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_001472 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (-4x² +3x +3) dx. | {
"A": "4.16667",
"B": "3.16667",
"C": "6.33333",
"D": "1.58333"
} | B | 3.16667 | An antiderivative is (-4/3)x³+(3/2)x²+(3)x. Evaluating between 0 and 1 gives (-4/3)(1)³+(3/2)(1)²+(3)(1)=3.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.16667, not 4.16667.",
"B": "Correct. The worked calculation gives 3.16667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.16667, not 6.33333.",
"D": "Incorrect. Substituting the stated va... | [
"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_008403 | 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 1.14 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "6.56 K",
"B": "1.456 K",
"C": "-4.56 K",
"D": "4.56 K"
} | D | 4.56 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×1.0×1.14=4.56 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.56 K, not 6.56 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.56 K, not 1.456 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.56 K, not -4.56 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_007660 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 67 mL of 0.10 M HCl is mixed with 16 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.42302",
"B": "3.21151",
"C": "1.21151",
"D": "1.12115"
} | C | 1.21151 | Excess H⁺ moles=0.10×(67−16)/1000=0.005100 mol. Total volume=0.083 L, so [H⁺]=0.061446 M and pH=−log₁₀[H⁺]=1.21151. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.21151, not 2.42302.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.21151, not 3.21151.",
"C": "Correct. The worked calculation gives 1.21151.",
"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_008411 | 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 1.75 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": "3.2 K",
"B": "1.42 K",
"C": "5.2 K",
"D": "4.2 K"
} | D | 4.2 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.6×1.75=4.2 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.2 K, not 3.2 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.2 K, not 1.42 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.2 K, not 5.2 K.",
"D"... | [
"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_006068 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 31 cm in front of a thin convex lens of focal length 7 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.29167",
"B": "0.29167",
"C": "2.29167",
"D": "-1.70833"
} | B | 0.29167 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(31)(7)/(31−7)=9.04167 cm. Thus |m|=v/u=9.04167/31=0.29167. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29167, not 1.29167.",
"B": "Correct. The worked calculation gives 0.29167.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29167, not 2.29167.",
"D": "Incorrect. Substituting the stated va... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009448 | 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_16H_28N_3X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "5",
"B": "4.5",
"C": "3",
"D": "2.25"
} | C | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×16+2+3−28−3)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.5.",
"C": "Correct. The worked calculation gives 3.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003906 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block initially moves at 2 m s⁻¹. A constant net force does 30 N of work over 18 m in the direction of motion. Find its final kinetic energy. | {
"A": "550 J",
"B": "-550 J",
"C": "551 J",
"D": "412.5 J"
} | A | 550 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(5)(2)²+(30)(18)=550 J. | {
"A": "Correct. The worked calculation gives 550 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 550 J, not -550 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 550 J, not 551 J.",
"D": "Incorrect. Substituting the stated values into... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000183 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 -1x +10=0, let its roots be α and β. What is α²+β²? | {
"A": "0.16327",
"B": "-2.12755",
"C": "-0.83673",
"D": "-2.83673"
} | D | -2.83673 | By Vieta's relations, α+β = 1/7 and αβ = 10/7. Then α²+β²=(α+β)²−2αβ = (1/7)²−2(10/7) = -2.83673. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2.83673, not 0.16327.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2.83673, not -2.12755.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2.83673, not -... | [
"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_006168 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 89 cm in front of a thin convex lens of focal length 23 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-2.65152",
"B": "0.17424",
"C": "0.69697",
"D": "0.34848"
} | D | 0.34848 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(89)(23)/(89−23)=31.01515 cm. Thus |m|=v/u=31.01515/89=0.34848. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34848, not -2.65152.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34848, not 0.17424.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34848, not 0.69... | [
"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_003102 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(15+7i)/(1+3i). What is Re(z), the real part of z? | {
"A": "5.4",
"B": "3.6",
"C": "1.6",
"D": "2.7"
} | B | 3.6 | Multiply numerator and denominator by the conjugate (1-3i). Then Re(z)=(ac+bd)/(c²+d²)=((15)(1)+(7)(3))/(1²+(3)²)=3.6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.6, not 5.4.",
"B": "Correct. The worked calculation gives 3.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.6, not 1.6.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_001646 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (3x² -3x -1) dx. | {
"A": "156",
"B": "78",
"C": "154",
"D": "117"
} | A | 156 | An antiderivative is (3/3)x³+(-3/2)x²+(-1)x. Evaluating between 0 and 6 gives (3/3)(6)³+(-3/2)(6)²+(-1)(6)=156. | {
"A": "Correct. The worked calculation gives 156.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 156, not 78.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 156, not 154.",
"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_005002 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 3 Ω and 15 Ω are connected in series; this combination is connected in parallel with a 13 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.38462 A",
"B": "1.78846 A",
"C": "0.38462 A",
"D": "4.76923 A"
} | A | 2.38462 A | Series branch resistance=3+15=18 Ω. Parallel equivalent R_eq=(18×13)/(18+13)=7.54839 Ω. Total current I=V/R_eq=18/7.54839=2.38462 A. | {
"A": "Correct. The worked calculation gives 2.38462 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.38462 A, not 1.78846 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.38462 A, not 0.38462 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001325 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ -5x² +10x+7. Evaluate f′(-2). | {
"A": "-102",
"B": "102",
"C": "103",
"D": "51"
} | B | 102 | Differentiate: f′(x)=3(6)x²+2(-5)x+(10). At x=-2, f′(-2)=3(6)(-2)²+2(-5)(-2)+(10)=102. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 102, not -102.",
"B": "Correct. The worked calculation gives 102.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 102, not 103.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_002576 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, -4], [3, -1]]. | {
"A": "0",
"B": "2.25",
"C": "1.5",
"D": "3"
} | D | 3 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(-1)−(-4)(3)=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.5.",
"D": "Correct. The work... | [
"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_006885 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 25 mol H₂ and 21 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "26 mol",
"B": "25 mol",
"C": "50 mol",
"D": "3.5 mol"
} | B | 25 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 25 mol H₂O; O₂ can produce 42 mol H₂O. The limiting condition is H₂; product=25 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 25 mol, not 26 mol.",
"B": "Correct. The worked calculation gives 25 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 25 mol, not 50 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_008290 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 11 A for 20390 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": "74.7949 g",
"B": "73.7949 g",
"C": "71.7949 g",
"D": "55.34617 g"
} | B | 73.7949 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×20390/(2×96500)=73.7949 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 73.7949 g, not 74.7949 g.",
"B": "Correct. The worked calculation gives 73.7949 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 73.7949 g, not 71.7949 g.",
"D": "Incorrect. Substituting the... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005735 | 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 5 atm at 450 K. What is its pressure at 617 K? | {
"A": "4.85556 atm",
"B": "6.85556 atm",
"C": "5.14167 atm",
"D": "8.85556 atm"
} | B | 6.85556 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(5)(617)/(450)=6.85556 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.85556 atm, not 4.85556 atm.",
"B": "Correct. The worked calculation gives 6.85556 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.85556 atm, not 5.14167 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_001093 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-3x³ +7x² -9x+7. Evaluate f′(-3). | {
"A": "-133",
"B": "-105.6",
"C": "-132",
"D": "-198"
} | C | -132 | Differentiate: f′(x)=3(-3)x²+2(7)x+(-9). At x=-3, f′(-3)=3(-3)(-3)²+2(7)(-3)+(-9)=-132. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -132, not -133.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -132, not -105.6.",
"C": "Correct. The worked calculation gives -132.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_005550 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 48 μF capacitor is charged to a potential difference of 9 V. Calculate the energy stored, expressed in μJ. | {
"A": "2916 μJ",
"B": "1458 μJ",
"C": "-1944 μJ",
"D": "1944 μJ"
} | D | 1944 μJ | U=½CV². Since C=48 μF, U in μJ is ½×48×(9)²=1944 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1944 μJ, not 2916 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1944 μJ, not 1458 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1944 μJ, not -1944... | [
"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_002211 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 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": "3.32806",
"B": "0.16403",
"C": "0.49209",
"D": "0.32806"
} | D | 0.32806 | Favourable pairs = C(8,2)+C(5,2)+C(10,2)=83. Total pairs=C(23,2)=253. Therefore P=83/253=0.32806. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32806, not 3.32806.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32806, not 0.16403.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32806, not 0.492... | [
"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_002908 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-2, -5, 3) and v=(-6, -3, 8), calculate u·v. | {
"A": "53",
"B": "50",
"C": "51",
"D": "76.5"
} | C | 51 | The dot product is the sum of corresponding component products: (-2)(-6)+(-5)(-3)+(3)(8)=51. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 51, not 53.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 51, not 50.",
"C": "Correct. The worked calculation gives 51.",
"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_007438 | 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 45 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.21568",
"B": "1.47712",
"C": "2.47712",
"D": "-1.52288"
} | B | 1.47712 | Excess H⁺ moles=0.10×(90−45)/1000=0.004500 mol. Total volume=0.135 L, so [H⁺]=0.033333 M and pH=−log₁₀[H⁺]=1.47712. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.47712, not 2.21568.",
"B": "Correct. The worked calculation gives 1.47712.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.47712, not 2.47712.",
"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_000575 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 28 and common difference 6. Find the sum of its first 21 terms. | {
"A": "3696",
"B": "1849",
"C": "1848",
"D": "-1848"
} | C | 1848 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=28, d=6, n=21: Sₙ=21/2[2(28)+(21−1)(6)]=1848. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1848, not 3696.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1848, not 1849.",
"C": "Correct. The worked calculation gives 1848.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007786 | 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 69 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "-1.73047 mmol L⁻¹",
"B": "0.26953 mmol L⁻¹",
"C": "0.4043 mmol L⁻¹",
"D": "1.26953 mmol L⁻¹"
} | B | 0.26953 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=69/2^8=0.26953 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.26953 mmol L⁻¹, not -1.73047 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.26953 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.26953 mmol L⁻¹, not 0.4043 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_002833 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, -4, 7) and v=(-4, -5, -2), calculate u·v. | {
"A": "1",
"B": "2",
"C": "3",
"D": "4"
} | B | 2 | The dot product is the sum of corresponding component products: (1)(-4)+(-4)(-5)+(7)(-2)=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004573 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 3 kg and radius 4 m is acted on by a constant torque of 66 N m about its central axis. Find its angular acceleration. | {
"A": "0.75 rad s⁻²",
"B": "2.0625 rad s⁻²",
"C": "2.75 rad s⁻²",
"D": "4.125 rad s⁻²"
} | C | 2.75 rad s⁻² | For a solid disc, I=½MR²=½(3)(4)²=24 kg m². Using τ=Iα, α=66/24=2.75 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.75 rad s⁻², not 0.75 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.75 rad s⁻², not 2.0625 rad s⁻².",
"C": "Correct. The worked calculation gives 2.75 rad s⁻².",
"D": "Incorrect.... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008366 | 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 1.29 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.87 K",
"B": "-3.87 K",
"C": "3.87 K",
"D": "7.74 K"
} | C | 3.87 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×1.0×1.29=3.87 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.87 K, not 1.87 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.87 K, not -3.87 K.",
"C": "Correct. The worked calculation gives 3.87 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006357 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 5 kg is attached to an ideal spring of force constant 1197 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.87074 s",
"B": "0.12926 s",
"C": "-0.87074 s",
"D": "1.01293 s"
} | B | 0.12926 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(5/1197)=0.12926 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.12926 s, not -2.87074 s.",
"B": "Correct. The worked calculation gives 0.12926 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.12926 s, not -0.87074 s.",
"D": "Incorrect. Substituting t... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000189 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 +9x -2=0, let its roots be α and β. What is α²+β²? | {
"A": "85",
"B": "87",
"C": "-85",
"D": "170"
} | A | 85 | By Vieta's relations, α+β = -9/1 and αβ = -2/1. Then α²+β²=(α+β)²−2αβ = (-9/1)²−2(-2/1) = 85. | {
"A": "Correct. The worked calculation gives 85.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 85, not 87.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 85, not -85.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009596 | 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_13N_2X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "6",
"B": "7",
"C": "4",
"D": "12"
} | A | 6 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+2−13−1)/2=6. | {
"A": "Correct. The worked calculation gives 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.",
"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_001365 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (5x² +7x +7) dx. | {
"A": "97.5",
"B": "195",
"C": "95.5",
"D": "48.75"
} | A | 97.5 | An antiderivative is (5/3)x³+(7/2)x²+(7)x. Evaluating between 0 and 3 gives (5/3)(3)³+(7/2)(3)²+(7)(3)=97.5. | {
"A": "Correct. The worked calculation gives 97.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 97.5, not 195.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 97.5, not 95.5.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_006046 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 54 cm in front of a thin convex lens of focal length 13 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.2378",
"B": "3.31707",
"C": "0.31707",
"D": "1.31707"
} | C | 0.31707 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(54)(13)/(54−13)=17.12195 cm. Thus |m|=v/u=17.12195/54=0.31707. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31707, not 0.2378.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31707, not 3.31707.",
"C": "Correct. The worked calculation gives 0.31707.",
"D": "Incorrect. Substituting the stated val... | [
"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_007543 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 89 mL of 0.10 M HCl is mixed with 91 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "9.04576",
"B": "2.10458",
"C": "5.52288",
"D": "11.04576"
} | D | 11.04576 | Excess OH⁻ moles=0.10×(91−89)/1000=0.000200 mol. Total volume=0.180 L, so [OH⁻]=0.001111 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=11.04576. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.04576, not 9.04576.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.04576, not 2.10458.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.04576, not 5.... | [
"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_008077 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 4 A for 9693 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": "25.51318 g",
"B": "9.56744 g",
"C": "10.75659 g",
"D": "12.75659 g"
} | D | 12.75659 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×9693/(2×96500)=12.75659 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.75659 g, not 25.51318 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.75659 g, not 9.56744 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.7565... | [
"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_007980 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 56 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "7 mmol L⁻¹",
"B": "12 mmol L⁻¹",
"C": "14 mmol L⁻¹",
"D": "16 mmol L⁻¹"
} | C | 14 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=56/2^2=14 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14 mmol L⁻¹, not 7 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14 mmol L⁻¹, not 12 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 14 mmol L⁻¹.",
"D": "Incorrect. Substit... | [
"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_005951 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.8 atm at 258 K. What is its pressure at 627 K? | {
"A": "8.74884 atm",
"B": "6.37442 atm",
"C": "4.37442 atm",
"D": "-4.37442 atm"
} | C | 4.37442 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.8)(627)/(258)=4.37442 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.37442 atm, not 8.74884 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.37442 atm, not 6.37442 atm.",
"C": "Correct. The worked calculation gives 4.37442 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_007402 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 36 mL of 0.10 M HCl is mixed with 68 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "11.48812",
"B": "10.48812",
"C": "15.48812",
"D": "12.48812"
} | D | 12.48812 | Excess OH⁻ moles=0.10×(68−36)/1000=0.003200 mol. Total volume=0.104 L, so [OH⁻]=0.030769 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.48812. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.48812, not 11.48812.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.48812, not 10.48812.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.48812, not ... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004210 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 13 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.28. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "58.656 N",
"B": "48.88 N",
"C": "46.88 N",
"D": "-48.88 N"
} | B | 48.88 N | Net force=mg(sinθ−μcosθ)=13×10×(0.6−0.28×0.8)=48.88 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 48.88 N, not 58.656 N.",
"B": "Correct. The worked calculation gives 48.88 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 48.88 N, not 46.88 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_005317 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +8 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": "41 N",
"B": "40 N",
"C": "38 N",
"D": "48 N"
} | B | 40 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(8×10⁻⁶)(2×10⁻⁶)/(6×10⁻²)²=40 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 40 N, not 41 N.",
"B": "Correct. The worked calculation gives 40 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 40 N, not 38 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_002960 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-6, 0, -5) and v=(8, -6, 0), calculate u·v. | {
"A": "-72",
"B": "48",
"C": "-38.4",
"D": "-48"
} | D | -48 | The dot product is the sum of corresponding component products: (-6)(8)+(0)(-6)+(-5)(0)=-48. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -48, not -72.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -48, not 48.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -48, not -38.4.",
"D": "Correct. ... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004592 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 1 m is acted on by a constant torque of 82 N m about its central axis. Find its angular acceleration. | {
"A": "30.8 rad s⁻²",
"B": "34.8 rad s⁻²",
"C": "32.8 rad s⁻²",
"D": "33.8 rad s⁻²"
} | C | 32.8 rad s⁻² | For a solid disc, I=½MR²=½(5)(1)²=2.5 kg m². Using τ=Iα, α=82/2.5=32.8 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 32.8 rad s⁻², not 30.8 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 32.8 rad s⁻², not 34.8 rad s⁻².",
"C": "Correct. The worked calculation gives 32.8 rad s⁻².",
"D": "Incorrect. S... | [
"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_000551 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 10 and common difference 5. Find the sum of its first 19 terms. | {
"A": "-1045",
"B": "1047",
"C": "1045",
"D": "105.5"
} | C | 1045 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=10, d=5, n=19: Sₙ=19/2[2(10)+(19−1)(5)]=1045. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1045, not -1045.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1045, not 1047.",
"C": "Correct. The worked calculation gives 1045.",
"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_002969 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(3, -3, 0) and v=(4, 5, 8), calculate u·v. | {
"A": "0",
"B": "-2.25",
"C": "-3",
"D": "-2"
} | C | -3 | The dot product is the sum of corresponding component products: (3)(4)+(-3)(5)+(0)(8)=-3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -3, not 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -3, not -2.25.",
"C": "Correct. The worked calculation gives -3.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009735 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(Cl)_3]^+2, each Cl ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "10",
"B": "8",
"C": "5",
"D": "3.75"
} | C | 5 | Let the formal oxidation state of Cr be x. Charge balance gives x+(3)(−1)=+2; hence x=2+3=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 8.",
"C": "Correct. The worked calculation gives 5.",
"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_008826 | 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 0.46 mol L⁻¹ and initially B is absent. At equilibrium, 20% of A has dissociated at constant volume. Find K_c. | {
"A": "0.138",
"B": "2.092",
"C": "0.092",
"D": "1.0092"
} | C | 0.092 | Let α=0.2. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.46)(0.2)²/(1−0.2)=0.092. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.092, not 0.138.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.092, not 2.092.",
"C": "Correct. The worked calculation gives 0.092.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_009682 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(Cl)_6]^-3, each Cl ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "2",
"B": "2.25",
"C": "4.5",
"D": "3"
} | D | 3 | Let the formal oxidation state of Pd be x. Charge balance gives x+(6)(−1)=-3; hence x=-3+6=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.5.",
"D": "Correct. The work... | [
"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_003864 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block initially moves at 11 m s⁻¹. A constant net force does 9 N of work over 5 m in the direction of motion. Find its final kinetic energy. | {
"A": "952.5 J",
"B": "950.5 J",
"C": "1143 J",
"D": "714.375 J"
} | A | 952.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(15)(11)²+(9)(5)=952.5 J. | {
"A": "Correct. The worked calculation gives 952.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 952.5 J, not 950.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 952.5 J, not 1143 J.",
"D": "Incorrect. Substituting the stated val... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004856 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 5 Ω are connected in series; this combination is connected in parallel with a 4 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "8.16667 A",
"B": "10.16667 A",
"C": "9.16667 A",
"D": "4.58333 A"
} | C | 9.16667 A | Series branch resistance=13+5=18 Ω. Parallel equivalent R_eq=(18×4)/(18+4)=3.27273 Ω. Total current I=V/R_eq=30/3.27273=9.16667 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.16667 A, not 8.16667 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.16667 A, not 10.16667 A.",
"C": "Correct. The worked calculation gives 9.16667 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000104 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -11x -2=0, let its roots be α and β. What is α²+β²? | {
"A": "-32.25",
"B": "32.25",
"C": "34.25",
"D": "31.25"
} | B | 32.25 | By Vieta's relations, α+β = 11/2 and αβ = -2/2. Then α²+β²=(α+β)²−2αβ = (11/2)²−2(-2/2) = 32.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 32.25, not -32.25.",
"B": "Correct. The worked calculation gives 32.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 32.25, not 34.25.",
"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_001731 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 6 elements can be selected from a set of 76 distinct elements? | {
"A": "262342728",
"B": "218618939",
"C": "218618940",
"D": "218618941"
} | C | 218618940 | Order does not matter, so the count is C(76,6)=76!/[6!(70)!]=218618940. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 218618940, not 262342728.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 218618940, not 218618939.",
"C": "Correct. The worked calculation gives 218618940.",
"D": "Incorrect. Substituting the... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002838 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(7, 1, 5) and v=(6, 4, -1), calculate u·v. | {
"A": "20.5",
"B": "41",
"C": "40",
"D": "30.75"
} | B | 41 | The dot product is the sum of corresponding component products: (7)(6)+(1)(4)+(5)(-1)=41. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 41, not 20.5.",
"B": "Correct. The worked calculation gives 41.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 41, not 40.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003868 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 7 m s⁻¹. A constant net force does 7 N of work over 6 m in the direction of motion. Find its final kinetic energy. | {
"A": "213.5 J",
"B": "256.2 J",
"C": "215.5 J",
"D": "22.35 J"
} | A | 213.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(7)²+(7)(6)=213.5 J. | {
"A": "Correct. The worked calculation gives 213.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 213.5 J, not 256.2 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 213.5 J, not 215.5 J.",
"D": "Incorrect. Substituting the stated va... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004338 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 43 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.13. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "255.936 N",
"B": "213.28 N",
"C": "215.28 N",
"D": "214.28 N"
} | B | 213.28 N | Net force=mg(sinθ−μcosθ)=43×10×(0.6−0.13×0.8)=213.28 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 213.28 N, not 255.936 N.",
"B": "Correct. The worked calculation gives 213.28 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 213.28 N, not 215.28 N.",
"D": "Incorrect. Substituting the sta... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008348 | 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 1 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-1.808 K",
"B": "2.192 K",
"C": "0.192 K",
"D": "0.384 K"
} | C | 0.192 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.6×0.32=0.192 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.192 K, not -1.808 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.192 K, not 2.192 K.",
"C": "Correct. The worked calculation gives 0.192 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_001385 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (5x² +7x -3) dx. | {
"A": "1264",
"B": "1052.33333",
"C": "1053.33333",
"D": "106.33333"
} | C | 1053.33333 | An antiderivative is (5/3)x³+(7/2)x²+(-3)x. Evaluating between 0 and 8 gives (5/3)(8)³+(7/2)(8)²+(-3)(8)=1053.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1053.33333, not 1264.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1053.33333, not 1052.33333.",
"C": "Correct. The worked calculation gives 1053.33333.",
"D": "Incorrect. Substituting the ... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001307 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-1x³ -8x² -5x+7. Evaluate f′(-1). | {
"A": "6",
"B": "4",
"C": "8",
"D": "11"
} | C | 8 | Differentiate: f′(x)=3(-1)x²+2(-8)x+(-5). At x=-1, f′(-1)=3(-1)(-1)²+2(-8)(-1)+(-5)=8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 4.",
"C": "Correct. The worked calculation gives 8.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_002811 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-1, -3, -5) and v=(-2, 5, -7), calculate u·v. | {
"A": "11",
"B": "23",
"C": "22",
"D": "33"
} | C | 22 | The dot product is the sum of corresponding component products: (-1)(-2)+(-3)(5)+(-5)(-7)=22. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22, not 11.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22, not 23.",
"C": "Correct. The worked calculation gives 22.",
"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_008339 | 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 1.94 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "4.0352 K",
"B": "2.0176 K",
"C": "0.0176 K",
"D": "-0.9824 K"
} | B | 2.0176 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×1.94=2.0176 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.0176 K, not 4.0352 K.",
"B": "Correct. The worked calculation gives 2.0176 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.0176 K, not 0.0176 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 |
openstem_002459 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, -2], [3, 6]]. | {
"A": "-60",
"B": "48",
"C": "61",
"D": "60"
} | D | 60 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(6)−(-2)(3)=60. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 60, not -60.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 60, not 48.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 60, not 61.",
"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_002531 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, 3], [3, 6]]. | {
"A": "46",
"B": "-45",
"C": "45",
"D": "43"
} | C | 45 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(6)−(3)(3)=45. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45, not 46.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 45, not -45.",
"C": "Correct. The worked calculation gives 45.",
"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_007309 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 7 mol of gas at 446 K and 0.55 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "463.78537 L",
"B": "465.78537 L",
"C": "466.78537 L",
"D": "467.78537 L"
} | B | 465.78537 L | PV=nRT, so V=nRT/P=(7)(0.082057)(446)/(0.55)=465.78537 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 465.78537 L, not 463.78537 L.",
"B": "Correct. The worked calculation gives 465.78537 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 465.78537 L, not 466.78537 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_007795 | 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 17 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "0.13281 mmol L⁻¹",
"B": "-2.86719 mmol L⁻¹",
"C": "2.13281 mmol L⁻¹",
"D": "3.13281 mmol L⁻¹"
} | A | 0.13281 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=17/2^7=0.13281 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 0.13281 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.13281 mmol L⁻¹, not -2.86719 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.13281 mmol L⁻¹, not 2.13281 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_002808 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(5, -2, 2) and v=(-1, -4, 8), calculate u·v. | {
"A": "19",
"B": "17",
"C": "9.5",
"D": "15.2"
} | A | 19 | The dot product is the sum of corresponding component products: (5)(-1)+(-2)(-4)+(2)(8)=19. | {
"A": "Correct. The worked calculation gives 19.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19, not 17.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19, not 9.5.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005544 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 46 μF capacitor is charged to a potential difference of 17 V. Calculate the energy stored, expressed in μJ. | {
"A": "6647 μJ",
"B": "6649 μJ",
"C": "4985.25 μJ",
"D": "6645 μJ"
} | A | 6647 μJ | U=½CV². Since C=46 μF, U in μJ is ½×46×(17)²=6647 μJ. | {
"A": "Correct. The worked calculation gives 6647 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6647 μJ, not 6649 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6647 μJ, not 4985.25 μJ.",
"D": "Incorrect. Substituting the stated... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000345 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -13 and common difference 4. Find the sum of its first 19 terms. | {
"A": "524.4",
"B": "437",
"C": "44.7",
"D": "435"
} | B | 437 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-13, d=4, n=19: Sₙ=19/2[2(-13)+(19−1)(4)]=437. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 437, not 524.4.",
"B": "Correct. The worked calculation gives 437.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 437, not 44.7.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_002874 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, 0, -6) and v=(-6, -5, 3), calculate u·v. | {
"A": "-48",
"B": "-22",
"C": "-24",
"D": "-23"
} | C | -24 | The dot product is the sum of corresponding component products: (1)(-6)+(0)(-5)+(-6)(3)=-24. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -24, not -48.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -24, not -22.",
"C": "Correct. The worked calculation gives -24.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004803 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 15 Ω are connected in series; this combination is connected in parallel with a 19 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.13158 A",
"B": "2.13158 A",
"C": "3.13158 A",
"D": "1.11316 A"
} | A | 1.13158 A | Series branch resistance=9+15=24 Ω. Parallel equivalent R_eq=(24×19)/(24+19)=10.60465 Ω. Total current I=V/R_eq=12/10.60465=1.13158 A. | {
"A": "Correct. The worked calculation gives 1.13158 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.13158 A, not 2.13158 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.13158 A, not 3.13158 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005821 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.8 atm at 322 K. What is its pressure at 572 K? | {
"A": "17.05342 atm",
"B": "7.52671 atm",
"C": "1.85267 atm",
"D": "8.52671 atm"
} | D | 8.52671 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.8)(572)/(322)=8.52671 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.52671 atm, not 17.05342 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.52671 atm, not 7.52671 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8... | [
"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_001216 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=2x³ +2x² -2x+7. Evaluate f′(5). | {
"A": "168",
"B": "170",
"C": "-168",
"D": "126"
} | A | 168 | Differentiate: f′(x)=3(2)x²+2(2)x+(-2). At x=5, f′(5)=3(2)(5)²+2(2)(5)+(-2)=168. | {
"A": "Correct. The worked calculation gives 168.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 168, not 170.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 168, not -168.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_005315 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +2 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "-10.41322 N",
"B": "7.80992 N",
"C": "7.41322 N",
"D": "10.41322 N"
} | D | 10.41322 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(2×10⁻⁶)/(11×10⁻²)²=10.41322 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.41322 N, not -10.41322 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.41322 N, not 7.80992 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10.413... | [
"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_008656 | 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 1.53 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "4.3868 K",
"B": "1.3868 K",
"C": "2.3868 K",
"D": "3.5802 K"
} | C | 2.3868 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.52×1.53=2.3868 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.3868 K, not 4.3868 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.3868 K, not 1.3868 K.",
"C": "Correct. The worked calculation gives 2.3868 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 |
openstem_003468 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 14 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "20.41798 m",
"B": "9.20899 m",
"C": "18.41798 m",
"D": "17.41798 m"
} | C | 18.41798 m | Range R=u²sin(2θ)/g. Substituting u=14, θ=55° and g=10 gives R=(14)²sin(110°)/10=18.41798 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18.41798 m, not 20.41798 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18.41798 m, not 9.20899 m.",
"C": "Correct. The worked calculation gives 18.41798 m.",
"D": "Incorrect. Substituting... | [
"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_005465 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 48 μF capacitor is charged to a potential difference of 7 V. Calculate the energy stored, expressed in μJ. | {
"A": "118.6 μJ",
"B": "2352 μJ",
"C": "1176 μJ",
"D": "1177 μJ"
} | C | 1176 μJ | U=½CV². Since C=48 μF, U in μJ is ½×48×(7)²=1176 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1176 μJ, not 118.6 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1176 μJ, not 2352 μJ.",
"C": "Correct. The worked calculation gives 1176 μJ.",
"D": "Incorrect. Substituting the stated v... | [
"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_001910 | 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 62 distinct elements? | {
"A": "2592183747769.2002",
"B": "3240229684711.5",
"C": "1080076561570.5",
"D": "2160153123141"
} | D | 2160153123141 | Order does not matter, so the count is C(62,12)=62!/[12!(50)!]=2160153123141. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2160153123141, not 2592183747769.2002.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2160153123141, not 3240229684711.5.",
"C": "Incorrect. Substituting the stated values into the governing re... | [
"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_001324 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ +3x² +10x+7. Evaluate f′(-1). | {
"A": "-10",
"B": "-9",
"C": "-7",
"D": "-8"
} | D | -8 | Differentiate: f′(x)=3(-4)x²+2(3)x+(10). At x=-1, f′(-1)=3(-4)(-1)²+2(3)(-1)+(10)=-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 -9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -8, not -7.",
"D": "Correct. The wo... | [
"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_003283 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-8+11i)/(4+8i). What is Re(z), the real part of z? | {
"A": "0.7",
"B": "1.4",
"C": "0.525",
"D": "1.7"
} | A | 0.7 | Multiply numerator and denominator by the conjugate (4-8i). Then Re(z)=(ac+bd)/(c²+d²)=((-8)(4)+(11)(8))/(4²+(8)²)=0.7. | {
"A": "Correct. The worked calculation gives 0.7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7, not 1.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7, not 0.525.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_004436 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 10 kg and radius 5 m is acted on by a constant torque of 83 N m about its central axis. Find its angular acceleration. | {
"A": "2.664 rad s⁻²",
"B": "1.328 rad s⁻²",
"C": "1.0664 rad s⁻²",
"D": "0.664 rad s⁻²"
} | D | 0.664 rad s⁻² | For a solid disc, I=½MR²=½(10)(5)²=125 kg m². Using τ=Iα, α=83/125=0.664 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.664 rad s⁻², not 2.664 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.664 rad s⁻², not 1.328 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation ... | [
"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_002900 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(8, 8, -1) and v=(2, 3, -7), calculate u·v. | {
"A": "35.25",
"B": "47",
"C": "94",
"D": "23.5"
} | B | 47 | The dot product is the sum of corresponding component products: (8)(2)+(8)(3)+(-1)(-7)=47. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 47, not 35.25.",
"B": "Correct. The worked calculation gives 47.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 47, not 94.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000686 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio -3. What is the sum of its first 6 terms? | {
"A": "-1092",
"B": "-108.2",
"C": "-1090",
"D": "-2184"
} | A | -1092 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(-3^6−1)/(-3−1)=-1092. | {
"A": "Correct. The worked calculation gives -1092.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1092, not -108.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1092, not -1090.",
"D": "Incorrect. Substituting the stated values into... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008351 | 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 1.79 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.18616 K",
"B": "1.8616 K",
"C": "2.8616 K",
"D": "4.8616 K"
} | B | 1.8616 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×1.79=1.8616 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.8616 K, not 1.18616 K.",
"B": "Correct. The worked calculation gives 1.8616 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.8616 K, not 2.8616 K.",
"D": "Incorrect. Substituting the sta... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001430 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (2x² +5x -3) dx. | {
"A": "329.16667",
"B": "331.16667",
"C": "330.16667",
"D": "264.13333"
} | C | 330.16667 | An antiderivative is (2/3)x³+(5/2)x²+(-3)x. Evaluating between 0 and 7 gives (2/3)(7)³+(5/2)(7)²+(-3)(7)=330.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 330.16667, not 329.16667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 330.16667, not 331.16667.",
"C": "Correct. The worked calculation gives 330.16667.",
"D": "Incorrect. Substituting the... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005944 | 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 atm at 404 K. What is its pressure at 521 K? | {
"A": "1.86881 atm",
"B": "5.86881 atm",
"C": "3.86881 atm",
"D": "2.86881 atm"
} | C | 3.86881 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3)(521)/(404)=3.86881 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.86881 atm, not 1.86881 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.86881 atm, not 5.86881 atm.",
"C": "Correct. The worked calculation gives 3.86881 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_000889 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio 5. What is the sum of its first 7 terms? | {
"A": "195310",
"B": "97655",
"C": "73241.25",
"D": "48827.5"
} | B | 97655 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(5^7−1)/(5−1)=97655. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 97655, not 195310.",
"B": "Correct. The worked calculation gives 97655.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 97655, not 73241.25.",
"D": "Incorrect. Substituting the stated values i... | [
"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_003856 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 4 m s⁻¹. A constant net force does 17 N of work over 9 m in the direction of motion. Find its final kinetic energy. | {
"A": "361.5 J",
"B": "241 J",
"C": "240 J",
"D": "243 J"
} | B | 241 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(4)²+(17)(9)=241 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 241 J, not 361.5 J.",
"B": "Correct. The worked calculation gives 241 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 241 J, not 240 J.",
"D": "Incorrect. Substituting the stated values int... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009693 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(CN)_6]^+0, each CN ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "-6",
"B": "6",
"C": "9",
"D": "3"
} | B | 6 | Let the formal oxidation state of Mn be x. Charge balance gives x+(6)(−1)=+0; hence x=0+6=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not -6.",
"B": "Correct. The worked calculation gives 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"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_009839 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(CN)_4]^-4, each CN ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "0",
"B": "-3",
"C": "3",
"D": "2"
} | A | 0 | Let the formal oxidation state of Co be x. Charge balance gives x+(4)(−1)=-4; hence x=-4+4=+0. | {
"A": "Correct. The worked calculation gives 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 3.",
"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_006875 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 29 mol H₂ and 2 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "5 mol",
"B": "3 mol",
"C": "4 mol",
"D": "1.4 mol"
} | C | 4 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 29 mol H₂O; O₂ can produce 4 mol H₂O. The limiting condition is O₂; product=4 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4 mol, not 5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4 mol, not 3 mol.",
"C": "Correct. The worked calculation gives 4 mol.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_004914 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 10 Ω are connected in series; this combination is connected in parallel with a 6 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "7.89474 A",
"B": "5.92105 A",
"C": "3.94737 A",
"D": "1.78947 A"
} | A | 7.89474 A | Series branch resistance=9+10=19 Ω. Parallel equivalent R_eq=(19×6)/(19+6)=4.56 Ω. Total current I=V/R_eq=36/4.56=7.89474 A. | {
"A": "Correct. The worked calculation gives 7.89474 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.89474 A, not 5.92105 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.89474 A, not 3.94737 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003895 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 3 kg block initially moves at 9 m s⁻¹. A constant net force does 19 N of work over 15 m in the direction of motion. Find its final kinetic energy. | {
"A": "203.25 J",
"B": "41.65 J",
"C": "406.5 J",
"D": "405.5 J"
} | C | 406.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(3)(9)²+(19)(15)=406.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 406.5 J, not 203.25 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 406.5 J, not 41.65 J.",
"C": "Correct. The worked calculation gives 406.5 J.",
"D": "Incorrect. Substituting the stated v... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005442 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 21 μF capacitor is charged to a potential difference of 20 V. Calculate the energy stored, expressed in μJ. | {
"A": "4201 μJ",
"B": "5040 μJ",
"C": "8400 μJ",
"D": "4200 μJ"
} | D | 4200 μJ | U=½CV². Since C=21 μF, U in μJ is ½×21×(20)²=4200 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4200 μJ, not 4201 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4200 μJ, not 5040 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4200 μJ, not 8400 ... | [
"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_009688 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(CN)_6]^+3, each CN ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "9",
"B": "6.75",
"C": "7",
"D": "1.9"
} | A | 9 | Let the formal oxidation state of Pt be x. Charge balance gives x+(6)(−1)=+3; hence x=3+6=+9. | {
"A": "Correct. The worked calculation gives 9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9, not 6.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9, not 7.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"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_000923 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio -3. What is the sum of its first 8 terms? | {
"A": "-16398",
"B": "-16400",
"C": "-16402",
"D": "-32800"
} | B | -16400 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(-3^8−1)/(-3−1)=-16400. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -16400, not -16398.",
"B": "Correct. The worked calculation gives -16400.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -16400, not -16402.",
"D": "Incorrect. Substituting the stated values ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002888 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(7, 6, 9) and v=(-2, 1, -6), calculate u·v. | {
"A": "-31",
"B": "-62",
"C": "-93",
"D": "-46.5"
} | B | -62 | The dot product is the sum of corresponding component products: (7)(-2)+(6)(1)+(9)(-6)=-62. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -62, not -31.",
"B": "Correct. The worked calculation gives -62.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -62, not -93.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007425 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 38 mL of 0.10 M HCl is mixed with 47 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "13.02482",
"B": "14.02482",
"C": "-12.02482",
"D": "12.02482"
} | D | 12.02482 | Excess OH⁻ moles=0.10×(47−38)/1000=0.000900 mol. Total volume=0.085 L, so [OH⁻]=0.010588 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.02482. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.02482, not 13.02482.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.02482, not 14.02482.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.02482, not ... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000620 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 16 and common difference 14. Find the sum of its first 10 terms. | {
"A": "791",
"B": "790",
"C": "788",
"D": "789"
} | B | 790 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=16, d=14, n=10: Sₙ=10/2[2(16)+(10−1)(14)]=790. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 790, not 791.",
"B": "Correct. The worked calculation gives 790.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 790, not 788.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008782 | 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 0.18 mol L⁻¹ and initially B is absent. At equilibrium, 64% of A has dissociated at constant volume. Find K_c. | {
"A": "1.2288",
"B": "0.8192",
"C": "1.8192",
"D": "-1.1808"
} | B | 0.8192 | Let α=0.64. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.18)(0.64)²/(1−0.64)=0.8192. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8192, not 1.2288.",
"B": "Correct. The worked calculation gives 0.8192.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8192, not 1.8192.",
"D": "Incorrect. Substituting the stated values ... | [
"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_006253 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 75 cm in front of a thin convex lens of focal length 27 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.4375",
"B": "-1.4375",
"C": "0.84375",
"D": "0.5625"
} | D | 0.5625 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(75)(27)/(75−27)=42.1875 cm. Thus |m|=v/u=42.1875/75=0.5625. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5625, not -0.4375.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.5625, not -1.4375.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5625, not 0.84375.... | [
"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_002116 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 11 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.53",
"B": "0.35333",
"C": "0.265",
"D": "-1.64667"
} | B | 0.35333 | Favourable pairs = C(10,2)+C(11,2)+C(4,2)=106. Total pairs=C(25,2)=300. Therefore P=106/300=0.35333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35333, not 0.53.",
"B": "Correct. The worked calculation gives 0.35333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35333, not 0.265.",
"D": "Incorrect. Substituting the stated values ... | [
"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_004513 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 14 kg and radius 1 m is acted on by a constant torque of 64 N m about its central axis. Find its angular acceleration. | {
"A": "12.14286 rad s⁻²",
"B": "9.14286 rad s⁻²",
"C": "6.14286 rad s⁻²",
"D": "13.71429 rad s⁻²"
} | B | 9.14286 rad s⁻² | For a solid disc, I=½MR²=½(14)(1)²=7 kg m². Using τ=Iα, α=64/7=9.14286 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.14286 rad s⁻², not 12.14286 rad s⁻².",
"B": "Correct. The worked calculation gives 9.14286 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.14286 rad s⁻², not 6.14286 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_002508 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, 1], [5, -2]]. | {
"A": "-19",
"B": "-9.5",
"C": "-28.5",
"D": "-22.8"
} | A | -19 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(-2)−(1)(5)=-19. | {
"A": "Correct. The worked calculation gives -19.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -19, not -9.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -19, not -28.5.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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 |
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