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_007250 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 4 mol of gas at 513 K and 1.54 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "54.66914 L",
"B": "-109.33829 L",
"C": "109.33829 L",
"D": "87.47063 L"
} | C | 109.33829 L | PV=nRT, so V=nRT/P=(4)(0.082057)(513)/(1.54)=109.33829 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 109.33829 L, not 54.66914 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 109.33829 L, not -109.33829 L.",
"C": "Correct. The worked calculation gives 109.33829 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_006853 | 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 13 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "14.4 mol",
"B": "18 mol",
"C": "13.5 mol",
"D": "20 mol"
} | B | 18 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 18 mol H₂O; O₂ can produce 26 mol H₂O. The limiting condition is H₂; product=18 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18 mol, not 14.4 mol.",
"B": "Correct. The worked calculation gives 18 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18 mol, not 13.5 mol.",
"D": "Incorrect. Substituting the stated val... | [
"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_001450 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (0x² +3x +7) dx. | {
"A": "30",
"B": "22",
"C": "20",
"D": "40"
} | C | 20 | An antiderivative is (0/3)x³+(3/2)x²+(7)x. Evaluating between 0 and 2 gives (0/3)(2)³+(3/2)(2)²+(7)(2)=20. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20, not 30.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20, not 22.",
"C": "Correct. The worked calculation gives 20.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_006854 | 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 28 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "61.5 mol",
"B": "32.8 mol",
"C": "20.5 mol",
"D": "41 mol"
} | D | 41 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 41 mol H₂O; O₂ can produce 56 mol H₂O. The limiting condition is H₂; product=41 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 41 mol, not 61.5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 41 mol, not 32.8 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 41 mol, not 20.5 m... | [
"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_003978 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 6 m s⁻¹. A constant net force does 20 N of work over 6 m in the direction of motion. Find its final kinetic energy. | {
"A": "299 J",
"B": "150 J",
"C": "300 J",
"D": "31 J"
} | C | 300 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(6)²+(20)(6)=300 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 300 J, not 299 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 300 J, not 150 J.",
"C": "Correct. The worked calculation gives 300 J.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_008282 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 13 A for 16968 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": "72.57556 g",
"B": "70.57556 g",
"C": "73.57556 g",
"D": "74.57556 g"
} | A | 72.57556 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×16968/(2×96500)=72.57556 g. | {
"A": "Correct. The worked calculation gives 72.57556 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 72.57556 g, not 70.57556 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 72.57556 g, not 73.57556 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003572 | 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 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "529.48992 m",
"B": "564.78925 m",
"C": "707.98656 m",
"D": "705.98656 m"
} | D | 705.98656 m | Range R=u²sin(2θ)/g. Substituting u=96, θ=25° and g=10 gives R=(96)²sin(50°)/10=705.98656 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 705.98656 m, not 529.48992 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 705.98656 m, not 564.78925 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 70... | [
"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_002377 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 8], [2, 7]]. | {
"A": "2.5",
"B": "7",
"C": "-5",
"D": "5"
} | D | 5 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(7)−(8)(2)=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not -5.",
"D": "Correct. The worked... | [
"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_009628 | 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_15H_7N_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "11",
"B": "-14",
"C": "2.4",
"D": "14"
} | D | 14 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×15+2+3−7−0)/2=14. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14, not 11.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14, not -14.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14, not 2.4.",
"D": "Correct. The w... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000413 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -11 and common difference 10. Find the sum of its first 28 terms. | {
"A": "3470",
"B": "3472",
"C": "2604",
"D": "1736"
} | B | 3472 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-11, d=10, n=28: Sₙ=28/2[2(-11)+(28−1)(10)]=3472. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3472, not 3470.",
"B": "Correct. The worked calculation gives 3472.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3472, not 2604.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008815 | 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 0.05 mol L⁻¹ and initially B is absent. At equilibrium, 54% of A has dissociated at constant volume. Find K_c. | {
"A": "0.12678",
"B": "0.09509",
"C": "3.12678",
"D": "-0.12678"
} | A | 0.12678 | Let α=0.54. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.05)(0.54)²/(1−0.54)=0.12678. | {
"A": "Correct. The worked calculation gives 0.12678.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.12678, not 0.09509.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.12678, not 3.12678.",
"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_007391 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 41 mL of 0.10 M HCl is mixed with 23 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "0.77545",
"B": "2.55091",
"C": "1.55091",
"D": "0.55091"
} | C | 1.55091 | Excess H⁺ moles=0.10×(41−23)/1000=0.001800 mol. Total volume=0.064 L, so [H⁺]=0.028125 M and pH=−log₁₀[H⁺]=1.55091. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.55091, not 0.77545.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.55091, not 2.55091.",
"C": "Correct. The worked calculation gives 1.55091.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003700 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block initially moves at 8 m s⁻¹. A constant net force does 30 N of work over 9 m in the direction of motion. Find its final kinetic energy. | {
"A": "720 J",
"B": "1436 J",
"C": "718 J",
"D": "719 J"
} | C | 718 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(14)(8)²+(30)(9)=718 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 718 J, not 720 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 718 J, not 1436 J.",
"C": "Correct. The worked calculation gives 718 J.",
"D": "Incorrect. Substituting the stated values into... | [
"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_007130 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 5 mol of gas at 280 K and 1.96 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "117.22429 L",
"B": "59.61214 L",
"C": "-58.61214 L",
"D": "58.61214 L"
} | D | 58.61214 L | PV=nRT, so V=nRT/P=(5)(0.082057)(280)/(1.96)=58.61214 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 58.61214 L, not 117.22429 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 58.61214 L, not 59.61214 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 58.61... | [
"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_000863 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio 2. What is the sum of its first 11 terms? | {
"A": "6141",
"B": "8188",
"C": "4094",
"D": "9825.6"
} | B | 8188 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(2^11−1)/(2−1)=8188. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8188, not 6141.",
"B": "Correct. The worked calculation gives 8188.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8188, not 4094.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_000415 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 16 and common difference 8. Find the sum of its first 30 terms. | {
"A": "3960",
"B": "4752",
"C": "3958",
"D": "5940"
} | A | 3960 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=16, d=8, n=30: Sₙ=30/2[2(16)+(30−1)(8)]=3960. | {
"A": "Correct. The worked calculation gives 3960.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3960, not 4752.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3960, not 3958.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005858 | 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 3.6 atm at 247 K. What is its pressure at 664 K? | {
"A": "19.35547 atm",
"B": "-9.67773 atm",
"C": "9.67773 atm",
"D": "10.67773 atm"
} | C | 9.67773 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.6)(664)/(247)=9.67773 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.67773 atm, not 19.35547 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.67773 atm, not -9.67773 atm.",
"C": "Correct. The worked calculation gives 9.67773 atm.",
"D": "Incorrect. Subs... | [
"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_009110 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.69 V, transfers 1 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.03354 V",
"B": "0.3354 V",
"C": "2.3354 V",
"D": "-1.6646 V"
} | B | 0.3354 V | Apply the Nernst equation: E=0.69−(0.0591/1)(6)=0.3354 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3354 V, not 1.03354 V.",
"B": "Correct. The worked calculation gives 0.3354 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3354 V, not 2.3354 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008248 | 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 11 A for 13894 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": "49.28476 g",
"B": "-50.28476 g",
"C": "50.28476 g",
"D": "51.28476 g"
} | C | 50.28476 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×13894/(2×96500)=50.28476 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 50.28476 g, not 49.28476 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 50.28476 g, not -50.28476 g.",
"C": "Correct. The worked calculation gives 50.28476 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000684 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio 2. What is the sum of its first 11 terms? | {
"A": "28658",
"B": "14328",
"C": "1433.9",
"D": "14329"
} | D | 14329 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(2^11−1)/(2−1)=14329. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14329, not 28658.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14329, not 14328.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14329, not 1433.9.",
"D"... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000583 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -2 and common difference 2. Find the sum of its first 13 terms. | {
"A": "130",
"B": "132",
"C": "65",
"D": "129"
} | A | 130 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-2, d=2, n=13: Sₙ=13/2[2(-2)+(13−1)(2)]=130. | {
"A": "Correct. The worked calculation gives 130.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 130, not 132.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 130, not 65.",
"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_000429 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 27 and common difference 4. Find the sum of its first 15 terms. | {
"A": "823",
"B": "-825",
"C": "824",
"D": "825"
} | D | 825 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=27, d=4, n=15: Sₙ=15/2[2(27)+(15−1)(4)]=825. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 825, not 823.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 825, not -825.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 825, not 824.",
"D": "Correct. ... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007073 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 16 mol of gas at 261 K and 1.72 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "159.38141 L",
"B": "20.92268 L",
"C": "197.22676 L",
"D": "199.22676 L"
} | D | 199.22676 L | PV=nRT, so V=nRT/P=(16)(0.082057)(261)/(1.72)=199.22676 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 199.22676 L, not 159.38141 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 199.22676 L, not 20.92268 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 199... | [
"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_008105 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 3 A for 13499 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": "16.32414 g",
"B": "13.32414 g",
"C": "19.98621 g",
"D": "14.32414 g"
} | B | 13.32414 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×3×13499/(2×96500)=13.32414 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13.32414 g, not 16.32414 g.",
"B": "Correct. The worked calculation gives 13.32414 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13.32414 g, not 19.98621 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005153 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +4 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "6.34694 N",
"B": "10.34694 N",
"C": "-7.34694 N",
"D": "7.34694 N"
} | D | 7.34694 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(4×10⁻⁶)/(7×10⁻²)²=7.34694 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.34694 N, not 6.34694 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.34694 N, not 10.34694 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.34694 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_004724 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 9 Ω are connected in series; this combination is connected in parallel with a 3 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "13.63636 A",
"B": "27.27273 A",
"C": "14.63636 A",
"D": "6.81818 A"
} | A | 13.63636 A | Series branch resistance=13+9=22 Ω. Parallel equivalent R_eq=(22×3)/(22+3)=2.64 Ω. Total current I=V/R_eq=36/2.64=13.63636 A. | {
"A": "Correct. The worked calculation gives 13.63636 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13.63636 A, not 27.27273 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13.63636 A, not 14.63636 A.",
"D": "Incorrect. Substitutin... | [
"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_007532 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 66 mL of 0.10 M HCl is mixed with 25 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.01939",
"B": "1.34626",
"C": "3.34626",
"D": "0.34626"
} | B | 1.34626 | Excess H⁺ moles=0.10×(66−25)/1000=0.004100 mol. Total volume=0.091 L, so [H⁺]=0.045055 M and pH=−log₁₀[H⁺]=1.34626. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.34626, not 2.01939.",
"B": "Correct. The worked calculation gives 1.34626.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.34626, not 3.34626.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003198 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(15-12i)/(8+7i). What is Re(z), the real part of z? | {
"A": "-0.68142",
"B": "-1.68142",
"C": "0.31858",
"D": "1.03186"
} | C | 0.31858 | Multiply numerator and denominator by the conjugate (8-7i). Then Re(z)=(ac+bd)/(c²+d²)=((15)(8)+(-12)(7))/(8²+(7)²)=0.31858. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31858, not -0.68142.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31858, not -1.68142.",
"C": "Correct. The worked calculation gives 0.31858.",
"D": "Incorrect. Substituting the stated ... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002036 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 4 blue and 10 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.69474",
"B": "0.34737",
"C": "-0.34737",
"D": "0.17368"
} | B | 0.34737 | Favourable pairs = C(6,2)+C(4,2)+C(10,2)=66. Total pairs=C(20,2)=190. Therefore P=66/190=0.34737. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34737, not 0.69474.",
"B": "Correct. The worked calculation gives 0.34737.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34737, not -0.34737.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000138 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +5x -9=0, let its roots be α and β. What is α²+β²? | {
"A": "5.77778",
"B": "8.77778",
"C": "7.77778",
"D": "6.77778"
} | B | 8.77778 | By Vieta's relations, α+β = -5/3 and αβ = -9/3. Then α²+β²=(α+β)²−2αβ = (-5/3)²−2(-9/3) = 8.77778. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.77778, not 5.77778.",
"B": "Correct. The worked calculation gives 8.77778.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.77778, not 7.77778.",
"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_003450 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 14 m s⁻¹ at 75° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "6.8 m",
"B": "19.6 m",
"C": "-9.8 m",
"D": "9.8 m"
} | D | 9.8 m | Range R=u²sin(2θ)/g. Substituting u=14, θ=75° and g=10 gives R=(14)²sin(150°)/10=9.8 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.8 m, not 6.8 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.8 m, not 19.6 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.8 m, not -9.8 m.",
"D... | [
"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_007973 | 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 15 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "8.5 mmol L⁻¹",
"B": "7.5 mmol L⁻¹",
"C": "-7.5 mmol L⁻¹",
"D": "6.5 mmol L⁻¹"
} | B | 7.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=15/2^1=7.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.5 mmol L⁻¹, not 8.5 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 7.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.5 mmol L⁻¹, not -7.5 mmol L⁻¹.",
"D": "Incorrect. ... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000647 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 13 and common difference 11. Find the sum of its first 23 terms. | {
"A": "3082",
"B": "6164",
"C": "3084",
"D": "3081"
} | A | 3082 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=13, d=11, n=23: Sₙ=23/2[2(13)+(23−1)(11)]=3082. | {
"A": "Correct. The worked calculation gives 3082.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3082, not 6164.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3082, not 3084.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001429 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (5x² +0x -1) dx. | {
"A": "354",
"B": "531",
"C": "-354",
"D": "708"
} | A | 354 | An antiderivative is (5/3)x³+(0/2)x²+(-1)x. Evaluating between 0 and 6 gives (5/3)(6)³+(0/2)(6)²+(-1)(6)=354. | {
"A": "Correct. The worked calculation gives 354.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 354, not 531.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 354, not -354.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_002533 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, 8], [7, 6]]. | {
"A": "-28",
"B": "14",
"C": "-12",
"D": "-14"
} | D | -14 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(6)−(8)(7)=-14. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -14, not -28.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -14, not 14.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -14, not -12.",
"D": "Correct. Th... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007932 | 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 61 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "30.5 mmol L⁻¹",
"B": "-30.5 mmol L⁻¹",
"C": "24.4 mmol L⁻¹",
"D": "32.5 mmol L⁻¹"
} | A | 30.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=61/2^1=30.5 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 30.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30.5 mmol L⁻¹, not -30.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30.5 mmol L⁻¹, not 24.4 mmol L⁻¹.",
"D": "Incorr... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005901 | 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 4.5 atm at 427 K. What is its pressure at 657 K? | {
"A": "6.92389 atm",
"B": "5.19292 atm",
"C": "-6.92389 atm",
"D": "1.69239 atm"
} | A | 6.92389 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.5)(657)/(427)=6.92389 atm. | {
"A": "Correct. The worked calculation gives 6.92389 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.92389 atm, not 5.19292 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.92389 atm, not -6.92389 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_004568 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 12 kg and radius 1 m is acted on by a constant torque of 49 N m about its central axis. Find its angular acceleration. | {
"A": "11.16667 rad s⁻²",
"B": "12.25 rad s⁻²",
"C": "5.16667 rad s⁻²",
"D": "8.16667 rad s⁻²"
} | D | 8.16667 rad s⁻² | For a solid disc, I=½MR²=½(12)(1)²=6 kg m². Using τ=Iα, α=49/6=8.16667 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.16667 rad s⁻², not 11.16667 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.16667 rad s⁻², not 12.25 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing re... | [
"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_009316 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.46 V, transfers 1 electrons, and has reaction quotient Q=10^3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.7173 V",
"B": "1.2827 V",
"C": "3.2827 V",
"D": "-1.2827 V"
} | B | 1.2827 V | Apply the Nernst equation: E=1.46−(0.0591/1)(3)=1.2827 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.2827 V, not -1.7173 V.",
"B": "Correct. The worked calculation gives 1.2827 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2827 V, not 3.2827 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001124 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ +4x² +2x+7. Evaluate f′(4). | {
"A": "-164.8",
"B": "-205",
"C": "-208",
"D": "-206"
} | D | -206 | Differentiate: f′(x)=3(-5)x²+2(4)x+(2). At x=4, f′(4)=3(-5)(4)²+2(4)(4)+(2)=-206. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -206, not -164.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -206, not -205.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -206, not -208.",
"D": "Co... | [
"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_007153 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 15 mol of gas at 361 K and 0.35 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "2539.07803 L",
"B": "1268.53901 L",
"C": "-1269.53901 L",
"D": "1269.53901 L"
} | D | 1269.53901 L | PV=nRT, so V=nRT/P=(15)(0.082057)(361)/(0.35)=1269.53901 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1269.53901 L, not 2539.07803 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1269.53901 L, not 1268.53901 L.",
"C": "Incorrect. Substituting the stated values into the governing relation give... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008559 | 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 0.34 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-1.66 K",
"B": "0.34 K",
"C": "3.34 K",
"D": "2.34 K"
} | B | 0.34 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×1.0×0.34=0.34 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34 K, not -1.66 K.",
"B": "Correct. The worked calculation gives 0.34 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34 K, not 3.34 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005658 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 26 μF capacitor is charged to a potential difference of 2 V. Calculate the energy stored, expressed in μJ. | {
"A": "54 μJ",
"B": "39 μJ",
"C": "52 μJ",
"D": "50 μJ"
} | C | 52 μJ | U=½CV². Since C=26 μF, U in μJ is ½×26×(2)²=52 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 52 μJ, not 54 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 52 μJ, not 39 μJ.",
"C": "Correct. The worked calculation gives 52 μJ.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_005880 | 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 0.2 atm at 210 K. What is its pressure at 409 K? | {
"A": "1.03895 atm",
"B": "3.38952 atm",
"C": "0.58429 atm",
"D": "0.38952 atm"
} | D | 0.38952 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.2)(409)/(210)=0.38952 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.38952 atm, not 1.03895 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.38952 atm, not 3.38952 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.... | [
"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_009907 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(Cl)_6]^+2, each Cl ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "9",
"B": "5",
"C": "8",
"D": "6"
} | C | 8 | Let the formal oxidation state of Cr be x. Charge balance gives x+(6)(−1)=+2; hence x=2+6=+8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 5.",
"C": "Correct. The worked calculation gives 8.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005329 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +4 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "358 N",
"B": "360 N",
"C": "361 N",
"D": "359 N"
} | B | 360 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(4×10⁻⁶)/(2×10⁻²)²=360 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 360 N, not 358 N.",
"B": "Correct. The worked calculation gives 360 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 360 N, not 361 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_004310 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 3 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.34. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "11.84 N",
"B": "4.92 N",
"C": "19.68 N",
"D": "9.84 N"
} | D | 9.84 N | Net force=mg(sinθ−μcosθ)=3×10×(0.6−0.34×0.8)=9.84 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.84 N, not 11.84 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.84 N, not 4.92 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.84 N, not 19.68 N."... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002251 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 11 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": "-0.32333",
"B": "0.32333",
"C": "1.32333",
"D": "0.485"
} | B | 0.32333 | Favourable pairs = C(11,2)+C(7,2)+C(7,2)=97. Total pairs=C(25,2)=300. Therefore P=97/300=0.32333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32333, not -0.32333.",
"B": "Correct. The worked calculation gives 0.32333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32333, not 1.32333.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009305 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.94 V, transfers 2 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.2327 V",
"B": "0.8218 V",
"C": "-1.1782 V",
"D": "0.61635 V"
} | B | 0.8218 V | Apply the Nernst equation: E=0.94−(0.0591/2)(4)=0.8218 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8218 V, not 1.2327 V.",
"B": "Correct. The worked calculation gives 0.8218 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8218 V, not -1.1782 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008009 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 12 A for 1611 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "6.36053 g",
"B": "12.72106 g",
"C": "9.54079 g",
"D": "1.63605 g"
} | A | 6.36053 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×12×1611/(2×96500)=6.36053 g. | {
"A": "Correct. The worked calculation gives 6.36053 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.36053 g, not 12.72106 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.36053 g, not 9.54079 g.",
"D": "Incorrect. Substituting th... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000898 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio 2. What is the sum of its first 6 terms? | {
"A": "316",
"B": "315",
"C": "236.25",
"D": "32.5"
} | B | 315 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(2^6−1)/(2−1)=315. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 315, not 316.",
"B": "Correct. The worked calculation gives 315.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 315, not 236.25.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_005521 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 71 μF capacitor is charged to a potential difference of 7 V. Calculate the energy stored, expressed in μJ. | {
"A": "1739.5 μJ",
"B": "1740.5 μJ",
"C": "2087.4 μJ",
"D": "1391.6 μJ"
} | A | 1739.5 μJ | U=½CV². Since C=71 μF, U in μJ is ½×71×(7)²=1739.5 μJ. | {
"A": "Correct. The worked calculation gives 1739.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1739.5 μJ, not 1740.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1739.5 μJ, not 2087.4 μJ.",
"D": "Incorrect. Substituting the... | [
"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_009644 | 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_18N_1X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "-1",
"B": "1",
"C": "3",
"D": "-2"
} | B | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×10+2+1−18−3)/2=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not -1.",
"B": "Correct. The worked calculation gives 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 3.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009857 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(OH)_6]^-4, each OH ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "1.5",
"B": "-1",
"C": "1",
"D": "2"
} | D | 2 | Let the formal oxidation state of Ni be x. Charge balance gives x+(6)(−1)=-4; hence x=-4+6=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not -1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"D": "Correct. The worked... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000968 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio 5. What is the sum of its first 8 terms? | {
"A": "97656",
"B": "-195312",
"C": "195312",
"D": "195311"
} | C | 195312 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(5^8−1)/(5−1)=195312. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 195312, not 97656.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 195312, not -195312.",
"C": "Correct. The worked calculation gives 195312.",
"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_002625 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, 0], [1, 5]]. | {
"A": "54",
"B": "-45",
"C": "67.5",
"D": "45"
} | D | 45 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(5)−(0)(1)=45. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45, not 54.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 45, not -45.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 45, not 67.5.",
"D": "Correct. The ... | [
"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_003940 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 9 m s⁻¹. A constant net force does 10 N of work over 20 m in the direction of motion. Find its final kinetic energy. | {
"A": "684 J",
"B": "686 J",
"C": "-686 J",
"D": "1029 J"
} | B | 686 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(9)²+(10)(20)=686 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 686 J, not 684 J.",
"B": "Correct. The worked calculation gives 686 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 686 J, not -686 J.",
"D": "Incorrect. Substituting the stated values into... | [
"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_001404 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (0x² +4x -3) dx. | {
"A": "-1",
"B": "-2",
"C": "0",
"D": "-3"
} | A | -1 | An antiderivative is (0/3)x³+(4/2)x²+(-3)x. Evaluating between 0 and 1 gives (0/3)(1)³+(4/2)(1)²+(-3)(1)=-1. | {
"A": "Correct. The worked calculation gives -1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1, not -2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1, not 0.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_000200 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +1x +9=0, let its roots be α and β. What is α²+β²? | {
"A": "-5.88889",
"B": "5.88889",
"C": "-4.88889",
"D": "-6.88889"
} | A | -5.88889 | By Vieta's relations, α+β = -1/3 and αβ = 9/3. Then α²+β²=(α+β)²−2αβ = (-1/3)²−2(9/3) = -5.88889. | {
"A": "Correct. The worked calculation gives -5.88889.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -5.88889, not 5.88889.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -5.88889, not -4.88889.",
"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_009978 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(Cl)_3]^+0, each Cl ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "5",
"B": "4.5",
"C": "1.3",
"D": "3"
} | D | 3 | Let the formal oxidation state of Mn be x. Charge balance gives x+(3)(−1)=+0; hence x=0+3=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"D": "Correct. The worke... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006484 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 12 kg is attached to an ideal spring of force constant 406 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.34384 s",
"B": "0.17192 s",
"C": "-0.65616 s",
"D": "3.34384 s"
} | A | 0.34384 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(12/406)=0.34384 s. | {
"A": "Correct. The worked calculation gives 0.34384 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34384 s, not 0.17192 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34384 s, not -0.65616 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_005463 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 63 μF capacitor is charged to a potential difference of 6 V. Calculate the energy stored, expressed in μJ. | {
"A": "907.2 μJ",
"B": "567 μJ",
"C": "1134 μJ",
"D": "1136 μJ"
} | C | 1134 μJ | U=½CV². Since C=63 μF, U in μJ is ½×63×(6)²=1134 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1134 μJ, not 907.2 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1134 μJ, not 567 μJ.",
"C": "Correct. The worked calculation gives 1134 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003084 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(2-15i)/(9+9i). What is Re(z), the real part of z? | {
"A": "-0.72222",
"B": "-1.08333",
"C": "-2.72222",
"D": "0.27778"
} | A | -0.72222 | Multiply numerator and denominator by the conjugate (9-9i). Then Re(z)=(ac+bd)/(c²+d²)=((2)(9)+(-15)(9))/(9²+(9)²)=-0.72222. | {
"A": "Correct. The worked calculation gives -0.72222.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.72222, not -1.08333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.72222, not -2.72222.",
"D": "Incorrect. Substituting the stat... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009610 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_11H_2N_3X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "14",
"B": "11",
"C": "-12",
"D": "12"
} | D | 12 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+3−2−1)/2=12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12, not 14.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12, not 11.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12, not -12.",
"D": "Correct. The wo... | [
"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_001927 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 12 elements can be selected from a set of 20 distinct elements? | {
"A": "188955",
"B": "125970",
"C": "125968",
"D": "125971"
} | B | 125970 | Order does not matter, so the count is C(20,12)=20!/[12!(8)!]=125970. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 125970, not 188955.",
"B": "Correct. The worked calculation gives 125970.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 125970, not 125968.",
"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_002742 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-2, -7, 2) and v=(5, 0, 7), calculate u·v. | {
"A": "6",
"B": "4",
"C": "8",
"D": "3"
} | B | 4 | The dot product is the sum of corresponding component products: (-2)(5)+(-7)(0)+(2)(7)=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 8.",
"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_005470 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 60 μF capacitor is charged to a potential difference of 21 V. Calculate the energy stored, expressed in μJ. | {
"A": "13230 μJ",
"B": "10584 μJ",
"C": "9922.5 μJ",
"D": "-13230 μJ"
} | A | 13230 μJ | U=½CV². Since C=60 μF, U in μJ is ½×60×(21)²=13230 μJ. | {
"A": "Correct. The worked calculation gives 13230 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13230 μJ, not 10584 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13230 μJ, not 9922.5 μJ.",
"D": "Incorrect. Substituting the sta... | [
"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_004716 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 6 Ω and 9 Ω are connected in series; this combination is connected in parallel with a 16 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.775 A",
"B": "2.325 A",
"C": "-0.45 A",
"D": "1.55 A"
} | D | 1.55 A | Series branch resistance=6+9=15 Ω. Parallel equivalent R_eq=(15×16)/(15+16)=7.74194 Ω. Total current I=V/R_eq=12/7.74194=1.55 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.55 A, not 0.775 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.55 A, not 2.325 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.55 A, not -0.45 A.... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008935 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.78 mol L⁻¹ and initially B is absent. At equilibrium, 66% of A has dissociated at constant volume. Find K_c. | {
"A": "5.99591",
"B": "5.99727",
"C": "3.99727",
"D": "7.99454"
} | C | 3.99727 | Let α=0.66. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.78)(0.66)²/(1−0.66)=3.99727. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.99727, not 5.99591.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.99727, not 5.99727.",
"C": "Correct. The worked calculation gives 3.99727.",
"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_005173 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +5 μC are separated by 5 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "162 N",
"B": "164 N",
"C": "194.4 N",
"D": "121.5 N"
} | A | 162 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(5×10⁻⁶)/(5×10⁻²)²=162 N. | {
"A": "Correct. The worked calculation gives 162 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 162 N, not 164 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 162 N, not 194.4 N.",
"D": "Incorrect. Substituting the stated values int... | [
"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_003715 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 7 m s⁻¹. A constant net force does 12 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "242.8 J",
"B": "303.5 J",
"C": "227.625 J",
"D": "301.5 J"
} | B | 303.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(7)²+(12)(11)=303.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 303.5 J, not 242.8 J.",
"B": "Correct. The worked calculation gives 303.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 303.5 J, not 227.625 J.",
"D": "Incorrect. Substituting the stated ... | [
"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_004703 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 6 Ω and 13 Ω are connected in series; this combination is connected in parallel with a 12 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "7.89474 A",
"B": "3.67105 A",
"C": "4.89474 A",
"D": "9.78947 A"
} | C | 4.89474 A | Series branch resistance=6+13=19 Ω. Parallel equivalent R_eq=(19×12)/(19+12)=7.35484 Ω. Total current I=V/R_eq=36/7.35484=4.89474 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.89474 A, not 7.89474 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.89474 A, not 3.67105 A.",
"C": "Correct. The worked calculation gives 4.89474 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_004878 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 6 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 12 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.76923 A",
"B": "-5.76923 A",
"C": "5.76923 A",
"D": "2.88462 A"
} | C | 5.76923 A | Series branch resistance=6+7=13 Ω. Parallel equivalent R_eq=(13×12)/(13+12)=6.24 Ω. Total current I=V/R_eq=36/6.24=5.76923 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.76923 A, not 2.76923 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.76923 A, not -5.76923 A.",
"C": "Correct. The worked calculation gives 5.76923 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_007810 | 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 19 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "5.75 mmol L⁻¹",
"B": "9.5 mmol L⁻¹",
"C": "7.125 mmol L⁻¹",
"D": "4.75 mmol L⁻¹"
} | D | 4.75 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=19/2^2=4.75 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.75 mmol L⁻¹, not 5.75 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.75 mmol L⁻¹, not 9.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation g... | [
"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_004992 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 14 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 16 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "-1.9375 A",
"B": "0.79688 A",
"C": "1.0625 A",
"D": "0.0625 A"
} | C | 1.0625 A | Series branch resistance=14+4=18 Ω. Parallel equivalent R_eq=(18×16)/(18+16)=8.47059 Ω. Total current I=V/R_eq=9/8.47059=1.0625 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0625 A, not -1.9375 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0625 A, not 0.79688 A.",
"C": "Correct. The worked calculation gives 1.0625 A.",
"D": "Incorrect. Substituting the st... | [
"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_009464 | 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_15H_15N_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "10",
"B": "12",
"C": "7",
"D": "8"
} | A | 10 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×15+2+3−15−0)/2=10. | {
"A": "Correct. The worked calculation gives 10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 7.",
"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_005027 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +6 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "288 N",
"B": "242 N",
"C": "240 N",
"D": "360 N"
} | C | 240 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(6×10⁻⁶)/(3×10⁻²)²=240 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 240 N, not 288 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 240 N, not 242 N.",
"C": "Correct. The worked calculation gives 240 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_005383 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 28 μF capacitor is charged to a potential difference of 38 V. Calculate the energy stored, expressed in μJ. | {
"A": "15162 μJ",
"B": "2022.6 μJ",
"C": "20216 μJ",
"D": "-20216 μJ"
} | C | 20216 μJ | U=½CV². Since C=28 μF, U in μJ is ½×28×(38)²=20216 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20216 μJ, not 15162 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20216 μJ, not 2022.6 μJ.",
"C": "Correct. The worked calculation gives 20216 μJ.",
"D": "Incorrect. Substituting the sta... | [
"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_004080 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 27 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.33. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "89.72 N",
"B": "90.72 N",
"C": "88.72 N",
"D": "-90.72 N"
} | B | 90.72 N | Net force=mg(sinθ−μcosθ)=27×10×(0.6−0.33×0.8)=90.72 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 90.72 N, not 89.72 N.",
"B": "Correct. The worked calculation gives 90.72 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 90.72 N, not 88.72 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002338 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 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": "-0.35714",
"B": "-1.64286",
"C": "0.35714",
"D": "-0.64286"
} | C | 0.35714 | Favourable pairs = C(3,2)+C(9,2)+C(9,2)=75. Total pairs=C(21,2)=210. Therefore P=75/210=0.35714. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35714, not -0.35714.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35714, not -1.64286.",
"C": "Correct. The worked calculation gives 0.35714.",
"D": "Incorrect. Substituting the stated ... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002066 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 11 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.31724",
"B": "-0.31724",
"C": "0.23793",
"D": "1.31724"
} | A | 0.31724 | Favourable pairs = C(8,2)+C(11,2)+C(11,2)=138. Total pairs=C(30,2)=435. Therefore P=138/435=0.31724. | {
"A": "Correct. The worked calculation gives 0.31724.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31724, not -0.31724.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31724, not 0.23793.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003697 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 3 kg block initially moves at 6 m s⁻¹. A constant net force does 29 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "447.6 J",
"B": "373 J",
"C": "186.5 J",
"D": "38.3 J"
} | B | 373 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(3)(6)²+(29)(11)=373 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 373 J, not 447.6 J.",
"B": "Correct. The worked calculation gives 373 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 373 J, not 186.5 J.",
"D": "Incorrect. Substituting the stated values i... | [
"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_006601 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 4 kg is attached to an ideal spring of force constant 96 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.30619 s",
"B": "1.04082 s",
"C": "0.40825 s",
"D": "2.40825 s"
} | C | 0.40825 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(4/96)=0.40825 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.40825 s, not 0.30619 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.40825 s, not 1.04082 s.",
"C": "Correct. The worked calculation gives 0.40825 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000730 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio 2. What is the sum of its first 7 terms? | {
"A": "762",
"B": "760",
"C": "761",
"D": "571.5"
} | A | 762 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(2^7−1)/(2−1)=762. | {
"A": "Correct. The worked calculation gives 762.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 762, not 760.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 762, not 761.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006044 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 54 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": "0.74194",
"B": "-1.25806",
"C": "2.74194",
"D": "-2.25806"
} | A | 0.74194 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(54)(23)/(54−23)=40.06452 cm. Thus |m|=v/u=40.06452/54=0.74194. | {
"A": "Correct. The worked calculation gives 0.74194.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.74194, not -1.25806.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.74194, not 2.74194.",
"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_000092 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 -12x -10=0, let its roots be α and β. What is α²+β²? | {
"A": "-7.33333",
"B": "7.33333",
"C": "3.66667",
"D": "8.33333"
} | B | 7.33333 | By Vieta's relations, α+β = 12/6 and αβ = -10/6. Then α²+β²=(α+β)²−2αβ = (12/6)²−2(-10/6) = 7.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.33333, not -7.33333.",
"B": "Correct. The worked calculation gives 7.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.33333, not 3.66667.",
"D": "Incorrect. Substituting the stated v... | [
"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_007947 | 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 94 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "-1.46875 mmol L⁻¹",
"B": "4.46875 mmol L⁻¹",
"C": "2.46875 mmol L⁻¹",
"D": "1.46875 mmol L⁻¹"
} | D | 1.46875 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=94/2^6=1.46875 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.46875 mmol L⁻¹, not -1.46875 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.46875 mmol L⁻¹, not 4.46875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the govern... | [
"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_006239 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 49 cm in front of a thin convex lens of focal length 15 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.44118",
"B": "-2.55882",
"C": "-0.55882",
"D": "0.22059"
} | A | 0.44118 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(49)(15)/(49−15)=21.61765 cm. Thus |m|=v/u=21.61765/49=0.44118. | {
"A": "Correct. The worked calculation gives 0.44118.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.44118, not -2.55882.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.44118, not -0.55882.",
"D": "Incorrect. Substituting the stated ... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003279 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(10-1i)/(2+7i). What is Re(z), the real part of z? | {
"A": "-1.75472",
"B": "0.24528",
"C": "1.02453",
"D": "0.18396"
} | B | 0.24528 | Multiply numerator and denominator by the conjugate (2-7i). Then Re(z)=(ac+bd)/(c²+d²)=((10)(2)+(-1)(7))/(2²+(7)²)=0.24528. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.24528, not -1.75472.",
"B": "Correct. The worked calculation gives 0.24528.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.24528, not 1.02453.",
"D": "Incorrect. Substituting the stated v... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002747 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-7, 4, -1) and v=(1, -1, 7), calculate u·v. | {
"A": "-18",
"B": "-9",
"C": "-20",
"D": "-17"
} | A | -18 | The dot product is the sum of corresponding component products: (-7)(1)+(4)(-1)+(-1)(7)=-18. | {
"A": "Correct. The worked calculation gives -18.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -18, not -9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -18, not -20.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_009535 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_7H_10X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "4",
"C": "0",
"D": "1"
} | D | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+0−10−4)/2=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.",
"D": "Correct. The worked ca... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006218 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 83 cm in front of a thin convex lens of focal length 26 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.45614",
"B": "0.91228",
"C": "0.45614",
"D": "0.22807"
} | C | 0.45614 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(83)(26)/(83−26)=37.85965 cm. Thus |m|=v/u=37.85965/83=0.45614. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.45614, not -0.45614.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.45614, not 0.91228.",
"C": "Correct. The worked calculation gives 0.45614.",
"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_007541 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 33 mL of 0.10 M HCl is mixed with 65 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "11.51392",
"B": "25.02785",
"C": "14.51392",
"D": "12.51392"
} | D | 12.51392 | Excess OH⁻ moles=0.10×(65−33)/1000=0.003200 mol. Total volume=0.098 L, so [OH⁻]=0.032653 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.51392. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.51392, not 11.51392.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.51392, not 25.02785.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.51392, not ... | [
"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_007891 | 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 88 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "2.75 mmol L⁻¹",
"B": "4.75 mmol L⁻¹",
"C": "1.275 mmol L⁻¹",
"D": "5.5 mmol L⁻¹"
} | A | 2.75 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=88/2^5=2.75 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 2.75 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.75 mmol L⁻¹, not 4.75 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.75 mmol L⁻¹, not 1.275 mmol L⁻¹.",
"D": "Incorr... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003805 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 11 m s⁻¹. A constant net force does 7 N of work over 12 m in the direction of motion. Find its final kinetic energy. | {
"A": "-810 J",
"B": "82 J",
"C": "1215 J",
"D": "810 J"
} | D | 810 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(11)²+(7)(12)=810 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 810 J, not -810 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 810 J, not 82 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 810 J, not 1215 J.",
"D"... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007663 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 56 mL of 0.10 M HCl is mixed with 84 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "11.30103",
"B": "12.30103",
"C": "13.30103",
"D": "9.30103"
} | B | 12.30103 | Excess OH⁻ moles=0.10×(84−56)/1000=0.002800 mol. Total volume=0.140 L, so [OH⁻]=0.020000 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.30103. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.30103, not 11.30103.",
"B": "Correct. The worked calculation gives 12.30103.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.30103, not 13.30103.",
"D": "Incorrect. Substituting the stat... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002240 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 8 blue and 8 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.48947",
"B": "0.65263",
"C": "1.32632",
"D": "0.32632"
} | D | 0.32632 | Favourable pairs = C(4,2)+C(8,2)+C(8,2)=62. Total pairs=C(20,2)=190. Therefore P=62/190=0.32632. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32632, not 0.48947.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32632, not 0.65263.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32632, not 1.326... | [
"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_000269 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -2x +4=0, let its roots be α and β. What is α²+β²? | {
"A": "-4",
"B": "-3",
"C": "-2",
"D": "-6"
} | B | -3 | By Vieta's relations, α+β = 2/2 and αβ = 4/2. Then α²+β²=(α+β)²−2αβ = (2/2)²−2(4/2) = -3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -3, not -4.",
"B": "Correct. The worked calculation gives -3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -3, not -2.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_002581 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 0], [7, -4]]. | {
"A": "-16",
"B": "-18",
"C": "-19.2",
"D": "-8"
} | A | -16 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(-4)−(0)(7)=-16. | {
"A": "Correct. The worked calculation gives -16.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -16, not -18.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -16, not -19.2.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_005842 | 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 4.5 atm at 373 K. What is its pressure at 742 K? | {
"A": "6.71381 atm",
"B": "8.95174 atm",
"C": "9.95174 atm",
"D": "5.95174 atm"
} | B | 8.95174 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.5)(742)/(373)=8.95174 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.95174 atm, not 6.71381 atm.",
"B": "Correct. The worked calculation gives 8.95174 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.95174 atm, not 9.95174 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 |
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