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_008835 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.62 mol L⁻¹ and initially B is absent. At equilibrium, 78% of A has dissociated at constant volume. Find K_c. | {
"A": "21.50417",
"B": "18.92015",
"C": "17.92015",
"D": "15.92015"
} | C | 17.92015 | Let α=0.78. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.62)(0.78)²/(1−0.78)=17.92015. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 17.92015, not 21.50417.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17.92015, not 18.92015.",
"C": "Correct. The worked calculation gives 17.92015.",
"D": "Incorrect. Substituting the stat... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004779 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 14 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 15 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.67273 A",
"B": "-2.32727 A",
"C": "-0.67273 A",
"D": "1.00909 A"
} | A | 0.67273 A | Series branch resistance=14+8=22 Ω. Parallel equivalent R_eq=(22×15)/(22+15)=8.91892 Ω. Total current I=V/R_eq=6/8.91892=0.67273 A. | {
"A": "Correct. The worked calculation gives 0.67273 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.67273 A, not -2.32727 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.67273 A, not -0.67273 A.",
"D": "Incorrect. Substituting t... | [
"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_005780 | 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 249 K. What is its pressure at 727 K? | {
"A": "1.52554 atm",
"B": "7.88313 atm",
"C": "5.25542 atm",
"D": "3.94157 atm"
} | C | 5.25542 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.8)(727)/(249)=5.25542 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.25542 atm, not 1.52554 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.25542 atm, not 7.88313 atm.",
"C": "Correct. The worked calculation gives 5.25542 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_002772 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(8, 2, -5) and v=(8, 5, -5), calculate u·v. | {
"A": "101",
"B": "100",
"C": "99",
"D": "-99"
} | C | 99 | The dot product is the sum of corresponding component products: (8)(8)+(2)(5)+(-5)(-5)=99. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 99, not 101.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 99, not 100.",
"C": "Correct. The worked calculation gives 99.",
"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_000931 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 3 and common ratio 4. What is the sum of its first 9 terms? | {
"A": "131071.5",
"B": "524286",
"C": "262143",
"D": "262145"
} | C | 262143 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=3(4^9−1)/(4−1)=262143. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 262143, not 131071.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 262143, not 524286.",
"C": "Correct. The worked calculation gives 262143.",
"D": "Incorrect. Substituting the stated value... | [
"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_000728 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio 2. What is the sum of its first 6 terms? | {
"A": "251",
"B": "250",
"C": "378",
"D": "252"
} | D | 252 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(2^6−1)/(2−1)=252. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 252, not 251.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 252, not 250.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 252, not 378.",
"D": "Correct. T... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001883 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 50 distinct elements? | {
"A": "2118761",
"B": "2118760",
"C": "-2118760",
"D": "1589070"
} | B | 2118760 | Order does not matter, so the count is C(50,5)=50!/[5!(45)!]=2118760. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2118760, not 2118761.",
"B": "Correct. The worked calculation gives 2118760.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2118760, not -2118760.",
"D": "Incorrect. Substituting the stated v... | [
"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_004296 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 47 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.17. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "261.696 N",
"B": "219.08 N",
"C": "218.08 N",
"D": "22.808 N"
} | C | 218.08 N | Net force=mg(sinθ−μcosθ)=47×10×(0.6−0.17×0.8)=218.08 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 218.08 N, not 261.696 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 218.08 N, not 219.08 N.",
"C": "Correct. The worked calculation gives 218.08 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_008727 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.53 mol L⁻¹ and initially B is absent. At equilibrium, 17% of A has dissociated at constant volume. Find K_c. | {
"A": "0.21309",
"B": "3.21309",
"C": "0.31964",
"D": "-0.78691"
} | A | 0.21309 | Let α=0.17. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.53)(0.17)²/(1−0.17)=0.21309. | {
"A": "Correct. The worked calculation gives 0.21309.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.21309, not 3.21309.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.21309, not 0.31964.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009502 | 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_8H_6N_3X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "-7",
"B": "5",
"C": "5.25",
"D": "7"
} | D | 7 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×8+2+3−6−1)/2=7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not -7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 5.25.",
"D": "Correct. The worke... | [
"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_001195 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ +0x² -2x+7. Evaluate f′(-1). | {
"A": "-25.5",
"B": "-17",
"C": "-8.5",
"D": "-18"
} | B | -17 | Differentiate: f′(x)=3(-5)x²+2(0)x+(-2). At x=-1, f′(-1)=3(-5)(-1)²+2(0)(-1)+(-2)=-17. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -17, not -25.5.",
"B": "Correct. The worked calculation gives -17.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -17, not -8.5.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_000636 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 8 and common difference 4. Find the sum of its first 29 terms. | {
"A": "1484.8",
"B": "1856",
"C": "1857",
"D": "928"
} | B | 1856 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=8, d=4, n=29: Sₙ=29/2[2(8)+(29−1)(4)]=1856. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1856, not 1484.8.",
"B": "Correct. The worked calculation gives 1856.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1856, not 1857.",
"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_001166 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-2x³ +3x² +4x+7. Evaluate f′(-2). | {
"A": "-2.2",
"B": "-32",
"C": "-30",
"D": "-33"
} | B | -32 | Differentiate: f′(x)=3(-2)x²+2(3)x+(4). At x=-2, f′(-2)=3(-2)(-2)²+2(3)(-2)+(4)=-32. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -32, not -2.2.",
"B": "Correct. The worked calculation gives -32.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -32, not -30.",
"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_006355 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 18 kg is attached to an ideal spring of force constant 534 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.63281 s",
"B": "0.1836 s",
"C": "0.36719 s",
"D": "3.36719 s"
} | C | 0.36719 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(18/534)=0.36719 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.36719 s, not -1.63281 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36719 s, not 0.1836 s.",
"C": "Correct. The worked calculation gives 0.36719 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001455 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (1x² -5x +3) dx. | {
"A": "25.66667",
"B": "15.83333",
"C": "12.83333",
"D": "10.83333"
} | C | 12.83333 | An antiderivative is (1/3)x³+(-5/2)x²+(3)x. Evaluating between 0 and 7 gives (1/3)(7)³+(-5/2)(7)²+(3)(7)=12.83333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.83333, not 25.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.83333, not 15.83333.",
"C": "Correct. The worked calculation gives 12.83333.",
"D": "Incorrect. Substituting the stat... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007120 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 18 mol of gas at 559 K and 0.79 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "-1045.13612 L",
"B": "1046.13612 L",
"C": "1045.13612 L",
"D": "1047.13612 L"
} | C | 1045.13612 L | PV=nRT, so V=nRT/P=(18)(0.082057)(559)/(0.79)=1045.13612 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1045.13612 L, not -1045.13612 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1045.13612 L, not 1046.13612 L.",
"C": "Correct. The worked calculation gives 1045.13612 L.",
"D": "Incorrect. ... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001601 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (4x² -8x +0) dx. | {
"A": "0.73333",
"B": "-2.66667",
"C": "-0.66667",
"D": "0.33333"
} | B | -2.66667 | An antiderivative is (4/3)x³+(-8/2)x²+(0)x. Evaluating between 0 and 1 gives (4/3)(1)³+(-8/2)(1)²+(0)(1)=-2.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2.66667, not 0.73333.",
"B": "Correct. The worked calculation gives -2.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2.66667, not -0.66667.",
"D": "Incorrect. Substituting the state... | [
"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_000480 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 22 and common difference 4. Find the sum of its first 30 terms. | {
"A": "-2400",
"B": "2400",
"C": "2401",
"D": "2399"
} | B | 2400 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=22, d=4, n=30: Sₙ=30/2[2(22)+(30−1)(4)]=2400. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2400, not -2400.",
"B": "Correct. The worked calculation gives 2400.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2400, not 2401.",
"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_009300 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.98 V, transfers 1 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.77932 V",
"B": "-1.9609 V",
"C": "3.0391 V",
"D": "1.0391 V"
} | D | 1.0391 V | Apply the Nernst equation: E=0.98−(0.0591/1)(-1)=1.0391 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0391 V, not 0.77932 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0391 V, not -1.9609 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0391 V, no... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002795 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(2, 7, 1) and v=(-4, 6, -7), calculate u·v. | {
"A": "54",
"B": "27",
"C": "20.25",
"D": "13.5"
} | B | 27 | The dot product is the sum of corresponding component products: (2)(-4)+(7)(6)+(1)(-7)=27. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 27, not 54.",
"B": "Correct. The worked calculation gives 27.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 27, not 20.25.",
"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_003491 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 87 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "72.12533 m",
"B": "712.25334 m",
"C": "711.25334 m",
"D": "1422.50669 m"
} | C | 711.25334 m | Range R=u²sin(2θ)/g. Substituting u=87, θ=55° and g=10 gives R=(87)²sin(110°)/10=711.25334 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 711.25334 m, not 72.12533 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 711.25334 m, not 712.25334 m.",
"C": "Correct. The worked calculation gives 711.25334 m.",
"D": "Incorrect. Substit... | [
"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_002096 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 10 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.36",
"B": "1.36",
"C": "-0.64",
"D": "0.54"
} | A | 0.36 | Favourable pairs = C(4,2)+C(10,2)+C(12,2)=117. Total pairs=C(26,2)=325. Therefore P=117/325=0.36. | {
"A": "Correct. The worked calculation gives 0.36.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36, not 1.36.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.36, not -0.64.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_002700 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(0, 1, 5) and v=(-6, 3, 0), calculate u·v. | {
"A": "1.3",
"B": "3",
"C": "4.5",
"D": "2"
} | B | 3 | The dot product is the sum of corresponding component products: (0)(-6)+(1)(3)+(5)(0)=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.5.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_003624 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 89 m s⁻¹ at 75° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "396.05 m",
"B": "394.05 m",
"C": "475.26 m",
"D": "594.075 m"
} | A | 396.05 m | Range R=u²sin(2θ)/g. Substituting u=89, θ=75° and g=10 gives R=(89)²sin(150°)/10=396.05 m. | {
"A": "Correct. The worked calculation gives 396.05 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 396.05 m, not 394.05 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 396.05 m, not 475.26 m.",
"D": "Incorrect. Substituting the stat... | [
"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_006971 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 44 mol H₂ and 28 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "46 mol",
"B": "44 mol",
"C": "22 mol",
"D": "45 mol"
} | B | 44 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 44 mol H₂O; O₂ can produce 56 mol H₂O. The limiting condition is H₂; product=44 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 44 mol, not 46 mol.",
"B": "Correct. The worked calculation gives 44 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 44 mol, not 22 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_009599 | 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_27N_1X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "6",
"C": "-3",
"D": "1.3"
} | A | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×16+2+1−27−2)/2=3. | {
"A": "Correct. The worked calculation gives 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not -3.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007682 | 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 21 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "-5.25 mmol L⁻¹",
"B": "5.25 mmol L⁻¹",
"C": "3.25 mmol L⁻¹",
"D": "8.25 mmol L⁻¹"
} | B | 5.25 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=21/2^2=5.25 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.25 mmol L⁻¹, not -5.25 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 5.25 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.25 mmol L⁻¹, not 3.25 mmol L⁻¹.",
"D": "Incorr... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005662 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 47 μF capacitor is charged to a potential difference of 8 V. Calculate the energy stored, expressed in μJ. | {
"A": "1505 μJ",
"B": "1128 μJ",
"C": "1504 μJ",
"D": "2256 μJ"
} | C | 1504 μJ | U=½CV². Since C=47 μF, U in μJ is ½×47×(8)²=1504 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1504 μJ, not 1505 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1504 μJ, not 1128 μJ.",
"C": "Correct. The worked calculation gives 1504 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008013 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 7 A for 9237 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": "42.54763 g",
"B": "10.63691 g",
"C": "21.27382 g",
"D": "25.52858 g"
} | C | 21.27382 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×7×9237/(2×96500)=21.27382 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21.27382 g, not 42.54763 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21.27382 g, not 10.63691 g.",
"C": "Correct. The worked calculation gives 21.27382 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005713 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.6 atm at 291 K. What is its pressure at 345 K? | {
"A": "1.54536 atm",
"B": "2.45361 atm",
"C": "8.18041 atm",
"D": "5.45361 atm"
} | D | 5.45361 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.6)(345)/(291)=5.45361 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.45361 atm, not 1.54536 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.45361 atm, not 2.45361 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.... | [
"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_000235 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 -18x -3=0, let its roots be α and β. What is α²+β²? | {
"A": "37",
"B": "38",
"C": "36",
"D": "76"
} | B | 38 | By Vieta's relations, α+β = 18/3 and αβ = -3/3. Then α²+β²=(α+β)²−2αβ = (18/3)²−2(-3/3) = 38. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 38, not 37.",
"B": "Correct. The worked calculation gives 38.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 38, not 36.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003160 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(4+5i)/(1+8i). What is Re(z), the real part of z? | {
"A": "-1.32308",
"B": "-0.67692",
"C": "-2.32308",
"D": "0.67692"
} | D | 0.67692 | Multiply numerator and denominator by the conjugate (1-8i). Then Re(z)=(ac+bd)/(c²+d²)=((4)(1)+(5)(8))/(1²+(8)²)=0.67692. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.67692, not -1.32308.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.67692, not -0.67692.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.67692, not -2.... | [
"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_000270 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -7x +12=0, let its roots be α and β. What is α²+β²? | {
"A": "-0.25",
"B": "2.25",
"C": "1.25",
"D": "0.25"
} | D | 0.25 | By Vieta's relations, α+β = 7/2 and αβ = 12/2. Then α²+β²=(α+β)²−2αβ = (7/2)²−2(12/2) = 0.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25, not -0.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25, not 2.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25, not 1.25.",
"D": "Cor... | [
"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_005418 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 72 μF capacitor is charged to a potential difference of 26 V. Calculate the energy stored, expressed in μJ. | {
"A": "24336 μJ",
"B": "48672 μJ",
"C": "24337 μJ",
"D": "2434.6 μJ"
} | A | 24336 μJ | U=½CV². Since C=72 μF, U in μJ is ½×72×(26)²=24336 μJ. | {
"A": "Correct. The worked calculation gives 24336 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24336 μJ, not 48672 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24336 μJ, not 24337 μJ.",
"D": "Incorrect. Substituting the stat... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001661 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (4x² -3x -5) dx. | {
"A": "31",
"B": "41.33333",
"C": "40.33333",
"D": "20.66667"
} | B | 41.33333 | An antiderivative is (4/3)x³+(-3/2)x²+(-5)x. Evaluating between 0 and 4 gives (4/3)(4)³+(-3/2)(4)²+(-5)(4)=41.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 41.33333, not 31.",
"B": "Correct. The worked calculation gives 41.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 41.33333, not 40.33333.",
"D": "Incorrect. Substituting the stated val... | [
"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_004795 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 3 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 18 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "-3.51515 A",
"B": "3.51515 A",
"C": "1.35152 A",
"D": "4.51515 A"
} | B | 3.51515 A | Series branch resistance=3+8=11 Ω. Parallel equivalent R_eq=(11×18)/(11+18)=6.82759 Ω. Total current I=V/R_eq=24/6.82759=3.51515 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.51515 A, not -3.51515 A.",
"B": "Correct. The worked calculation gives 3.51515 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.51515 A, not 1.35152 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_008418 | 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 0.16 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.384 K",
"B": "-0.616 K",
"C": "-2.616 K",
"D": "0.288 K"
} | A | 0.384 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.6×0.16=0.384 K. | {
"A": "Correct. The worked calculation gives 0.384 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.384 K, not -0.616 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.384 K, not -2.616 K.",
"D": "Incorrect. Substituting the stated ... | [
"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_001474 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (-1x² +5x -2) dx. | {
"A": "1.75",
"B": "3.75",
"C": "15",
"D": "7.5"
} | D | 7.5 | An antiderivative is (-1/3)x³+(5/2)x²+(-2)x. Evaluating between 0 and 3 gives (-1/3)(3)³+(5/2)(3)²+(-2)(3)=7.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.5, not 1.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.5, not 3.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.5, not 15.",
"D": "Correct. ... | [
"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_009217 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.30 V, transfers 2 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.61135 V",
"B": "1.38865 V",
"C": "-1.38865 V",
"D": "4.38865 V"
} | B | 1.38865 V | Apply the Nernst equation: E=1.30−(0.0591/2)(-3)=1.38865 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.38865 V, not -1.61135 V.",
"B": "Correct. The worked calculation gives 1.38865 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.38865 V, not -1.38865 V.",
"D": "Incorrect. Substituting t... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006502 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 11 kg is attached to an ideal spring of force constant 883 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.11161 s",
"B": "0.22323 s",
"C": "2.22323 s",
"D": "0.16742 s"
} | B | 0.22323 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(11/883)=0.22323 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.22323 s, not 0.11161 s.",
"B": "Correct. The worked calculation gives 0.22323 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.22323 s, not 2.22323 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003687 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 10 m s⁻¹. A constant net force does 24 N of work over 20 m in the direction of motion. Find its final kinetic energy. | {
"A": "109 J",
"B": "1078 J",
"C": "864 J",
"D": "1080 J"
} | D | 1080 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(10)²+(24)(20)=1080 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1080 J, not 109 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1080 J, not 1078 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1080 J, not 864 J.",
... | [
"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_008081 | 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 8 A for 15386 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": "48.59744 g",
"B": "60.7468 g",
"C": "41.49787 g",
"D": "40.49787 g"
} | D | 40.49787 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×8×15386/(2×96500)=40.49787 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 40.49787 g, not 48.59744 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 40.49787 g, not 60.7468 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 40.4978... | [
"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_000610 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -13 and common difference 13. Find the sum of its first 16 terms. | {
"A": "2028",
"B": "1081.6",
"C": "1353",
"D": "1352"
} | D | 1352 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-13, d=13, n=16: Sₙ=16/2[2(-13)+(16−1)(13)]=1352. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1352, not 2028.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1352, not 1081.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1352, not 1353.",
"D": "Co... | [
"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_006387 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 14 kg is attached to an ideal spring of force constant 162 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.41206 s",
"B": "0.88192 s",
"C": "0.58794 s",
"D": "-0.58794 s"
} | C | 0.58794 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(14/162)=0.58794 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.58794 s, not -0.41206 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.58794 s, not 0.88192 s.",
"C": "Correct. The worked calculation gives 0.58794 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001949 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 71 distinct elements? | {
"A": "15623890.8",
"B": "13019909",
"C": "10415927.2",
"D": "1301991.9"
} | B | 13019909 | Order does not matter, so the count is C(71,5)=71!/[5!(66)!]=13019909. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13019909, not 15623890.8.",
"B": "Correct. The worked calculation gives 13019909.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13019909, not 10415927.2.",
"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_001081 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ -6x² -8x+7. Evaluate f′(2). | {
"A": "26",
"B": "56",
"C": "28",
"D": "14"
} | C | 28 | Differentiate: f′(x)=3(5)x²+2(-6)x+(-8). At x=2, f′(2)=3(5)(2)²+2(-6)(2)+(-8)=28. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28, not 26.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28, not 56.",
"C": "Correct. The worked calculation gives 28.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008980 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.94 mol L⁻¹ and initially B is absent. At equilibrium, 62% of A has dissociated at constant volume. Find K_c. | {
"A": "7.84985",
"B": "6.84985",
"C": "-7.84985",
"D": "15.69971"
} | A | 7.84985 | Let α=0.62. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.94)(0.62)²/(1−0.62)=7.84985. | {
"A": "Correct. The worked calculation gives 7.84985.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.84985, not 6.84985.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.84985, not -7.84985.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001203 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-2x³ +9x² +2x+7. Evaluate f′(3). | {
"A": "4",
"B": "1.2",
"C": "2",
"D": "1"
} | C | 2 | Differentiate: f′(x)=3(-2)x²+2(9)x+(2). At x=3, f′(3)=3(-2)(3)²+2(9)(3)+(2)=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.2.",
"C": "Correct. The worked calculation gives 2.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_004484 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 11 kg and radius 3 m is acted on by a constant torque of 41 N m about its central axis. Find its angular acceleration. | {
"A": "0.62121 rad s⁻²",
"B": "3.82828 rad s⁻²",
"C": "1.65657 rad s⁻²",
"D": "0.82828 rad s⁻²"
} | D | 0.82828 rad s⁻² | For a solid disc, I=½MR²=½(11)(3)²=49.5 kg m². Using τ=Iα, α=41/49.5=0.82828 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.82828 rad s⁻², not 0.62121 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.82828 rad s⁻², not 3.82828 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing r... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003821 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 7 m s⁻¹. A constant net force does 10 N of work over 5 m in the direction of motion. Find its final kinetic energy. | {
"A": "354 J",
"B": "296 J",
"C": "295 J",
"D": "236 J"
} | C | 295 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(7)²+(10)(5)=295 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 295 J, not 354 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 295 J, not 296 J.",
"C": "Correct. The worked calculation gives 295 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_000514 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -1 and common difference 9. Find the sum of its first 33 terms. | {
"A": "4721",
"B": "2359.5",
"C": "4718",
"D": "4719"
} | D | 4719 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-1, d=9, n=33: Sₙ=33/2[2(-1)+(33−1)(9)]=4719. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4719, not 4721.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4719, not 2359.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4719, not 4718.",
"D": "Co... | [
"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_004036 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 35 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.29. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "126.8 N",
"B": "128.8 N",
"C": "64.4 N",
"D": "13.88 N"
} | B | 128.8 N | Net force=mg(sinθ−μcosθ)=35×10×(0.6−0.29×0.8)=128.8 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 128.8 N, not 126.8 N.",
"B": "Correct. The worked calculation gives 128.8 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 128.8 N, not 64.4 N.",
"D": "Incorrect. Substituting the stated val... | [
"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_002447 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, 3], [8, 7]]. | {
"A": "39",
"B": "19.5",
"C": "78",
"D": "40"
} | A | 39 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(7)−(3)(8)=39. | {
"A": "Correct. The worked calculation gives 39.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39, not 19.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39, not 78.",
"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_006178 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 29 cm in front of a thin convex lens of focal length 10 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.26316",
"B": "0.52632",
"C": "-2.47368",
"D": "2.52632"
} | B | 0.52632 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(29)(10)/(29−10)=15.26316 cm. Thus |m|=v/u=15.26316/29=0.52632. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.52632, not 0.26316.",
"B": "Correct. The worked calculation gives 0.52632.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.52632, not -2.47368.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009369 | 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_18H_30N_2X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "6",
"B": "5",
"C": "1.5",
"D": "3"
} | D | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+2−30−4)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.5.",
"D": "Correct. The worked ... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007020 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 4 mol of gas at 317 K and 2.87 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "36.25375 L",
"B": "37.25375 L",
"C": "43.50451 L",
"D": "-36.25375 L"
} | A | 36.25375 L | PV=nRT, so V=nRT/P=(4)(0.082057)(317)/(2.87)=36.25375 L. | {
"A": "Correct. The worked calculation gives 36.25375 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 36.25375 L, not 37.25375 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 36.25375 L, not 43.50451 L.",
"D": "Incorrect. Substitutin... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001934 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 3 elements can be selected from a set of 73 distinct elements? | {
"A": "46647",
"B": "62196",
"C": "62198",
"D": "93294"
} | B | 62196 | Order does not matter, so the count is C(73,3)=73!/[3!(70)!]=62196. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 62196, not 46647.",
"B": "Correct. The worked calculation gives 62196.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 62196, not 62198.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_000680 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio 3. What is the sum of its first 12 terms? | {
"A": "1062880",
"B": "1275456",
"C": "1062879",
"D": "2125760"
} | A | 1062880 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(3^12−1)/(3−1)=1062880. | {
"A": "Correct. The worked calculation gives 1062880.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1062880, not 1275456.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1062880, not 1062879.",
"D": "Incorrect. Substituting the stated va... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001074 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-3x³ +6x² +7x+7. Evaluate f′(-2). | {
"A": "53",
"B": "-53",
"C": "-4.3",
"D": "-52"
} | B | -53 | Differentiate: f′(x)=3(-3)x²+2(6)x+(7). At x=-2, f′(-2)=3(-3)(-2)²+2(6)(-2)+(7)=-53. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -53, not 53.",
"B": "Correct. The worked calculation gives -53.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -53, not -4.3.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004946 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 2 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 11 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.31818 A",
"B": "1.15909 A",
"C": "-0.68182 A",
"D": "3.31818 A"
} | A | 2.31818 A | Series branch resistance=2+4=6 Ω. Parallel equivalent R_eq=(6×11)/(6+11)=3.88235 Ω. Total current I=V/R_eq=9/3.88235=2.31818 A. | {
"A": "Correct. The worked calculation gives 2.31818 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.31818 A, not 1.15909 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.31818 A, not -0.68182 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_005273 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +2 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "17.0625 N",
"B": "14.0625 N",
"C": "11.0625 N",
"D": "7.03125 N"
} | B | 14.0625 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(2×10⁻⁶)/(8×10⁻²)²=14.0625 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14.0625 N, not 17.0625 N.",
"B": "Correct. The worked calculation gives 14.0625 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14.0625 N, not 11.0625 N.",
"D": "Incorrect. Substituting the... | [
"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_000244 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 -3x -11=0, let its roots be α and β. What is α²+β²? | {
"A": "4.91667",
"B": "5.91667",
"C": "3.91667",
"D": "1.91667"
} | C | 3.91667 | By Vieta's relations, α+β = 3/6 and αβ = -11/6. Then α²+β²=(α+β)²−2αβ = (3/6)²−2(-11/6) = 3.91667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.91667, not 4.91667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.91667, not 5.91667.",
"C": "Correct. The worked calculation gives 3.91667.",
"D": "Incorrect. Substituting the stated va... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003020 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-12+8i)/(1+2i). What is Re(z), the real part of z? | {
"A": "2.8",
"B": "0.4",
"C": "-0.2",
"D": "0.8"
} | D | 0.8 | Multiply numerator and denominator by the conjugate (1-2i). Then Re(z)=(ac+bd)/(c²+d²)=((-12)(1)+(8)(2))/(1²+(2)²)=0.8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8, not 2.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8, not 0.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8, not -0.2.",
"D": "Correct. ... | [
"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_007329 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 4 mol of gas at 333 K and 1.51 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "72.38406 L",
"B": "144.76811 L",
"C": "73.38406 L",
"D": "71.38406 L"
} | A | 72.38406 L | PV=nRT, so V=nRT/P=(4)(0.082057)(333)/(1.51)=72.38406 L. | {
"A": "Correct. The worked calculation gives 72.38406 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 72.38406 L, not 144.76811 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 72.38406 L, not 73.38406 L.",
"D": "Incorrect. Substituti... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001176 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=1x³ +8x² +5x+7. Evaluate f′(-2). | {
"A": "-30",
"B": "-12",
"C": "-15",
"D": "-0.5"
} | C | -15 | Differentiate: f′(x)=3(1)x²+2(8)x+(5). At x=-2, f′(-2)=3(1)(-2)²+2(8)(-2)+(5)=-15. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -15, not -30.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -15, not -12.",
"C": "Correct. The worked calculation gives -15.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002476 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, -4], [7, 8]]. | {
"A": "78",
"B": "-52",
"C": "52",
"D": "41.6"
} | C | 52 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(8)−(-4)(7)=52. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 52, not 78.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 52, not -52.",
"C": "Correct. The worked calculation gives 52.",
"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_004523 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 6 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": "20.33333 rad s⁻²",
"B": "21.33333 rad s⁻²",
"C": "16 rad s⁻²",
"D": "23.33333 rad s⁻²"
} | B | 21.33333 rad s⁻² | For a solid disc, I=½MR²=½(6)(1)²=3 kg m². Using τ=Iα, α=64/3=21.33333 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21.33333 rad s⁻², not 20.33333 rad s⁻².",
"B": "Correct. The worked calculation gives 21.33333 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21.33333 rad s⁻², not 16 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_000741 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 2. What is the sum of its first 9 terms? | {
"A": "5111",
"B": "5110",
"C": "2555",
"D": "5112"
} | B | 5110 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(2^9−1)/(2−1)=5110. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5110, not 5111.",
"B": "Correct. The worked calculation gives 5110.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5110, not 2555.",
"D": "Incorrect. Substituting the stated values into the g... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000329 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 -1x +3=0, let its roots be α and β. What is α²+β²? | {
"A": "-8",
"B": "-10",
"C": "-2",
"D": "-5"
} | D | -5 | By Vieta's relations, α+β = 1/1 and αβ = 3/1. Then α²+β²=(α+β)²−2αβ = (1/1)²−2(3/1) = -5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -5, not -8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -5, not -10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -5, not -2.",
"D": "Correct. The wo... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005720 | 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 2.6 atm at 320 K. What is its pressure at 665 K? | {
"A": "-5.40313 atm",
"B": "8.40312 atm",
"C": "5.40313 atm",
"D": "2.40313 atm"
} | C | 5.40313 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.6)(665)/(320)=5.40313 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.40313 atm, not -5.40313 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.40313 atm, not 8.40312 atm.",
"C": "Correct. The worked calculation gives 5.40313 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003449 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 114 m s⁻¹ at 50° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1280.85616 m",
"B": "1281.85616 m",
"C": "1277.85616 m",
"D": "1279.85616 m"
} | D | 1279.85616 m | Range R=u²sin(2θ)/g. Substituting u=114, θ=50° and g=10 gives R=(114)²sin(100°)/10=1279.85616 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1279.85616 m, not 1280.85616 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1279.85616 m, not 1281.85616 m.",
"C": "Incorrect. Substituting the stated values into the governing relation give... | [
"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_003292 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(4+9i)/(2+1i). What is Re(z), the real part of z? | {
"A": "5.4",
"B": "3.4",
"C": "1.34",
"D": "1.4"
} | B | 3.4 | Multiply numerator and denominator by the conjugate (2-1i). Then Re(z)=(ac+bd)/(c²+d²)=((4)(2)+(9)(1))/(2²+(1)²)=3.4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.4, not 5.4.",
"B": "Correct. The worked calculation gives 3.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.4, not 1.34.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_004092 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 38 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.42. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "150.48 N",
"B": "200.64 N",
"C": "100.32 N",
"D": "120.384 N"
} | C | 100.32 N | Net force=mg(sinθ−μcosθ)=38×10×(0.6−0.42×0.8)=100.32 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 100.32 N, not 150.48 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 100.32 N, not 200.64 N.",
"C": "Correct. The worked calculation gives 100.32 N.",
"D": "Incorrect. Substituting the stat... | [
"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_003748 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block initially moves at 10 m s⁻¹. A constant net force does 5 N of work over 15 m in the direction of motion. Find its final kinetic energy. | {
"A": "930 J",
"B": "776 J",
"C": "1550 J",
"D": "775 J"
} | D | 775 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(14)(10)²+(5)(15)=775 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 775 J, not 930 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 775 J, not 776 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 775 J, not 1550 J.",
"D"... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009546 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_14H_21N_1X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "2",
"B": "0",
"C": "3",
"D": "4"
} | C | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×14+2+1−21−4)/2=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 0.",
"C": "Correct. The worked calculation gives 3.",
"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_009660 | 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_5H_9X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "-2",
"B": "0",
"C": "3",
"D": "1"
} | B | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×5+2+0−9−3)/2=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"B": "Correct. The worked calculation gives 0.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 3.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006014 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 35 cm in front of a thin convex lens of focal length 20 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1",
"B": "0.33333",
"C": "-0.66667",
"D": "1.33333"
} | D | 1.33333 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(35)(20)/(35−20)=46.66667 cm. Thus |m|=v/u=46.66667/35=1.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.33333, not 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.33333, not 0.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.33333, not -0.66667.",... | [
"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_002956 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(2, 7, -6) and v=(-5, -6, -7), calculate u·v. | {
"A": "-15",
"B": "-10",
"C": "-11",
"D": "-7"
} | B | -10 | The dot product is the sum of corresponding component products: (2)(-5)+(7)(-6)+(-6)(-7)=-10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -10, not -15.",
"B": "Correct. The worked calculation gives -10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -10, not -11.",
"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_008198 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 5 A for 17152 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": "28.21637 g",
"B": "56.43275 g",
"C": "27.21637 g",
"D": "21.16228 g"
} | A | 28.21637 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×5×17152/(2×96500)=28.21637 g. | {
"A": "Correct. The worked calculation gives 28.21637 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28.21637 g, not 56.43275 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28.21637 g, not 27.21637 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002369 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, -6], [3, 7]]. | {
"A": "32",
"B": "64",
"C": "4.2",
"D": "25.6"
} | A | 32 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(7)−(-6)(3)=32. | {
"A": "Correct. The worked calculation gives 32.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 32, not 64.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 32, not 4.2.",
"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_007788 | 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 51 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "3.39844 mmol L⁻¹",
"B": "0.39844 mmol L⁻¹",
"C": "-2.60156 mmol L⁻¹",
"D": "1.03984 mmol L⁻¹"
} | B | 0.39844 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=51/2^7=0.39844 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.39844 mmol L⁻¹, not 3.39844 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.39844 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.39844 mmol L⁻¹, not -2.60156 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_004711 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 11 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 3 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "14.4 A",
"B": "4.8 A",
"C": "9.6 A",
"D": "11.6 A"
} | C | 9.6 A | Series branch resistance=11+4=15 Ω. Parallel equivalent R_eq=(15×3)/(15+3)=2.5 Ω. Total current I=V/R_eq=24/2.5=9.6 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.6 A, not 14.4 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.6 A, not 4.8 A.",
"C": "Correct. The worked calculation gives 9.6 A.",
"D": "Incorrect. Substituting the stated values into... | [
"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_007003 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 8 mol H₂ and 16 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "6 mol",
"B": "8 mol",
"C": "7 mol",
"D": "12 mol"
} | B | 8 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 8 mol H₂O; O₂ can produce 32 mol H₂O. The limiting condition is H₂; product=8 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8 mol, not 6 mol.",
"B": "Correct. The worked calculation gives 8 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8 mol, not 7 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_001132 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=1x³ +5x² -5x+7. Evaluate f′(-4). | {
"A": "1.5",
"B": "1.3",
"C": "3",
"D": "2.25"
} | C | 3 | Differentiate: f′(x)=3(1)x²+2(5)x+(-5). At x=-4, f′(-4)=3(1)(-4)²+2(5)(-4)+(-5)=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"C": "Correct. The worked calculation gives 3.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_001796 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 3 elements can be selected from a set of 40 distinct elements? | {
"A": "9879",
"B": "7904",
"C": "19760",
"D": "9880"
} | D | 9880 | Order does not matter, so the count is C(40,3)=40!/[3!(37)!]=9880. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9880, not 9879.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9880, not 7904.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9880, not 19760.",
"D": "Cor... | [
"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_007210 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 12 mol of gas at 261 K and 1.26 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "203.97026 L",
"B": "163.17621 L",
"C": "244.76431 L",
"D": "202.97026 L"
} | A | 203.97026 L | PV=nRT, so V=nRT/P=(12)(0.082057)(261)/(1.26)=203.97026 L. | {
"A": "Correct. The worked calculation gives 203.97026 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 203.97026 L, not 163.17621 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 203.97026 L, not 244.76431 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_003849 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 6 m s⁻¹. A constant net force does 16 N of work over 15 m in the direction of motion. Find its final kinetic energy. | {
"A": "366 J",
"B": "549 J",
"C": "274.5 J",
"D": "732 J"
} | A | 366 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(6)²+(16)(15)=366 J. | {
"A": "Correct. The worked calculation gives 366 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 366 J, not 549 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 366 J, not 274.5 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_003274 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-14+10i)/(5+11i). What is Re(z), the real part of z? | {
"A": "0.13699",
"B": "1.0274",
"C": "3.27397",
"D": "0.27397"
} | D | 0.27397 | Multiply numerator and denominator by the conjugate (5-11i). Then Re(z)=(ac+bd)/(c²+d²)=((-14)(5)+(10)(11))/(5²+(11)²)=0.27397. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.27397, not 0.13699.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.27397, not 1.0274.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.27397, not 3.2739... | [
"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_005209 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +8 μC and +1 μC are separated by 12 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "5 N",
"B": "7.5 N",
"C": "2 N",
"D": "3 N"
} | A | 5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(8×10⁻⁶)(1×10⁻⁶)/(12×10⁻²)²=5 N. | {
"A": "Correct. The worked calculation gives 5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5 N, not 7.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5 N, not 2 N.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_009567 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_6H_1X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "2.5",
"B": "7",
"C": "5",
"D": "2"
} | C | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+0−1−3)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.",
"C": "Correct. The worked calculation gives 5.",
"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_007380 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 22 mL of 0.10 M HCl is mixed with 65 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "9.52046",
"B": "6.34697",
"C": "12.69395",
"D": "13.69395"
} | C | 12.69395 | Excess OH⁻ moles=0.10×(65−22)/1000=0.004300 mol. Total volume=0.087 L, so [OH⁻]=0.049425 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.69395. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.69395, not 9.52046.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.69395, not 6.34697.",
"C": "Correct. The worked calculation gives 12.69395.",
"D": "Incorrect. Substituting the stated... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001647 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (-3x² -2x +4) dx. | {
"A": "130",
"B": "-12",
"C": "-128",
"D": "-130"
} | D | -130 | An antiderivative is (-3/3)x³+(-2/2)x²+(4)x. Evaluating between 0 and 5 gives (-3/3)(5)³+(-2/2)(5)²+(4)(5)=-130. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -130, not 130.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -130, not -12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -130, not -128.",
"D": "Correc... | [
"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_004727 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 15 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 14 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.63547 A",
"B": "1.06355 A",
"C": "-1.36453 A",
"D": "2.63547 A"
} | A | 0.63547 A | Series branch resistance=15+14=29 Ω. Parallel equivalent R_eq=(29×14)/(29+14)=9.44186 Ω. Total current I=V/R_eq=6/9.44186=0.63547 A. | {
"A": "Correct. The worked calculation gives 0.63547 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.63547 A, not 1.06355 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.63547 A, not -1.36453 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_006535 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 4 kg is attached to an ideal spring of force constant 252 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.37796 s",
"B": "0.18898 s",
"C": "3.25198 s",
"D": "0.25198 s"
} | D | 0.25198 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(4/252)=0.25198 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25198 s, not 0.37796 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25198 s, not 0.18898 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25198 s,... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008637 | 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 0.3 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.03 K",
"B": "0.3 K",
"C": "1.3 K",
"D": "0.45 K"
} | B | 0.3 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×1.0×0.3=0.3 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3 K, not 1.03 K.",
"B": "Correct. The worked calculation gives 0.3 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3 K, not 1.3 K.",
"D": "Incorrect. Substituting the stated values into... | [
"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_003473 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 108 m s⁻¹ at 30° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1010.13203 m",
"B": "1012.13203 m",
"C": "1515.19805 m",
"D": "808.10562 m"
} | A | 1010.13203 m | Range R=u²sin(2θ)/g. Substituting u=108, θ=30° and g=10 gives R=(108)²sin(60°)/10=1010.13203 m. | {
"A": "Correct. The worked calculation gives 1010.13203 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1010.13203 m, not 1012.13203 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1010.13203 m, not 1515.19805 m.",
"D": "Incorrect. S... | [
"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_004960 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 14 Ω and 9 Ω are connected in series; this combination is connected in parallel with a 9 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.92754 A",
"B": "-1.07246 A",
"C": "-0.92754 A",
"D": "0.92754 A"
} | D | 0.92754 A | Series branch resistance=14+9=23 Ω. Parallel equivalent R_eq=(23×9)/(23+9)=6.46875 Ω. Total current I=V/R_eq=6/6.46875=0.92754 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.92754 A, not 1.92754 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.92754 A, not -1.07246 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.92754 A... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005318 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +3 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "67.5 N",
"B": "101.25 N",
"C": "65.5 N",
"D": "66.5 N"
} | A | 67.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(3×10⁻⁶)/(4×10⁻²)²=67.5 N. | {
"A": "Correct. The worked calculation gives 67.5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 67.5 N, not 101.25 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 67.5 N, not 65.5 N.",
"D": "Incorrect. Substituting the stated value... | [
"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_003965 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 9 m s⁻¹. A constant net force does 15 N of work over 3 m in the direction of motion. Find its final kinetic energy. | {
"A": "450 J",
"B": "-450 J",
"C": "225 J",
"D": "360 J"
} | A | 450 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(9)²+(15)(3)=450 J. | {
"A": "Correct. The worked calculation gives 450 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 450 J, not -450 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 450 J, not 225 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_005197 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +1 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "7.77778 N",
"B": "9.77778 N",
"C": "5.77778 N",
"D": "5.83333 N"
} | A | 7.77778 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(1×10⁻⁶)/(9×10⁻²)²=7.77778 N. | {
"A": "Correct. The worked calculation gives 7.77778 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.77778 N, not 9.77778 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.77778 N, not 5.77778 N.",
"D": "Incorrect. Substituting the... | [
"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 |
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