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_002381 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, 3], [9, 0]]. | {
"A": "-25",
"B": "-27",
"C": "-1.7",
"D": "-32.4"
} | B | -27 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(0)−(3)(9)=-27. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -27, not -25.",
"B": "Correct. The worked calculation gives -27.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -27, not -1.7.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_002799 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(7, 7, 9) and v=(0, -2, 8), calculate u·v. | {
"A": "57",
"B": "116",
"C": "58",
"D": "43.5"
} | C | 58 | The dot product is the sum of corresponding component products: (7)(0)+(7)(-2)+(9)(8)=58. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 58, not 57.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 58, not 116.",
"C": "Correct. The worked calculation gives 58.",
"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_003696 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block initially moves at 7 m s⁻¹. A constant net force does 29 N of work over 5 m in the direction of motion. Find its final kinetic energy. | {
"A": "512.5 J",
"B": "768.75 J",
"C": "1025 J",
"D": "52.25 J"
} | A | 512.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(15)(7)²+(29)(5)=512.5 J. | {
"A": "Correct. The worked calculation gives 512.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 512.5 J, not 768.75 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 512.5 J, not 1025 J.",
"D": "Incorrect. Substituting the stated va... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009794 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(Cl)_6]^-4, each Cl ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "-2",
"B": "-1",
"C": "2",
"D": "3"
} | C | 2 | Let the formal oxidation state of Co be x. Charge balance gives x+(6)(−1)=-4; hence x=-4+6=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not -1.",
"C": "Correct. The worked calculation gives 2.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000781 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio -3. What is the sum of its first 11 terms? | {
"A": "354296",
"B": "265722",
"C": "354297",
"D": "531444"
} | A | 354296 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(-3^11−1)/(-3−1)=354296. | {
"A": "Correct. The worked calculation gives 354296.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 354296, not 265722.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 354296, not 354297.",
"D": "Incorrect. Substituting the stated values ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005191 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +8 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "88.16327 N",
"B": "86.16327 N",
"C": "87.16327 N",
"D": "132.2449 N"
} | A | 88.16327 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(8×10⁻⁶)/(7×10⁻²)²=88.16327 N. | {
"A": "Correct. The worked calculation gives 88.16327 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 88.16327 N, not 86.16327 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 88.16327 N, not 87.16327 N.",
"D": "Incorrect. Substitutin... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009814 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(CN)_2]^+3, each CN ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "5",
"B": "8",
"C": "7",
"D": "3.75"
} | A | 5 | Let the formal oxidation state of Cr be x. Charge balance gives x+(2)(−1)=+3; hence x=3+2=+5. | {
"A": "Correct. The worked calculation gives 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000725 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio -3. What is the sum of its first 7 terms? | {
"A": "5743.5",
"B": "1914.5",
"C": "3829",
"D": "3827"
} | C | 3829 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(-3^7−1)/(-3−1)=3829. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3829, not 5743.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3829, not 1914.5.",
"C": "Correct. The worked calculation gives 3829.",
"D": "Incorrect. Substituting the stated values into t... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009276 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.02 V, transfers 1 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.0791 V",
"B": "0.53955 V",
"C": "3.0791 V",
"D": "1.0791 V"
} | D | 1.0791 V | Apply the Nernst equation: E=1.02−(0.0591/1)(-1)=1.0791 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0791 V, not 2.0791 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0791 V, not 0.53955 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0791 V, not... | [
"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_001483 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (-2x² -2x +5) dx. | {
"A": "1.66667",
"B": "2.5",
"C": "3.33333",
"D": "5"
} | C | 3.33333 | An antiderivative is (-2/3)x³+(-2/2)x²+(5)x. Evaluating between 0 and 1 gives (-2/3)(1)³+(-2/2)(1)²+(5)(1)=3.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.33333, not 1.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.33333, not 2.5.",
"C": "Correct. The worked calculation gives 3.33333.",
"D": "Incorrect. Substituting the stated values... | [
"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_000224 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +16x +2=0, let its roots be α and β. What is α²+β²? | {
"A": "4.72",
"B": "6.44",
"C": "9.44",
"D": "12.44"
} | C | 9.44 | By Vieta's relations, α+β = -16/5 and αβ = 2/5. Then α²+β²=(α+β)²−2αβ = (-16/5)²−2(2/5) = 9.44. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.44, not 4.72.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.44, not 6.44.",
"C": "Correct. The worked calculation gives 9.44.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_007835 | 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 75 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "7.375 mmol L⁻¹",
"B": "11.375 mmol L⁻¹",
"C": "9.375 mmol L⁻¹",
"D": "8.375 mmol L⁻¹"
} | C | 9.375 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=75/2^3=9.375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.375 mmol L⁻¹, not 7.375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.375 mmol L⁻¹, not 11.375 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 9.375 mmol L⁻¹.",
"D": "I... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009759 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(CN)_6]^-1, each CN ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "7",
"B": "5",
"C": "7.5",
"D": "4"
} | B | 5 | Let the formal oxidation state of Pt be x. Charge balance gives x+(6)(−1)=-1; hence x=-1+6=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.",
"B": "Correct. The worked calculation gives 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.5.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003937 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block initially moves at 4 m s⁻¹. A constant net force does 12 N of work over 15 m in the direction of motion. Find its final kinetic energy. | {
"A": "30.2 J",
"B": "292 J",
"C": "291 J",
"D": "290 J"
} | B | 292 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(14)(4)²+(12)(15)=292 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 292 J, not 30.2 J.",
"B": "Correct. The worked calculation gives 292 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 292 J, not 291 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_004316 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 25 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.28. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "10.4 N",
"B": "93 N",
"C": "141 N",
"D": "94 N"
} | D | 94 N | Net force=mg(sinθ−μcosθ)=25×10×(0.6−0.28×0.8)=94 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 94 N, not 10.4 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 94 N, not 93 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 94 N, not 141 N.",
"D": "C... | [
"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_006457 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 6 kg is attached to an ideal spring of force constant 613 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.19787 s",
"B": "3.19787 s",
"C": "1.19787 s",
"D": "0.2968 s"
} | A | 0.19787 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(6/613)=0.19787 s. | {
"A": "Correct. The worked calculation gives 0.19787 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.19787 s, not 3.19787 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.19787 s, not 1.19787 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_000665 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -11 and common difference 5. Find the sum of its first 15 terms. | {
"A": "360",
"B": "288",
"C": "-360",
"D": "270"
} | A | 360 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-11, d=5, n=15: Sₙ=15/2[2(-11)+(15−1)(5)]=360. | {
"A": "Correct. The worked calculation gives 360.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 360, not 288.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 360, not -360.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_000108 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +6x -6=0, let its roots be α and β. What is α²+β²? | {
"A": "1.84",
"B": "0.84",
"C": "3.84",
"D": "1.384"
} | C | 3.84 | By Vieta's relations, α+β = -6/5 and αβ = -6/5. Then α²+β²=(α+β)²−2αβ = (-6/5)²−2(-6/5) = 3.84. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.84, not 1.84.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.84, not 0.84.",
"C": "Correct. The worked calculation gives 3.84.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_006795 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 3 mol H₂ and 6 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "0 mol",
"B": "3 mol",
"C": "4.5 mol",
"D": "1 mol"
} | B | 3 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 3 mol H₂O; O₂ can produce 12 mol H₂O. The limiting condition is H₂; product=3 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3 mol, not 0 mol.",
"B": "Correct. The worked calculation gives 3 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3 mol, not 4.5 mol.",
"D": "Incorrect. Substituting the stated values int... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005528 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 8 μF capacitor is charged to a potential difference of 18 V. Calculate the energy stored, expressed in μJ. | {
"A": "1555.2 μJ",
"B": "1296 μJ",
"C": "1036.8 μJ",
"D": "130.6 μJ"
} | B | 1296 μJ | U=½CV². Since C=8 μF, U in μJ is ½×8×(18)²=1296 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1296 μJ, not 1555.2 μJ.",
"B": "Correct. The worked calculation gives 1296 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1296 μJ, not 1036.8 μJ.",
"D": "Incorrect. Substituting the state... | [
"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_001711 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 4 elements can be selected from a set of 10 distinct elements? | {
"A": "210",
"B": "-210",
"C": "22",
"D": "315"
} | A | 210 | Order does not matter, so the count is C(10,4)=10!/[4!(6)!]=210. | {
"A": "Correct. The worked calculation gives 210.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 210, not -210.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 210, not 22.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_001774 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 63 distinct elements? | {
"A": "3872894696",
"B": "3872894697",
"C": "4647473636.4",
"D": "1936447348.5"
} | B | 3872894697 | Order does not matter, so the count is C(63,8)=63!/[8!(55)!]=3872894697. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3872894697, not 3872894696.",
"B": "Correct. The worked calculation gives 3872894697.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3872894697, not 4647473636.4.",
"D": "Incorrect. Substitut... | [
"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_009492 | 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_6. Treat X as the total number of monovalent halogen atoms. | {
"A": "-3",
"B": "3",
"C": "2",
"D": "5"
} | B | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×5+2+0−6−0)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not -3.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.",
"D": "Incorrect. Substituting the stated values into the governing 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_000989 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio 5. What is the sum of its first 5 terms? | {
"A": "5467",
"B": "5468",
"C": "547.7",
"D": "4373.6"
} | A | 5467 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(5^5−1)/(5−1)=5467. | {
"A": "Correct. The worked calculation gives 5467.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5467, not 5468.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5467, not 547.7.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_009968 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(OH)_6]^+0, each OH ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "3",
"B": "6",
"C": "1.6",
"D": "7"
} | B | 6 | Let the formal oxidation state of Co be x. Charge balance gives x+(6)(−1)=+0; hence x=0+6=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"B": "Correct. The worked calculation gives 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 1.6.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008563 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.07 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "2.2256 K",
"B": "5.2256 K",
"C": "1.2256 K",
"D": "3.2256 K"
} | A | 2.2256 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.52×1.07=2.2256 K. | {
"A": "Correct. The worked calculation gives 2.2256 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.2256 K, not 5.2256 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.2256 K, not 1.2256 K.",
"D": "Incorrect. Substituting the stat... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004495 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 4 m is acted on by a constant torque of 31 N m about its central axis. Find its angular acceleration. | {
"A": "-0.225 rad s⁻²",
"B": "-1.225 rad s⁻²",
"C": "0.775 rad s⁻²",
"D": "1.775 rad s⁻²"
} | C | 0.775 rad s⁻² | For a solid disc, I=½MR²=½(5)(4)²=40 kg m². Using τ=Iα, α=31/40=0.775 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.775 rad s⁻², not -0.225 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.775 rad s⁻², not -1.225 rad s⁻².",
"C": "Correct. The worked calculation gives 0.775 rad s⁻².",
"D": "Incor... | [
"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_009207 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.41 V, transfers 1 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "4.5873 V",
"B": "3.1746 V",
"C": "1.19047 V",
"D": "1.5873 V"
} | D | 1.5873 V | Apply the Nernst equation: E=1.41−(0.0591/1)(-3)=1.5873 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.5873 V, not 4.5873 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.5873 V, not 3.1746 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.5873 V, not ... | [
"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_000832 | 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 11 terms? | {
"A": "177148",
"B": "354296",
"C": "141718.4",
"D": "-177148"
} | A | 177148 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(-3^11−1)/(-3−1)=177148. | {
"A": "Correct. The worked calculation gives 177148.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 177148, not 354296.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 177148, not 141718.4.",
"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_004011 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 18 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.23. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "75.88 N",
"B": "74.88 N",
"C": "-74.88 N",
"D": "149.76 N"
} | B | 74.88 N | Net force=mg(sinθ−μcosθ)=18×10×(0.6−0.23×0.8)=74.88 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 74.88 N, not 75.88 N.",
"B": "Correct. The worked calculation gives 74.88 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 74.88 N, not -74.88 N.",
"D": "Incorrect. Substituting the stated v... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001798 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 12 elements can be selected from a set of 55 distinct elements? | {
"A": "438729741450",
"B": "877459482900",
"C": "43872974146",
"D": "438729741448"
} | A | 438729741450 | Order does not matter, so the count is C(55,12)=55!/[12!(43)!]=438729741450. | {
"A": "Correct. The worked calculation gives 438729741450.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 438729741450, not 877459482900.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 438729741450, not 43872974146.",
"D": "Incorrect. Su... | [
"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_009264 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.65 V, transfers 2 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-2.5273 V",
"B": "1.04727 V",
"C": "0.4727 V",
"D": "3.4727 V"
} | C | 0.4727 V | Apply the Nernst equation: E=0.65−(0.0591/2)(6)=0.4727 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.4727 V, not -2.5273 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.4727 V, not 1.04727 V.",
"C": "Correct. The worked calculation gives 0.4727 V.",
"D": "Incorrect. Substituting the st... | [
"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_005094 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +8 μC and +8 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "10 N",
"B": "135 N",
"C": "90 N",
"D": "45 N"
} | C | 90 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(8×10⁻⁶)(8×10⁻⁶)/(8×10⁻²)²=90 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 90 N, not 10 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 90 N, not 135 N.",
"C": "Correct. The worked calculation gives 90 N.",
"D": "Incorrect. Substituting the stated values into 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_004085 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 44 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.15. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "213.2 N",
"B": "210.2 N",
"C": "211.2 N",
"D": "316.8 N"
} | C | 211.2 N | Net force=mg(sinθ−μcosθ)=44×10×(0.6−0.15×0.8)=211.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 211.2 N, not 213.2 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 211.2 N, not 210.2 N.",
"C": "Correct. The worked calculation gives 211.2 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002135 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 11 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.35145",
"B": "-0.64855",
"C": "3.35145",
"D": "-0.35145"
} | A | 0.35145 | Favourable pairs = C(9,2)+C(11,2)+C(4,2)=97. Total pairs=C(24,2)=276. Therefore P=97/276=0.35145. | {
"A": "Correct. The worked calculation gives 0.35145.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35145, not -0.64855.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35145, not 3.35145.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003643 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 91 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "64.43614 m",
"B": "634.3614 m",
"C": "951.54211 m",
"D": "633.3614 m"
} | B | 634.3614 m | Range R=u²sin(2θ)/g. Substituting u=91, θ=25° and g=10 gives R=(91)²sin(50°)/10=634.3614 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 634.3614 m, not 64.43614 m.",
"B": "Correct. The worked calculation gives 634.3614 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 634.3614 m, not 951.54211 m.",
"D": "Incorrect. Substituti... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006850 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 39 mol H₂ and 30 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "31.2 mol",
"B": "39 mol",
"C": "-39 mol",
"D": "58.5 mol"
} | B | 39 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 39 mol H₂O; O₂ can produce 60 mol H₂O. The limiting condition is H₂; product=39 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 39 mol, not 31.2 mol.",
"B": "Correct. The worked calculation gives 39 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39 mol, not -39 mol.",
"D": "Incorrect. Substituting the stated valu... | [
"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_001134 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ +7x² -3x+7. Evaluate f′(-1). | {
"A": "-33",
"B": "-30",
"C": "-32",
"D": "-16"
} | C | -32 | Differentiate: f′(x)=3(-5)x²+2(7)x+(-3). At x=-1, f′(-1)=3(-5)(-1)²+2(7)(-1)+(-3)=-32. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -32, not -33.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -32, not -30.",
"C": "Correct. The worked calculation gives -32.",
"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_006882 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 5 mol H₂ and 21 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "7.5 mol",
"B": "1.5 mol",
"C": "5 mol",
"D": "3 mol"
} | C | 5 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 5 mol H₂O; O₂ can produce 42 mol H₂O. The limiting condition is H₂; product=5 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5 mol, not 7.5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5 mol, not 1.5 mol.",
"C": "Correct. The worked calculation gives 5 mol.",
"D": "Incorrect. Substituting the stated values i... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001518 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (1x² +8x +5) dx. | {
"A": "57.33333",
"B": "28.66667",
"C": "3.86667",
"D": "27.66667"
} | B | 28.66667 | An antiderivative is (1/3)x³+(8/2)x²+(5)x. Evaluating between 0 and 2 gives (1/3)(2)³+(8/2)(2)²+(5)(2)=28.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28.66667, not 57.33333.",
"B": "Correct. The worked calculation gives 28.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28.66667, not 3.86667.",
"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_005701 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.7 atm at 371 K. What is its pressure at 730 K? | {
"A": "5.28032 atm",
"B": "7.28032 atm",
"C": "14.56065 atm",
"D": "3.64016 atm"
} | B | 7.28032 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.7)(730)/(371)=7.28032 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.28032 atm, not 5.28032 atm.",
"B": "Correct. The worked calculation gives 7.28032 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.28032 atm, not 14.56065 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_003520 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 70 m s⁻¹ at 18° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "288.01477 m",
"B": "290.01477 m",
"C": "576.02955 m",
"D": "289.01477 m"
} | A | 288.01477 m | Range R=u²sin(2θ)/g. Substituting u=70, θ=18° and g=10 gives R=(70)²sin(36°)/10=288.01477 m. | {
"A": "Correct. The worked calculation gives 288.01477 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 288.01477 m, not 290.01477 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 288.01477 m, not 576.02955 m.",
"D": "Incorrect. Substi... | [
"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_007529 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 44 mL of 0.10 M HCl is mixed with 13 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.26451",
"B": "-0.73549",
"C": "3.26451",
"D": "0.94838"
} | A | 1.26451 | Excess H⁺ moles=0.10×(44−13)/1000=0.003100 mol. Total volume=0.057 L, so [H⁺]=0.054386 M and pH=−log₁₀[H⁺]=1.26451. | {
"A": "Correct. The worked calculation gives 1.26451.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.26451, not -0.73549.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.26451, not 3.26451.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003561 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 107 m s⁻¹ at 30° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "793.20999 m",
"B": "100.15125 m",
"C": "-991.51248 m",
"D": "991.51248 m"
} | D | 991.51248 m | Range R=u²sin(2θ)/g. Substituting u=107, θ=30° and g=10 gives R=(107)²sin(60°)/10=991.51248 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 991.51248 m, not 793.20999 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 991.51248 m, not 100.15125 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 99... | [
"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_000274 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +0x -4=0, let its roots be α and β. What is α²+β²? | {
"A": "1.6",
"B": "3.6",
"C": "4.6",
"D": "2.4"
} | A | 1.6 | By Vieta's relations, α+β = 0/5 and αβ = -4/5. Then α²+β²=(α+β)²−2αβ = (0/5)²−2(-4/5) = 1.6. | {
"A": "Correct. The worked calculation gives 1.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.6, not 3.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.6, not 4.6.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_001699 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 2 elements can be selected from a set of 41 distinct elements? | {
"A": "656",
"B": "820",
"C": "83",
"D": "984"
} | B | 820 | Order does not matter, so the count is C(41,2)=41!/[2!(39)!]=820. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 820, not 656.",
"B": "Correct. The worked calculation gives 820.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 820, not 83.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_008831 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.37 mol L⁻¹ and initially B is absent. At equilibrium, 21% of A has dissociated at constant volume. Find K_c. | {
"A": "0.04131",
"B": "-2.91738",
"C": "3.08262",
"D": "0.08262"
} | D | 0.08262 | Let α=0.21. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.37)(0.21)²/(1−0.21)=0.08262. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.08262, not 0.04131.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.08262, not -2.91738.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.08262, not 3.08... | [
"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_002368 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, 5], [6, 5]]. | {
"A": "15",
"B": "12",
"C": "11.25",
"D": "-15"
} | A | 15 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(5)−(5)(6)=15. | {
"A": "Correct. The worked calculation gives 15.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15, not 12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15, not 11.25.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002610 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, -3], [3, -1]]. | {
"A": "6",
"B": "8",
"C": "-8",
"D": "10"
} | B | 8 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(-1)−(-3)(3)=8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 6.",
"B": "Correct. The worked calculation gives 8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not -8.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_000373 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 5 and common difference 11. Find the sum of its first 9 terms. | {
"A": "443",
"B": "441",
"C": "330.75",
"D": "442"
} | B | 441 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=5, d=11, n=9: Sₙ=9/2[2(5)+(9−1)(11)]=441. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 441, not 443.",
"B": "Correct. The worked calculation gives 441.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 441, not 330.75.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004485 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 5 m is acted on by a constant torque of 39 N m about its central axis. Find its angular acceleration. | {
"A": "0.624 rad s⁻²",
"B": "3.624 rad s⁻²",
"C": "2.624 rad s⁻²",
"D": "1.248 rad s⁻²"
} | A | 0.624 rad s⁻² | For a solid disc, I=½MR²=½(5)(5)²=62.5 kg m². Using τ=Iα, α=39/62.5=0.624 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.624 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.624 rad s⁻², not 3.624 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.624 rad s⁻², not 2.624 rad s⁻².",
"D": "Incorre... | [
"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_000817 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 12 and common ratio 5. What is the sum of its first 12 terms? | {
"A": "732421870",
"B": "878906246.4",
"C": "585937497.6",
"D": "732421872"
} | D | 732421872 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=12(5^12−1)/(5−1)=732421872. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 732421872, not 732421870.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 732421872, not 878906246.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 73242187... | [
"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_006416 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 25 kg is attached to an ideal spring of force constant 248 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.635 s",
"B": "-1.365 s",
"C": "-0.635 s",
"D": "-2.365 s"
} | A | 0.635 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(25/248)=0.635 s. | {
"A": "Correct. The worked calculation gives 0.635 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.635 s, not -1.365 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.635 s, not -0.635 s.",
"D": "Incorrect. Substituting the stated ... | [
"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_009044 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.60 V, transfers 3 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-2.3803 V",
"B": "1.06197 V",
"C": "0.6197 V",
"D": "1.2394 V"
} | C | 0.6197 V | Apply the Nernst equation: E=0.60−(0.0591/3)(-1)=0.6197 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6197 V, not -2.3803 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6197 V, not 1.06197 V.",
"C": "Correct. The worked calculation gives 0.6197 V.",
"D": "Incorrect. Substituting the st... | [
"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_009961 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(Cl)_6]^+2, each Cl ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "8",
"B": "10",
"C": "5",
"D": "11"
} | A | 8 | Let the formal oxidation state of Pd be x. Charge balance gives x+(6)(−1)=+2; hence x=2+6=+8. | {
"A": "Correct. The worked calculation gives 8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 5.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001778 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 4 elements can be selected from a set of 50 distinct elements? | {
"A": "230300",
"B": "-230300",
"C": "230302",
"D": "230298"
} | A | 230300 | Order does not matter, so the count is C(50,4)=50!/[4!(46)!]=230300. | {
"A": "Correct. The worked calculation gives 230300.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 230300, not -230300.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 230300, not 230302.",
"D": "Incorrect. Substituting the stated values... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007412 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 48 mL of 0.10 M HCl is mixed with 78 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "9.28256",
"B": "24.7535",
"C": "12.37675",
"D": "-12.37675"
} | C | 12.37675 | Excess OH⁻ moles=0.10×(78−48)/1000=0.003000 mol. Total volume=0.126 L, so [OH⁻]=0.023810 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.37675. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.37675, not 9.28256.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.37675, not 24.7535.",
"C": "Correct. The worked calculation gives 12.37675.",
"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_009803 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(CN)_2]^-3, each CN ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "-2",
"B": "0",
"C": "-1.5",
"D": "-1"
} | D | -1 | Let the formal oxidation state of Ni be x. Charge balance gives x+(2)(−1)=-3; hence x=-3+2=-1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1, not 0.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1, not -1.5.",
"D": "Correct. The wo... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001109 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=0x³ +2x² +2x+7. Evaluate f′(2). | {
"A": "13",
"B": "12",
"C": "10",
"D": "20"
} | C | 10 | Differentiate: f′(x)=3(0)x²+2(2)x+(2). At x=2, f′(2)=3(0)(2)²+2(2)(2)+(2)=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 13.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 12.",
"C": "Correct. The worked calculation gives 10.",
"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_008051 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 3 A for 22317 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": "22.02792 g",
"B": "3.20279 g",
"C": "11.01396 g",
"D": "24.02792 g"
} | A | 22.02792 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×3×22317/(2×96500)=22.02792 g. | {
"A": "Correct. The worked calculation gives 22.02792 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22.02792 g, not 3.20279 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22.02792 g, not 11.01396 g.",
"D": "Incorrect. Substituting... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002783 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(9, 1, 4) and v=(5, 2, 8), calculate u·v. | {
"A": "79",
"B": "118.5",
"C": "80",
"D": "94.8"
} | A | 79 | The dot product is the sum of corresponding component products: (9)(5)+(1)(2)+(4)(8)=79. | {
"A": "Correct. The worked calculation gives 79.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 79, not 118.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 79, not 80.",
"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_004634 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 5 m is acted on by a constant torque of 29 N m about its central axis. Find its angular acceleration. | {
"A": "-2.66857 rad s⁻²",
"B": "0.33143 rad s⁻²",
"C": "-1.66857 rad s⁻²",
"D": "0.49714 rad s⁻²"
} | B | 0.33143 rad s⁻² | For a solid disc, I=½MR²=½(7)(5)²=87.5 kg m². Using τ=Iα, α=29/87.5=0.33143 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33143 rad s⁻², not -2.66857 rad s⁻².",
"B": "Correct. The worked calculation gives 0.33143 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33143 rad s⁻², not -1.66857 rad s⁻².",
"... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004655 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 4 kg and radius 5 m is acted on by a constant torque of 87 N m about its central axis. Find its angular acceleration. | {
"A": "-1.26 rad s⁻²",
"B": "1.174 rad s⁻²",
"C": "1.74 rad s⁻²",
"D": "3.48 rad s⁻²"
} | C | 1.74 rad s⁻² | For a solid disc, I=½MR²=½(4)(5)²=50 kg m². Using τ=Iα, α=87/50=1.74 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.74 rad s⁻², not -1.26 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.74 rad s⁻², not 1.174 rad s⁻².",
"C": "Correct. The worked calculation gives 1.74 rad s⁻².",
"D": "Incorrect.... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007446 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 55 mL of 0.10 M HCl is mixed with 44 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-1.95424",
"B": "1.95424",
"C": "1.46568",
"D": "4.95424"
} | B | 1.95424 | Excess H⁺ moles=0.10×(55−44)/1000=0.001100 mol. Total volume=0.099 L, so [H⁺]=0.011111 M and pH=−log₁₀[H⁺]=1.95424. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.95424, not -1.95424.",
"B": "Correct. The worked calculation gives 1.95424.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.95424, not 1.46568.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000217 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 +1x -11=0, let its roots be α and β. What is α²+β²? | {
"A": "3.16327",
"B": "0.16327",
"C": "1.16327",
"D": "1.31633"
} | A | 3.16327 | By Vieta's relations, α+β = -1/7 and αβ = -11/7. Then α²+β²=(α+β)²−2αβ = (-1/7)²−2(-11/7) = 3.16327. | {
"A": "Correct. The worked calculation gives 3.16327.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.16327, not 0.16327.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.16327, not 1.16327.",
"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_003672 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 56 m s⁻¹ at 15° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "117.6 m",
"B": "16.68 m",
"C": "125.44 m",
"D": "156.8 m"
} | D | 156.8 m | Range R=u²sin(2θ)/g. Substituting u=56, θ=15° and g=10 gives R=(56)²sin(30°)/10=156.8 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 156.8 m, not 117.6 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 156.8 m, not 16.68 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 156.8 m, not 125.4... | [
"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_007228 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 3 mol of gas at 491 K and 1.3 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "91.97689 L",
"B": "92.97689 L",
"C": "-92.97689 L",
"D": "46.48845 L"
} | B | 92.97689 L | PV=nRT, so V=nRT/P=(3)(0.082057)(491)/(1.3)=92.97689 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 92.97689 L, not 91.97689 L.",
"B": "Correct. The worked calculation gives 92.97689 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 92.97689 L, not -92.97689 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_008923 | 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 1.07 mol L⁻¹ and initially B is absent. At equilibrium, 77% of A has dissociated at constant volume. Find K_c. | {
"A": "11.0331",
"B": "2.10331",
"C": "14.0331",
"D": "8.0331"
} | A | 11.0331 | Let α=0.77. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.07)(0.77)²/(1−0.77)=11.0331. | {
"A": "Correct. The worked calculation gives 11.0331.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.0331, not 2.10331.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.0331, not 14.0331.",
"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_008414 | 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 0.29 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "3.522 K",
"B": "-0.522 K",
"C": "0.522 K",
"D": "2.522 K"
} | C | 0.522 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.6×0.29=0.522 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.522 K, not 3.522 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.522 K, not -0.522 K.",
"C": "Correct. The worked calculation gives 0.522 K.",
"D": "Incorrect. Substituting the stated v... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006408 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 20 kg is attached to an ideal spring of force constant 1004 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.28228 s",
"B": "0.28228 s",
"C": "-0.28228 s",
"D": "0.42342 s"
} | B | 0.28228 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(20/1004)=0.28228 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.28228 s, not 1.28228 s.",
"B": "Correct. The worked calculation gives 0.28228 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.28228 s, not -0.28228 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_001544 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (6x² +7x -3) dx. | {
"A": "542",
"B": "270",
"C": "540",
"D": "810"
} | C | 540 | An antiderivative is (6/3)x³+(7/2)x²+(-3)x. Evaluating between 0 and 6 gives (6/3)(6)³+(7/2)(6)²+(-3)(6)=540. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 540, not 542.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 540, not 270.",
"C": "Correct. The worked calculation gives 540.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_009734 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(OH)_4]^-4, each OH ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "2",
"B": "1",
"C": "-3",
"D": "0"
} | D | 0 | Let the formal oxidation state of Pd be x. Charge balance gives x+(4)(−1)=-4; hence x=-4+4=+0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"D": "Correct. The worked c... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002117 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 11 blue and 10 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.2358",
"B": "0.31439",
"C": "3.31439",
"D": "0.62879"
} | B | 0.31439 | Favourable pairs = C(12,2)+C(11,2)+C(10,2)=166. Total pairs=C(33,2)=528. Therefore P=166/528=0.31439. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31439, not 0.2358.",
"B": "Correct. The worked calculation gives 0.31439.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31439, not 3.31439.",
"D": "Incorrect. Substituting the stated val... | [
"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_006348 | 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 1015 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.76511 s",
"B": "2.23489 s",
"C": "0.23489 s",
"D": "1.23489 s"
} | C | 0.23489 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(14/1015)=0.23489 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.23489 s, not -1.76511 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.23489 s, not 2.23489 s.",
"C": "Correct. The worked calculation gives 0.23489 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_001578 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (-1x² +2x -1) dx. | {
"A": "-3.66667",
"B": "-0.66667",
"C": "-2.66667",
"D": "0.66667"
} | B | -0.66667 | An antiderivative is (-1/3)x³+(2/2)x²+(-1)x. Evaluating between 0 and 2 gives (-1/3)(2)³+(2/2)(2)²+(-1)(2)=-0.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.66667, not -3.66667.",
"B": "Correct. The worked calculation gives -0.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.66667, not -2.66667.",
"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_005459 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 60 μF capacitor is charged to a potential difference of 40 V. Calculate the energy stored, expressed in μJ. | {
"A": "48000 μJ",
"B": "38400 μJ",
"C": "48001 μJ",
"D": "4801 μJ"
} | A | 48000 μJ | U=½CV². Since C=60 μF, U in μJ is ½×60×(40)²=48000 μJ. | {
"A": "Correct. The worked calculation gives 48000 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 48000 μJ, not 38400 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 48000 μJ, not 48001 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_000950 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio 4. What is the sum of its first 11 terms? | {
"A": "6990504",
"B": "699051.5",
"C": "6990505",
"D": "8388606"
} | C | 6990505 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(4^11−1)/(4−1)=6990505. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6990505, not 6990504.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6990505, not 699051.5.",
"C": "Correct. The worked calculation gives 6990505.",
"D": "Incorrect. Substituting the stated v... | [
"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_002812 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(9, 1, -1) and v=(4, 6, 9), calculate u·v. | {
"A": "31",
"B": "24.75",
"C": "33",
"D": "-33"
} | C | 33 | The dot product is the sum of corresponding component products: (9)(4)+(1)(6)+(-1)(9)=33. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33, not 31.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33, not 24.75.",
"C": "Correct. The worked calculation gives 33.",
"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_002718 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(5, -5, -7) and v=(-3, 3, 3), calculate u·v. | {
"A": "-49",
"B": "-51",
"C": "-76.5",
"D": "-50"
} | B | -51 | The dot product is the sum of corresponding component products: (5)(-3)+(-5)(3)+(-7)(3)=-51. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -51, not -49.",
"B": "Correct. The worked calculation gives -51.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -51, not -76.5.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004487 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 3 kg and radius 4 m is acted on by a constant torque of 60 N m about its central axis. Find its angular acceleration. | {
"A": "3.5 rad s⁻²",
"B": "2.5 rad s⁻²",
"C": "0.5 rad s⁻²",
"D": "1.875 rad s⁻²"
} | B | 2.5 rad s⁻² | For a solid disc, I=½MR²=½(3)(4)²=24 kg m². Using τ=Iα, α=60/24=2.5 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.5 rad s⁻², not 3.5 rad s⁻².",
"B": "Correct. The worked calculation gives 2.5 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.5 rad s⁻², not 0.5 rad s⁻².",
"D": "Incorrect. Substi... | [
"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_002262 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 11 red, 8 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.23793",
"B": "2.31724",
"C": "0.31724",
"D": "-1.68276"
} | C | 0.31724 | Favourable pairs = C(11,2)+C(8,2)+C(11,2)=138. Total pairs=C(30,2)=435. Therefore P=138/435=0.31724. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31724, not 0.23793.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31724, not 2.31724.",
"C": "Correct. The worked calculation gives 0.31724.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001409 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (-4x² +0x +7) dx. | {
"A": "-628.66667",
"B": "-1253.33333",
"C": "-626.66667",
"D": "-627.66667"
} | C | -626.66667 | An antiderivative is (-4/3)x³+(0/2)x²+(7)x. Evaluating between 0 and 8 gives (-4/3)(8)³+(0/2)(8)²+(7)(8)=-626.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -626.66667, not -628.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -626.66667, not -1253.33333.",
"C": "Correct. The worked calculation gives -626.66667.",
"D": "Incorrect. Substituti... | [
"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_003763 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 11 m s⁻¹. A constant net force does 22 N of work over 5 m in the direction of motion. Find its final kinetic energy. | {
"A": "715 J",
"B": "357.5 J",
"C": "717 J",
"D": "714 J"
} | A | 715 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(11)²+(22)(5)=715 J. | {
"A": "Correct. The worked calculation gives 715 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 715 J, not 357.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 715 J, not 717 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_001147 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ -7x² +9x+7. Evaluate f′(2). | {
"A": "82",
"B": "5.1",
"C": "-41",
"D": "41"
} | D | 41 | Differentiate: f′(x)=3(5)x²+2(-7)x+(9). At x=2, f′(2)=3(5)(2)²+2(-7)(2)+(9)=41. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 41, not 82.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 41, not 5.1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 41, not -41.",
"D": "Correct. The w... | [
"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_008802 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.28 mol L⁻¹ and initially B is absent. At equilibrium, 50% of A has dissociated at constant volume. Find K_c. | {
"A": "0.56",
"B": "1.12",
"C": "0.42",
"D": "0.28"
} | A | 0.56 | Let α=0.5. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.28)(0.5)²/(1−0.5)=0.56. | {
"A": "Correct. The worked calculation gives 0.56.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.56, not 1.12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.56, not 0.42.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_002281 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 4 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.20455",
"B": "2.27273",
"C": "3.27273",
"D": "0.27273"
} | D | 0.27273 | Favourable pairs = C(4,2)+C(4,2)+C(3,2)=15. Total pairs=C(11,2)=55. Therefore P=15/55=0.27273. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.27273, not 0.20455.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.27273, not 2.27273.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.27273, not 3.272... | [
"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_009057 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.48 V, transfers 1 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.6573 V",
"B": "3.6573 V",
"C": "1.16573 V",
"D": "-0.3427 V"
} | A | 1.6573 V | Apply the Nernst equation: E=1.48−(0.0591/1)(-3)=1.6573 V. | {
"A": "Correct. The worked calculation gives 1.6573 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.6573 V, not 3.6573 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.6573 V, not 1.16573 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004461 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 5 m is acted on by a constant torque of 16 N m about its central axis. Find its angular acceleration. | {
"A": "-0.18286 rad s⁻²",
"B": "0.09143 rad s⁻²",
"C": "0.18286 rad s⁻²",
"D": "-2.81714 rad s⁻²"
} | C | 0.18286 rad s⁻² | For a solid disc, I=½MR²=½(7)(5)²=87.5 kg m². Using τ=Iα, α=16/87.5=0.18286 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.18286 rad s⁻², not -0.18286 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.18286 rad s⁻², not 0.09143 rad s⁻².",
"C": "Correct. The worked calculation gives 0.18286 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_002698 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-6, 8, -2) and v=(-7, 6, -7), calculate u·v. | {
"A": "103",
"B": "208",
"C": "52",
"D": "104"
} | D | 104 | The dot product is the sum of corresponding component products: (-6)(-7)+(8)(6)+(-2)(-7)=104. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 104, not 103.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 104, not 208.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 104, not 52.",
"D": "Correct. Th... | [
"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_002101 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 8 blue and 9 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "2.35263",
"B": "0.70526",
"C": "1.03526",
"D": "0.35263"
} | D | 0.35263 | Favourable pairs = C(3,2)+C(8,2)+C(9,2)=67. Total pairs=C(20,2)=190. Therefore P=67/190=0.35263. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35263, not 2.35263.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35263, not 0.70526.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35263, not 1.035... | [
"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_005541 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 53 μF capacitor is charged to a potential difference of 16 V. Calculate the energy stored, expressed in μJ. | {
"A": "5088 μJ",
"B": "6784 μJ",
"C": "5427.2 μJ",
"D": "3392 μJ"
} | B | 6784 μJ | U=½CV². Since C=53 μF, U in μJ is ½×53×(16)²=6784 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6784 μJ, not 5088 μJ.",
"B": "Correct. The worked calculation gives 6784 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6784 μJ, not 5427.2 μJ.",
"D": "Incorrect. Substituting the stated ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004866 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 12 Ω and 13 Ω are connected in series; this combination is connected in parallel with a 19 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.66737 A",
"B": "2.50105 A",
"C": "-1.33263 A",
"D": "1.66737 A"
} | D | 1.66737 A | Series branch resistance=12+13=25 Ω. Parallel equivalent R_eq=(25×19)/(25+19)=10.79545 Ω. Total current I=V/R_eq=18/10.79545=1.66737 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.66737 A, not 2.66737 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.66737 A, not 2.50105 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.66737 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_002631 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, -3], [3, -5]]. | {
"A": "4",
"B": "5",
"C": "1.4",
"D": "6"
} | A | 4 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(-5)−(-3)(3)=4. | {
"A": "Correct. The worked calculation gives 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.4.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_009749 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(CN)_5]^-2, each CN ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "2",
"B": "3",
"C": "1",
"D": "2.25"
} | B | 3 | Let the formal oxidation state of Pd be x. Charge balance gives x+(5)(−1)=-2; hence x=-2+5=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008152 | 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 9478 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": "10.91443 g",
"B": "21.82887 g",
"C": "26.19464 g",
"D": "23.82887 g"
} | B | 21.82887 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×7×9478/(2×96500)=21.82887 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21.82887 g, not 10.91443 g.",
"B": "Correct. The worked calculation gives 21.82887 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21.82887 g, not 26.19464 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_007710 | 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 33 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "5.125 mmol L⁻¹",
"B": "6.1875 mmol L⁻¹",
"C": "2.0625 mmol L⁻¹",
"D": "4.125 mmol L⁻¹"
} | D | 4.125 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=33/2^3=4.125 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.125 mmol L⁻¹, not 5.125 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.125 mmol L⁻¹, not 6.1875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing rela... | [
"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_008381 | 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 3 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.288 K",
"B": "0.576 K",
"C": "0.432 K",
"D": "0.288 K"
} | D | 0.288 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.6×0.16=0.288 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.288 K, not -0.288 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.288 K, not 0.576 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.288 K, not 0.43... | [
"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_006532 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 5 kg is attached to an ideal spring of force constant 744 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.83604 s",
"B": "0.16396 s",
"C": "3.16396 s",
"D": "0.32791 s"
} | B | 0.16396 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(5/744)=0.16396 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.16396 s, not -1.83604 s.",
"B": "Correct. The worked calculation gives 0.16396 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.16396 s, not 3.16396 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_001902 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 46 distinct elements? | {
"A": "3057262815.75",
"B": "4076350421",
"C": "3261080336.8",
"D": "-4076350421"
} | B | 4076350421 | Order does not matter, so the count is C(46,10)=46!/[10!(36)!]=4076350421. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4076350421, not 3057262815.75.",
"B": "Correct. The worked calculation gives 4076350421.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4076350421, not 3261080336.8.",
"D": "Incorrect. Substi... | [
"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_003759 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block initially moves at 6 m s⁻¹. A constant net force does 26 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "300.8 J",
"B": "378 J",
"C": "376 J",
"D": "282 J"
} | C | 376 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(5)(6)²+(26)(11)=376 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 376 J, not 300.8 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 376 J, not 378 J.",
"C": "Correct. The worked calculation gives 376 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 |
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