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_002505 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, -2], [4, 8]]. | {
"A": "81",
"B": "80",
"C": "160",
"D": "82"
} | B | 80 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(8)−(-2)(4)=80. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 80, not 81.",
"B": "Correct. The worked calculation gives 80.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 80, not 160.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000024 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 -11x -4=0, let its roots be α and β. What is α²+β²? | {
"A": "7.17188",
"B": "11.5625",
"C": "6.5625",
"D": "9.5625"
} | D | 9.5625 | By Vieta's relations, α+β = 11/4 and αβ = -4/4. Then α²+β²=(α+β)²−2αβ = (11/4)²−2(-4/4) = 9.5625. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.5625, not 7.17188.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.5625, not 11.5625.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.5625, not 6.5625."... | [
"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_005927 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.3 atm at 186 K. What is its pressure at 566 K? | {
"A": "-0.0871 atm",
"B": "0.68468 atm",
"C": "-2.0871 atm",
"D": "0.9129 atm"
} | D | 0.9129 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.3)(566)/(186)=0.9129 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9129 atm, not -0.0871 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9129 atm, not 0.68468 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.91... | [
"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_004404 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 12 kg and radius 4 m is acted on by a constant torque of 37 N m about its central axis. Find its angular acceleration. | {
"A": "0.77083 rad s⁻²",
"B": "0.57812 rad s⁻²",
"C": "0.38542 rad s⁻²",
"D": "1.03854 rad s⁻²"
} | C | 0.38542 rad s⁻² | For a solid disc, I=½MR²=½(12)(4)²=96 kg m². Using τ=Iα, α=37/96=0.38542 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.38542 rad s⁻², not 0.77083 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.38542 rad s⁻², not 0.57812 rad s⁻².",
"C": "Correct. The worked calculation gives 0.38542 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_001996 | 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 30 distinct elements? | {
"A": "54627301",
"B": "65552760",
"C": "43701840",
"D": "54627300"
} | D | 54627300 | Order does not matter, so the count is C(30,11)=30!/[11!(19)!]=54627300. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 54627300, not 54627301.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 54627300, not 65552760.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 54627300, not ... | [
"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_008842 | 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 0.65 mol L⁻¹ and initially B is absent. At equilibrium, 56% of A has dissociated at constant volume. Find K_c. | {
"A": "-1.14691",
"B": "1.18531",
"C": "1.85309",
"D": "2.85309"
} | C | 1.85309 | Let α=0.56. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.65)(0.56)²/(1−0.56)=1.85309. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.85309, not -1.14691.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.85309, not 1.18531.",
"C": "Correct. The worked calculation gives 1.85309.",
"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_003727 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block initially moves at 1 m s⁻¹. A constant net force does 6 N of work over 4 m in the direction of motion. Find its final kinetic energy. | {
"A": "15.75 J",
"B": "30.5 J",
"C": "31.5 J",
"D": "47.25 J"
} | C | 31.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(15)(1)²+(6)(4)=31.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 31.5 J, not 15.75 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 31.5 J, not 30.5 J.",
"C": "Correct. The worked calculation gives 31.5 J.",
"D": "Incorrect. Substituting the stated values... | [
"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_005457 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 48 μF capacitor is charged to a potential difference of 3 V. Calculate the energy stored, expressed in μJ. | {
"A": "432 μJ",
"B": "215 μJ",
"C": "216 μJ",
"D": "214 μJ"
} | C | 216 μJ | U=½CV². Since C=48 μF, U in μJ is ½×48×(3)²=216 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 216 μJ, not 432 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 216 μJ, not 215 μJ.",
"C": "Correct. The worked calculation gives 216 μJ.",
"D": "Incorrect. Substituting the stated values ... | [
"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_002857 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-2, -1, 6) and v=(8, -6, 3), calculate u·v. | {
"A": "8",
"B": "7",
"C": "6",
"D": "12"
} | A | 8 | The dot product is the sum of corresponding component products: (-2)(8)+(-1)(-6)+(6)(3)=8. | {
"A": "Correct. The worked calculation gives 8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 6.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_006290 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 63 cm in front of a thin convex lens of focal length 23 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.43125",
"B": "0.8625",
"C": "1.0575",
"D": "0.575"
} | D | 0.575 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(63)(23)/(63−23)=36.225 cm. Thus |m|=v/u=36.225/63=0.575. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.575, not 0.43125.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.575, not 0.8625.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.575, not 1.0575.",
... | [
"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_007421 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 55 mL of 0.10 M HCl is mixed with 43 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.1912",
"B": "3.91204",
"C": "0.95602",
"D": "1.91204"
} | D | 1.91204 | Excess H⁺ moles=0.10×(55−43)/1000=0.001200 mol. Total volume=0.098 L, so [H⁺]=0.012245 M and pH=−log₁₀[H⁺]=1.91204. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.91204, not 1.1912.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.91204, not 3.91204.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.91204, not 0.9560... | [
"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_000087 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 -5x +5=0, let its roots be α and β. What is α²+β²? | {
"A": "-0.97222",
"B": "0.97222",
"C": "-2.97222",
"D": "-1.97222"
} | A | -0.97222 | By Vieta's relations, α+β = 5/6 and αβ = 5/6. Then α²+β²=(α+β)²−2αβ = (5/6)²−2(5/6) = -0.97222. | {
"A": "Correct. The worked calculation gives -0.97222.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.97222, not 0.97222.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.97222, not -2.97222.",
"D": "Incorrect. Substituting the state... | [
"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_002524 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 0], [8, -4]]. | {
"A": "-15",
"B": "-18",
"C": "-16",
"D": "-17"
} | C | -16 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(-4)−(0)(8)=-16. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -16, not -15.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -16, not -18.",
"C": "Correct. The worked calculation gives -16.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000335 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 3 and common difference 7. Find the sum of its first 26 terms. | {
"A": "2353",
"B": "2823.6",
"C": "1764.75",
"D": "-2353"
} | A | 2353 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=3, d=7, n=26: Sₙ=26/2[2(3)+(26−1)(7)]=2353. | {
"A": "Correct. The worked calculation gives 2353.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2353, not 2823.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2353, not 1764.75.",
"D": "Incorrect. Substituting the stated values into ... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006846 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 18 mol H₂ and 6 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "12 mol",
"B": "15 mol",
"C": "14 mol",
"D": "2.2 mol"
} | A | 12 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 18 mol H₂O; O₂ can produce 12 mol H₂O. The limiting condition is O₂; product=12 mol. | {
"A": "Correct. The worked calculation gives 12 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 15 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 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_009001 | 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 0.5 mol L⁻¹ and initially B is absent. At equilibrium, 28% of A has dissociated at constant volume. Find K_c. | {
"A": "0.43556",
"B": "0.10889",
"C": "0.21778",
"D": "0.16333"
} | C | 0.21778 | Let α=0.28. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.5)(0.28)²/(1−0.28)=0.21778. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.21778, not 0.43556.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.21778, not 0.10889.",
"C": "Correct. The worked calculation gives 0.21778.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000409 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 0 and common difference 11. Find the sum of its first 15 terms. | {
"A": "1155",
"B": "116.5",
"C": "577.5",
"D": "1154"
} | A | 1155 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=0, d=11, n=15: Sₙ=15/2[2(0)+(15−1)(11)]=1155. | {
"A": "Correct. The worked calculation gives 1155.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1155, not 116.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1155, not 577.5.",
"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_005922 | 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 atm at 276 K. What is its pressure at 695 K? | {
"A": "1.25906 atm",
"B": "2.51812 atm",
"C": "5.51812 atm",
"D": "-0.48188 atm"
} | B | 2.51812 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1)(695)/(276)=2.51812 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.51812 atm, not 1.25906 atm.",
"B": "Correct. The worked calculation gives 2.51812 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.51812 atm, not 5.51812 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_007278 | 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 525 K and 0.56 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "2615.56687 L",
"B": "1307.78344 L",
"C": "-1307.78344 L",
"D": "1961.67516 L"
} | B | 1307.78344 L | PV=nRT, so V=nRT/P=(17)(0.082057)(525)/(0.56)=1307.78344 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1307.78344 L, not 2615.56687 L.",
"B": "Correct. The worked calculation gives 1307.78344 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1307.78344 L, not -1307.78344 L.",
"D": "Incorrect. ... | [
"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_007462 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 61 mL of 0.10 M HCl is mixed with 40 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.6821",
"B": "2.6821",
"C": "1.26158",
"D": "4.6821"
} | A | 1.6821 | Excess H⁺ moles=0.10×(61−40)/1000=0.002100 mol. Total volume=0.101 L, so [H⁺]=0.020792 M and pH=−log₁₀[H⁺]=1.6821. | {
"A": "Correct. The worked calculation gives 1.6821.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.6821, not 2.6821.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.6821, not 1.26158.",
"D": "Incorrect. Substituting the stated values... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005338 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +7 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "33.5 N",
"B": "23.625 N",
"C": "15.75 N",
"D": "31.5 N"
} | D | 31.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(7×10⁻⁶)/(10×10⁻²)²=31.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 31.5 N, not 33.5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 31.5 N, not 23.625 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 31.5 N, not 15.75 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_001114 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ -10x² +6x+7. Evaluate f′(0). | {
"A": "1.6",
"B": "12",
"C": "8",
"D": "6"
} | D | 6 | Differentiate: f′(x)=3(-4)x²+2(-10)x+(6). At x=0, f′(0)=3(-4)(0)²+2(-10)(0)+(6)=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 1.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 8.",
"D": "Correct. The worked... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005731 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4 atm at 255 K. What is its pressure at 780 K? | {
"A": "14.23529 atm",
"B": "9.23529 atm",
"C": "10.23529 atm",
"D": "12.23529 atm"
} | D | 12.23529 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4)(780)/(255)=12.23529 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.23529 atm, not 14.23529 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.23529 atm, not 9.23529 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005930 | 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 369 K. What is its pressure at 421 K? | {
"A": "1.93957 atm",
"B": "2.90935 atm",
"C": "-1.06043 atm",
"D": "1.19396 atm"
} | A | 1.93957 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.7)(421)/(369)=1.93957 atm. | {
"A": "Correct. The worked calculation gives 1.93957 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.93957 atm, not 2.90935 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.93957 atm, not -1.06043 atm.",
"D": "Incorrect. Subst... | [
"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_009609 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_10H_6. Treat X as the total number of monovalent halogen atoms. | {
"A": "12",
"B": "8",
"C": "11",
"D": "6"
} | B | 8 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×10+2+0−6−0)/2=8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 12.",
"B": "Correct. The worked calculation gives 8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 11.",
"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_002458 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, -6], [8, -1]]. | {
"A": "47",
"B": "44",
"C": "22.5",
"D": "45"
} | D | 45 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(-1)−(-6)(8)=45. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45, not 47.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 45, not 44.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 45, not 22.5.",
"D": "Correct. The w... | [
"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_003961 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block initially moves at 2 m s⁻¹. A constant net force does 17 N of work over 17 m in the direction of motion. Find its final kinetic energy. | {
"A": "361.2 J",
"B": "31.1 J",
"C": "301 J",
"D": "451.5 J"
} | C | 301 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(6)(2)²+(17)(17)=301 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 301 J, not 361.2 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 301 J, not 31.1 J.",
"C": "Correct. The worked calculation gives 301 J.",
"D": "Incorrect. Substituting the stated values in... | [
"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_000450 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -5 and common difference 10. Find the sum of its first 9 terms. | {
"A": "317",
"B": "314",
"C": "313",
"D": "315"
} | D | 315 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-5, d=10, n=9: Sₙ=9/2[2(-5)+(9−1)(10)]=315. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 315, not 317.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 315, not 314.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 315, not 313.",
"D": "Correct. T... | [
"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_003547 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 96 m s⁻¹ at 30° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "598.59676 m",
"B": "796.12901 m",
"C": "798.12901 m",
"D": "797.12901 m"
} | C | 798.12901 m | Range R=u²sin(2θ)/g. Substituting u=96, θ=30° and g=10 gives R=(96)²sin(60°)/10=798.12901 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 798.12901 m, not 598.59676 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 798.12901 m, not 796.12901 m.",
"C": "Correct. The worked calculation gives 798.12901 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_006834 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 41 mol H₂ and 35 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "20.5 mol",
"B": "41 mol",
"C": "43 mol",
"D": "32.8 mol"
} | B | 41 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 41 mol H₂O; O₂ can produce 70 mol H₂O. The limiting condition is H₂; product=41 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 41 mol, not 20.5 mol.",
"B": "Correct. The worked calculation gives 41 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 41 mol, not 43 mol.",
"D": "Incorrect. Substituting the stated value... | [
"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_008881 | 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 1.52 mol L⁻¹ and initially B is absent. At equilibrium, 70% of A has dissociated at constant volume. Find K_c. | {
"A": "7.93067",
"B": "9.93067",
"C": "6.93067",
"D": "10.93067"
} | B | 9.93067 | Let α=0.7. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.52)(0.7)²/(1−0.7)=9.93067. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.93067, not 7.93067.",
"B": "Correct. The worked calculation gives 9.93067.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.93067, not 6.93067.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002884 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(9, 2, -3) and v=(0, 1, 2), calculate u·v. | {
"A": "-6",
"B": "-4",
"C": "0.6",
"D": "-1"
} | B | -4 | The dot product is the sum of corresponding component products: (9)(0)+(2)(1)+(-3)(2)=-4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4, not -6.",
"B": "Correct. The worked calculation gives -4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -4, not 0.6.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005763 | 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 1.1 atm at 406 K. What is its pressure at 655 K? | {
"A": "1.77463 atm",
"B": "0.77463 atm",
"C": "2.77463 atm",
"D": "1.33097 atm"
} | A | 1.77463 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.1)(655)/(406)=1.77463 atm. | {
"A": "Correct. The worked calculation gives 1.77463 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.77463 atm, not 0.77463 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.77463 atm, not 2.77463 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_009362 | 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_3H_2X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "1.5",
"B": "1.1",
"C": "1",
"D": "0.5"
} | C | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×3+2+0−2−4)/2=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.1.",
"C": "Correct. The worked calculation gives 1.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_007939 | 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 56 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "0.65625 mmol L⁻¹",
"B": "0.4375 mmol L⁻¹",
"C": "2.875 mmol L⁻¹",
"D": "0.875 mmol L⁻¹"
} | D | 0.875 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=56/2^6=0.875 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.875 mmol L⁻¹, not 0.65625 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.875 mmol L⁻¹, not 0.4375 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing re... | [
"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_004922 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 13 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "-1.41026 A",
"B": "3.58974 A",
"C": "1.58974 A",
"D": "0.58974 A"
} | C | 1.58974 A | Series branch resistance=4+14=18 Ω. Parallel equivalent R_eq=(18×13)/(18+13)=7.54839 Ω. Total current I=V/R_eq=12/7.54839=1.58974 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.58974 A, not -1.41026 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.58974 A, not 3.58974 A.",
"C": "Correct. The worked calculation gives 1.58974 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_003519 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 12 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "7.2 m",
"B": "11.4 m",
"C": "14.4 m",
"D": "12.4 m"
} | C | 14.4 m | Range R=u²sin(2θ)/g. Substituting u=12, θ=45° and g=10 gives R=(12)²sin(90°)/10=14.4 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14.4 m, not 7.2 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14.4 m, not 11.4 m.",
"C": "Correct. The worked calculation gives 14.4 m.",
"D": "Incorrect. Substituting the stated values i... | [
"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_000853 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio 3. What is the sum of its first 8 terms? | {
"A": "36080",
"B": "-36080",
"C": "36078",
"D": "36081"
} | A | 36080 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(3^8−1)/(3−1)=36080. | {
"A": "Correct. The worked calculation gives 36080.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 36080, not -36080.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 36080, not 36078.",
"D": "Incorrect. Substituting the stated values into... | [
"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_000928 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio -3. What is the sum of its first 10 terms? | {
"A": "-103334",
"B": "-82667.2",
"C": "-51667",
"D": "-10332.4"
} | A | -103334 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(-3^10−1)/(-3−1)=-103334. | {
"A": "Correct. The worked calculation gives -103334.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -103334, not -82667.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -103334, not -51667.",
"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_001613 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (-2x² +2x +3) dx. | {
"A": "-79.33333",
"B": "-158.66667",
"C": "-160.66667",
"D": "158.66667"
} | B | -158.66667 | An antiderivative is (-2/3)x³+(2/2)x²+(3)x. Evaluating between 0 and 7 gives (-2/3)(7)³+(2/2)(7)²+(3)(7)=-158.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -158.66667, not -79.33333.",
"B": "Correct. The worked calculation gives -158.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -158.66667, not -160.66667.",
"D": "Incorrect. Substituting... | [
"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_000214 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 -4x -3=0, let its roots be α and β. What is α²+β²? | {
"A": "1.77551",
"B": "1.18367",
"C": "3.18367",
"D": "2.36735"
} | B | 1.18367 | By Vieta's relations, α+β = 4/7 and αβ = -3/7. Then α²+β²=(α+β)²−2αβ = (4/7)²−2(-3/7) = 1.18367. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.18367, not 1.77551.",
"B": "Correct. The worked calculation gives 1.18367.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.18367, not 3.18367.",
"D": "Incorrect. Substituting the stated va... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000167 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -18x +1=0, let its roots be α and β. What is α²+β²? | {
"A": "-80",
"B": "64",
"C": "78",
"D": "80"
} | D | 80 | By Vieta's relations, α+β = 18/2 and αβ = 1/2. Then α²+β²=(α+β)²−2αβ = (18/2)²−2(1/2) = 80. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 80, not -80.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 80, not 64.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 80, not 78.",
"D": "Correct. The wo... | [
"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_001492 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (1x² +3x +7) dx. | {
"A": "24.66667",
"B": "21.66667",
"C": "45.33333",
"D": "22.66667"
} | D | 22.66667 | An antiderivative is (1/3)x³+(3/2)x²+(7)x. Evaluating between 0 and 2 gives (1/3)(2)³+(3/2)(2)²+(7)(2)=22.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22.66667, not 24.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22.66667, not 21.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22.66667, 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_008372 | 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 0.54 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.972 K",
"B": "-2.028 K",
"C": "1.458 K",
"D": "-0.028 K"
} | A | 0.972 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.6×0.54=0.972 K. | {
"A": "Correct. The worked calculation gives 0.972 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.972 K, not -2.028 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.972 K, not 1.458 K.",
"D": "Incorrect. Substituting the stated v... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005333 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +3 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "30 N",
"B": "60 N",
"C": "45 N",
"D": "28 N"
} | A | 30 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(3×10⁻⁶)/(3×10⁻²)²=30 N. | {
"A": "Correct. The worked calculation gives 30 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30 N, not 60 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30 N, not 45 N.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_005967 | 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 4.6 atm at 296 K. What is its pressure at 491 K? | {
"A": "10.63041 atm",
"B": "4.63041 atm",
"C": "7.63041 atm",
"D": "1.76304 atm"
} | C | 7.63041 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.6)(491)/(296)=7.63041 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.63041 atm, not 10.63041 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.63041 atm, not 4.63041 atm.",
"C": "Correct. The worked calculation gives 7.63041 atm.",
"D": "Incorrect. Subst... | [
"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_000953 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio 4. What is the sum of its first 5 terms? | {
"A": "4092",
"B": "2046",
"C": "2455.2",
"D": "1023"
} | B | 2046 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(4^5−1)/(4−1)=2046. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2046, not 4092.",
"B": "Correct. The worked calculation gives 2046.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2046, not 2455.2.",
"D": "Incorrect. Substituting the stated values into the... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007188 | 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 568 K and 2.01 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "139.12948 L",
"B": "104.34711 L",
"C": "208.69422 L",
"D": "140.12948 L"
} | A | 139.12948 L | PV=nRT, so V=nRT/P=(6)(0.082057)(568)/(2.01)=139.12948 L. | {
"A": "Correct. The worked calculation gives 139.12948 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 139.12948 L, not 104.34711 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 139.12948 L, not 208.69422 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_008960 | 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 1.29 mol L⁻¹ and initially B is absent. At equilibrium, 55% of A has dissociated at constant volume. Find K_c. | {
"A": "2.6015",
"B": "3.46867",
"C": "6.46867",
"D": "6.93733"
} | B | 3.46867 | Let α=0.55. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.29)(0.55)²/(1−0.55)=3.46867. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.46867, not 2.6015.",
"B": "Correct. The worked calculation gives 3.46867.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.46867, not 6.46867.",
"D": "Incorrect. Substituting the stated val... | [
"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_007401 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 87 mL of 0.10 M HCl is mixed with 59 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.71719",
"B": "2.71719",
"C": "-1.28281",
"D": "0.8586"
} | A | 1.71719 | Excess H⁺ moles=0.10×(87−59)/1000=0.002800 mol. Total volume=0.146 L, so [H⁺]=0.019178 M and pH=−log₁₀[H⁺]=1.71719. | {
"A": "Correct. The worked calculation gives 1.71719.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.71719, not 2.71719.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.71719, not -1.28281.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006115 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 29 cm in front of a thin convex lens of focal length 9 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.9",
"B": "2.45",
"C": "-2.55",
"D": "0.45"
} | D | 0.45 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(29)(9)/(29−9)=13.05 cm. Thus |m|=v/u=13.05/29=0.45. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.45, not 0.9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.45, not 2.45.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.45, not -2.55.",
"D": "Corr... | [
"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_007755 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 27 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "6.75 mmol L⁻¹",
"B": "3.375 mmol L⁻¹",
"C": "10.125 mmol L⁻¹",
"D": "4.75 mmol L⁻¹"
} | A | 6.75 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=27/2^2=6.75 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 6.75 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.75 mmol L⁻¹, not 3.375 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.75 mmol L⁻¹, not 10.125 mmol L⁻¹.",
"D": "Inco... | [
"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_004586 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 5 m is acted on by a constant torque of 43 N m about its central axis. Find its angular acceleration. | {
"A": "0.43 rad s⁻²",
"B": "-0.57 rad s⁻²",
"C": "0.215 rad s⁻²",
"D": "2.43 rad s⁻²"
} | A | 0.43 rad s⁻² | For a solid disc, I=½MR²=½(8)(5)²=100 kg m². Using τ=Iα, α=43/100=0.43 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.43 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.43 rad s⁻², not -0.57 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.43 rad s⁻², not 0.215 rad s⁻².",
"D": "Incorrect.... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000348 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 2 and common difference 7. Find the sum of its first 10 terms. | {
"A": "335",
"B": "333",
"C": "337",
"D": "670"
} | A | 335 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=2, d=7, n=10: Sₙ=10/2[2(2)+(10−1)(7)]=335. | {
"A": "Correct. The worked calculation gives 335.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 335, not 333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 335, not 337.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_006939 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 18 mol H₂ and 21 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "18 mol",
"B": "19 mol",
"C": "27 mol",
"D": "21.6 mol"
} | A | 18 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 18 mol H₂O; O₂ can produce 42 mol H₂O. The limiting condition is H₂; product=18 mol. | {
"A": "Correct. The worked calculation gives 18 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18 mol, not 19 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18 mol, not 27 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_004173 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.38. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "18.76 N",
"B": "19.76 N",
"C": "15.76 N",
"D": "17.76 N"
} | D | 17.76 N | Net force=mg(sinθ−μcosθ)=6×10×(0.6−0.38×0.8)=17.76 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 17.76 N, not 18.76 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17.76 N, not 19.76 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17.76 N, not 15.76... | [
"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_005120 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +5 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "56.25 N",
"B": "57.25 N",
"C": "58.25 N",
"D": "67.5 N"
} | A | 56.25 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(5×10⁻⁶)/(4×10⁻²)²=56.25 N. | {
"A": "Correct. The worked calculation gives 56.25 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 56.25 N, not 57.25 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 56.25 N, not 58.25 N.",
"D": "Incorrect. Substituting the stated va... | [
"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_000152 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 +2x +8=0, let its roots be α and β. What is α²+β²? | {
"A": "-7",
"B": "-14",
"C": "-5",
"D": "-3.5"
} | A | -7 | By Vieta's relations, α+β = -2/2 and αβ = 8/2. Then α²+β²=(α+β)²−2αβ = (-2/2)²−2(8/2) = -7. | {
"A": "Correct. The worked calculation gives -7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -7, not -14.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -7, not -5.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"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_001974 | 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 82 distinct elements? | {
"A": "27285336",
"B": "54570672",
"C": "20464002",
"D": "27285335"
} | A | 27285336 | Order does not matter, so the count is C(82,5)=82!/[5!(77)!]=27285336. | {
"A": "Correct. The worked calculation gives 27285336.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 27285336, not 54570672.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 27285336, not 20464002.",
"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_005638 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 37 μF capacitor is charged to a potential difference of 29 V. Calculate the energy stored, expressed in μJ. | {
"A": "15558.5 μJ",
"B": "15557.5 μJ",
"C": "31117 μJ",
"D": "15556.5 μJ"
} | A | 15558.5 μJ | U=½CV². Since C=37 μF, U in μJ is ½×37×(29)²=15558.5 μJ. | {
"A": "Correct. The worked calculation gives 15558.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15558.5 μJ, not 15557.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15558.5 μJ, not 31117 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_001779 | 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 45 distinct elements? | {
"A": "1221758",
"B": "1221759",
"C": "1221757",
"D": "1221760"
} | B | 1221759 | Order does not matter, so the count is C(45,5)=45!/[5!(40)!]=1221759. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1221759, not 1221758.",
"B": "Correct. The worked calculation gives 1221759.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1221759, not 1221757.",
"D": "Incorrect. Substituting the stated va... | [
"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_007175 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 3 mol of gas at 444 K and 0.74 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "147.7026 L",
"B": "149.7026 L",
"C": "15.77026 L",
"D": "148.7026 L"
} | A | 147.7026 L | PV=nRT, so V=nRT/P=(3)(0.082057)(444)/(0.74)=147.7026 L. | {
"A": "Correct. The worked calculation gives 147.7026 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 147.7026 L, not 149.7026 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 147.7026 L, not 15.77026 L.",
"D": "Incorrect. Substitutin... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008154 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 15 A for 20050 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": "197.90285 g",
"B": "148.42714 g",
"C": "98.95142 g",
"D": "10.89514 g"
} | C | 98.95142 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×15×20050/(2×96500)=98.95142 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 98.95142 g, not 197.90285 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 98.95142 g, not 148.42714 g.",
"C": "Correct. The worked calculation gives 98.95142 g.",
"D": "Incorrect. Substitut... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004737 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 12 Ω and 15 Ω are connected in series; this combination is connected in parallel with a 9 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "5.33333 A",
"B": "3.33333 A",
"C": "1.53333 A",
"D": "8 A"
} | A | 5.33333 A | Series branch resistance=12+15=27 Ω. Parallel equivalent R_eq=(27×9)/(27+9)=6.75 Ω. Total current I=V/R_eq=36/6.75=5.33333 A. | {
"A": "Correct. The worked calculation gives 5.33333 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.33333 A, not 3.33333 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.33333 A, not 1.53333 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005964 | 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 0.8 atm at 309 K. What is its pressure at 653 K? | {
"A": "1.16906 atm",
"B": "1.69061 atm",
"C": "-0.30939 atm",
"D": "-1.30939 atm"
} | B | 1.69061 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.8)(653)/(309)=1.69061 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.69061 atm, not 1.16906 atm.",
"B": "Correct. The worked calculation gives 1.69061 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.69061 atm, not -0.30939 atm.",
"D": "Incorrect. Subst... | [
"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_008714 | 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 0.35 mol L⁻¹ and initially B is absent. At equilibrium, 31% of A has dissociated at constant volume. Find K_c. | {
"A": "0.09749",
"B": "0.19499",
"C": "3.19499",
"D": "-0.19499"
} | B | 0.19499 | Let α=0.31. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.35)(0.31)²/(1−0.31)=0.19499. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.19499, not 0.09749.",
"B": "Correct. The worked calculation gives 0.19499.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.19499, not 3.19499.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006287 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 36 cm in front of a thin convex lens of focal length 9 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.66667",
"B": "-0.66667",
"C": "0.33333",
"D": "1.03333"
} | C | 0.33333 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(36)(9)/(36−9)=12 cm. Thus |m|=v/u=12/36=0.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not 0.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not -0.66667.",
"C": "Correct. The worked calculation gives 0.33333.",
"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_002441 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, -4], [2, 5]]. | {
"A": "17.25",
"B": "23",
"C": "34.5",
"D": "25"
} | B | 23 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(5)−(-4)(2)=23. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 23, not 17.25.",
"B": "Correct. The worked calculation gives 23.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23, not 34.5.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008729 | 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 0.21 mol L⁻¹ and initially B is absent. At equilibrium, 74% of A has dissociated at constant volume. Find K_c. | {
"A": "3.76917",
"B": "4.76917",
"C": "3.53834",
"D": "1.76917"
} | D | 1.76917 | Let α=0.74. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.21)(0.74)²/(1−0.74)=1.76917. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.76917, not 3.76917.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.76917, not 4.76917.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.76917, not 3.538... | [
"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_004579 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 9 kg and radius 6 m is acted on by a constant torque of 33 N m about its central axis. Find its angular acceleration. | {
"A": "2.2037 rad s⁻²",
"B": "0.2037 rad s⁻²",
"C": "3.2037 rad s⁻²",
"D": "-0.7963 rad s⁻²"
} | B | 0.2037 rad s⁻² | For a solid disc, I=½MR²=½(9)(6)²=162 kg m². Using τ=Iα, α=33/162=0.2037 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.2037 rad s⁻², not 2.2037 rad s⁻².",
"B": "Correct. The worked calculation gives 0.2037 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.2037 rad s⁻², not 3.2037 rad s⁻².",
"D": "In... | [
"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_007863 | 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 100 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "1.5625 mmol L⁻¹",
"B": "3.125 mmol L⁻¹",
"C": "2.34375 mmol L⁻¹",
"D": "1.17188 mmol L⁻¹"
} | A | 1.5625 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=100/2^6=1.5625 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 1.5625 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.5625 mmol L⁻¹, not 3.125 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.5625 mmol L⁻¹, not 2.34375 mmol L⁻¹.",
"D"... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005888 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.1 atm at 232 K. What is its pressure at 316 K? | {
"A": "4.22241 atm",
"B": "5.22241 atm",
"C": "-4.22241 atm",
"D": "1.42224 atm"
} | A | 4.22241 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.1)(316)/(232)=4.22241 atm. | {
"A": "Correct. The worked calculation gives 4.22241 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.22241 atm, not 5.22241 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.22241 atm, not -4.22241 atm.",
"D": "Incorrect. Subst... | [
"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_008806 | 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 0.89 mol L⁻¹ and initially B is absent. At equilibrium, 45% of A has dissociated at constant volume. Find K_c. | {
"A": "0.31073",
"B": "1.31073",
"C": "1.13107",
"D": "-1.31073"
} | B | 1.31073 | Let α=0.45. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.89)(0.45)²/(1−0.45)=1.31073. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.31073, not 0.31073.",
"B": "Correct. The worked calculation gives 1.31073.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.31073, not 1.13107.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003527 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 64 m s⁻¹ at 70° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "263.2858 m",
"B": "262.2858 m",
"C": "261.2858 m",
"D": "27.32858 m"
} | A | 263.2858 m | Range R=u²sin(2θ)/g. Substituting u=64, θ=70° and g=10 gives R=(64)²sin(140°)/10=263.2858 m. | {
"A": "Correct. The worked calculation gives 263.2858 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 263.2858 m, not 262.2858 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 263.2858 m, not 261.2858 m.",
"D": "Incorrect. Substitutin... | [
"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_005057 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +3 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "268 N",
"B": "216 N",
"C": "270 N",
"D": "540 N"
} | C | 270 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(3×10⁻⁶)/(3×10⁻²)²=270 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 270 N, not 268 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 270 N, not 216 N.",
"C": "Correct. The worked calculation gives 270 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002744 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-5, 5, -6) and v=(-2, 0, 8), calculate u·v. | {
"A": "38",
"B": "-38",
"C": "-45.6",
"D": "-19"
} | B | -38 | The dot product is the sum of corresponding component products: (-5)(-2)+(5)(0)+(-6)(8)=-38. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -38, not 38.",
"B": "Correct. The worked calculation gives -38.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -38, not -45.6.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_002006 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 7 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": "0.22807",
"B": "1.03041",
"C": "-0.30409",
"D": "0.30409"
} | D | 0.30409 | Favourable pairs = C(5,2)+C(7,2)+C(7,2)=52. Total pairs=C(19,2)=171. Therefore P=52/171=0.30409. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30409, not 0.22807.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30409, not 1.03041.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30409, not -0.30... | [
"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_004635 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 9 kg and radius 1 m is acted on by a constant torque of 5 N m about its central axis. Find its angular acceleration. | {
"A": "2.22222 rad s⁻²",
"B": "0.55556 rad s⁻²",
"C": "-1.88889 rad s⁻²",
"D": "1.11111 rad s⁻²"
} | D | 1.11111 rad s⁻² | For a solid disc, I=½MR²=½(9)(1)²=4.5 kg m². Using τ=Iα, α=5/4.5=1.11111 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.11111 rad s⁻², not 2.22222 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.11111 rad s⁻², not 0.55556 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing r... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000903 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio 4. What is the sum of its first 9 terms? | {
"A": "87381",
"B": "65535.75",
"C": "104857.2",
"D": "87382"
} | A | 87381 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(4^9−1)/(4−1)=87381. | {
"A": "Correct. The worked calculation gives 87381.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 87381, not 65535.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 87381, not 104857.2.",
"D": "Incorrect. Substituting the stated values... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005522 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 4 μF capacitor is charged to a potential difference of 31 V. Calculate the energy stored, expressed in μJ. | {
"A": "1924 μJ",
"B": "193.2 μJ",
"C": "961 μJ",
"D": "1922 μJ"
} | D | 1922 μJ | U=½CV². Since C=4 μF, U in μJ is ½×4×(31)²=1922 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1922 μJ, not 1924 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1922 μJ, not 193.2 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1922 μJ, not 961 ... | [
"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_004790 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 10 Ω are connected in series; this combination is connected in parallel with a 8 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.575 A",
"B": "3.15 A",
"C": "2.15 A",
"D": "4.15 A"
} | B | 3.15 A | Series branch resistance=10+10=20 Ω. Parallel equivalent R_eq=(20×8)/(20+8)=5.71429 Ω. Total current I=V/R_eq=18/5.71429=3.15 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.15 A, not 1.575 A.",
"B": "Correct. The worked calculation gives 3.15 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.15 A, not 2.15 A.",
"D": "Incorrect. Substituting the stated values... | [
"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_007993 | 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 91 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "44.5 mmol L⁻¹",
"B": "5.55 mmol L⁻¹",
"C": "45.5 mmol L⁻¹",
"D": "22.75 mmol L⁻¹"
} | C | 45.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=91/2^1=45.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45.5 mmol L⁻¹, not 44.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 45.5 mmol L⁻¹, not 5.55 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 45.5 mmol L⁻¹.",
"D": "Incorre... | [
"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_001692 | 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 30 distinct elements? | {
"A": "14251.6",
"B": "142507",
"C": "142506",
"D": "142505"
} | C | 142506 | Order does not matter, so the count is C(30,5)=30!/[5!(25)!]=142506. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 142506, not 14251.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 142506, not 142507.",
"C": "Correct. The worked calculation gives 142506.",
"D": "Incorrect. Substituting the stated values... | [
"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_002312 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 9 blue and 9 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.67589",
"B": "1.03241",
"C": "0.16206",
"D": "0.32411"
} | D | 0.32411 | Favourable pairs = C(5,2)+C(9,2)+C(9,2)=82. Total pairs=C(23,2)=253. Therefore P=82/253=0.32411. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32411, not -0.67589.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32411, not 1.03241.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32411, not 0.16... | [
"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_001194 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ -9x² +0x+7. Evaluate f′(1). | {
"A": "-30",
"B": "-36",
"C": "-32",
"D": "30"
} | A | -30 | Differentiate: f′(x)=3(-4)x²+2(-9)x+(0). At x=1, f′(1)=3(-4)(1)²+2(-9)(1)+(0)=-30. | {
"A": "Correct. The worked calculation gives -30.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -30, not -36.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -30, not -32.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000157 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 -8x -10=0, let its roots be α and β. What is α²+β²? | {
"A": "6.11111",
"B": "7.11111",
"C": "5.11111",
"D": "8.11111"
} | C | 5.11111 | By Vieta's relations, α+β = 8/6 and αβ = -10/6. Then α²+β²=(α+β)²−2αβ = (8/6)²−2(-10/6) = 5.11111. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.11111, not 6.11111.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.11111, not 7.11111.",
"C": "Correct. The worked calculation gives 5.11111.",
"D": "Incorrect. Substituting the stated va... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000139 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 -10x -4=0, let its roots be α and β. What is α²+β²? | {
"A": "8.25",
"B": "1.825",
"C": "5.25",
"D": "7.25"
} | A | 8.25 | By Vieta's relations, α+β = 10/4 and αβ = -4/4. Then α²+β²=(α+β)²−2αβ = (10/4)²−2(-4/4) = 8.25. | {
"A": "Correct. The worked calculation gives 8.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.25, not 1.825.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.25, not 5.25.",
"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_006398 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 14 kg is attached to an ideal spring of force constant 836 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.25882 s",
"B": "0.19411 s",
"C": "0.25882 s",
"D": "0.12941 s"
} | C | 0.25882 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(14/836)=0.25882 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25882 s, not -0.25882 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25882 s, not 0.19411 s.",
"C": "Correct. The worked calculation gives 0.25882 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_003955 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block initially moves at 3 m s⁻¹. A constant net force does 24 N of work over 10 m in the direction of motion. Find its final kinetic energy. | {
"A": "309.5 J",
"B": "246 J",
"C": "307.5 J",
"D": "305.5 J"
} | C | 307.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(15)(3)²+(24)(10)=307.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 307.5 J, not 309.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 307.5 J, not 246 J.",
"C": "Correct. The worked calculation gives 307.5 J.",
"D": "Incorrect. Substituting the stated valu... | [
"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_008764 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.48 mol L⁻¹ and initially B is absent. At equilibrium, 53% of A has dissociated at constant volume. Find K_c. | {
"A": "-3.53814",
"B": "6.53814",
"C": "3.53814",
"D": "1.76907"
} | C | 3.53814 | Let α=0.53. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.48)(0.53)²/(1−0.53)=3.53814. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.53814, not -3.53814.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.53814, not 6.53814.",
"C": "Correct. The worked calculation gives 3.53814.",
"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_003777 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block initially moves at 11 m s⁻¹. A constant net force does 10 N of work over 16 m in the direction of motion. Find its final kinetic energy. | {
"A": "283 J",
"B": "281 J",
"C": "224.8 J",
"D": "279 J"
} | B | 281 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(2)(11)²+(10)(16)=281 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 281 J, not 283 J.",
"B": "Correct. The worked calculation gives 281 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 281 J, not 224.8 J.",
"D": "Incorrect. Substituting the stated values int... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007579 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 64 mL of 0.10 M HCl is mixed with 45 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-1.75867",
"B": "-1.24133",
"C": "4.75867",
"D": "1.75867"
} | D | 1.75867 | Excess H⁺ moles=0.10×(64−45)/1000=0.001900 mol. Total volume=0.109 L, so [H⁺]=0.017431 M and pH=−log₁₀[H⁺]=1.75867. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.75867, not -1.75867.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.75867, not -1.24133.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.75867, not 4.7... | [
"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_006699 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 38 mol H₂ and 26 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "39 mol",
"B": "19 mol",
"C": "38 mol",
"D": "4.8 mol"
} | C | 38 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 38 mol H₂O; O₂ can produce 52 mol H₂O. The limiting condition is H₂; product=38 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 38 mol, not 39 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 38 mol, not 19 mol.",
"C": "Correct. The worked calculation gives 38 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_003545 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 17 m s⁻¹ at 65° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "26.56642 m",
"B": "22.13868 m",
"C": "44.27737 m",
"D": "23.13868 m"
} | B | 22.13868 m | Range R=u²sin(2θ)/g. Substituting u=17, θ=65° and g=10 gives R=(17)²sin(130°)/10=22.13868 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22.13868 m, not 26.56642 m.",
"B": "Correct. The worked calculation gives 22.13868 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22.13868 m, not 44.27737 m.",
"D": "Incorrect. Substitutin... | [
"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_000653 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -12 and common difference 4. Find the sum of its first 25 terms. | {
"A": "720",
"B": "900",
"C": "91",
"D": "899"
} | B | 900 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-12, d=4, n=25: Sₙ=25/2[2(-12)+(25−1)(4)]=900. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 900, not 720.",
"B": "Correct. The worked calculation gives 900.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 900, not 91.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_000911 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio 4. What is the sum of its first 8 terms? | {
"A": "174759",
"B": "174760",
"C": "174762",
"D": "349520"
} | B | 174760 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(4^8−1)/(4−1)=174760. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 174760, not 174759.",
"B": "Correct. The worked calculation gives 174760.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 174760, not 174762.",
"D": "Incorrect. Substituting the stated values ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000662 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 8 and common difference 14. Find the sum of its first 32 terms. | {
"A": "7200",
"B": "7202",
"C": "10800",
"D": "7198"
} | A | 7200 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=8, d=14, n=32: Sₙ=32/2[2(8)+(32−1)(14)]=7200. | {
"A": "Correct. The worked calculation gives 7200.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7200, not 7202.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7200, not 10800.",
"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_000873 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio 4. What is the sum of its first 6 terms? | {
"A": "12285",
"B": "18427.5",
"C": "12284",
"D": "1229.5"
} | A | 12285 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(4^6−1)/(4−1)=12285. | {
"A": "Correct. The worked calculation gives 12285.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12285, not 18427.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12285, not 12284.",
"D": "Incorrect. Substituting the stated values int... | [
"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_007773 | 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 47 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "23.5 mmol L⁻¹",
"B": "25.5 mmol L⁻¹",
"C": "22.5 mmol L⁻¹",
"D": "18.8 mmol L⁻¹"
} | A | 23.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=47/2^1=23.5 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 23.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23.5 mmol L⁻¹, not 25.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23.5 mmol L⁻¹, not 22.5 mmol L⁻¹.",
"D": "Incorre... | [
"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_000743 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 5. What is the sum of its first 12 terms? | {
"A": "610351560",
"B": "915527340",
"C": "610351558",
"D": "732421872"
} | A | 610351560 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(5^12−1)/(5−1)=610351560. | {
"A": "Correct. The worked calculation gives 610351560.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 610351560, not 915527340.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 610351560, not 610351558.",
"D": "Incorrect. Substituting the... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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