ideal spring of force constant 30 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.41421 s",
"B": "2.41421 s",
"C": "1.41421 s",
"D": "2.82843 s"
} | C | 1.41421 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(15/30)=1.41421 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.41421 s, not 0.41421 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.41421 s, not 2.41421 s.",
"C": "Correct. The worked calculation gives 1.41421 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002354 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, 5], [2, 8]]. | {
"A": "-2",
"B": "-1",
"C": "-4",
"D": "-3"
} | A | -2 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(8)−(5)(2)=-2. | {
"A": "Correct. The worked calculation gives -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2, not -1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2, not -4.",
"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_006295 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 66 cm in front of a thin convex lens of focal length 29 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "3.78378",
"B": "0.78378",
"C": "1.56757",
"D": "1.78378"
} | B | 0.78378 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(66)(29)/(66−29)=51.72973 cm. Thus |m|=v/u=51.72973/66=0.78378. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.78378, not 3.78378.",
"B": "Correct. The worked calculation gives 0.78378.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.78378, not 1.56757.",
"D": "Incorrect. Substituting the stated va... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003488 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 79 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "703.7546 m",
"B": "586.46216 m",
"C": "879.69325 m",
"D": "439.84662 m"
} | B | 586.46216 m | Range R=u²sin(2θ)/g. Substituting u=79, θ=55° and g=10 gives R=(79)²sin(110°)/10=586.46216 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 586.46216 m, not 703.7546 m.",
"B": "Correct. The worked calculation gives 586.46216 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 586.46216 m, not 879.69325 m.",
"D": "Incorrect. Substit... | [
"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_005447 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 22 μF capacitor is charged to a potential difference of 18 V. Calculate the energy stored, expressed in μJ. | {
"A": "1782 μJ",
"B": "3563 μJ",
"C": "3564 μJ",
"D": "2673 μJ"
} | C | 3564 μJ | U=½CV². Since C=22 μF, U in μJ is ½×22×(18)²=3564 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3564 μJ, not 1782 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3564 μJ, not 3563 μJ.",
"C": "Correct. The worked calculation gives 3564 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_006349 | 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 984 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.83131 s",
"B": "2.16869 s",
"C": "0.25303 s",
"D": "0.16869 s"
} | D | 0.16869 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(7/984)=0.16869 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.16869 s, not -2.83131 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.16869 s, not 2.16869 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.16869 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007231 | 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 312 K and 0.28 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "146.29591 L",
"B": "183.86989 L",
"C": "182.86989 L",
"D": "184.86989 L"
} | C | 182.86989 L | PV=nRT, so V=nRT/P=(2)(0.082057)(312)/(0.28)=182.86989 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 182.86989 L, not 146.29591 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 182.86989 L, not 183.86989 L.",
"C": "Correct. The worked calculation gives 182.86989 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_006931 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 38 mol H₂ and 20 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "40 mol",
"B": "38 mol",
"C": "19 mol",
"D": "30.4 mol"
} | B | 38 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 38 mol H₂O; O₂ can produce 40 mol H₂O. The limiting condition is H₂; product=38 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 38 mol, not 40 mol.",
"B": "Correct. The worked calculation gives 38 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 38 mol, not 19 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005054 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +5 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "675 N",
"B": "225 N",
"C": "540 N",
"D": "450 N"
} | D | 450 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(5×10⁻⁶)/(3×10⁻²)²=450 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 450 N, not 675 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 450 N, not 225 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 450 N, not 540 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_005240 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +7 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "33 N",
"B": "4.5 N",
"C": "17.5 N",
"D": "35 N"
} | D | 35 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(7×10⁻⁶)/(6×10⁻²)²=35 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 35 N, not 33 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 35 N, not 4.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 35 N, not 17.5 N.",
"D": "C... | [
"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_002617 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, -1], [1, -6]]. | {
"A": "-70",
"B": "35",
"C": "-42",
"D": "-35"
} | D | -35 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(-6)−(-1)(1)=-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 35.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -35, not -42.",
"D": "Correct. Th... | [
"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_006306 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 85 cm in front of a thin convex lens of focal length 19 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-2.71212",
"B": "-0.28788",
"C": "0.28788",
"D": "-0.71212"
} | C | 0.28788 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(85)(19)/(85−19)=24.4697 cm. Thus |m|=v/u=24.4697/85=0.28788. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.28788, not -2.71212.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.28788, not -0.28788.",
"C": "Correct. The worked calculation gives 0.28788.",
"D": "Incorrect. Substituting the stated ... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003024 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-10+8i)/(5+2i). What is Re(z), the real part of z? | {
"A": "-0.17241",
"B": "-3.17241",
"C": "-1.17241",
"D": "1.82759"
} | C | -1.17241 | Multiply numerator and denominator by the conjugate (5-2i). Then Re(z)=(ac+bd)/(c²+d²)=((-10)(5)+(8)(2))/(5²+(2)²)=-1.17241. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.17241, not -0.17241.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.17241, not -3.17241.",
"C": "Correct. The worked calculation gives -1.17241.",
"D": "Incorrect. Substituting the stat... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001122 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ +1x² +10x+7. Evaluate f′(-3). | {
"A": "141",
"B": "-139",
"C": "140",
"D": "139"
} | D | 139 | Differentiate: f′(x)=3(5)x²+2(1)x+(10). At x=-3, f′(-3)=3(5)(-3)²+2(1)(-3)+(10)=139. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 139, not 141.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 139, not -139.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 139, not 140.",
"D": "Correct. ... | [
"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_009451 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_10H_15N_1X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "4.5",
"C": "4",
"D": "5"
} | A | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×10+2+1−15−2)/2=3. | {
"A": "Correct. The worked calculation gives 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.",
"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_000936 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio -2. What is the sum of its first 7 terms? | {
"A": "473",
"B": "475",
"C": "471",
"D": "567.6"
} | A | 473 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(-2^7−1)/(-2−1)=473. | {
"A": "Correct. The worked calculation gives 473.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 473, not 475.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 473, not 471.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002015 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 9 blue and 5 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.32749",
"B": "-1.67251",
"C": "-0.67251",
"D": "0.24561"
} | A | 0.32749 | Favourable pairs = C(5,2)+C(9,2)+C(5,2)=56. Total pairs=C(19,2)=171. Therefore P=56/171=0.32749. | {
"A": "Correct. The worked calculation gives 0.32749.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32749, not -1.67251.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32749, not -0.67251.",
"D": "Incorrect. Substituting the stated ... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009470 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_7H_14X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "0",
"B": "1",
"C": "-3",
"D": "3"
} | A | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+0−14−2)/2=0. | {
"A": "Correct. The worked calculation gives 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000522 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 11 and common difference 14. Find the sum of its first 34 terms. | {
"A": "6171",
"B": "823.8",
"C": "-8228",
"D": "8228"
} | D | 8228 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=11, d=14, n=34: Sₙ=34/2[2(11)+(34−1)(14)]=8228. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8228, not 6171.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8228, not 823.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8228, not -8228.",
"D": "Co... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008057 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 13 A for 9882 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": "42.26731 g",
"B": "50.72077 g",
"C": "41.26731 g",
"D": "63.40097 g"
} | A | 42.26731 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×9882/(2×96500)=42.26731 g. | {
"A": "Correct. The worked calculation gives 42.26731 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 42.26731 g, not 50.72077 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 42.26731 g, not 41.26731 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008024 | 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 17320 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": "2.13971 g",
"B": "17.09565 g",
"C": "11.3971 g",
"D": "12.3971 g"
} | C | 11.3971 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×2×17320/(2×96500)=11.3971 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.3971 g, not 2.13971 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.3971 g, not 17.09565 g.",
"C": "Correct. The worked calculation gives 11.3971 g.",
"D": "Incorrect. Substituting th... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004043 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 16 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.42. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "5.224 N",
"B": "42.24 N",
"C": "21.12 N",
"D": "41.24 N"
} | B | 42.24 N | Net force=mg(sinθ−μcosθ)=16×10×(0.6−0.42×0.8)=42.24 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 42.24 N, not 5.224 N.",
"B": "Correct. The worked calculation gives 42.24 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 42.24 N, not 21.12 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_007245 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 5 mol of gas at 613 K and 2.58 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "146.22367 L",
"B": "96.48244 L",
"C": "97.48244 L",
"D": "73.11183 L"
} | C | 97.48244 L | PV=nRT, so V=nRT/P=(5)(0.082057)(613)/(2.58)=97.48244 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 97.48244 L, not 146.22367 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 97.48244 L, not 96.48244 L.",
"C": "Correct. The worked calculation gives 97.48244 L.",
"D": "Incorrect. Substituti... | [
"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_008613 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "4.8 K",
"B": "2.4 K",
"C": "1.8 K",
"D": "3.6 K"
} | B | 2.4 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.6×1=2.4 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.4 K, not 4.8 K.",
"B": "Correct. The worked calculation gives 2.4 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.4 K, not 1.8 K.",
"D": "Incorrect. Substituting the stated values into ... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000982 | 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 9 terms? | {
"A": "1023",
"B": "1022",
"C": "766.5",
"D": "1226.4"
} | B | 1022 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(2^9−1)/(2−1)=1022. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1022, not 1023.",
"B": "Correct. The worked calculation gives 1022.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1022, not 766.5.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_002946 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-3, 4, 8) and v=(-7, 9, 7), calculate u·v. | {
"A": "111",
"B": "113",
"C": "114",
"D": "169.5"
} | B | 113 | The dot product is the sum of corresponding component products: (-3)(-7)+(4)(9)+(8)(7)=113. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 113, not 111.",
"B": "Correct. The worked calculation gives 113.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 113, not 114.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005305 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +9 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "50.625 N",
"B": "101.25 N",
"C": "40.5 N",
"D": "75.9375 N"
} | A | 50.625 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(9×10⁻⁶)/(8×10⁻²)²=50.625 N. | {
"A": "Correct. The worked calculation gives 50.625 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 50.625 N, not 101.25 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 50.625 N, not 40.5 N.",
"D": "Incorrect. Substituting the stated... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007373 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 66 mL of 0.10 M HCl is mixed with 85 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "6.04989",
"B": "12.09978",
"C": "9.09978",
"D": "9.07483"
} | B | 12.09978 | Excess OH⁻ moles=0.10×(85−66)/1000=0.001900 mol. Total volume=0.151 L, so [OH⁻]=0.012583 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.09978. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.09978, not 6.04989.",
"B": "Correct. The worked calculation gives 12.09978.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.09978, not 9.09978.",
"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_006365 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 14 kg is attached to an ideal spring of force constant 468 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.25944 s",
"B": "0.34592 s",
"C": "0.17296 s",
"D": "-1.65408 s"
} | B | 0.34592 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(14/468)=0.34592 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34592 s, not 0.25944 s.",
"B": "Correct. The worked calculation gives 0.34592 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34592 s, not 0.17296 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006403 | 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 230 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.60437 s",
"B": "0.39563 s",
"C": "-2.60437 s",
"D": "1.39563 s"
} | B | 0.39563 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(9/230)=0.39563 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.39563 s, not -1.60437 s.",
"B": "Correct. The worked calculation gives 0.39563 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.39563 s, not -2.60437 s.",
"D": "Incorrect. Substituting t... | [
"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_009325 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.05 V, transfers 1 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.84095 V",
"B": "1.2273 V",
"C": "1.12273 V",
"D": "0.61365 V"
} | B | 1.2273 V | Apply the Nernst equation: E=1.05−(0.0591/1)(-3)=1.2273 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.2273 V, not 1.84095 V.",
"B": "Correct. The worked calculation gives 1.2273 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2273 V, not 1.12273 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_006140 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 68 cm in front of a thin convex lens of focal length 20 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.20833",
"B": "0.3125",
"C": "0.41667",
"D": "2.41667"
} | C | 0.41667 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(68)(20)/(68−20)=28.33333 cm. Thus |m|=v/u=28.33333/68=0.41667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.41667, not 0.20833.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.41667, not 0.3125.",
"C": "Correct. The worked calculation gives 0.41667.",
"D": "Incorrect. Substituting the stated val... | [
"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_006263 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 63 cm in front of a thin convex lens of focal length 25 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.65789",
"B": "1.65789",
"C": "-0.34211",
"D": "2.65789"
} | A | 0.65789 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(63)(25)/(63−25)=41.44737 cm. Thus |m|=v/u=41.44737/63=0.65789. | {
"A": "Correct. The worked calculation gives 0.65789.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.65789, not 1.65789.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.65789, not -0.34211.",
"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_009958 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(Cl)_3]^+0, each Cl ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "3",
"B": "4.5",
"C": "5",
"D": "1.5"
} | A | 3 | Let the formal oxidation state of Pt be x. Charge balance gives x+(3)(−1)=+0; hence x=0+3=+3. | {
"A": "Correct. The worked calculation gives 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 5.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005346 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 80 μF capacitor is charged to a potential difference of 21 V. Calculate the energy stored, expressed in μJ. | {
"A": "13230 μJ",
"B": "26460 μJ",
"C": "17639 μJ",
"D": "17640 μJ"
} | D | 17640 μJ | U=½CV². Since C=80 μF, U in μJ is ½×80×(21)²=17640 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 17640 μJ, not 13230 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17640 μJ, not 26460 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17640 μJ, not ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001198 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ +6x² +11x+7. Evaluate f′(4). | {
"A": "299",
"B": "300",
"C": "298",
"D": "448.5"
} | A | 299 | Differentiate: f′(x)=3(5)x²+2(6)x+(11). At x=4, f′(4)=3(5)(4)²+2(6)(4)+(11)=299. | {
"A": "Correct. The worked calculation gives 299.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 299, not 300.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 299, not 298.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007534 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 73 mL of 0.10 M HCl is mixed with 56 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "4.88014",
"B": "1.88014",
"C": "2.88014",
"D": "1.18801"
} | B | 1.88014 | Excess H⁺ moles=0.10×(73−56)/1000=0.001700 mol. Total volume=0.129 L, so [H⁺]=0.013178 M and pH=−log₁₀[H⁺]=1.88014. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.88014, not 4.88014.",
"B": "Correct. The worked calculation gives 1.88014.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.88014, not 2.88014.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004865 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 10 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.02857 A",
"B": "0.02857 A",
"C": "2.05714 A",
"D": "1.02857 A"
} | D | 1.02857 A | Series branch resistance=7+7=14 Ω. Parallel equivalent R_eq=(14×10)/(14+10)=5.83333 Ω. Total current I=V/R_eq=6/5.83333=1.02857 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.02857 A, not 4.02857 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.02857 A, not 0.02857 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.02857 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_003430 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 72 m s⁻¹ at 35° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "730.70498 m",
"B": "49.71367 m",
"C": "487.13665 m",
"D": "486.13665 m"
} | C | 487.13665 m | Range R=u²sin(2θ)/g. Substituting u=72, θ=35° and g=10 gives R=(72)²sin(70°)/10=487.13665 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 487.13665 m, not 730.70498 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 487.13665 m, not 49.71367 m.",
"C": "Correct. The worked calculation gives 487.13665 m.",
"D": "Incorrect. Substit... | [
"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_001425 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (6x² +3x +4) dx. | {
"A": "510",
"B": "509",
"C": "52",
"D": "1020"
} | A | 510 | An antiderivative is (6/3)x³+(3/2)x²+(4)x. Evaluating between 0 and 6 gives (6/3)(6)³+(3/2)(6)²+(4)(6)=510. | {
"A": "Correct. The worked calculation gives 510.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 510, not 509.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 510, not 52.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_001453 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (6x² -6x +0) dx. | {
"A": "29",
"B": "27",
"C": "40.5",
"D": "21.6"
} | B | 27 | An antiderivative is (6/3)x³+(-6/2)x²+(0)x. Evaluating between 0 and 3 gives (6/3)(3)³+(-6/2)(3)²+(0)(3)=27. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 27, not 29.",
"B": "Correct. The worked calculation gives 27.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 27, not 40.5.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008173 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 10 A for 20781 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": "51.27954 g",
"B": "68.37272 g",
"C": "54.69818 g",
"D": "69.37272 g"
} | B | 68.37272 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×10×20781/(2×96500)=68.37272 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 68.37272 g, not 51.27954 g.",
"B": "Correct. The worked calculation gives 68.37272 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 68.37272 g, not 54.69818 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004858 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 15 Ω and 5 Ω are connected in series; this combination is connected in parallel with a 18 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.95 A",
"B": "-0.63333 A",
"C": "0.31667 A",
"D": "0.63333 A"
} | D | 0.63333 A | Series branch resistance=15+5=20 Ω. Parallel equivalent R_eq=(20×18)/(20+18)=9.47368 Ω. Total current I=V/R_eq=6/9.47368=0.63333 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.63333 A, not 0.95 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.63333 A, not -0.63333 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.63333 A, n... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004903 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 15 Ω and 11 Ω are connected in series; this combination is connected in parallel with a 5 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "5.29231 A",
"B": "6.43846 A",
"C": "4.29231 A",
"D": "7.29231 A"
} | C | 4.29231 A | Series branch resistance=15+11=26 Ω. Parallel equivalent R_eq=(26×5)/(26+5)=4.19355 Ω. Total current I=V/R_eq=18/4.19355=4.29231 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.29231 A, not 5.29231 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.29231 A, not 6.43846 A.",
"C": "Correct. The worked calculation gives 4.29231 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_009013 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.81 V, transfers 3 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.7115 V",
"B": "1.7115 V",
"C": "0.7115 V",
"D": "1.06725 V"
} | C | 0.7115 V | Apply the Nernst equation: E=0.81−(0.0591/3)(5)=0.7115 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7115 V, not 2.7115 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7115 V, not 1.7115 V.",
"C": "Correct. The worked calculation gives 0.7115 V.",
"D": "Incorrect. Substituting the stat... | [
"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_004861 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 13 Ω are connected in series; this combination is connected in parallel with a 11 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.09091 A",
"B": "6.13636 A",
"C": "4.09091 A",
"D": "1.40909 A"
} | C | 4.09091 A | Series branch resistance=9+13=22 Ω. Parallel equivalent R_eq=(22×11)/(22+11)=7.33333 Ω. Total current I=V/R_eq=30/7.33333=4.09091 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.09091 A, not 2.09091 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.09091 A, not 6.13636 A.",
"C": "Correct. The worked calculation gives 4.09091 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_005656 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 73 μF capacitor is charged to a potential difference of 15 V. Calculate the energy stored, expressed in μJ. | {
"A": "-8212.5 μJ",
"B": "8211.5 μJ",
"C": "9855 μJ",
"D": "8212.5 μJ"
} | D | 8212.5 μJ | U=½CV². Since C=73 μF, U in μJ is ½×73×(15)²=8212.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8212.5 μJ, not -8212.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8212.5 μJ, not 8211.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8212.5 μJ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004740 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 5 Ω and 12 Ω are connected in series; this combination is connected in parallel with a 3 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "8.41176 A",
"B": "9.41176 A",
"C": "18.82353 A",
"D": "10.41176 A"
} | B | 9.41176 A | Series branch resistance=5+12=17 Ω. Parallel equivalent R_eq=(17×3)/(17+3)=2.55 Ω. Total current I=V/R_eq=24/2.55=9.41176 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.41176 A, not 8.41176 A.",
"B": "Correct. The worked calculation gives 9.41176 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.41176 A, not 18.82353 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008696 | 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 1.71 mol L⁻¹ and initially B is absent. At equilibrium, 41% of A has dissociated at constant volume. Find K_c. | {
"A": "0.94882",
"B": "1.19488",
"C": "1.94882",
"D": "3.94882"
} | C | 1.94882 | Let α=0.41. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.71)(0.41)²/(1−0.41)=1.94882. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.94882, not 0.94882.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.94882, not 1.19488.",
"C": "Correct. The worked calculation gives 1.94882.",
"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_008850 | 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 0.78 mol L⁻¹ and initially B is absent. At equilibrium, 31% of A has dissociated at constant volume. Find K_c. | {
"A": "0.43454",
"B": "-0.56546",
"C": "0.86908",
"D": "0.21727"
} | A | 0.43454 | Let α=0.31. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.78)(0.31)²/(1−0.31)=0.43454. | {
"A": "Correct. The worked calculation gives 0.43454.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.43454, not -0.56546.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.43454, not 0.86908.",
"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_004350 | 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 16 N m about its central axis. Find its angular acceleration. | {
"A": "-1.87302 rad s⁻²",
"B": "0.06349 rad s⁻²",
"C": "0.12698 rad s⁻²",
"D": "-0.87302 rad s⁻²"
} | C | 0.12698 rad s⁻² | For a solid disc, I=½MR²=½(7)(6)²=126 kg m². Using τ=Iα, α=16/126=0.12698 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.12698 rad s⁻², not -1.87302 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.12698 rad s⁻², not 0.06349 rad s⁻².",
"C": "Correct. The worked calculation gives 0.12698 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_006401 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 16 kg is attached to an ideal spring of force constant 378 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.04115 s",
"B": "0.30861 s",
"C": "0.61721 s",
"D": "0.41148 s"
} | D | 0.41148 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(16/378)=0.41148 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.41148 s, not 1.04115 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.41148 s, not 0.30861 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.41148 s,... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005781 | 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 2.9 atm at 315 K. What is its pressure at 661 K? | {
"A": "5.0854 atm",
"B": "6.0854 atm",
"C": "9.0854 atm",
"D": "9.1281 atm"
} | B | 6.0854 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.9)(661)/(315)=6.0854 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.0854 atm, not 5.0854 atm.",
"B": "Correct. The worked calculation gives 6.0854 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.0854 atm, not 9.0854 atm.",
"D": "Incorrect. Substitutin... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007560 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 39 mL of 0.10 M HCl is mixed with 19 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.4624",
"B": "0.7312",
"C": "2.1936",
"D": "4.4624"
} | A | 1.4624 | Excess H⁺ moles=0.10×(39−19)/1000=0.002000 mol. Total volume=0.058 L, so [H⁺]=0.034483 M and pH=−log₁₀[H⁺]=1.4624. | {
"A": "Correct. The worked calculation gives 1.4624.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4624, not 0.7312.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.4624, not 2.1936.",
"D": "Incorrect. Substituting the stated values ... | [
"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_006901 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 44 mol H₂ and 30 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "43 mol",
"B": "44 mol",
"C": "5.4 mol",
"D": "22 mol"
} | B | 44 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 44 mol H₂O; O₂ can produce 60 mol H₂O. The limiting condition is H₂; product=44 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 44 mol, not 43 mol.",
"B": "Correct. The worked calculation gives 44 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 44 mol, not 5.4 mol.",
"D": "Incorrect. Substituting the stated values... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003673 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 34 m s⁻¹ at 50° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "113.84378 m",
"B": "114.84378 m",
"C": "112.84378 m",
"D": "170.76566 m"
} | A | 113.84378 m | Range R=u²sin(2θ)/g. Substituting u=34, θ=50° and g=10 gives R=(34)²sin(100°)/10=113.84378 m. | {
"A": "Correct. The worked calculation gives 113.84378 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 113.84378 m, not 114.84378 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 113.84378 m, not 112.84378 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_004536 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 14 kg and radius 3 m is acted on by a constant torque of 20 N m about its central axis. Find its angular acceleration. | {
"A": "0.31746 rad s⁻²",
"B": "3.31746 rad s⁻²",
"C": "0.63492 rad s⁻²",
"D": "-0.68254 rad s⁻²"
} | A | 0.31746 rad s⁻² | For a solid disc, I=½MR²=½(14)(3)²=63 kg m². Using τ=Iα, α=20/63=0.31746 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.31746 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31746 rad s⁻², not 3.31746 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31746 rad s⁻², not 0.63492 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_008459 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.64 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-3.35872 K",
"B": "1.35872 K",
"C": "3.35872 K",
"D": "2.35872 K"
} | C | 3.35872 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.512×1.64=3.35872 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.35872 K, not -3.35872 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.35872 K, not 1.35872 K.",
"C": "Correct. The worked calculation gives 3.35872 K.",
"D": "Incorrect. Substituting th... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008236 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 6 A for 9915 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "14.67985 g",
"B": "39.14627 g",
"C": "19.57313 g",
"D": "29.3597 g"
} | C | 19.57313 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×6×9915/(2×96500)=19.57313 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19.57313 g, not 14.67985 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19.57313 g, not 39.14627 g.",
"C": "Correct. The worked calculation gives 19.57313 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005931 | 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 1.6 atm at 296 K. What is its pressure at 540 K? | {
"A": "3.91892 atm",
"B": "4.37838 atm",
"C": "0.91892 atm",
"D": "2.91892 atm"
} | D | 2.91892 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.6)(540)/(296)=2.91892 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.91892 atm, not 3.91892 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.91892 atm, not 4.37838 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.... | [
"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_007333 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 14 mol of gas at 285 K and 1.11 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "147.48082 L",
"B": "235.96932 L",
"C": "30.49616 L",
"D": "294.96165 L"
} | D | 294.96165 L | PV=nRT, so V=nRT/P=(14)(0.082057)(285)/(1.11)=294.96165 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 294.96165 L, not 147.48082 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 294.96165 L, not 235.96932 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29... | [
"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_000497 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 20 and common difference 12. Find the sum of its first 29 terms. | {
"A": "5452",
"B": "5450",
"C": "4361.6",
"D": "-5452"
} | A | 5452 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=20, d=12, n=29: Sₙ=29/2[2(20)+(29−1)(12)]=5452. | {
"A": "Correct. The worked calculation gives 5452.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5452, not 5450.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5452, not 4361.6.",
"D": "Incorrect. Substituting the stated values into the... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009328 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.63 V, transfers 2 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.77775 V",
"B": "0.58331 V",
"C": "1.16662 V",
"D": "-1.22225 V"
} | A | 0.77775 V | Apply the Nernst equation: E=0.63−(0.0591/2)(-5)=0.77775 V. | {
"A": "Correct. The worked calculation gives 0.77775 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.77775 V, not 0.58331 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.77775 V, not 1.16662 V.",
"D": "Incorrect. Substituting the... | [
"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_007470 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 94 mL of 0.10 M HCl is mixed with 95 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.07235",
"B": "12.72354",
"C": "10.72354",
"D": "16.08531"
} | C | 10.72354 | Excess OH⁻ moles=0.10×(95−94)/1000=0.000100 mol. Total volume=0.189 L, so [OH⁻]=0.000529 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=10.72354. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.72354, not 2.07235.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.72354, not 12.72354.",
"C": "Correct. The worked calculation gives 10.72354.",
"D": "Incorrect. Substituting the state... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009096 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.72 V, transfers 2 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.1027 V",
"B": "-0.1027 V",
"C": "0.8973 V",
"D": "2.8973 V"
} | C | 0.8973 V | Apply the Nernst equation: E=0.72−(0.0591/2)(-6)=0.8973 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8973 V, not -1.1027 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8973 V, not -0.1027 V.",
"C": "Correct. The worked calculation gives 0.8973 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_006464 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 25 kg is attached to an ideal spring of force constant 275 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.60302 s",
"B": "1.60302 s",
"C": "0.60302 s",
"D": "-0.39698 s"
} | C | 0.60302 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(25/275)=0.60302 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.60302 s, not -0.60302 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.60302 s, not 1.60302 s.",
"C": "Correct. The worked calculation gives 0.60302 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_004451 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 15 kg and radius 1 m is acted on by a constant torque of 63 N m about its central axis. Find its angular acceleration. | {
"A": "9.4 rad s⁻²",
"B": "8.4 rad s⁻²",
"C": "12.6 rad s⁻²",
"D": "6.4 rad s⁻²"
} | B | 8.4 rad s⁻² | For a solid disc, I=½MR²=½(15)(1)²=7.5 kg m². Using τ=Iα, α=63/7.5=8.4 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.4 rad s⁻², not 9.4 rad s⁻².",
"B": "Correct. The worked calculation gives 8.4 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.4 rad s⁻², not 12.6 rad s⁻².",
"D": "Incorrect. Subst... | [
"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_000204 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 +5x +2=0, let its roots be α and β. What is α²+β²? | {
"A": "-3.06122",
"B": "-0.12245",
"C": "-0.06122",
"D": "-0.09184"
} | C | -0.06122 | By Vieta's relations, α+β = -5/7 and αβ = 2/7. Then α²+β²=(α+β)²−2αβ = (-5/7)²−2(2/7) = -0.06122. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.06122, not -3.06122.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.06122, not -0.12245.",
"C": "Correct. The worked calculation gives -0.06122.",
"D": "Incorrect. Substituting the stat... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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