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_006776 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 21 mol H₂ and 13 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "21 mol",
"B": "3.1 mol",
"C": "-21 mol",
"D": "31.5 mol"
} | A | 21 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 21 mol H₂O; O₂ can produce 26 mol H₂O. The limiting condition is H₂; product=21 mol. | {
"A": "Correct. The worked calculation gives 21 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21 mol, not 3.1 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21 mol, not -21 mol.",
"D": "Incorrect. Substituting the stated value... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004834 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 5 Ω are connected in series; this combination is connected in parallel with a 11 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.56818 A",
"B": "0.78409 A",
"C": "1.15682 A",
"D": "2.56818 A"
} | A | 1.56818 A | Series branch resistance=7+5=12 Ω. Parallel equivalent R_eq=(12×11)/(12+11)=5.73913 Ω. Total current I=V/R_eq=9/5.73913=1.56818 A. | {
"A": "Correct. The worked calculation gives 1.56818 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.56818 A, not 0.78409 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.56818 A, not 1.15682 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_002042 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 6 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.25",
"B": "0.16667",
"C": "0.33333",
"D": "-2.66667"
} | C | 0.33333 | Favourable pairs = C(10,2)+C(6,2)+C(12,2)=126. Total pairs=C(28,2)=378. Therefore P=126/378=0.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not 0.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not 0.16667.",
"C": "Correct. The worked calculation gives 0.33333.",
"D": "Incorrect. Substituting the stated value... | [
"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_008194 | 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 5 A for 24415 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": "40.16457 g",
"B": "41.16457 g",
"C": "30.12343 g",
"D": "5.01646 g"
} | A | 40.16457 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×5×24415/(2×96500)=40.16457 g. | {
"A": "Correct. The worked calculation gives 40.16457 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 40.16457 g, not 41.16457 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 40.16457 g, not 30.12343 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_001829 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 38 distinct elements? | {
"A": "36677619",
"B": "24451746",
"C": "97806984",
"D": "48903492"
} | D | 48903492 | Order does not matter, so the count is C(38,8)=38!/[8!(30)!]=48903492. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 48903492, not 36677619.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 48903492, not 24451746.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 48903492, not ... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001035 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-1x³ +3x² -8x+7. Evaluate f′(-2). | {
"A": "-33",
"B": "-32",
"C": "-34",
"D": "-31"
} | B | -32 | Differentiate: f′(x)=3(-1)x²+2(3)x+(-8). At x=-2, f′(-2)=3(-1)(-2)²+2(3)(-2)+(-8)=-32. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -32, not -33.",
"B": "Correct. The worked calculation gives -32.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -32, not -34.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003137 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-13-2i)/(2+2i). What is Re(z), the real part of z? | {
"A": "-3.75",
"B": "-1.875",
"C": "-5.75",
"D": "0.625"
} | A | -3.75 | Multiply numerator and denominator by the conjugate (2-2i). Then Re(z)=(ac+bd)/(c²+d²)=((-13)(2)+(-2)(2))/(2²+(2)²)=-3.75. | {
"A": "Correct. The worked calculation gives -3.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -3.75, not -1.875.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -3.75, not -5.75.",
"D": "Incorrect. Substituting the stated values into... | [
"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_005875 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.4 atm at 391 K. What is its pressure at 468 K? | {
"A": "0.47877 atm",
"B": "-1.52123 atm",
"C": "-0.47877 atm",
"D": "3.47877 atm"
} | A | 0.47877 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.4)(468)/(391)=0.47877 atm. | {
"A": "Correct. The worked calculation gives 0.47877 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.47877 atm, not -1.52123 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.47877 atm, not -0.47877 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_000382 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 27 and common difference 11. Find the sum of its first 16 terms. | {
"A": "1401.6",
"B": "876",
"C": "1314",
"D": "1752"
} | D | 1752 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=27, d=11, n=16: Sₙ=16/2[2(27)+(16−1)(11)]=1752. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1752, not 1401.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1752, not 876.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1752, not 1314.",
"D": "Cor... | [
"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_009705 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(CN)_3]^-3, each CN ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "-1",
"B": "3",
"C": "1",
"D": "0"
} | D | 0 | Let the formal oxidation state of Ni be x. Charge balance gives x+(3)(−1)=-3; hence x=-3+3=+0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not -1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"D": "Correct. The worked c... | [
"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_008619 | 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 0.37 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.7696 K",
"B": "1.7696 K",
"C": "-2.2304 K",
"D": "1.5392 K"
} | A | 0.7696 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.52×0.37=0.7696 K. | {
"A": "Correct. The worked calculation gives 0.7696 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7696 K, not 1.7696 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7696 K, not -2.2304 K.",
"D": "Incorrect. Substituting the sta... | [
"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_007079 | 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 492 K and 2.18 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "296.30858 L",
"B": "-296.30858 L",
"C": "298.30858 L",
"D": "444.46287 L"
} | A | 296.30858 L | PV=nRT, so V=nRT/P=(16)(0.082057)(492)/(2.18)=296.30858 L. | {
"A": "Correct. The worked calculation gives 296.30858 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 296.30858 L, not -296.30858 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 296.30858 L, not 298.30858 L.",
"D": "Incorrect. Subst... | [
"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_005680 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.5 atm at 309 K. What is its pressure at 753 K? | {
"A": "1.82767 atm",
"B": "7.31068 atm",
"C": "3.65534 atm",
"D": "2.65534 atm"
} | C | 3.65534 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.5)(753)/(309)=3.65534 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.65534 atm, not 1.82767 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.65534 atm, not 7.31068 atm.",
"C": "Correct. The worked calculation gives 3.65534 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007626 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 26 mL of 0.10 M HCl is mixed with 73 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.67646",
"B": "9.67646",
"C": "6.33823",
"D": "2.26765"
} | A | 12.67646 | Excess OH⁻ moles=0.10×(73−26)/1000=0.004700 mol. Total volume=0.099 L, so [OH⁻]=0.047475 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.67646. | {
"A": "Correct. The worked calculation gives 12.67646.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.67646, not 9.67646.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.67646, not 6.33823.",
"D": "Incorrect. Substituting the stated... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002826 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-1, -5, -5) and v=(-5, 1, 6), calculate u·v. | {
"A": "-22.5",
"B": "-45",
"C": "-24",
"D": "-30"
} | D | -30 | The dot product is the sum of corresponding component products: (-1)(-5)+(-5)(1)+(-5)(6)=-30. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -30, not -22.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -30, not -45.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -30, not -24.",
"D": "Correct.... | [
"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_009947 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(Cl)_2]^-1, each Cl ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "4",
"B": "-1",
"C": "0.5",
"D": "1"
} | D | 1 | Let the formal oxidation state of Fe be x. Charge balance gives x+(2)(−1)=-1; hence x=-1+2=+1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not -1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.5.",
"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_001337 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (2x² -1x +3) dx. | {
"A": "42.91667",
"B": "85.83333",
"C": "87.83333",
"D": "128.75"
} | B | 85.83333 | An antiderivative is (2/3)x³+(-1/2)x²+(3)x. Evaluating between 0 and 5 gives (2/3)(5)³+(-1/2)(5)²+(3)(5)=85.83333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 85.83333, not 42.91667.",
"B": "Correct. The worked calculation gives 85.83333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 85.83333, not 87.83333.",
"D": "Incorrect. Substituting the stat... | [
"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_003338 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(11+9i)/(1+12i). What is Re(z), the real part of z? | {
"A": "-0.17931",
"B": "0.41034",
"C": "0.61552",
"D": "0.82069"
} | D | 0.82069 | Multiply numerator and denominator by the conjugate (1-12i). Then Re(z)=(ac+bd)/(c²+d²)=((11)(1)+(9)(12))/(1²+(12)²)=0.82069. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.82069, not -0.17931.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.82069, not 0.41034.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.82069, not 0.61... | [
"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_002310 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 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": "-0.34387",
"B": "0.17194",
"C": "0.34387",
"D": "1.34387"
} | C | 0.34387 | Favourable pairs = C(9,2)+C(4,2)+C(10,2)=87. Total pairs=C(23,2)=253. Therefore P=87/253=0.34387. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34387, not -0.34387.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34387, not 0.17194.",
"C": "Correct. The worked calculation gives 0.34387.",
"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_005378 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 9 μF capacitor is charged to a potential difference of 32 V. Calculate the energy stored, expressed in μJ. | {
"A": "3686.4 μJ",
"B": "4608 μJ",
"C": "2304 μJ",
"D": "6912 μJ"
} | B | 4608 μJ | U=½CV². Since C=9 μF, U in μJ is ½×9×(32)²=4608 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4608 μJ, not 3686.4 μJ.",
"B": "Correct. The worked calculation gives 4608 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4608 μJ, not 2304 μJ.",
"D": "Incorrect. Substituting the stated ... | [
"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_007222 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 17 mol of gas at 204 K and 2.74 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "102.85901 L",
"B": "103.85901 L",
"C": "124.63081 L",
"D": "77.89425 L"
} | B | 103.85901 L | PV=nRT, so V=nRT/P=(17)(0.082057)(204)/(2.74)=103.85901 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 103.85901 L, not 102.85901 L.",
"B": "Correct. The worked calculation gives 103.85901 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 103.85901 L, not 124.63081 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_009976 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(OH)_3]^+3, each OH ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "3",
"B": "8",
"C": "6",
"D": "9"
} | C | 6 | Let the formal oxidation state of Pd be x. Charge balance gives x+(3)(−1)=+3; hence x=3+3=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 8.",
"C": "Correct. The worked calculation gives 6.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006659 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 20 kg is attached to an ideal spring of force constant 842 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.30824 s",
"B": "1.30824 s",
"C": "-0.69176 s",
"D": "2.30824 s"
} | A | 0.30824 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(20/842)=0.30824 s. | {
"A": "Correct. The worked calculation gives 0.30824 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30824 s, not 1.30824 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30824 s, not -0.69176 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_001045 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ -3x² +10x+7. Evaluate f′(1). | {
"A": "38",
"B": "19",
"C": "21",
"D": "22.8"
} | B | 19 | Differentiate: f′(x)=3(5)x²+2(-3)x+(10). At x=1, f′(1)=3(5)(1)²+2(-3)(1)+(10)=19. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19, not 38.",
"B": "Correct. The worked calculation gives 19.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19, not 21.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_007193 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 2 mol of gas at 215 K and 2.67 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "9.91138 L",
"B": "14.21517 L",
"C": "19.82276 L",
"D": "13.21517 L"
} | D | 13.21517 L | PV=nRT, so V=nRT/P=(2)(0.082057)(215)/(2.67)=13.21517 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13.21517 L, not 9.91138 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13.21517 L, not 14.21517 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13.2151... | [
"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_002522 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, 0], [1, 5]]. | {
"A": "30",
"B": "45",
"C": "15",
"D": "36"
} | A | 30 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(5)−(0)(1)=30. | {
"A": "Correct. The worked calculation gives 30.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30, not 45.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30, not 15.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003154 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(2+10i)/(7+1i). What is Re(z), the real part of z? | {
"A": "1.048",
"B": "0.48",
"C": "0.96",
"D": "-0.48"
} | B | 0.48 | Multiply numerator and denominator by the conjugate (7-1i). Then Re(z)=(ac+bd)/(c²+d²)=((2)(7)+(10)(1))/(7²+(1)²)=0.48. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.48, not 1.048.",
"B": "Correct. The worked calculation gives 0.48.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.48, not 0.96.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_004479 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 13 kg and radius 2 m is acted on by a constant torque of 43 N m about its central axis. Find its angular acceleration. | {
"A": "1.65385 rad s⁻²",
"B": "1.24038 rad s⁻²",
"C": "3.65385 rad s⁻²",
"D": "-0.34615 rad s⁻²"
} | A | 1.65385 rad s⁻² | For a solid disc, I=½MR²=½(13)(2)²=26 kg m². Using τ=Iα, α=43/26=1.65385 rad s⁻². | {
"A": "Correct. The worked calculation gives 1.65385 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.65385 rad s⁻², not 1.24038 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.65385 rad s⁻², not 3.65385 rad s⁻².",
"D"... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007214 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 1 mol of gas at 595 K and 2.93 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "-16.66345 L",
"B": "18.66345 L",
"C": "16.66345 L",
"D": "19.99614 L"
} | C | 16.66345 L | PV=nRT, so V=nRT/P=(1)(0.082057)(595)/(2.93)=16.66345 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16.66345 L, not -16.66345 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16.66345 L, not 18.66345 L.",
"C": "Correct. The worked calculation gives 16.66345 L.",
"D": "Incorrect. Substituti... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004900 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 10 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.29091 A",
"B": "1.71818 A",
"C": "4.58182 A",
"D": "1.22909 A"
} | A | 2.29091 A | Series branch resistance=4+7=11 Ω. Parallel equivalent R_eq=(11×10)/(11+10)=5.2381 Ω. Total current I=V/R_eq=12/5.2381=2.29091 A. | {
"A": "Correct. The worked calculation gives 2.29091 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.29091 A, not 1.71818 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.29091 A, not 4.58182 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_008275 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 2 A for 1564 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": "1.02916 g",
"B": "2.05832 g",
"C": "0.77187 g",
"D": "1.10292 g"
} | A | 1.02916 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×2×1564/(2×96500)=1.02916 g. | {
"A": "Correct. The worked calculation gives 1.02916 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.02916 g, not 2.05832 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.02916 g, not 0.77187 g.",
"D": "Incorrect. Substituting the... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009910 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(Cl)_6]^+2, each Cl ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "6",
"B": "12",
"C": "16",
"D": "8"
} | D | 8 | Let the formal oxidation state of Fe 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 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 16.",
"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_007039 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 2 mol of gas at 498 K and 1.93 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "21.17326 L",
"B": "40.34651 L",
"C": "42.34651 L",
"D": "41.34651 L"
} | C | 42.34651 L | PV=nRT, so V=nRT/P=(2)(0.082057)(498)/(1.93)=42.34651 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 42.34651 L, not 21.17326 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 42.34651 L, not 40.34651 L.",
"C": "Correct. The worked calculation gives 42.34651 L.",
"D": "Incorrect. Substitutin... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001243 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=0x³ -10x² +4x+7. Evaluate f′(0). | {
"A": "4",
"B": "-4",
"C": "1",
"D": "6"
} | A | 4 | Differentiate: f′(x)=3(0)x²+2(-10)x+(4). At x=0, f′(0)=3(0)(0)²+2(-10)(0)+(4)=4. | {
"A": "Correct. The worked calculation gives 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not -4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_000410 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 3 and common difference 4. Find the sum of its first 22 terms. | {
"A": "1188",
"B": "990",
"C": "1980",
"D": "1485"
} | B | 990 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=3, d=4, n=22: Sₙ=22/2[2(3)+(22−1)(4)]=990. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 990, not 1188.",
"B": "Correct. The worked calculation gives 990.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 990, not 1980.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_001795 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 9 elements can be selected from a set of 26 distinct elements? | {
"A": "3124548",
"B": "3124550",
"C": "3124551",
"D": "2343412.5"
} | B | 3124550 | Order does not matter, so the count is C(26,9)=26!/[9!(17)!]=3124550. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3124550, not 3124548.",
"B": "Correct. The worked calculation gives 3124550.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3124550, not 3124551.",
"D": "Incorrect. Substituting the stated va... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002518 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, 4], [3, -2]]. | {
"A": "-44",
"B": "-33",
"C": "-21",
"D": "-22"
} | D | -22 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(-2)−(4)(3)=-22. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -22, not -44.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -22, not -33.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -22, not -21.",
"D": "Correct. T... | [
"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_007449 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 85 mL of 0.10 M HCl is mixed with 42 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "0.47034",
"B": "1.47034",
"C": "1.14703",
"D": "3.47034"
} | B | 1.47034 | Excess H⁺ moles=0.10×(85−42)/1000=0.004300 mol. Total volume=0.127 L, so [H⁺]=0.033858 M and pH=−log₁₀[H⁺]=1.47034. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.47034, not 0.47034.",
"B": "Correct. The worked calculation gives 1.47034.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.47034, not 1.14703.",
"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_007137 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 17 mol of gas at 277 K and 0.64 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "452.82002 L",
"B": "603.76002 L",
"C": "905.64003 L",
"D": "602.76002 L"
} | B | 603.76002 L | PV=nRT, so V=nRT/P=(17)(0.082057)(277)/(0.64)=603.76002 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 603.76002 L, not 452.82002 L.",
"B": "Correct. The worked calculation gives 603.76002 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 603.76002 L, not 905.64003 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_007934 | 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 73 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "18.25 mmol L⁻¹",
"B": "-18.25 mmol L⁻¹",
"C": "9.125 mmol L⁻¹",
"D": "20.25 mmol L⁻¹"
} | A | 18.25 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=73/2^2=18.25 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 18.25 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18.25 mmol L⁻¹, not -18.25 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18.25 mmol L⁻¹, not 9.125 mmol L⁻¹.",
"D": "I... | [
"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_001545 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (4x² -5x +6) dx. | {
"A": "135.16667",
"B": "134.16667",
"C": "67.08333",
"D": "14.41667"
} | B | 134.16667 | An antiderivative is (4/3)x³+(-5/2)x²+(6)x. Evaluating between 0 and 5 gives (4/3)(5)³+(-5/2)(5)²+(6)(5)=134.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 134.16667, not 135.16667.",
"B": "Correct. The worked calculation gives 134.16667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 134.16667, not 67.08333.",
"D": "Incorrect. Substituting the ... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004176 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 41 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.36. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "102.336 N",
"B": "125.92 N",
"C": "127.92 N",
"D": "191.88 N"
} | C | 127.92 N | Net force=mg(sinθ−μcosθ)=41×10×(0.6−0.36×0.8)=127.92 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 127.92 N, not 102.336 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 127.92 N, not 125.92 N.",
"C": "Correct. The worked calculation gives 127.92 N.",
"D": "Incorrect. Substituting the sta... | [
"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_008550 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.39 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.4456 K",
"B": "-1.4456 K",
"C": "2.1684 K",
"D": "2.8912 K"
} | A | 1.4456 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×1.39=1.4456 K. | {
"A": "Correct. The worked calculation gives 1.4456 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4456 K, not -1.4456 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.4456 K, not 2.1684 K.",
"D": "Incorrect. Substituting the sta... | [
"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_000893 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio -3. What is the sum of its first 9 terms? | {
"A": "39370",
"B": "29526",
"C": "-39368",
"D": "39368"
} | D | 39368 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(-3^9−1)/(-3−1)=39368. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 39368, not 39370.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39368, not 29526.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39368, not -39368.",
"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_007183 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 18 mol of gas at 522 K and 2.36 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "324.69812 L",
"B": "490.04719 L",
"C": "326.69812 L",
"D": "328.69812 L"
} | C | 326.69812 L | PV=nRT, so V=nRT/P=(18)(0.082057)(522)/(2.36)=326.69812 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 326.69812 L, not 324.69812 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 326.69812 L, not 490.04719 L.",
"C": "Correct. The worked calculation gives 326.69812 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_002734 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(0, -3, -2) and v=(3, -4, -7), calculate u·v. | {
"A": "39",
"B": "13",
"C": "26",
"D": "20.8"
} | C | 26 | The dot product is the sum of corresponding component products: (0)(3)+(-3)(-4)+(-2)(-7)=26. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26, not 39.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26, not 13.",
"C": "Correct. The worked calculation gives 26.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_002138 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 9 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.27273",
"B": "0.36364",
"C": "1.36364",
"D": "0.18182"
} | B | 0.36364 | Favourable pairs = C(10,2)+C(9,2)+C(3,2)=84. Total pairs=C(22,2)=231. Therefore P=84/231=0.36364. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.36364, not 0.27273.",
"B": "Correct. The worked calculation gives 0.36364.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.36364, not 1.36364.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009183 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.14 V, transfers 2 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.22865 V",
"B": "2.4573 V",
"C": "-1.77135 V",
"D": "0.61433 V"
} | A | 1.22865 V | Apply the Nernst equation: E=1.14−(0.0591/2)(-3)=1.22865 V. | {
"A": "Correct. The worked calculation gives 1.22865 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.22865 V, not 2.4573 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.22865 V, not -1.77135 V.",
"D": "Incorrect. Substituting the... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006051 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 43 cm in front of a thin convex lens of focal length 20 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.86957",
"B": "1.86957",
"C": "3.86957",
"D": "1.08696"
} | A | 0.86957 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(43)(20)/(43−20)=37.3913 cm. Thus |m|=v/u=37.3913/43=0.86957. | {
"A": "Correct. The worked calculation gives 0.86957.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.86957, not 1.86957.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.86957, not 3.86957.",
"D": "Incorrect. Substituting the stated va... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009692 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(Cl)_3]^+3, each Cl ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "9",
"B": "5",
"C": "6",
"D": "3"
} | C | 6 | Let the formal oxidation state of Co be x. Charge balance gives x+(3)(−1)=+3; hence x=3+3=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 5.",
"C": "Correct. The worked calculation gives 6.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004632 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 14 kg and radius 1 m is acted on by a constant torque of 28 N m about its central axis. Find its angular acceleration. | {
"A": "3 rad s⁻²",
"B": "5 rad s⁻²",
"C": "7 rad s⁻²",
"D": "4 rad s⁻²"
} | D | 4 rad s⁻² | For a solid disc, I=½MR²=½(14)(1)²=7 kg m². Using τ=Iα, α=28/7=4 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4 rad s⁻², not 3 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4 rad s⁻², not 5 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4 rad s⁻²,... | [
"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_007471 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 23 mL of 0.10 M HCl is mixed with 48 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.25467",
"B": "18.82002",
"C": "12.54668",
"D": "15.54668"
} | C | 12.54668 | Excess OH⁻ moles=0.10×(48−23)/1000=0.002500 mol. Total volume=0.071 L, so [OH⁻]=0.035211 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.54668. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.54668, not 2.25467.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.54668, not 18.82002.",
"C": "Correct. The worked calculation gives 12.54668.",
"D": "Incorrect. Substituting the state... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000750 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio -3. What is the sum of its first 10 terms? | {
"A": "-177144",
"B": "-118096",
"C": "-118098",
"D": "-141715.2"
} | B | -118096 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(-3^10−1)/(-3−1)=-118096. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -118096, not -177144.",
"B": "Correct. The worked calculation gives -118096.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -118096, not -118098.",
"D": "Incorrect. Substituting the stated va... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002493 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, -4], [2, 3]]. | {
"A": "34.8",
"B": "23.2",
"C": "-29",
"D": "29"
} | D | 29 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(3)−(-4)(2)=29. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 29, not 34.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 29, not 23.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29, not -29.",
"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_002875 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(6, -3, 4) and v=(9, -1, -7), calculate u·v. | {
"A": "34.8",
"B": "29",
"C": "3.9",
"D": "14.5"
} | B | 29 | The dot product is the sum of corresponding component products: (6)(9)+(-3)(-1)+(4)(-7)=29. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 29, not 34.8.",
"B": "Correct. The worked calculation gives 29.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29, not 3.9.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007420 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 74 mL of 0.10 M HCl is mixed with 34 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.43136",
"B": "1.14314",
"C": "-1.56864",
"D": "3.43136"
} | A | 1.43136 | Excess H⁺ moles=0.10×(74−34)/1000=0.004000 mol. Total volume=0.108 L, so [H⁺]=0.037037 M and pH=−log₁₀[H⁺]=1.43136. | {
"A": "Correct. The worked calculation gives 1.43136.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.43136, not 1.14314.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.43136, not -1.56864.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009964 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(OH)_6]^-2, each OH ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "7",
"B": "4",
"C": "1",
"D": "3"
} | B | 4 | Let the formal oxidation state of Co be x. Charge balance gives x+(6)(−1)=-2; hence x=-2+6=+4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 7.",
"B": "Correct. The worked calculation gives 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.",
"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_000634 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 10 and common difference 6. Find the sum of its first 31 terms. | {
"A": "3100",
"B": "2325",
"C": "4650",
"D": "3720"
} | A | 3100 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=10, d=6, n=31: Sₙ=31/2[2(10)+(31−1)(6)]=3100. | {
"A": "Correct. The worked calculation gives 3100.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3100, not 2325.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3100, not 4650.",
"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_004758 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 10 Ω are connected in series; this combination is connected in parallel with a 16 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "6.375 A",
"B": "3.375 A",
"C": "6.75 A",
"D": "1.6875 A"
} | B | 3.375 A | Series branch resistance=10+10=20 Ω. Parallel equivalent R_eq=(20×16)/(20+16)=8.88889 Ω. Total current I=V/R_eq=30/8.88889=3.375 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.375 A, not 6.375 A.",
"B": "Correct. The worked calculation gives 3.375 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.375 A, not 6.75 A.",
"D": "Incorrect. Substituting the stated val... | [
"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_008821 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.01 mol L⁻¹ and initially B is absent. At equilibrium, 77% of A has dissociated at constant volume. Find K_c. | {
"A": "10.41442",
"B": "13.41442",
"C": "-10.41442",
"D": "2.04144"
} | A | 10.41442 | Let α=0.77. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.01)(0.77)²/(1−0.77)=10.41442. | {
"A": "Correct. The worked calculation gives 10.41442.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.41442, not 13.41442.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10.41442, not -10.41442.",
"D": "Incorrect. Substituting the sta... | [
"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_000942 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio 2. What is the sum of its first 12 terms? | {
"A": "36855",
"B": "36853",
"C": "73710",
"D": "-36855"
} | A | 36855 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(2^12−1)/(2−1)=36855. | {
"A": "Correct. The worked calculation gives 36855.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 36855, not 36853.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 36855, not 73710.",
"D": "Incorrect. Substituting the stated values into ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008631 | 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 0.87 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "2.00448 K",
"B": "2.67264 K",
"C": "0.33632 K",
"D": "1.33632 K"
} | D | 1.33632 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.512×0.87=1.33632 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.33632 K, not 2.00448 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.33632 K, not 2.67264 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.33632 K,... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008520 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.97 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.0244 K",
"B": "4.0488 K",
"C": "0.0488 K",
"D": "2.0488 K"
} | D | 2.0488 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×1.97=2.0488 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.0488 K, not 1.0244 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.0488 K, not 4.0488 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.0488 K, not ... | [
"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_006674 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 39 mol H₂ and 17 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "25.5 mol",
"B": "34 mol",
"C": "33 mol",
"D": "32 mol"
} | B | 34 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 39 mol H₂O; O₂ can produce 34 mol H₂O. The limiting condition is O₂; product=34 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 34 mol, not 25.5 mol.",
"B": "Correct. The worked calculation gives 34 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 34 mol, not 33 mol.",
"D": "Incorrect. Substituting the stated value... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006845 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 45 mol H₂ and 5 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "9 mol",
"B": "20 mol",
"C": "10 mol",
"D": "12 mol"
} | C | 10 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 45 mol H₂O; O₂ can produce 10 mol H₂O. The limiting condition is O₂; product=10 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 9 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 20 mol.",
"C": "Correct. The worked calculation gives 10 mol.",
"D": "Incorrect. Substituting the stated values i... | [
"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_001021 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=0x³ -8x² -1x+7. Evaluate f′(-1). | {
"A": "15",
"B": "2.5",
"C": "16",
"D": "30"
} | A | 15 | Differentiate: f′(x)=3(0)x²+2(-8)x+(-1). At x=-1, f′(-1)=3(0)(-1)²+2(-8)(-1)+(-1)=15. | {
"A": "Correct. The worked calculation gives 15.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15, not 2.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15, not 16.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"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_003003 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-5, 0, 8) and v=(8, 1, -7), calculate u·v. | {
"A": "-94",
"B": "-8.6",
"C": "-72",
"D": "-96"
} | D | -96 | The dot product is the sum of corresponding component products: (-5)(8)+(0)(1)+(8)(-7)=-96. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -96, not -94.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -96, not -8.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -96, not -72.",
"D": "Correct. ... | [
"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_008716 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.13 mol L⁻¹ and initially B is absent. At equilibrium, 41% of A has dissociated at constant volume. Find K_c. | {
"A": "1.93173",
"B": "-0.71218",
"C": "1.28782",
"D": "2.57563"
} | C | 1.28782 | Let α=0.41. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.13)(0.41)²/(1−0.41)=1.28782. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.28782, not 1.93173.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.28782, not -0.71218.",
"C": "Correct. The worked calculation gives 1.28782.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004196 | 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 0.14. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "131.76 N",
"B": "263.52 N",
"C": "-131.76 N",
"D": "132.76 N"
} | A | 131.76 N | Net force=mg(sinθ−μcosθ)=27×10×(0.6−0.14×0.8)=131.76 N. | {
"A": "Correct. The worked calculation gives 131.76 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 131.76 N, not 263.52 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 131.76 N, not -131.76 N.",
"D": "Incorrect. Substituting the sta... | [
"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_006588 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 11 kg is attached to an ideal spring of force constant 622 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.39895 s",
"B": "0.13298 s",
"C": "-0.73403 s",
"D": "0.26597 s"
} | D | 0.26597 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(11/622)=0.26597 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.26597 s, not 0.39895 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.26597 s, not 0.13298 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.26597 s,... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007554 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 88 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": "-1.17704",
"B": "1.1823",
"C": "1.82296",
"D": "0.91148"
} | C | 1.82296 | Excess H⁺ moles=0.10×(88−65)/1000=0.002300 mol. Total volume=0.153 L, so [H⁺]=0.015033 M and pH=−log₁₀[H⁺]=1.82296. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.82296, not -1.17704.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.82296, not 1.1823.",
"C": "Correct. The worked calculation gives 1.82296.",
"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_008143 | 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 7531 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": "-7.43345 g",
"B": "6.43345 g",
"C": "7.43345 g",
"D": "5.43345 g"
} | C | 7.43345 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×3×7531/(2×96500)=7.43345 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.43345 g, not -7.43345 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.43345 g, not 6.43345 g.",
"C": "Correct. The worked calculation gives 7.43345 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_003751 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block initially moves at 6 m s⁻¹. A constant net force does 17 N of work over 6 m in the direction of motion. Find its final kinetic energy. | {
"A": "144 J",
"B": "191 J",
"C": "192 J",
"D": "384 J"
} | C | 192 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(5)(6)²+(17)(6)=192 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 192 J, not 144 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 192 J, not 191 J.",
"C": "Correct. The worked calculation gives 192 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_002678 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(9, 8, 4) and v=(6, 5, 9), calculate u·v. | {
"A": "97.5",
"B": "132",
"C": "130",
"D": "-130"
} | C | 130 | The dot product is the sum of corresponding component products: (9)(6)+(8)(5)+(4)(9)=130. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 130, not 97.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 130, not 132.",
"C": "Correct. The worked calculation gives 130.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005349 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 30 μF capacitor is charged to a potential difference of 40 V. Calculate the energy stored, expressed in μJ. | {
"A": "19200 μJ",
"B": "23998 μJ",
"C": "2401 μJ",
"D": "24000 μJ"
} | D | 24000 μJ | U=½CV². Since C=30 μF, U in μJ is ½×30×(40)²=24000 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24000 μJ, not 19200 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24000 μJ, not 23998 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24000 μJ, not ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003145 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(11-11i)/(6+9i). What is Re(z), the real part of z? | {
"A": "-1.28205",
"B": "-0.5641",
"C": "-0.28205",
"D": "0.71795"
} | C | -0.28205 | Multiply numerator and denominator by the conjugate (6-9i). Then Re(z)=(ac+bd)/(c²+d²)=((11)(6)+(-11)(9))/(6²+(9)²)=-0.28205. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.28205, not -1.28205.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.28205, not -0.5641.",
"C": "Correct. The worked calculation gives -0.28205.",
"D": "Incorrect. Substituting the state... | [
"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_006553 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 24 kg is attached to an ideal spring of force constant 1077 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.29856 s",
"B": "0.22392 s",
"C": "-1.70144 s",
"D": "0.29856 s"
} | D | 0.29856 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(24/1077)=0.29856 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29856 s, not -0.29856 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29856 s, not 0.22392 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29856 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000554 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 27 and common difference 15. Find the sum of its first 17 terms. | {
"A": "2499",
"B": "4998",
"C": "2497",
"D": "-2499"
} | A | 2499 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=27, d=15, n=17: Sₙ=17/2[2(27)+(17−1)(15)]=2499. | {
"A": "Correct. The worked calculation gives 2499.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2499, not 4998.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2499, not 2497.",
"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_005362 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 66 μF capacitor is charged to a potential difference of 30 V. Calculate the energy stored, expressed in μJ. | {
"A": "29700 μJ",
"B": "22275 μJ",
"C": "29702 μJ",
"D": "29699 μJ"
} | A | 29700 μJ | U=½CV². Since C=66 μF, U in μJ is ½×66×(30)²=29700 μJ. | {
"A": "Correct. The worked calculation gives 29700 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 29700 μJ, not 22275 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29700 μJ, not 29702 μJ.",
"D": "Incorrect. Substituting the stat... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000716 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 3 and common ratio -3. What is the sum of its first 8 terms? | {
"A": "-491",
"B": "-9840",
"C": "-4920",
"D": "-4919"
} | C | -4920 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=3(-3^8−1)/(-3−1)=-4920. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4920, not -491.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -4920, not -9840.",
"C": "Correct. The worked calculation gives -4920.",
"D": "Incorrect. Substituting the stated values into t... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007034 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 14 mol of gas at 311 K and 1.39 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "385.54983 L",
"B": "26.70332 L",
"C": "257.03322 L",
"D": "258.03322 L"
} | C | 257.03322 L | PV=nRT, so V=nRT/P=(14)(0.082057)(311)/(1.39)=257.03322 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 257.03322 L, not 385.54983 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 257.03322 L, not 26.70332 L.",
"C": "Correct. The worked calculation gives 257.03322 L.",
"D": "Incorrect. Substit... | [
"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_008307 | 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 14 A for 3423 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": "18.9205 g",
"B": "15.76708 g",
"C": "13.76708 g",
"D": "14.76708 g"
} | B | 15.76708 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×3423/(2×96500)=15.76708 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15.76708 g, not 18.9205 g.",
"B": "Correct. The worked calculation gives 15.76708 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15.76708 g, not 13.76708 g.",
"D": "Incorrect. Substituting... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003846 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 10 m s⁻¹. A constant net force does 5 N of work over 13 m in the direction of motion. Find its final kinetic energy. | {
"A": "565 J",
"B": "-565 J",
"C": "678 J",
"D": "847.5 J"
} | A | 565 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(10)²+(5)(13)=565 J. | {
"A": "Correct. The worked calculation gives 565 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 565 J, not -565 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 565 J, not 678 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_004480 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 5 m is acted on by a constant torque of 74 N m about its central axis. Find its angular acceleration. | {
"A": "1.1184 rad s⁻²",
"B": "3.184 rad s⁻²",
"C": "1.184 rad s⁻²",
"D": "0.888 rad s⁻²"
} | C | 1.184 rad s⁻² | For a solid disc, I=½MR²=½(5)(5)²=62.5 kg m². Using τ=Iα, α=74/62.5=1.184 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.184 rad s⁻², not 1.1184 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.184 rad s⁻², not 3.184 rad s⁻².",
"C": "Correct. The worked calculation gives 1.184 rad s⁻².",
"D": "Incorr... | [
"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_000414 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -3 and common difference 10. Find the sum of its first 25 terms. | {
"A": "2925",
"B": "293.5",
"C": "-2925",
"D": "2340"
} | A | 2925 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-3, d=10, n=25: Sₙ=25/2[2(-3)+(25−1)(10)]=2925. | {
"A": "Correct. The worked calculation gives 2925.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2925, not 293.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2925, not -2925.",
"D": "Incorrect. Substituting the stated values into the... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008404 | 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 0.73 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.56064 K",
"B": "0.74752 K",
"C": "1.49504 K",
"D": "0.37376 K"
} | B | 0.74752 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×0.73=0.74752 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.74752 K, not 0.56064 K.",
"B": "Correct. The worked calculation gives 0.74752 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.74752 K, not 1.49504 K.",
"D": "Incorrect. Substituting the... | [
"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_003134 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-10+8i)/(4+6i). What is Re(z), the real part of z? | {
"A": "3.15385",
"B": "0.11538",
"C": "0.15385",
"D": "0.07692"
} | C | 0.15385 | Multiply numerator and denominator by the conjugate (4-6i). Then Re(z)=(ac+bd)/(c²+d²)=((-10)(4)+(8)(6))/(4²+(6)²)=0.15385. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.15385, not 3.15385.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.15385, not 0.11538.",
"C": "Correct. The worked calculation gives 0.15385.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002064 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 5 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": "0.34462",
"B": "0.51692",
"C": "1.03446",
"D": "0.25846"
} | A | 0.34462 | Favourable pairs = C(12,2)+C(5,2)+C(9,2)=112. Total pairs=C(26,2)=325. Therefore P=112/325=0.34462. | {
"A": "Correct. The worked calculation gives 0.34462.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34462, not 0.51692.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34462, not 1.03446.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003211 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(1-1i)/(11+3i). What is Re(z), the real part of z? | {
"A": "0.06154",
"B": "0.09231",
"C": "3.06154",
"D": "0.04615"
} | A | 0.06154 | Multiply numerator and denominator by the conjugate (11-3i). Then Re(z)=(ac+bd)/(c²+d²)=((1)(11)+(-1)(3))/(11²+(3)²)=0.06154. | {
"A": "Correct. The worked calculation gives 0.06154.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.06154, not 0.09231.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.06154, not 3.06154.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009834 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(Cl)_6]^-3, each Cl ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "0",
"B": "3",
"C": "5",
"D": "4.5"
} | B | 3 | Let the formal oxidation state of Co be x. Charge balance gives x+(6)(−1)=-3; hence x=-3+6=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 0.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 5.",
"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_004295 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 34 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.20. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "151.6 N",
"B": "149.6 N",
"C": "119.68 N",
"D": "74.8 N"
} | B | 149.6 N | Net force=mg(sinθ−μcosθ)=34×10×(0.6−0.20×0.8)=149.6 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 149.6 N, not 151.6 N.",
"B": "Correct. The worked calculation gives 149.6 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 149.6 N, not 119.68 N.",
"D": "Incorrect. Substituting the stated v... | [
"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_002827 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(2, -2, 8) and v=(0, -6, -4), calculate u·v. | {
"A": "-20",
"B": "-24",
"C": "20",
"D": "-21"
} | A | -20 | The dot product is the sum of corresponding component products: (2)(0)+(-2)(-6)+(8)(-4)=-20. | {
"A": "Correct. The worked calculation gives -20.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -20, not -24.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -20, 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_008899 | 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 0.73 mol L⁻¹ and initially B is absent. At equilibrium, 77% of A has dissociated at constant volume. Find K_c. | {
"A": "7.52725",
"B": "4.52725",
"C": "6.52725",
"D": "5.52725"
} | A | 7.52725 | Let α=0.77. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.73)(0.77)²/(1−0.77)=7.52725. | {
"A": "Correct. The worked calculation gives 7.52725.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.52725, not 4.52725.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.52725, not 6.52725.",
"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_003201 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-3-3i)/(4+11i). What is Re(z), the real part of z? | {
"A": "-0.24635",
"B": "-0.65693",
"C": "-2.32847",
"D": "-0.32847"
} | D | -0.32847 | Multiply numerator and denominator by the conjugate (4-11i). Then Re(z)=(ac+bd)/(c²+d²)=((-3)(4)+(-3)(11))/(4²+(11)²)=-0.32847. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.32847, not -0.24635.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.32847, not -0.65693.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.32847, not ... | [
"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_009689 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(OH)_6]^+0, each OH ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "1.6",
"B": "6",
"C": "7",
"D": "3"
} | B | 6 | Let the formal oxidation state of Ni be x. Charge balance gives x+(6)(−1)=+0; hence x=0+6=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 1.6.",
"B": "Correct. The worked calculation gives 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 7.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000346 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -8 and common difference 14. Find the sum of its first 16 terms. | {
"A": "776",
"B": "1862.4",
"C": "1552",
"D": "1550"
} | C | 1552 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-8, d=14, n=16: Sₙ=16/2[2(-8)+(16−1)(14)]=1552. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1552, not 776.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1552, not 1862.4.",
"C": "Correct. The worked calculation gives 1552.",
"D": "Incorrect. Substituting the stated values into the ... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006345 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 25 kg is attached to an ideal spring of force constant 1088 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.30317 s",
"B": "0.22738 s",
"C": "1.03032 s",
"D": "0.30317 s"
} | D | 0.30317 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(25/1088)=0.30317 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30317 s, not -0.30317 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30317 s, not 0.22738 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30317 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007933 | 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 62 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "0.48438 mmol L⁻¹",
"B": "0.96875 mmol L⁻¹",
"C": "3.48438 mmol L⁻¹",
"D": "-0.48438 mmol L⁻¹"
} | A | 0.48438 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=62/2^7=0.48438 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 0.48438 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.48438 mmol L⁻¹, not 0.96875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.48438 mmol L⁻¹, not 3.48438 mmol L⁻¹.",
... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001696 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 6 elements can be selected from a set of 39 distinct elements? | {
"A": "1631311.5",
"B": "3262623",
"C": "6525246",
"D": "3262621"
} | B | 3262623 | Order does not matter, so the count is C(39,6)=39!/[6!(33)!]=3262623. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3262623, not 1631311.5.",
"B": "Correct. The worked calculation gives 3262623.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3262623, not 6525246.",
"D": "Incorrect. Substituting the stated ... | [
"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_002905 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-7, -5, 4) and v=(5, 4, -3), calculate u·v. | {
"A": "-67",
"B": "-5.7",
"C": "67",
"D": "-80.4"
} | A | -67 | The dot product is the sum of corresponding component products: (-7)(5)+(-5)(4)+(4)(-3)=-67. | {
"A": "Correct. The worked calculation gives -67.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -67, not -5.7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -67, not 67.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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