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_006755 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 43 mol H₂ and 18 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "34 mol",
"B": "-36 mol",
"C": "38 mol",
"D": "36 mol"
} | D | 36 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 43 mol H₂O; O₂ can produce 36 mol H₂O. The limiting condition is O₂; product=36 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 36 mol, not 34 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 36 mol, not -36 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 36 mol, not 38 mol.",... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000256 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 +18x -7=0, let its roots be α and β. What is α²+β²? | {
"A": "338",
"B": "253.5",
"C": "507",
"D": "270.4"
} | A | 338 | By Vieta's relations, α+β = -18/1 and αβ = -7/1. Then α²+β²=(α+β)²−2αβ = (-18/1)²−2(-7/1) = 338. | {
"A": "Correct. The worked calculation gives 338.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 338, not 253.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 338, not 507.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007824 | 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 99 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "1.15469 mmol L⁻¹",
"B": "-1.45312 mmol L⁻¹",
"C": "1.54688 mmol L⁻¹",
"D": "0.77344 mmol L⁻¹"
} | C | 1.54688 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=99/2^6=1.54688 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.54688 mmol L⁻¹, not 1.15469 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.54688 mmol L⁻¹, not -1.45312 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 1.54688 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_007483 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 95 mL of 0.10 M HCl is mixed with 39 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.37892",
"B": "0.68946",
"C": "2.37892",
"D": "3.37892"
} | A | 1.37892 | Excess H⁺ moles=0.10×(95−39)/1000=0.005600 mol. Total volume=0.134 L, so [H⁺]=0.041791 M and pH=−log₁₀[H⁺]=1.37892. | {
"A": "Correct. The worked calculation gives 1.37892.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.37892, not 0.68946.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.37892, not 2.37892.",
"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_007620 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 24 mL of 0.10 M HCl is mixed with 25 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "5.6549",
"B": "8.48235",
"C": "2.13098",
"D": "11.3098"
} | D | 11.3098 | Excess OH⁻ moles=0.10×(25−24)/1000=0.000100 mol. Total volume=0.049 L, so [OH⁻]=0.002041 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=11.3098. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.3098, not 5.6549.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.3098, not 8.48235.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.3098, not 2.1309... | [
"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_008331 | 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 7 A for 15144 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": "-34.87828 g",
"B": "34.87828 g",
"C": "35.87828 g",
"D": "27.90262 g"
} | B | 34.87828 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×7×15144/(2×96500)=34.87828 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 34.87828 g, not -34.87828 g.",
"B": "Correct. The worked calculation gives 34.87828 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 34.87828 g, not 35.87828 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001347 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (-1x² -5x +0) dx. | {
"A": "-355.25",
"B": "-238.83333",
"C": "-177.625",
"D": "-236.83333"
} | D | -236.83333 | An antiderivative is (-1/3)x³+(-5/2)x²+(0)x. Evaluating between 0 and 7 gives (-1/3)(7)³+(-5/2)(7)²+(0)(7)=-236.83333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -236.83333, not -355.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -236.83333, not -238.83333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -236.8333... | [
"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_002638 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, -6], [3, -8]]. | {
"A": "11",
"B": "7.5",
"C": "10",
"D": "-10"
} | C | 10 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(-8)−(-6)(3)=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 11.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 7.5.",
"C": "Correct. The worked calculation gives 10.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006874 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 35 mol H₂ and 6 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "10 mol",
"B": "12 mol",
"C": "24 mol",
"D": "13 mol"
} | B | 12 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 35 mol H₂O; O₂ can produce 12 mol H₂O. The limiting condition is O₂; product=12 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 10 mol.",
"B": "Correct. The worked calculation gives 12 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 24 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005475 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 43 μF capacitor is charged to a potential difference of 39 V. Calculate the energy stored, expressed in μJ. | {
"A": "32701.5 μJ",
"B": "32703.5 μJ",
"C": "3271.15 μJ",
"D": "39241.8 μJ"
} | A | 32701.5 μJ | U=½CV². Since C=43 μF, U in μJ is ½×43×(39)²=32701.5 μJ. | {
"A": "Correct. The worked calculation gives 32701.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 32701.5 μJ, not 32703.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 32701.5 μJ, not 3271.15 μJ.",
"D": "Incorrect. Substitutin... | [
"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_009537 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_14H_9N_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "12",
"B": "15",
"C": "10",
"D": "6"
} | A | 12 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×14+2+3−9−0)/2=12. | {
"A": "Correct. The worked calculation gives 12.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12, not 15.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12, not 10.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008472 | 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 0.71 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-2.574 K",
"B": "0.426 K",
"C": "1.426 K",
"D": "0.213 K"
} | B | 0.426 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.6×0.71=0.426 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.426 K, not -2.574 K.",
"B": "Correct. The worked calculation gives 0.426 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.426 K, not 1.426 K.",
"D": "Incorrect. Substituting the stated v... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002083 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 5 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": "0.66667",
"B": "-0.33333",
"C": "0.33333",
"D": "3.33333"
} | C | 0.33333 | Favourable pairs = C(6,2)+C(5,2)+C(10,2)=70. Total pairs=C(21,2)=210. Therefore P=70/210=0.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not 0.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not -0.33333.",
"C": "Correct. The worked calculation gives 0.33333.",
"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_003255 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-5+12i)/(4+5i). What is Re(z), the real part of z? | {
"A": "1.46341",
"B": "0.73171",
"C": "-0.02439",
"D": "0.97561"
} | D | 0.97561 | Multiply numerator and denominator by the conjugate (4-5i). Then Re(z)=(ac+bd)/(c²+d²)=((-5)(4)+(12)(5))/(4²+(5)²)=0.97561. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.97561, not 1.46341.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.97561, not 0.73171.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.97561, not -0.02... | [
"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_007975 | 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 58 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "1.90625 mmol L⁻¹",
"B": "2.90625 mmol L⁻¹",
"C": "0.90625 mmol L⁻¹",
"D": "0.45312 mmol L⁻¹"
} | C | 0.90625 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=58/2^6=0.90625 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.90625 mmol L⁻¹, not 1.90625 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.90625 mmol L⁻¹, not 2.90625 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.90625 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_008945 | 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 0.42 mol L⁻¹ and initially B is absent. At equilibrium, 51% of A has dissociated at constant volume. Find K_c. | {
"A": "0.89177",
"B": "1.78354",
"C": "1.08918",
"D": "2.89177"
} | A | 0.89177 | Let α=0.51. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.42)(0.51)²/(1−0.51)=0.89177. | {
"A": "Correct. The worked calculation gives 0.89177.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.89177, not 1.78354.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.89177, not 1.08918.",
"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_008780 | 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 1.18 mol L⁻¹ and initially B is absent. At equilibrium, 12% of A has dissociated at constant volume. Find K_c. | {
"A": "0.05793",
"B": "0.15447",
"C": "1.00772",
"D": "0.07724"
} | D | 0.07724 | Let α=0.12. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.18)(0.12)²/(1−0.12)=0.07724. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.07724, not 0.05793.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.07724, not 0.15447.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.07724, not 1.007... | [
"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_008396 | 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 1.88 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "4.512 K",
"B": "-4.512 K",
"C": "9.024 K",
"D": "5.512 K"
} | A | 4.512 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.6×1.88=4.512 K. | {
"A": "Correct. The worked calculation gives 4.512 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.512 K, not -4.512 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.512 K, not 9.024 K.",
"D": "Incorrect. Substituting the stated v... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008763 | 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 0.1 mol L⁻¹ and initially B is absent. At equilibrium, 74% of A has dissociated at constant volume. Find K_c. | {
"A": "3.84246",
"B": "0.63185",
"C": "0.84246",
"D": "0.42123"
} | C | 0.84246 | Let α=0.74. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.1)(0.74)²/(1−0.74)=0.84246. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.84246, not 3.84246.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.84246, not 0.63185.",
"C": "Correct. The worked calculation gives 0.84246.",
"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_002673 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-5, 7, 2) and v=(5, -6, -2), calculate u·v. | {
"A": "-69",
"B": "-71",
"C": "-142",
"D": "-6.1"
} | B | -71 | The dot product is the sum of corresponding component products: (-5)(5)+(7)(-6)+(2)(-2)=-71. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -71, not -69.",
"B": "Correct. The worked calculation gives -71.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -71, not -142.",
"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_000058 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 +16x +9=0, let its roots be α and β. What is α²+β²? | {
"A": "4.11111",
"B": "6.16667",
"C": "1.11111",
"D": "-4.11111"
} | A | 4.11111 | By Vieta's relations, α+β = -16/6 and αβ = 9/6. Then α²+β²=(α+β)²−2αβ = (-16/6)²−2(9/6) = 4.11111. | {
"A": "Correct. The worked calculation gives 4.11111.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.11111, not 6.16667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.11111, not 1.11111.",
"D": "Incorrect. Substituting the stated va... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004402 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 9 kg and radius 6 m is acted on by a constant torque of 19 N m about its central axis. Find its angular acceleration. | {
"A": "0.11728 rad s⁻²",
"B": "-0.88272 rad s⁻²",
"C": "-1.88272 rad s⁻²",
"D": "0.17593 rad s⁻²"
} | A | 0.11728 rad s⁻² | For a solid disc, I=½MR²=½(9)(6)²=162 kg m². Using τ=Iα, α=19/162=0.11728 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.11728 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.11728 rad s⁻², not -0.88272 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.11728 rad s⁻², not -1.88272 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_009683 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(CN)_4]^+2, each CN ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "3",
"B": "12",
"C": "5",
"D": "6"
} | D | 6 | Let the formal oxidation state of Mn be x. Charge balance gives x+(4)(−1)=+2; hence x=2+4=+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 12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 5.",
"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_007762 | 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 43 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "2.6875 mmol L⁻¹",
"B": "1.26875 mmol L⁻¹",
"C": "1.6875 mmol L⁻¹",
"D": "-2.6875 mmol L⁻¹"
} | A | 2.6875 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=43/2^4=2.6875 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 2.6875 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.6875 mmol L⁻¹, not 1.26875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.6875 mmol L⁻¹, not 1.6875 mmol L⁻¹.",
"D... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009409 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_17H_33N_3X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "-2",
"B": "1",
"C": "4",
"D": "2"
} | D | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×17+2+3−33−2)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 4.",
"D": "Correct. The worked c... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004287 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 26 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.37. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "59.28 N",
"B": "79.04 N",
"C": "118.56 N",
"D": "-79.04 N"
} | B | 79.04 N | Net force=mg(sinθ−μcosθ)=26×10×(0.6−0.37×0.8)=79.04 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 79.04 N, not 59.28 N.",
"B": "Correct. The worked calculation gives 79.04 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 79.04 N, not 118.56 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_009380 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_15H_17N_3X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "10",
"B": "12",
"C": "6",
"D": "8"
} | D | 8 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×15+2+3−17−2)/2=8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 10.",
"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 6.",
"D": "Correct. The worked ... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001631 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (5x² +8x +0) dx. | {
"A": "81",
"B": "97.2",
"C": "40.5",
"D": "80"
} | A | 81 | An antiderivative is (5/3)x³+(8/2)x²+(0)x. Evaluating between 0 and 3 gives (5/3)(3)³+(8/2)(3)²+(0)(3)=81. | {
"A": "Correct. The worked calculation gives 81.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 81, not 97.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 81, not 40.5.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009934 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(Cl)_4]^-4, each Cl ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "-2",
"B": "0",
"C": "1",
"D": "-1"
} | B | 0 | Let the formal oxidation state of Mn be x. Charge balance gives x+(4)(−1)=-4; hence x=-4+4=+0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"B": "Correct. The worked calculation gives 0.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_000279 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +2x +5=0, let its roots be α and β. What is α²+β²? | {
"A": "-0.88889",
"B": "0.71111",
"C": "-2.88889",
"D": "-2.16667"
} | C | -2.88889 | By Vieta's relations, α+β = -2/3 and αβ = 5/3. Then α²+β²=(α+β)²−2αβ = (-2/3)²−2(5/3) = -2.88889. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2.88889, not -0.88889.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2.88889, not 0.71111.",
"C": "Correct. The worked calculation gives -2.88889.",
"D": "Incorrect. Substituting the state... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008436 | 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 0.94 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": "4.44384 K",
"B": "0.44384 K",
"C": "1.44384 K",
"D": "1.14438 K"
} | C | 1.44384 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.512×0.94=1.44384 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.44384 K, not 4.44384 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.44384 K, not 0.44384 K.",
"C": "Correct. The worked calculation gives 1.44384 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_008562 | 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 0.2 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.72 K",
"B": "3.48 K",
"C": "-1.52 K",
"D": "0.48 K"
} | D | 0.48 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.6×0.2=0.48 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.48 K, not 0.72 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.48 K, not 3.48 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.48 K, not -1.52 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_000068 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 -13x -7=0, let its roots be α and β. What is α²+β²? | {
"A": "3.44898",
"B": "6.44898",
"C": "4.08673",
"D": "5.44898"
} | D | 5.44898 | By Vieta's relations, α+β = 13/7 and αβ = -7/7. Then α²+β²=(α+β)²−2αβ = (13/7)²−2(-7/7) = 5.44898. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.44898, not 3.44898.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.44898, not 6.44898.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.44898, not 4.086... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000748 | 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 6 terms? | {
"A": "567",
"B": "680.4",
"C": "283.5",
"D": "565"
} | A | 567 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(2^6−1)/(2−1)=567. | {
"A": "Correct. The worked calculation gives 567.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 567, not 680.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 567, not 283.5.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_004268 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 26 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.11. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "199.68 N",
"B": "159.744 N",
"C": "134.12 N",
"D": "133.12 N"
} | D | 133.12 N | Net force=mg(sinθ−μcosθ)=26×10×(0.6−0.11×0.8)=133.12 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 133.12 N, not 199.68 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 133.12 N, not 159.744 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 133.12 N, not... | [
"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_005437 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 34 μF capacitor is charged to a potential difference of 36 V. Calculate the energy stored, expressed in μJ. | {
"A": "22034 μJ",
"B": "22033 μJ",
"C": "22032 μJ",
"D": "22031 μJ"
} | C | 22032 μJ | U=½CV². Since C=34 μF, U in μJ is ½×34×(36)²=22032 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22032 μJ, not 22034 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22032 μJ, not 22033 μJ.",
"C": "Correct. The worked calculation gives 22032 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_002350 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, -5], [1, 6]]. | {
"A": "46",
"B": "56.4",
"C": "23.5",
"D": "47"
} | D | 47 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(6)−(-5)(1)=47. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 47, not 46.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 47, not 56.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 47, not 23.5.",
"D": "Correct. The... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002073 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 12 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": "0.67586",
"B": "0.33793",
"C": "-0.66207",
"D": "1.33793"
} | B | 0.33793 | Favourable pairs = C(6,2)+C(12,2)+C(12,2)=147. Total pairs=C(30,2)=435. Therefore P=147/435=0.33793. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33793, not 0.67586.",
"B": "Correct. The worked calculation gives 0.33793.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33793, not -0.66207.",
"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_006332 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 107 cm in front of a thin convex lens of focal length 26 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.67901",
"B": "0.32099",
"C": "-0.32099",
"D": "1.0321"
} | B | 0.32099 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(107)(26)/(107−26)=34.34568 cm. Thus |m|=v/u=34.34568/107=0.32099. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32099, not -0.67901.",
"B": "Correct. The worked calculation gives 0.32099.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32099, not -0.32099.",
"D": "Incorrect. Substituting the stated ... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004311 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 32 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": "16.616 N",
"B": "78.08 N",
"C": "156.16 N",
"D": "187.392 N"
} | C | 156.16 N | Net force=mg(sinθ−μcosθ)=32×10×(0.6−0.14×0.8)=156.16 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 156.16 N, not 16.616 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 156.16 N, not 78.08 N.",
"C": "Correct. The worked calculation gives 156.16 N.",
"D": "Incorrect. Substituting the state... | [
"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_002471 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, -4], [8, 5]]. | {
"A": "70",
"B": "-72",
"C": "74",
"D": "72"
} | D | 72 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(5)−(-4)(8)=72. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 72, not 70.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 72, not -72.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 72, not 74.",
"D": "Correct. The wo... | [
"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_007905 | 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 37 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "-9.25 mmol L⁻¹",
"B": "6.25 mmol L⁻¹",
"C": "18.5 mmol L⁻¹",
"D": "9.25 mmol L⁻¹"
} | D | 9.25 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=37/2^2=9.25 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.25 mmol L⁻¹, not -9.25 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.25 mmol L⁻¹, not 6.25 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation... | [
"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_002456 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, -6], [7, 3]]. | {
"A": "6.4",
"B": "64.8",
"C": "54",
"D": "40.5"
} | C | 54 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(3)−(-6)(7)=54. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 54, not 6.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 54, not 64.8.",
"C": "Correct. The worked calculation gives 54.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003505 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 97 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "705.675 m",
"B": "939.9 m",
"C": "470.45 m",
"D": "940.9 m"
} | D | 940.9 m | Range R=u²sin(2θ)/g. Substituting u=97, θ=45° and g=10 gives R=(97)²sin(90°)/10=940.9 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 940.9 m, not 705.675 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 940.9 m, not 939.9 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 940.9 m, not 470... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006686 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 4 mol H₂ and 14 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "2 mol",
"B": "4 mol",
"C": "1.4 mol",
"D": "5 mol"
} | B | 4 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 4 mol H₂O; O₂ can produce 28 mol H₂O. The limiting condition is H₂; product=4 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4 mol, not 2 mol.",
"B": "Correct. The worked calculation gives 4 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4 mol, not 1.4 mol.",
"D": "Incorrect. Substituting the stated values int... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005722 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.9 atm at 393 K. What is its pressure at 734 K? | {
"A": "5.28397 atm",
"B": "7.28397 atm",
"C": "3.64198 atm",
"D": "9.28397 atm"
} | B | 7.28397 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.9)(734)/(393)=7.28397 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.28397 atm, not 5.28397 atm.",
"B": "Correct. The worked calculation gives 7.28397 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.28397 atm, not 3.64198 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_003230 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-3+3i)/(2+6i). What is Re(z), the real part of z? | {
"A": "0.3",
"B": "-0.3",
"C": "0.225",
"D": "1.3"
} | A | 0.3 | Multiply numerator and denominator by the conjugate (2-6i). Then Re(z)=(ac+bd)/(c²+d²)=((-3)(2)+(3)(6))/(2²+(6)²)=0.3. | {
"A": "Correct. The worked calculation gives 0.3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3, not -0.3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3, not 0.225.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_003097 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(11-14i)/(12+7i). What is Re(z), the real part of z? | {
"A": "0.08808",
"B": "0.17617",
"C": "3.17617",
"D": "0.26425"
} | B | 0.17617 | Multiply numerator and denominator by the conjugate (12-7i). Then Re(z)=(ac+bd)/(c²+d²)=((11)(12)+(-14)(7))/(12²+(7)²)=0.17617. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.17617, not 0.08808.",
"B": "Correct. The worked calculation gives 0.17617.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.17617, not 3.17617.",
"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_000488 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -11 and common difference 2. Find the sum of its first 8 terms. | {
"A": "-32",
"B": "-38.4",
"C": "-33",
"D": "-34"
} | A | -32 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-11, d=2, n=8: Sₙ=8/2[2(-11)+(8−1)(2)]=-32. | {
"A": "Correct. The worked calculation gives -32.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -32, not -38.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -32, not -33.",
"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_005496 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 41 μF capacitor is charged to a potential difference of 4 V. Calculate the energy stored, expressed in μJ. | {
"A": "328 μJ",
"B": "329 μJ",
"C": "326 μJ",
"D": "330 μJ"
} | A | 328 μJ | U=½CV². Since C=41 μF, U in μJ is ½×41×(4)²=328 μJ. | {
"A": "Correct. The worked calculation gives 328 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 328 μJ, not 329 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 328 μJ, not 326 μJ.",
"D": "Incorrect. Substituting the stated values ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001220 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ -9x² +12x+7. Evaluate f′(3). | {
"A": "-176",
"B": "-179",
"C": "-177",
"D": "-141.6"
} | C | -177 | Differentiate: f′(x)=3(-5)x²+2(-9)x+(12). At x=3, f′(3)=3(-5)(3)²+2(-9)(3)+(12)=-177. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -177, not -176.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -177, not -179.",
"C": "Correct. The worked calculation gives -177.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_004908 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 8 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.7875 A",
"B": "-1.575 A",
"C": "1.18125 A",
"D": "1.575 A"
} | D | 1.575 A | Series branch resistance=13+7=20 Ω. Parallel equivalent R_eq=(20×8)/(20+8)=5.71429 Ω. Total current I=V/R_eq=9/5.71429=1.575 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.575 A, not 0.7875 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.575 A, not -1.575 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.575 A, not 1.1... | [
"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_003557 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 29 m s⁻¹ at 70° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "-54.05844 m",
"B": "54.05844 m",
"C": "40.54383 m",
"D": "27.02922 m"
} | B | 54.05844 m | Range R=u²sin(2θ)/g. Substituting u=29, θ=70° and g=10 gives R=(29)²sin(140°)/10=54.05844 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 54.05844 m, not -54.05844 m.",
"B": "Correct. The worked calculation gives 54.05844 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 54.05844 m, not 40.54383 m.",
"D": "Incorrect. Substituti... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002639 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 8], [3, -2]]. | {
"A": "-15",
"B": "-24",
"C": "-29",
"D": "-30"
} | D | -30 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(-2)−(8)(3)=-30. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -30, not -15.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -30, not -24.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -30, not -29.",
"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_007072 | 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 570 K and 0.81 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "736.23364 L",
"B": "981.64485 L",
"C": "490.82243 L",
"D": "99.16449 L"
} | B | 981.64485 L | PV=nRT, so V=nRT/P=(17)(0.082057)(570)/(0.81)=981.64485 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 981.64485 L, not 736.23364 L.",
"B": "Correct. The worked calculation gives 981.64485 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 981.64485 L, not 490.82243 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_005311 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +2 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "10 N",
"B": "15 N",
"C": "13 N",
"D": "7.5 N"
} | A | 10 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(2×10⁻⁶)/(6×10⁻²)²=10 N. | {
"A": "Correct. The worked calculation gives 10 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10 N, not 15 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10 N, not 13 N.",
"D": "Incorrect. Substituting the stated values into the g... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000513 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 18 and common difference 15. Find the sum of its first 22 terms. | {
"A": "3859",
"B": "1930.5",
"C": "3861",
"D": "387.1"
} | C | 3861 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=18, d=15, n=22: Sₙ=22/2[2(18)+(22−1)(15)]=3861. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3861, not 3859.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3861, not 1930.5.",
"C": "Correct. The worked calculation gives 3861.",
"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_000066 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 +9x +10=0, let its roots be α and β. What is α²+β²? | {
"A": "-10.25",
"B": "7.25",
"C": "10.25",
"D": "9.25"
} | C | 10.25 | By Vieta's relations, α+β = -9/2 and αβ = 10/2. Then α²+β²=(α+β)²−2αβ = (-9/2)²−2(10/2) = 10.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.25, not -10.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.25, not 7.25.",
"C": "Correct. The worked calculation gives 10.25.",
"D": "Incorrect. Substituting the stated values into ... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005629 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 47 μF capacitor is charged to a potential difference of 11 V. Calculate the energy stored, expressed in μJ. | {
"A": "2845.5 μJ",
"B": "2843.5 μJ",
"C": "2844.5 μJ",
"D": "-2843.5 μJ"
} | B | 2843.5 μJ | U=½CV². Since C=47 μF, U in μJ is ½×47×(11)²=2843.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2843.5 μJ, not 2845.5 μJ.",
"B": "Correct. The worked calculation gives 2843.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2843.5 μJ, not 2844.5 μJ.",
"D": "Incorrect. Substituting the... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000469 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -1 and common difference 10. Find the sum of its first 33 terms. | {
"A": "-5247",
"B": "5247",
"C": "3935.25",
"D": "7870.5"
} | B | 5247 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-1, d=10, n=33: Sₙ=33/2[2(-1)+(33−1)(10)]=5247. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5247, not -5247.",
"B": "Correct. The worked calculation gives 5247.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5247, not 3935.25.",
"D": "Incorrect. Substituting the stated values into t... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009653 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_11H_18N_3X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "-3",
"B": "1.3",
"C": "1.5",
"D": "3"
} | D | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+3−18−3)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not -3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.5.",
"D": "Correct. The work... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005416 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 13 μF capacitor is charged to a potential difference of 2 V. Calculate the energy stored, expressed in μJ. | {
"A": "39 μJ",
"B": "26 μJ",
"C": "25 μJ",
"D": "31.2 μJ"
} | B | 26 μJ | U=½CV². Since C=13 μF, U in μJ is ½×13×(2)²=26 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26 μJ, not 39 μJ.",
"B": "Correct. The worked calculation gives 26 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26 μJ, not 25 μJ.",
"D": "Incorrect. Substituting the stated values into ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004409 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 10 kg and radius 6 m is acted on by a constant torque of 40 N m about its central axis. Find its angular acceleration. | {
"A": "0.22222 rad s⁻²",
"B": "1.02222 rad s⁻²",
"C": "0.44444 rad s⁻²",
"D": "0.11111 rad s⁻²"
} | A | 0.22222 rad s⁻² | For a solid disc, I=½MR²=½(10)(6)²=180 kg m². Using τ=Iα, α=40/180=0.22222 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.22222 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.22222 rad s⁻², not 1.02222 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.22222 rad s⁻², not 0.44444 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_005566 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 78 μF capacitor is charged to a potential difference of 12 V. Calculate the energy stored, expressed in μJ. | {
"A": "2808 μJ",
"B": "5616 μJ",
"C": "5617 μJ",
"D": "11232 μJ"
} | B | 5616 μJ | U=½CV². Since C=78 μF, U in μJ is ½×78×(12)²=5616 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5616 μJ, not 2808 μJ.",
"B": "Correct. The worked calculation gives 5616 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5616 μJ, not 5617 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007621 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 90 mL of 0.10 M HCl is mixed with 49 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "0.53023",
"B": "1.53023",
"C": "2.53023",
"D": "3.06046"
} | B | 1.53023 | Excess H⁺ moles=0.10×(90−49)/1000=0.004100 mol. Total volume=0.139 L, so [H⁺]=0.029496 M and pH=−log₁₀[H⁺]=1.53023. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.53023, not 0.53023.",
"B": "Correct. The worked calculation gives 1.53023.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.53023, not 2.53023.",
"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_008527 | 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 0.32 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.576 K",
"B": "-2.232 K",
"C": "0.768 K",
"D": "-0.768 K"
} | C | 0.768 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.6×0.32=0.768 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.768 K, not 0.576 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.768 K, not -2.232 K.",
"C": "Correct. The worked calculation gives 0.768 K.",
"D": "Incorrect. Substituting the stated v... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005049 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +8 μC and +4 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "60.77551 N",
"B": "58.77551 N",
"C": "56.77551 N",
"D": "70.53061 N"
} | B | 58.77551 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(8×10⁻⁶)(4×10⁻⁶)/(7×10⁻²)²=58.77551 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 58.77551 N, not 60.77551 N.",
"B": "Correct. The worked calculation gives 58.77551 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 58.77551 N, not 56.77551 N.",
"D": "Incorrect. Substitutin... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000060 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 +2x +3=0, let its roots be α and β. What is α²+β²? | {
"A": "0.22449",
"B": "-0.77551",
"C": "-2.77551",
"D": "-1.55102"
} | B | -0.77551 | By Vieta's relations, α+β = -2/7 and αβ = 3/7. Then α²+β²=(α+β)²−2αβ = (-2/7)²−2(3/7) = -0.77551. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.77551, not 0.22449.",
"B": "Correct. The worked calculation gives -0.77551.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.77551, not -2.77551.",
"D": "Incorrect. Substituting the state... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000494 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -6 and common difference 14. Find the sum of its first 35 terms. | {
"A": "8121",
"B": "6496",
"C": "8119",
"D": "8120"
} | D | 8120 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-6, d=14, n=35: Sₙ=35/2[2(-6)+(35−1)(14)]=8120. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8120, not 8121.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8120, not 6496.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8120, not 8119.",
"D": "Corr... | [
"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_007008 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 4 mol of gas at 641 K and 2.46 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "83.52608 L",
"B": "102.63129 L",
"C": "68.42086 L",
"D": "85.52608 L"
} | D | 85.52608 L | PV=nRT, so V=nRT/P=(4)(0.082057)(641)/(2.46)=85.52608 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 85.52608 L, not 83.52608 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 85.52608 L, not 102.63129 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 85.52... | [
"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_008677 | 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 1.23 mol L⁻¹ and initially B is absent. At equilibrium, 79% of A has dissociated at constant volume. Find K_c. | {
"A": "29.24354",
"B": "12.62177",
"C": "14.62177",
"D": "15.62177"
} | C | 14.62177 | Let α=0.79. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.23)(0.79)²/(1−0.79)=14.62177. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14.62177, not 29.24354.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14.62177, not 12.62177.",
"C": "Correct. The worked calculation gives 14.62177.",
"D": "Incorrect. Substituting the stat... | [
"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_007142 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 15 mol of gas at 278 K and 2.43 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "168.97664 L",
"B": "140.81386 L",
"C": "211.2208 L",
"D": "70.40693 L"
} | B | 140.81386 L | PV=nRT, so V=nRT/P=(15)(0.082057)(278)/(2.43)=140.81386 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 140.81386 L, not 168.97664 L.",
"B": "Correct. The worked calculation gives 140.81386 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 140.81386 L, not 211.2208 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_005026 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +5 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "21.22222 N",
"B": "-22.22222 N",
"C": "22.22222 N",
"D": "3.22222 N"
} | C | 22.22222 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(5×10⁻⁶)/(9×10⁻²)²=22.22222 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22.22222 N, not 21.22222 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22.22222 N, not -22.22222 N.",
"C": "Correct. The worked calculation gives 22.22222 N.",
"D": "Incorrect. Substituti... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002919 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, 4, -5) and v=(-1, -7, 7), calculate u·v. | {
"A": "-67",
"B": "-69",
"C": "-80.4",
"D": "-33.5"
} | A | -67 | The dot product is the sum of corresponding component products: (4)(-1)+(4)(-7)+(-5)(7)=-67. | {
"A": "Correct. The worked calculation gives -67.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -67, not -69.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -67, not -80.4.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_006310 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 22 cm in front of a thin convex lens of focal length 8 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-2.42857",
"B": "-0.57143",
"C": "-1.42857",
"D": "0.57143"
} | D | 0.57143 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(22)(8)/(22−8)=12.57143 cm. Thus |m|=v/u=12.57143/22=0.57143. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.57143, not -2.42857.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.57143, not -0.57143.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.57143, not -1.... | [
"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_004154 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.38. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "-20.72 N",
"B": "24.864 N",
"C": "21.72 N",
"D": "20.72 N"
} | D | 20.72 N | Net force=mg(sinθ−μcosθ)=7×10×(0.6−0.38×0.8)=20.72 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20.72 N, not -20.72 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20.72 N, not 24.864 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20.72 N, not 21.... | [
"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_003590 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 60 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "336.28934 m",
"B": "676.57869 m",
"C": "339.28934 m",
"D": "338.28934 m"
} | D | 338.28934 m | Range R=u²sin(2θ)/g. Substituting u=60, θ=55° and g=10 gives R=(60)²sin(110°)/10=338.28934 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 338.28934 m, not 336.28934 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 338.28934 m, not 676.57869 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 33... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002754 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-6, 1, -3) and v=(-5, 5, 7), calculate u·v. | {
"A": "28",
"B": "15",
"C": "14",
"D": "12"
} | C | 14 | The dot product is the sum of corresponding component products: (-6)(-5)+(1)(5)+(-3)(7)=14. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14, not 28.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14, not 15.",
"C": "Correct. The worked calculation gives 14.",
"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_009778 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(Cl)_4]^-1, each Cl ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "4.5",
"B": "5",
"C": "2",
"D": "3"
} | D | 3 | Let the formal oxidation state of Ni be x. Charge balance gives x+(4)(−1)=-1; hence x=-1+4=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.",
"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_008564 | 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 0.08 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.072 K",
"B": "-2.856 K",
"C": "-0.856 K",
"D": "0.144 K"
} | D | 0.144 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.6×0.08=0.144 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.144 K, not 0.072 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.144 K, not -2.856 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.144 K, not -0.8... | [
"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_004926 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 3 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 13 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "6.25792 A",
"B": "1.32579 A",
"C": "4.88688 A",
"D": "3.25792 A"
} | D | 3.25792 A | Series branch resistance=3+14=17 Ω. Parallel equivalent R_eq=(17×13)/(17+13)=7.36667 Ω. Total current I=V/R_eq=24/7.36667=3.25792 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.25792 A, not 6.25792 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.25792 A, not 1.32579 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.25792 A,... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007941 | 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 10 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "0.25 mmol L⁻¹",
"B": "2.25 mmol L⁻¹",
"C": "1.875 mmol L⁻¹",
"D": "1.25 mmol L⁻¹"
} | D | 1.25 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=10/2^3=1.25 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.25 mmol L⁻¹, not 0.25 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.25 mmol L⁻¹, not 2.25 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation ... | [
"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_006962 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 22 mol H₂ and 23 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "22 mol",
"B": "11 mol",
"C": "24 mol",
"D": "33 mol"
} | A | 22 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 22 mol H₂O; O₂ can produce 46 mol H₂O. The limiting condition is H₂; product=22 mol. | {
"A": "Correct. The worked calculation gives 22 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22 mol, not 11 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22 mol, not 24 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008760 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.48 mol L⁻¹ and initially B is absent. At equilibrium, 59% of A has dissociated at constant volume. Find K_c. | {
"A": "3.02622",
"B": "5.02622",
"C": "4.02622",
"D": "-5.02622"
} | B | 5.02622 | Let α=0.59. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.48)(0.59)²/(1−0.59)=5.02622. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.02622, not 3.02622.",
"B": "Correct. The worked calculation gives 5.02622.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.02622, not 4.02622.",
"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_003040 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-10-3i)/(10+10i). What is Re(z), the real part of z? | {
"A": "-0.65",
"B": "-1.65",
"C": "-0.975",
"D": "-1.3"
} | A | -0.65 | Multiply numerator and denominator by the conjugate (10-10i). Then Re(z)=(ac+bd)/(c²+d²)=((-10)(10)+(-3)(10))/(10²+(10)²)=-0.65. | {
"A": "Correct. The worked calculation gives -0.65.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.65, not -1.65.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.65, not -0.975.",
"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_004229 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.15. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "24 N",
"B": "28.8 N",
"C": "12 N",
"D": "25 N"
} | A | 24 N | Net force=mg(sinθ−μcosθ)=5×10×(0.6−0.15×0.8)=24 N. | {
"A": "Correct. The worked calculation gives 24 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24 N, not 28.8 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24 N, not 12 N.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_009475 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_4H_4N_1X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "2.25",
"B": "0",
"C": "3",
"D": "1"
} | C | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×4+2+1−4−1)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 0.",
"C": "Correct. The worked calculation gives 3.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009755 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(OH)_6]^-4, each OH ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "2",
"B": "1",
"C": "-2",
"D": "1.5"
} | A | 2 | Let the formal oxidation state of Cr be x. Charge balance gives x+(6)(−1)=-4; hence x=-4+6=+2. | {
"A": "Correct. The worked calculation gives 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_007778 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 19 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "0.22266 mmol L⁻¹",
"B": "0.14844 mmol L⁻¹",
"C": "0.29688 mmol L⁻¹",
"D": "-2.85156 mmol L⁻¹"
} | B | 0.14844 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=19/2^7=0.14844 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.14844 mmol L⁻¹, not 0.22266 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.14844 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.14844 mmol L⁻¹, not 0.29688 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_002106 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 7 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-2.66013",
"B": "0.33987",
"C": "0.16993",
"D": "1.33987"
} | B | 0.33987 | Favourable pairs = C(8,2)+C(7,2)+C(3,2)=52. Total pairs=C(18,2)=153. Therefore P=52/153=0.33987. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33987, not -2.66013.",
"B": "Correct. The worked calculation gives 0.33987.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33987, not 0.16993.",
"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_009627 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_6H_5N_3X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "4",
"B": "6",
"C": "-4",
"D": "8"
} | A | 4 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+3−5−4)/2=4. | {
"A": "Correct. The worked calculation gives 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not -4.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001751 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 89 distinct elements? | {
"A": "5085018206136",
"B": "10170036412272",
"C": "5085018206135",
"D": "5085018206138"
} | A | 5085018206136 | Order does not matter, so the count is C(89,10)=89!/[10!(79)!]=5085018206136. | {
"A": "Correct. The worked calculation gives 5085018206136.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5085018206136, not 10170036412272.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5085018206136, not 5085018206135.",
"D": "Incorr... | [
"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_003067 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(5+5i)/(4+1i). What is Re(z), the real part of z? | {
"A": "1.47059",
"B": "-0.52941",
"C": "2.47059",
"D": "-1.52941"
} | A | 1.47059 | Multiply numerator and denominator by the conjugate (4-1i). Then Re(z)=(ac+bd)/(c²+d²)=((5)(4)+(5)(1))/(4²+(1)²)=1.47059. | {
"A": "Correct. The worked calculation gives 1.47059.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.47059, not -0.52941.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.47059, not 2.47059.",
"D": "Incorrect. Substituting the stated v... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001207 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=1x³ +10x² +12x+7. Evaluate f′(5). | {
"A": "93.5",
"B": "19.7",
"C": "185",
"D": "187"
} | D | 187 | Differentiate: f′(x)=3(1)x²+2(10)x+(12). At x=5, f′(5)=3(1)(5)²+2(10)(5)+(12)=187. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 187, not 93.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 187, not 19.7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 187, not 185.",
"D": "Correct.... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003100 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(6+12i)/(4+5i). What is Re(z), the real part of z? | {
"A": "1.53659",
"B": "2.04878",
"C": "5.04878",
"D": "4.09756"
} | B | 2.04878 | Multiply numerator and denominator by the conjugate (4-5i). Then Re(z)=(ac+bd)/(c²+d²)=((6)(4)+(12)(5))/(4²+(5)²)=2.04878. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.04878, not 1.53659.",
"B": "Correct. The worked calculation gives 2.04878.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.04878, not 5.04878.",
"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_001823 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 12 elements can be selected from a set of 61 distinct elements? | {
"A": "871029485137.5",
"B": "1742058970277",
"C": "-1742058970275",
"D": "1742058970275"
} | D | 1742058970275 | Order does not matter, so the count is C(61,12)=61!/[12!(49)!]=1742058970275. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1742058970275, not 871029485137.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1742058970275, not 1742058970277.",
"C": "Incorrect. Substituting the stated values into the governing relation... | [
"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_009467 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_7H_9N_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "2",
"B": "4",
"C": "1",
"D": "-4"
} | B | 4 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+1−9−0)/2=4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"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... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007248 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 3 mol of gas at 414 K and 2.19 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "46.53644 L",
"B": "44.53644 L",
"C": "47.53644 L",
"D": "5.65364 L"
} | A | 46.53644 L | PV=nRT, so V=nRT/P=(3)(0.082057)(414)/(2.19)=46.53644 L. | {
"A": "Correct. The worked calculation gives 46.53644 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 46.53644 L, not 44.53644 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 46.53644 L, not 47.53644 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_005580 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 72 μF capacitor is charged to a potential difference of 25 V. Calculate the energy stored, expressed in μJ. | {
"A": "22501 μJ",
"B": "22500 μJ",
"C": "22499 μJ",
"D": "-22500 μJ"
} | B | 22500 μJ | U=½CV². Since C=72 μF, U in μJ is ½×72×(25)²=22500 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22500 μJ, not 22501 μJ.",
"B": "Correct. The worked calculation gives 22500 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22500 μJ, not 22499 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_008496 | 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 1 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "3.0244 K",
"B": "2.0488 K",
"C": "1.0244 K",
"D": "0.7683 K"
} | C | 1.0244 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.52×1.97=1.0244 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0244 K, not 3.0244 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0244 K, not 2.0488 K.",
"C": "Correct. The worked calculation gives 1.0244 K.",
"D": "Incorrect. Substituting the stat... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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