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_004055 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.21. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "21.6 N",
"B": "3.16 N",
"C": "25.92 N",
"D": "43.2 N"
} | A | 21.6 N | Net force=mg(sinθ−μcosθ)=5×10×(0.6−0.21×0.8)=21.6 N. | {
"A": "Correct. The worked calculation gives 21.6 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21.6 N, not 3.16 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21.6 N, not 25.92 N.",
"D": "Incorrect. Substituting the stated values... | [
"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_007018 | 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 528 K and 0.24 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "37.10508 L",
"B": "-361.0508 L",
"C": "180.5254 L",
"D": "361.0508 L"
} | D | 361.0508 L | PV=nRT, so V=nRT/P=(2)(0.082057)(528)/(0.24)=361.0508 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 361.0508 L, not 37.10508 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 361.0508 L, not -361.0508 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 361.0... | [
"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_007676 | 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 57 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "28.5 mmol L⁻¹",
"B": "22.8 mmol L⁻¹",
"C": "14.25 mmol L⁻¹",
"D": "34.2 mmol L⁻¹"
} | A | 28.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=57/2^1=28.5 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 28.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28.5 mmol L⁻¹, not 22.8 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28.5 mmol L⁻¹, not 14.25 mmol L⁻¹.",
"D": "Incorr... | [
"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_004935 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 2 Ω are connected in series; this combination is connected in parallel with a 12 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.83333 A",
"B": "4.83333 A",
"C": "11.66667 A",
"D": "5.83333 A"
} | D | 5.83333 A | Series branch resistance=7+2=9 Ω. Parallel equivalent R_eq=(9×12)/(9+12)=5.14286 Ω. Total current I=V/R_eq=30/5.14286=5.83333 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.83333 A, not 2.83333 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.83333 A, not 4.83333 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.83333 A,... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002048 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 7 red, 3 blue and 8 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.03399",
"B": "0.67974",
"C": "0.33987",
"D": "0.16993"
} | C | 0.33987 | Favourable pairs = C(7,2)+C(3,2)+C(8,2)=52. Total pairs=C(18,2)=153. Therefore P=52/153=0.33987. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33987, not 1.03399.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33987, not 0.67974.",
"C": "Correct. The worked calculation gives 0.33987.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009022 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.36 V, transfers 3 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.3797 V",
"B": "1.03478 V",
"C": "2.7594 V",
"D": "0.68985 V"
} | A | 1.3797 V | Apply the Nernst equation: E=1.36−(0.0591/3)(-1)=1.3797 V. | {
"A": "Correct. The worked calculation gives 1.3797 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.3797 V, not 1.03478 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.3797 V, not 2.7594 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000438 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 1 and common difference 15. Find the sum of its first 12 terms. | {
"A": "1503",
"B": "1002",
"C": "751.5",
"D": "501"
} | B | 1002 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=1, d=15, n=12: Sₙ=12/2[2(1)+(12−1)(15)]=1002. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1002, not 1503.",
"B": "Correct. The worked calculation gives 1002.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1002, not 751.5.",
"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_004600 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 4 m is acted on by a constant torque of 75 N m about its central axis. Find its angular acceleration. | {
"A": "1.17188 rad s⁻²",
"B": "2.17188 rad s⁻²",
"C": "-1.17188 rad s⁻²",
"D": "2.34375 rad s⁻²"
} | A | 1.17188 rad s⁻² | For a solid disc, I=½MR²=½(8)(4)²=64 kg m². Using τ=Iα, α=75/64=1.17188 rad s⁻². | {
"A": "Correct. The worked calculation gives 1.17188 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.17188 rad s⁻², not 2.17188 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.17188 rad s⁻², not -1.17188 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_001833 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 4 elements can be selected from a set of 22 distinct elements? | {
"A": "7317",
"B": "8778",
"C": "7315",
"D": "7314"
} | C | 7315 | Order does not matter, so the count is C(22,4)=22!/[4!(18)!]=7315. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7315, not 7317.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7315, not 8778.",
"C": "Correct. The worked calculation gives 7315.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_002936 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(6, -5, -3) and v=(8, 8, -5), calculate u·v. | {
"A": "23",
"B": "3.3",
"C": "27.6",
"D": "17.25"
} | A | 23 | The dot product is the sum of corresponding component products: (6)(8)+(-5)(8)+(-3)(-5)=23. | {
"A": "Correct. The worked calculation gives 23.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23, not 3.3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23, not 27.6.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000525 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -15 and common difference 12. Find the sum of its first 32 terms. | {
"A": "5470",
"B": "5471",
"C": "5472",
"D": "4377.6"
} | C | 5472 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-15, d=12, n=32: Sₙ=32/2[2(-15)+(32−1)(12)]=5472. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5472, not 5470.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5472, not 5471.",
"C": "Correct. The worked calculation gives 5472.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005283 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +5 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "1012.5 N",
"B": "676 N",
"C": "506.25 N",
"D": "675 N"
} | D | 675 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(5×10⁻⁶)/(2×10⁻²)²=675 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 675 N, not 1012.5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 675 N, not 676 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 675 N, not 506.25 N.",
... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001158 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ +2x² +12x+7. Evaluate f′(3). | {
"A": "223.2",
"B": "186",
"C": "187",
"D": "188"
} | B | 186 | Differentiate: f′(x)=3(6)x²+2(2)x+(12). At x=3, f′(3)=3(6)(3)²+2(2)(3)+(12)=186. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 186, not 223.2.",
"B": "Correct. The worked calculation gives 186.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 186, not 187.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000231 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +10x -1=0, let its roots be α and β. What is α²+β²? | {
"A": "7.4",
"B": "5.4",
"C": "4.4",
"D": "1.44"
} | C | 4.4 | By Vieta's relations, α+β = -10/5 and αβ = -1/5. Then α²+β²=(α+β)²−2αβ = (-10/5)²−2(-1/5) = 4.4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.4, not 7.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.4, not 5.4.",
"C": "Correct. The worked calculation gives 4.4.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_000407 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -15 and common difference 9. Find the sum of its first 9 terms. | {
"A": "187",
"B": "94.5",
"C": "19.9",
"D": "189"
} | D | 189 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-15, d=9, n=9: Sₙ=9/2[2(-15)+(9−1)(9)]=189. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 189, not 187.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 189, not 94.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 189, not 19.9.",
"D": "Correct.... | [
"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_005484 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 34 μF capacitor is charged to a potential difference of 38 V. Calculate the energy stored, expressed in μJ. | {
"A": "24548 μJ",
"B": "49096 μJ",
"C": "24549 μJ",
"D": "24547 μJ"
} | A | 24548 μJ | U=½CV². Since C=34 μF, U in μJ is ½×34×(38)²=24548 μJ. | {
"A": "Correct. The worked calculation gives 24548 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24548 μJ, not 49096 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24548 μJ, not 24549 μJ.",
"D": "Incorrect. Substituting the stat... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008095 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 4 A for 13442 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": "17.69051 g",
"B": "8.84525 g",
"C": "26.53576 g",
"D": "-17.69051 g"
} | A | 17.69051 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×13442/(2×96500)=17.69051 g. | {
"A": "Correct. The worked calculation gives 17.69051 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17.69051 g, not 8.84525 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17.69051 g, not 26.53576 g.",
"D": "Incorrect. Substituting... | [
"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_001918 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 11 elements can be selected from a set of 31 distinct elements? | {
"A": "84672315",
"B": "84672316",
"C": "63504236.25",
"D": "84672313"
} | A | 84672315 | Order does not matter, so the count is C(31,11)=31!/[11!(20)!]=84672315. | {
"A": "Correct. The worked calculation gives 84672315.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 84672315, not 84672316.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 84672315, not 63504236.25.",
"D": "Incorrect. Substituting the s... | [
"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_009425 | 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_13H_17N_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "7",
"B": "10",
"C": "6",
"D": "5.25"
} | A | 7 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×13+2+3−17−0)/2=7. | {
"A": "Correct. The worked calculation gives 7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 6.",
"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_007217 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 17 mol of gas at 546 K and 2.94 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "26.90657 L",
"B": "259.06567 L",
"C": "-259.06567 L",
"D": "388.59851 L"
} | B | 259.06567 L | PV=nRT, so V=nRT/P=(17)(0.082057)(546)/(2.94)=259.06567 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 259.06567 L, not 26.90657 L.",
"B": "Correct. The worked calculation gives 259.06567 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 259.06567 L, not -259.06567 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_009655 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_5H_3N_3X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "5",
"C": "7.5",
"D": "3.75"
} | B | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×5+2+3−3−2)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.",
"B": "Correct. The worked calculation gives 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.5.",
"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_006200 | 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 23 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.27823",
"B": "-1.62903",
"C": "0.37097",
"D": "-2.62903"
} | C | 0.37097 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(85)(23)/(85−23)=31.53226 cm. Thus |m|=v/u=31.53226/85=0.37097. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.37097, not 0.27823.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.37097, not -1.62903.",
"C": "Correct. The worked calculation gives 0.37097.",
"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_007609 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 81 mL of 0.10 M HCl is mixed with 60 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "3.654",
"B": "3.827",
"C": "1.827",
"D": "-0.173"
} | C | 1.827 | Excess H⁺ moles=0.10×(81−60)/1000=0.002100 mol. Total volume=0.141 L, so [H⁺]=0.014894 M and pH=−log₁₀[H⁺]=1.827. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.827, not 3.654.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.827, not 3.827.",
"C": "Correct. The worked calculation gives 1.827.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_004223 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 13 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.26. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "52.96 N",
"B": "6.096 N",
"C": "50.96 N",
"D": "38.22 N"
} | C | 50.96 N | Net force=mg(sinθ−μcosθ)=13×10×(0.6−0.26×0.8)=50.96 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 50.96 N, not 52.96 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 50.96 N, not 6.096 N.",
"C": "Correct. The worked calculation gives 50.96 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_002012 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 11 red, 12 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": "-0.34656",
"B": "1.03466",
"C": "0.34656",
"D": "0.51984"
} | C | 0.34656 | Favourable pairs = C(11,2)+C(12,2)+C(5,2)=131. Total pairs=C(28,2)=378. Therefore P=131/378=0.34656. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34656, not -0.34656.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34656, not 1.03466.",
"C": "Correct. The worked calculation gives 0.34656.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008991 | 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 1.42 mol L⁻¹ and initially B is absent. At equilibrium, 71% of A has dissociated at constant volume. Find K_c. | {
"A": "7.40506",
"B": "1.98734",
"C": "10.87341",
"D": "9.87341"
} | D | 9.87341 | Let α=0.71. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.42)(0.71)²/(1−0.71)=9.87341. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.87341, not 7.40506.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.87341, not 1.98734.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.87341, not 10.87... | [
"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_008064 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 9 A for 14020 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": "41.51518 g",
"B": "62.27277 g",
"C": "31.13639 g",
"D": "5.15152 g"
} | A | 41.51518 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×9×14020/(2×96500)=41.51518 g. | {
"A": "Correct. The worked calculation gives 41.51518 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 41.51518 g, not 62.27277 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 41.51518 g, not 31.13639 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_001185 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=7x³ -7x² +12x+7. Evaluate f′(-3). | {
"A": "245",
"B": "242",
"C": "25.3",
"D": "243"
} | D | 243 | Differentiate: f′(x)=3(7)x²+2(-7)x+(12). At x=-3, f′(-3)=3(7)(-3)²+2(-7)(-3)+(12)=243. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 243, not 245.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 243, not 242.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 243, not 25.3.",
"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_009351 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_11H_15X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "4",
"B": "2",
"C": "-4",
"D": "3"
} | A | 4 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+0−15−1)/2=4. | {
"A": "Correct. The worked calculation gives 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not -4.",
"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_000917 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 3 and common ratio -3. What is the sum of its first 12 terms? | {
"A": "-398582",
"B": "-398580",
"C": "-797160",
"D": "-199290"
} | B | -398580 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=3(-3^12−1)/(-3−1)=-398580. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -398580, not -398582.",
"B": "Correct. The worked calculation gives -398580.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -398580, not -797160.",
"D": "Incorrect. Substituting the stated va... | [
"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_005676 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.9 atm at 354 K. What is its pressure at 501 K? | {
"A": "6.93475 atm",
"B": "4.93475 atm",
"C": "7.93475 atm",
"D": "8.93475 atm"
} | A | 6.93475 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.9)(501)/(354)=6.93475 atm. | {
"A": "Correct. The worked calculation gives 6.93475 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.93475 atm, not 4.93475 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.93475 atm, not 7.93475 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007873 | 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 48 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "0.14062 mmol L⁻¹",
"B": "0.1875 mmol L⁻¹",
"C": "-2.8125 mmol L⁻¹",
"D": "2.1875 mmol L⁻¹"
} | B | 0.1875 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=48/2^8=0.1875 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.1875 mmol L⁻¹, not 0.14062 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.1875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.1875 mmol L⁻¹, not -2.8125 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_002046 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 11 red, 4 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": "3.37368",
"B": "0.37368",
"C": "-2.62632",
"D": "0.56053"
} | B | 0.37368 | Favourable pairs = C(11,2)+C(4,2)+C(5,2)=71. Total pairs=C(20,2)=190. Therefore P=71/190=0.37368. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.37368, not 3.37368.",
"B": "Correct. The worked calculation gives 0.37368.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.37368, not -2.62632.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004548 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 9 kg and radius 5 m is acted on by a constant torque of 62 N m about its central axis. Find its angular acceleration. | {
"A": "0.55111 rad s⁻²",
"B": "0.27556 rad s⁻²",
"C": "1.05511 rad s⁻²",
"D": "3.55111 rad s⁻²"
} | A | 0.55111 rad s⁻² | For a solid disc, I=½MR²=½(9)(5)²=112.5 kg m². Using τ=Iα, α=62/112.5=0.55111 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.55111 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.55111 rad s⁻², not 0.27556 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.55111 rad s⁻², not 1.05511 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_000951 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio 5. What is the sum of its first 11 terms? | {
"A": "97656249",
"B": "97656250",
"C": "195312496",
"D": "97656248"
} | D | 97656248 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(5^11−1)/(5−1)=97656248. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 97656248, not 97656249.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 97656248, not 97656250.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 97656248, not ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002942 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(8, -7, -1) and v=(-5, 0, 4), calculate u·v. | {
"A": "-33",
"B": "-44",
"C": "-42",
"D": "-3.4"
} | B | -44 | The dot product is the sum of corresponding component products: (8)(-5)+(-7)(0)+(-1)(4)=-44. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -44, not -33.",
"B": "Correct. The worked calculation gives -44.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -44, not -42.",
"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_000626 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 28 and common difference 12. Find the sum of its first 23 terms. | {
"A": "2944",
"B": "3680",
"C": "-3680",
"D": "369"
} | B | 3680 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=28, d=12, n=23: Sₙ=23/2[2(28)+(23−1)(12)]=3680. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3680, not 2944.",
"B": "Correct. The worked calculation gives 3680.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3680, not -3680.",
"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_003455 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 26 m s⁻¹ at 35° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "63.52322 m",
"B": "95.28483 m",
"C": "127.04644 m",
"D": "50.81858 m"
} | A | 63.52322 m | Range R=u²sin(2θ)/g. Substituting u=26, θ=35° and g=10 gives R=(26)²sin(70°)/10=63.52322 m. | {
"A": "Correct. The worked calculation gives 63.52322 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 63.52322 m, not 95.28483 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 63.52322 m, not 127.04644 m.",
"D": "Incorrect. Substituti... | [
"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_003819 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 0 m s⁻¹. A constant net force does 20 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "222 J",
"B": "440 J",
"C": "176 J",
"D": "220 J"
} | D | 220 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(0)²+(20)(11)=220 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 220 J, not 222 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 220 J, not 440 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 220 J, not 176 J.",
"D":... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005201 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +6 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "99.25 N",
"B": "202.5 N",
"C": "101.25 N",
"D": "151.875 N"
} | C | 101.25 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(6×10⁻⁶)/(4×10⁻²)²=101.25 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 101.25 N, not 99.25 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 101.25 N, not 202.5 N.",
"C": "Correct. The worked calculation gives 101.25 N.",
"D": "Incorrect. Substituting the stated... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000377 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 30 and common difference 10. Find the sum of its first 18 terms. | {
"A": "2070",
"B": "-2070",
"C": "2484",
"D": "208"
} | A | 2070 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=30, d=10, n=18: Sₙ=18/2[2(30)+(18−1)(10)]=2070. | {
"A": "Correct. The worked calculation gives 2070.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2070, not -2070.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2070, not 2484.",
"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_007263 | 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 339 K and 0.17 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "981.78787 L",
"B": "99.17879 L",
"C": "1963.57574 L",
"D": "1178.14544 L"
} | A | 981.78787 L | PV=nRT, so V=nRT/P=(6)(0.082057)(339)/(0.17)=981.78787 L. | {
"A": "Correct. The worked calculation gives 981.78787 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 981.78787 L, not 99.17879 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 981.78787 L, not 1963.57574 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_005890 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.9 atm at 287 K. What is its pressure at 800 K? | {
"A": "3.76307 atm",
"B": "1.50871 atm",
"C": "2.50871 atm",
"D": "0.50871 atm"
} | C | 2.50871 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.9)(800)/(287)=2.50871 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.50871 atm, not 3.76307 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.50871 atm, not 1.50871 atm.",
"C": "Correct. The worked calculation gives 2.50871 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003629 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 55 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "209.57815 m",
"B": "392.95903 m",
"C": "261.97268 m",
"D": "259.97268 m"
} | C | 261.97268 m | Range R=u²sin(2θ)/g. Substituting u=55, θ=60° and g=10 gives R=(55)²sin(120°)/10=261.97268 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 261.97268 m, not 209.57815 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 261.97268 m, not 392.95903 m.",
"C": "Correct. The worked calculation gives 261.97268 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_007189 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 15 mol of gas at 566 K and 0.12 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "8708.29913 L",
"B": "5807.53275 L",
"C": "4354.14956 L",
"D": "5805.53275 L"
} | D | 5805.53275 L | PV=nRT, so V=nRT/P=(15)(0.082057)(566)/(0.12)=5805.53275 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5805.53275 L, not 8708.29913 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5805.53275 L, not 5807.53275 L.",
"C": "Incorrect. Substituting the stated values into the governing relation give... | [
"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_007264 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 15 mol of gas at 555 K and 2.68 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "509.79442 L",
"B": "382.34582 L",
"C": "254.89721 L",
"D": "256.89721 L"
} | C | 254.89721 L | PV=nRT, so V=nRT/P=(15)(0.082057)(555)/(2.68)=254.89721 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 254.89721 L, not 509.79442 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 254.89721 L, not 382.34582 L.",
"C": "Correct. The worked calculation gives 254.89721 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_008732 | 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 1.42 mol L⁻¹ and initially B is absent. At equilibrium, 45% of A has dissociated at constant volume. Find K_c. | {
"A": "3.13691",
"B": "2.09127",
"C": "-2.09127",
"D": "1.20913"
} | B | 2.09127 | Let α=0.45. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.42)(0.45)²/(1−0.45)=2.09127. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.09127, not 3.13691.",
"B": "Correct. The worked calculation gives 2.09127.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.09127, not -2.09127.",
"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_001979 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 9 elements can be selected from a set of 40 distinct elements? | {
"A": "546877760",
"B": "27343889",
"C": "273438880",
"D": "273438878"
} | C | 273438880 | Order does not matter, so the count is C(40,9)=40!/[9!(31)!]=273438880. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 273438880, not 546877760.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 273438880, not 27343889.",
"C": "Correct. The worked calculation gives 273438880.",
"D": "Incorrect. Substituting the ... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009145 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.27 V, transfers 3 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.6547 V",
"B": "1.9641 V",
"C": "1.3094 V",
"D": "-1.3094 V"
} | C | 1.3094 V | Apply the Nernst equation: E=1.27−(0.0591/3)(-2)=1.3094 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.3094 V, not 0.6547 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.3094 V, not 1.9641 V.",
"C": "Correct. The worked calculation gives 1.3094 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_006700 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 1 mol H₂ and 24 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "0.5 mol",
"B": "-1 mol",
"C": "0.75 mol",
"D": "1 mol"
} | D | 1 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 1 mol H₂O; O₂ can produce 48 mol H₂O. The limiting condition is H₂; product=1 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1 mol, not 0.5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1 mol, not -1 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1 mol, not 0.75 mol.",
... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007429 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 43 mL of 0.10 M HCl is mixed with 21 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.46376",
"B": "0.46376",
"C": "4.46376",
"D": "-0.53624"
} | A | 1.46376 | Excess H⁺ moles=0.10×(43−21)/1000=0.002200 mol. Total volume=0.064 L, so [H⁺]=0.034375 M and pH=−log₁₀[H⁺]=1.46376. | {
"A": "Correct. The worked calculation gives 1.46376.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.46376, not 0.46376.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.46376, not 4.46376.",
"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_006701 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 31 mol H₂ and 4 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "8 mol",
"B": "6 mol",
"C": "1.8 mol",
"D": "4 mol"
} | A | 8 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 31 mol H₂O; O₂ can produce 8 mol H₂O. The limiting condition is O₂; product=8 mol. | {
"A": "Correct. The worked calculation gives 8 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8 mol, not 6 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8 mol, not 1.8 mol.",
"D": "Incorrect. Substituting the stated values int... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008490 | 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 0.36 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.73728 K",
"B": "-2.63136 K",
"C": "-0.63136 K",
"D": "0.36864 K"
} | D | 0.36864 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×0.36=0.36864 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.36864 K, not 0.73728 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36864 K, not -2.63136 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.36864 K... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008045 | 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 1778 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "4.38742 g",
"B": "8.77484 g",
"C": "2.92495 g",
"D": "5.8499 g"
} | D | 5.8499 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×10×1778/(2×96500)=5.8499 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.8499 g, not 4.38742 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.8499 g, not 8.77484 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.8499 g, no... | [
"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_009051 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.34 V, transfers 3 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.86225 V",
"B": "1.2415 V",
"C": "2.483 V",
"D": "-1.2415 V"
} | B | 1.2415 V | Apply the Nernst equation: E=1.34−(0.0591/3)(5)=1.2415 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.2415 V, not 1.86225 V.",
"B": "Correct. The worked calculation gives 1.2415 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2415 V, not 2.483 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_002267 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 4 blue and 7 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.23162",
"B": "0.30882",
"C": "0.15441",
"D": "1.30882"
} | B | 0.30882 | Favourable pairs = C(6,2)+C(4,2)+C(7,2)=42. Total pairs=C(17,2)=136. Therefore P=42/136=0.30882. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30882, not 0.23162.",
"B": "Correct. The worked calculation gives 0.30882.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30882, not 0.15441.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004590 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 14 kg and radius 6 m is acted on by a constant torque of 36 N m about its central axis. Find its angular acceleration. | {
"A": "2.14286 rad s⁻²",
"B": "0.14286 rad s⁻²",
"C": "1.01429 rad s⁻²",
"D": "-1.85714 rad s⁻²"
} | B | 0.14286 rad s⁻² | For a solid disc, I=½MR²=½(14)(6)²=252 kg m². Using τ=Iα, α=36/252=0.14286 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.14286 rad s⁻², not 2.14286 rad s⁻².",
"B": "Correct. The worked calculation gives 0.14286 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.14286 rad s⁻², not 1.01429 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_006177 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 48 cm in front of a thin convex lens of focal length 18 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.6",
"B": "1.2",
"C": "0.3",
"D": "0.9"
} | A | 0.6 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(48)(18)/(48−18)=28.8 cm. Thus |m|=v/u=28.8/48=0.6. | {
"A": "Correct. The worked calculation gives 0.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6, not 1.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.6, not 0.3.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_002418 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, -7], [9, -8]]. | {
"A": "22.5",
"B": "15",
"C": "2.5",
"D": "17"
} | B | 15 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(-8)−(-7)(9)=15. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15, not 22.5.",
"B": "Correct. The worked calculation gives 15.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15, not 2.5.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005674 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.6 atm at 373 K. What is its pressure at 614 K? | {
"A": "0.98767 atm",
"B": "1.4815 atm",
"C": "1.09877 atm",
"D": "-1.01233 atm"
} | A | 0.98767 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.6)(614)/(373)=0.98767 atm. | {
"A": "Correct. The worked calculation gives 0.98767 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.98767 atm, not 1.4815 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.98767 atm, not 1.09877 atm.",
"D": "Incorrect. Substit... | [
"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_008942 | 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 0.68 mol L⁻¹ and initially B is absent. At equilibrium, 79% of A has dissociated at constant volume. Find K_c. | {
"A": "6.06269",
"B": "10.08358",
"C": "8.08358",
"D": "5.08358"
} | C | 8.08358 | Let α=0.79. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.68)(0.79)²/(1−0.79)=8.08358. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.08358, not 6.06269.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.08358, not 10.08358.",
"C": "Correct. The worked calculation gives 8.08358.",
"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_002175 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 8 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": "0.32806",
"B": "3.32806",
"C": "2.32806",
"D": "-0.32806"
} | A | 0.32806 | Favourable pairs = C(10,2)+C(8,2)+C(5,2)=83. Total pairs=C(23,2)=253. Therefore P=83/253=0.32806. | {
"A": "Correct. The worked calculation gives 0.32806.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32806, not 3.32806.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32806, not 2.32806.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008041 | 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 29950 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "9.85402 g",
"B": "19.70803 g",
"C": "20.70803 g",
"D": "2.9708 g"
} | B | 19.70803 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×2×29950/(2×96500)=19.70803 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19.70803 g, not 9.85402 g.",
"B": "Correct. The worked calculation gives 19.70803 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19.70803 g, not 20.70803 g.",
"D": "Incorrect. Substituting... | [
"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_008577 | 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 0.07 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "3.03584 K",
"B": "-2.96416 K",
"C": "0.03584 K",
"D": "0.01792 K"
} | C | 0.03584 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.512×0.07=0.03584 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.03584 K, not 3.03584 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.03584 K, not -2.96416 K.",
"C": "Correct. The worked calculation gives 0.03584 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_005364 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 49 μF capacitor is charged to a potential difference of 33 V. Calculate the energy stored, expressed in μJ. | {
"A": "40020.75 μJ",
"B": "26680.5 μJ",
"C": "53361 μJ",
"D": "21344.4 μJ"
} | B | 26680.5 μJ | U=½CV². Since C=49 μF, U in μJ is ½×49×(33)²=26680.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26680.5 μJ, not 40020.75 μJ.",
"B": "Correct. The worked calculation gives 26680.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26680.5 μJ, not 53361 μJ.",
"D": "Incorrect. Substituting... | [
"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_008183 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 3 A for 11837 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": "11.68367 g",
"B": "2.16837 g",
"C": "23.36734 g",
"D": "8.68367 g"
} | A | 11.68367 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×3×11837/(2×96500)=11.68367 g. | {
"A": "Correct. The worked calculation gives 11.68367 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.68367 g, not 2.16837 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.68367 g, not 23.36734 g.",
"D": "Incorrect. Substituting... | [
"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_005353 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 31 μF capacitor is charged to a potential difference of 8 V. Calculate the energy stored, expressed in μJ. | {
"A": "100.2 μJ",
"B": "991 μJ",
"C": "992 μJ",
"D": "1984 μJ"
} | C | 992 μJ | U=½CV². Since C=31 μF, U in μJ is ½×31×(8)²=992 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 992 μJ, not 100.2 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 992 μJ, not 991 μJ.",
"C": "Correct. The worked calculation gives 992 μJ.",
"D": "Incorrect. Substituting the stated value... | [
"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_001446 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (4x² +2x +3) dx. | {
"A": "206.66667",
"B": "165.33333",
"C": "413.33333",
"D": "248"
} | A | 206.66667 | An antiderivative is (4/3)x³+(2/2)x²+(3)x. Evaluating between 0 and 5 gives (4/3)(5)³+(2/2)(5)²+(3)(5)=206.66667. | {
"A": "Correct. The worked calculation gives 206.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 206.66667, not 165.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 206.66667, not 413.33333.",
"D": "Incorrect. Substituting the... | [
"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_004054 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.40. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "31.5 N",
"B": "44 N",
"C": "84 N",
"D": "42 N"
} | D | 42 N | Net force=mg(sinθ−μcosθ)=15×10×(0.6−0.40×0.8)=42 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 42 N, not 31.5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 42 N, not 44 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 42 N, not 84 N.",
"D": "Co... | [
"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_005525 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 14 μF capacitor is charged to a potential difference of 9 V. Calculate the energy stored, expressed in μJ. | {
"A": "567 μJ",
"B": "569 μJ",
"C": "680.4 μJ",
"D": "425.25 μJ"
} | A | 567 μJ | U=½CV². Since C=14 μF, U in μJ is ½×14×(9)²=567 μJ. | {
"A": "Correct. The worked calculation gives 567 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 567 μJ, not 569 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 567 μJ, not 680.4 μJ.",
"D": "Incorrect. Substituting the stated value... | [
"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_001073 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ +10x² +10x+7. Evaluate f′(2). | {
"A": "132",
"B": "220",
"C": "82.5",
"D": "110"
} | D | 110 | Differentiate: f′(x)=3(5)x²+2(10)x+(10). At x=2, f′(2)=3(5)(2)²+2(10)(2)+(10)=110. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 110, not 132.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 110, not 220.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 110, not 82.5.",
"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_009407 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_12H_22. Treat X as the total number of monovalent halogen atoms. | {
"A": "4",
"B": "-2",
"C": "2",
"D": "1"
} | C | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×12+2+0−22−0)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"C": "Correct. The worked calculation gives 2.",
"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_001075 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=3x³ +8x² +1x+7. Evaluate f′(-4). | {
"A": "81",
"B": "40.5",
"C": "9.1",
"D": "97.2"
} | A | 81 | Differentiate: f′(x)=3(3)x²+2(8)x+(1). At x=-4, f′(-4)=3(3)(-4)²+2(8)(-4)+(1)=81. | {
"A": "Correct. The worked calculation gives 81.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 81, not 40.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 81, not 9.1.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_002093 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 8 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "2.35263",
"B": "0.35263",
"C": "-1.64737",
"D": "3.35263"
} | B | 0.35263 | Favourable pairs = C(9,2)+C(8,2)+C(3,2)=67. Total pairs=C(20,2)=190. Therefore P=67/190=0.35263. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35263, not 2.35263.",
"B": "Correct. The worked calculation gives 0.35263.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35263, not -1.64737.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006579 | 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 603 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.18212 s",
"B": "-1.81788 s",
"C": "2.18212 s",
"D": "0.18212 s"
} | D | 0.18212 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(5/603)=0.18212 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.18212 s, not -0.18212 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.18212 s, not -1.81788 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.18212 ... | [
"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_006926 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 40 mol H₂ and 7 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "21 mol",
"B": "-14 mol",
"C": "14 mol",
"D": "12 mol"
} | C | 14 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 40 mol H₂O; O₂ can produce 14 mol H₂O. The limiting condition is O₂; product=14 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14 mol, not 21 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14 mol, not -14 mol.",
"C": "Correct. The worked calculation gives 14 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_005708 | 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 1.7 atm at 243 K. What is its pressure at 769 K? | {
"A": "2.37984 atm",
"B": "8.06975 atm",
"C": "10.75967 atm",
"D": "5.37984 atm"
} | D | 5.37984 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.7)(769)/(243)=5.37984 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.37984 atm, not 2.37984 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.37984 atm, not 8.06975 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.... | [
"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_004936 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 2 Ω are connected in series; this combination is connected in parallel with a 3 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "4 A",
"B": "2.5 A",
"C": "5 A",
"D": "-5 A"
} | C | 5 A | Series branch resistance=10+2=12 Ω. Parallel equivalent R_eq=(12×3)/(12+3)=2.4 Ω. Total current I=V/R_eq=12/2.4=5 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5 A, not 4 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5 A, not 2.5 A.",
"C": "Correct. The worked calculation gives 5 A.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_000704 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 3 and common ratio 2. What is the sum of its first 6 terms? | {
"A": "378",
"B": "188",
"C": "187",
"D": "189"
} | D | 189 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=3(2^6−1)/(2−1)=189. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 189, not 378.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 189, not 188.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 189, not 187.",
"D": "Correct. T... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002906 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-7, -3, 2) and v=(8, -5, 4), calculate u·v. | {
"A": "-24.75",
"B": "-35",
"C": "-33",
"D": "-16.5"
} | C | -33 | The dot product is the sum of corresponding component products: (-7)(8)+(-3)(-5)+(2)(4)=-33. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -33, not -24.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -33, not -35.",
"C": "Correct. The worked calculation gives -33.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001173 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ +1x² +8x+7. Evaluate f′(0). | {
"A": "6",
"B": "9",
"C": "-8",
"D": "8"
} | D | 8 | Differentiate: f′(x)=3(4)x²+2(1)x+(8). At x=0, f′(0)=3(4)(0)²+2(1)(0)+(8)=8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not -8.",
"D": "Correct. The worked c... | [
"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_001933 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 73 distinct elements? | {
"A": "22530501",
"B": "15020334",
"C": "15020332",
"D": "15020335"
} | B | 15020334 | Order does not matter, so the count is C(73,5)=73!/[5!(68)!]=15020334. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15020334, not 22530501.",
"B": "Correct. The worked calculation gives 15020334.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15020334, not 15020332.",
"D": "Incorrect. Substituting the stat... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006661 | 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 1135 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.70317 s",
"B": "0.29683 s",
"C": "-0.29683 s",
"D": "-0.70317 s"
} | B | 0.29683 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(25/1135)=0.29683 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29683 s, not -2.70317 s.",
"B": "Correct. The worked calculation gives 0.29683 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29683 s, not -0.29683 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_006583 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 11 kg is attached to an ideal spring of force constant 332 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.27304 s",
"B": "0.54607 s",
"C": "0.36405 s",
"D": "2.36405 s"
} | C | 0.36405 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(11/332)=0.36405 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.36405 s, not 0.27304 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36405 s, not 0.54607 s.",
"C": "Correct. The worked calculation gives 0.36405 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_007397 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 70 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": "-0.75818",
"B": "3.24182",
"C": "0.62091",
"D": "1.24182"
} | D | 1.24182 | Excess H⁺ moles=0.10×(70−19)/1000=0.005100 mol. Total volume=0.089 L, so [H⁺]=0.057303 M and pH=−log₁₀[H⁺]=1.24182. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.24182, not -0.75818.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.24182, not 3.24182.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.24182, not 0.62... | [
"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_004671 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 6 m is acted on by a constant torque of 41 N m about its central axis. Find its angular acceleration. | {
"A": "0.28472 rad s⁻²",
"B": "-0.71528 rad s⁻²",
"C": "2.28472 rad s⁻²",
"D": "0.56944 rad s⁻²"
} | A | 0.28472 rad s⁻² | For a solid disc, I=½MR²=½(8)(6)²=144 kg m². Using τ=Iα, α=41/144=0.28472 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.28472 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.28472 rad s⁻², not -0.71528 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.28472 rad s⁻², not 2.28472 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_008973 | 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 1.38 mol L⁻¹ and initially B is absent. At equilibrium, 25% of A has dissociated at constant volume. Find K_c. | {
"A": "0.46",
"B": "0.69",
"C": "2.46",
"D": "-0.46"
} | A | 0.46 | Let α=0.25. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.38)(0.25)²/(1−0.25)=0.46. | {
"A": "Correct. The worked calculation gives 0.46.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.46, not 0.69.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.46, not 2.46.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_006859 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 15 mol H₂ and 11 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "17 mol",
"B": "15 mol",
"C": "-15 mol",
"D": "14 mol"
} | B | 15 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 15 mol H₂O; O₂ can produce 22 mol H₂O. The limiting condition is H₂; product=15 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15 mol, not 17 mol.",
"B": "Correct. The worked calculation gives 15 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15 mol, not -15 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_009522 | 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_13H_4N_2X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "2.1",
"B": "14",
"C": "11",
"D": "12"
} | C | 11 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×13+2+2−4−4)/2=11. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11, not 2.1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11, not 14.",
"C": "Correct. The worked calculation gives 11.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006445 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 19 kg is attached to an ideal spring of force constant 645 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.65674 s",
"B": "0.34326 s",
"C": "3.34326 s",
"D": "1.03433 s"
} | B | 0.34326 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(19/645)=0.34326 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34326 s, not -0.65674 s.",
"B": "Correct. The worked calculation gives 0.34326 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34326 s, not 3.34326 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_004697 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 12 Ω and 12 Ω are connected in series; this combination is connected in parallel with a 10 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "-0.3 A",
"B": "1.275 A",
"C": "1.7 A",
"D": "3.7 A"
} | C | 1.7 A | Series branch resistance=12+12=24 Ω. Parallel equivalent R_eq=(24×10)/(24+10)=7.05882 Ω. Total current I=V/R_eq=12/7.05882=1.7 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.7 A, not -0.3 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.7 A, not 1.275 A.",
"C": "Correct. The worked calculation gives 1.7 A.",
"D": "Incorrect. Substituting the stated values in... | [
"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_001554 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (1x² -1x -1) dx. | {
"A": "22.16667",
"B": "23.16667",
"C": "-24.16667",
"D": "24.16667"
} | D | 24.16667 | An antiderivative is (1/3)x³+(-1/2)x²+(-1)x. Evaluating between 0 and 5 gives (1/3)(5)³+(-1/2)(5)²+(-1)(5)=24.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24.16667, not 22.16667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24.16667, not 23.16667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24.16667, not ... | [
"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_006235 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 32 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": "3.57143",
"B": "6.57143",
"C": "4.57143",
"D": "2.57143"
} | A | 3.57143 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(32)(25)/(32−25)=114.28571 cm. Thus |m|=v/u=114.28571/32=3.57143. | {
"A": "Correct. The worked calculation gives 3.57143.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.57143, not 6.57143.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.57143, not 4.57143.",
"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_001824 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 2 elements can be selected from a set of 31 distinct elements? | {
"A": "372",
"B": "697.5",
"C": "558",
"D": "465"
} | D | 465 | Order does not matter, so the count is C(31,2)=31!/[2!(29)!]=465. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 465, not 372.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 465, not 697.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 465, not 558.",
"D": "Correct.... | [
"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_003799 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 4 m s⁻¹. A constant net force does 30 N of work over 19 m in the direction of motion. Find its final kinetic energy. | {
"A": "481.6 J",
"B": "604 J",
"C": "301 J",
"D": "602 J"
} | D | 602 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(4)²+(30)(19)=602 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 602 J, not 481.6 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 602 J, not 604 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 602 J, not 301 J.",
"D... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007572 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 10 mL of 0.10 M HCl is mixed with 31 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "25.41887",
"B": "14.70944",
"C": "12.70944",
"D": "-12.70944"
} | C | 12.70944 | Excess OH⁻ moles=0.10×(31−10)/1000=0.002100 mol. Total volume=0.041 L, so [OH⁻]=0.051220 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.70944. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.70944, not 25.41887.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.70944, not 14.70944.",
"C": "Correct. The worked calculation gives 12.70944.",
"D": "Incorrect. Substituting the stat... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004934 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 5 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 14 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.64286 A",
"B": "2.64286 A",
"C": "-1.35714 A",
"D": "4.64286 A"
} | A | 1.64286 A | Series branch resistance=5+4=9 Ω. Parallel equivalent R_eq=(9×14)/(9+14)=5.47826 Ω. Total current I=V/R_eq=9/5.47826=1.64286 A. | {
"A": "Correct. The worked calculation gives 1.64286 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.64286 A, not 2.64286 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.64286 A, not -1.35714 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_000344 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 29 and common difference 14. Find the sum of its first 29 terms. | {
"A": "9787.5",
"B": "13050",
"C": "6525",
"D": "-6525"
} | C | 6525 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=29, d=14, n=29: Sₙ=29/2[2(29)+(29−1)(14)]=6525. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6525, not 9787.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6525, not 13050.",
"C": "Correct. The worked calculation gives 6525.",
"D": "Incorrect. Substituting the stated values into th... | [
"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_000106 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 -13x +6=0, let its roots be α and β. What is α²+β²? | {
"A": "1.436",
"B": "4.36",
"C": "5.36",
"D": "2.18"
} | B | 4.36 | By Vieta's relations, α+β = 13/5 and αβ = 6/5. Then α²+β²=(α+β)²−2αβ = (13/5)²−2(6/5) = 4.36. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.36, not 1.436.",
"B": "Correct. The worked calculation gives 4.36.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.36, not 5.36.",
"D": "Incorrect. Substituting the stated values into the ... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008751 | 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 0.99 mol L⁻¹ and initially B is absent. At equilibrium, 79% of A has dissociated at constant volume. Find K_c. | {
"A": "23.53749",
"B": "2.17687",
"C": "10.76874",
"D": "11.76874"
} | D | 11.76874 | Let α=0.79. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.99)(0.79)²/(1−0.79)=11.76874. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.76874, not 23.53749.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.76874, not 2.17687.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.76874, not 1... | [
"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 |
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