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_005985 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.4 atm at 429 K. What is its pressure at 703 K? | {
"A": "-0.70583 atm",
"B": "2.29417 atm",
"C": "1.29417 atm",
"D": "-2.29417 atm"
} | B | 2.29417 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.4)(703)/(429)=2.29417 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.29417 atm, not -0.70583 atm.",
"B": "Correct. The worked calculation gives 2.29417 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.29417 atm, not 1.29417 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_005126 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +8 μC are separated by 5 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "43.2 N",
"B": "88.4 N",
"C": "85.4 N",
"D": "86.4 N"
} | D | 86.4 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(8×10⁻⁶)/(5×10⁻²)²=86.4 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 86.4 N, not 43.2 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 86.4 N, not 88.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 86.4 N, not 85.4 N.",
... | [
"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_002234 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 3 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.03846",
"B": "1.38462",
"C": "0.38462",
"D": "3.38462"
} | C | 0.38462 | Favourable pairs = C(12,2)+C(3,2)+C(12,2)=135. Total pairs=C(27,2)=351. Therefore P=135/351=0.38462. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.38462, not 1.03846.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.38462, not 1.38462.",
"C": "Correct. The worked calculation gives 0.38462.",
"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_001498 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (5x² +4x -4) dx. | {
"A": "-2.33333",
"B": "-0.33333",
"C": "-0.66667",
"D": "-0.25"
} | B | -0.33333 | An antiderivative is (5/3)x³+(4/2)x²+(-4)x. Evaluating between 0 and 1 gives (5/3)(1)³+(4/2)(1)²+(-4)(1)=-0.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.33333, not -2.33333.",
"B": "Correct. The worked calculation gives -0.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.33333, not -0.66667.",
"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_001196 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ -4x² -6x+7. Evaluate f′(1). | {
"A": "-2",
"B": "-3",
"C": "-1",
"D": "0.8"
} | A | -2 | Differentiate: f′(x)=3(4)x²+2(-4)x+(-6). At x=1, f′(1)=3(4)(1)²+2(-4)(1)+(-6)=-2. | {
"A": "Correct. The worked calculation gives -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2, not -3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2, not -1.",
"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_000133 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 -14x -1=0, let its roots be α and β. What is α²+β²? | {
"A": "5.77778",
"B": "8.66667",
"C": "3.77778",
"D": "6.77778"
} | A | 5.77778 | By Vieta's relations, α+β = 14/6 and αβ = -1/6. Then α²+β²=(α+β)²−2αβ = (14/6)²−2(-1/6) = 5.77778. | {
"A": "Correct. The worked calculation gives 5.77778.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.77778, not 8.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.77778, not 3.77778.",
"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_006713 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 34 mol H₂ and 34 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "40.8 mol",
"B": "4.4 mol",
"C": "34 mol",
"D": "32 mol"
} | C | 34 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 34 mol H₂O; O₂ can produce 68 mol H₂O. The limiting condition is H₂; product=34 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 34 mol, not 40.8 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 34 mol, not 4.4 mol.",
"C": "Correct. The worked calculation gives 34 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_006615 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 18 kg is attached to an ideal spring of force constant 145 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.70466 s",
"B": "-0.70466 s",
"C": "-0.29534 s",
"D": "-1.29534 s"
} | A | 0.70466 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(18/145)=0.70466 s. | {
"A": "Correct. The worked calculation gives 0.70466 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.70466 s, not -0.70466 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.70466 s, not -0.29534 s.",
"D": "Incorrect. Substituting t... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005149 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +5 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "295.3125 N",
"B": "-196.875 N",
"C": "98.4375 N",
"D": "196.875 N"
} | D | 196.875 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(5×10⁻⁶)/(4×10⁻²)²=196.875 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 196.875 N, not 295.3125 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 196.875 N, not -196.875 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 196.875 ... | [
"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_006467 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 19 kg is attached to an ideal spring of force constant 157 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.04363 s",
"B": "0.34788 s",
"C": "0.69576 s",
"D": "0.52182 s"
} | C | 0.69576 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(19/157)=0.69576 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.69576 s, not 1.04363 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.69576 s, not 0.34788 s.",
"C": "Correct. The worked calculation gives 0.69576 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_007910 | 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 70 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "5.1875 mmol L⁻¹",
"B": "2.1875 mmol L⁻¹",
"C": "4.1875 mmol L⁻¹",
"D": "3.1875 mmol L⁻¹"
} | B | 2.1875 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=70/2^5=2.1875 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.1875 mmol L⁻¹, not 5.1875 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 2.1875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.1875 mmol L⁻¹, not 4.1875 mmol L⁻¹.",
"D"... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009106 | 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 2 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.25225 V",
"B": "0.74775 V",
"C": "1.12162 V",
"D": "-0.74775 V"
} | B | 0.74775 V | Apply the Nernst equation: E=0.60−(0.0591/2)(-5)=0.74775 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.74775 V, not -0.25225 V.",
"B": "Correct. The worked calculation gives 0.74775 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.74775 V, not 1.12162 V.",
"D": "Incorrect. Substituting th... | [
"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_009067 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.67 V, transfers 2 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.4927 V",
"B": "0.4927 V",
"C": "-0.5073 V",
"D": "-1.5073 V"
} | B | 0.4927 V | Apply the Nernst equation: E=0.67−(0.0591/2)(6)=0.4927 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.4927 V, not 1.4927 V.",
"B": "Correct. The worked calculation gives 0.4927 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.4927 V, not -0.5073 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_007111 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 10 mol of gas at 257 K and 1.86 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "136.0558 L",
"B": "226.75967 L",
"C": "90.70387 L",
"D": "113.37983 L"
} | D | 113.37983 L | PV=nRT, so V=nRT/P=(10)(0.082057)(257)/(1.86)=113.37983 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 113.37983 L, not 136.0558 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 113.37983 L, not 226.75967 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 113... | [
"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_005957 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.8 atm at 335 K. What is its pressure at 624 K? | {
"A": "8.21552 atm",
"B": "6.21552 atm",
"C": "5.21552 atm",
"D": "7.82328 atm"
} | C | 5.21552 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.8)(624)/(335)=5.21552 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.21552 atm, not 8.21552 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.21552 atm, not 6.21552 atm.",
"C": "Correct. The worked calculation gives 5.21552 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002832 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-3, -5, 8) and v=(0, -5, 4), calculate u·v. | {
"A": "28.5",
"B": "57",
"C": "58",
"D": "114"
} | B | 57 | The dot product is the sum of corresponding component products: (-3)(0)+(-5)(-5)+(8)(4)=57. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 57, not 28.5.",
"B": "Correct. The worked calculation gives 57.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 57, not 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_009774 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(OH)_5]^+1, each OH ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "5",
"B": "3",
"C": "6",
"D": "1.6"
} | C | 6 | Let the formal oxidation state of Mn be x. Charge balance gives x+(5)(−1)=+1; hence x=1+5=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"C": "Correct. The worked calculation gives 6.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000988 | 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 6 terms? | {
"A": "-1456",
"B": "-1747.2",
"C": "-1164.8",
"D": "-1458"
} | A | -1456 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(-3^6−1)/(-3−1)=-1456. | {
"A": "Correct. The worked calculation gives -1456.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1456, not -1747.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1456, not -1164.8.",
"D": "Incorrect. Substituting the stated values i... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005259 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +7 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "420 N",
"B": "281 N",
"C": "280 N",
"D": "279 N"
} | C | 280 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(7×10⁻⁶)/(3×10⁻²)²=280 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 280 N, not 420 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 280 N, not 281 N.",
"C": "Correct. The worked calculation gives 280 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_009214 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.66 V, transfers 1 electrons, and has reaction quotient Q=10^0. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.066 V",
"B": "-0.66 V",
"C": "0.66 V",
"D": "-2.34 V"
} | C | 0.66 V | Apply the Nernst equation: E=0.66−(0.0591/1)(0)=0.66 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.66 V, not 1.066 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.66 V, not -0.66 V.",
"C": "Correct. The worked calculation gives 0.66 V.",
"D": "Incorrect. Substituting the stated value... | [
"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_000735 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio -2. What is the sum of its first 5 terms? | {
"A": "88",
"B": "66",
"C": "89",
"D": "9.8"
} | A | 88 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(-2^5−1)/(-2−1)=88. | {
"A": "Correct. The worked calculation gives 88.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 88, not 66.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 88, not 89.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_005560 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 77 μF capacitor is charged to a potential difference of 22 V. Calculate the energy stored, expressed in μJ. | {
"A": "-18634 μJ",
"B": "18632 μJ",
"C": "18634 μJ",
"D": "13975.5 μJ"
} | C | 18634 μJ | U=½CV². Since C=77 μF, U in μJ is ½×77×(22)²=18634 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18634 μJ, not -18634 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18634 μJ, not 18632 μJ.",
"C": "Correct. The worked calculation gives 18634 μJ.",
"D": "Incorrect. Substituting the sta... | [
"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_002850 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, -6, 3) and v=(7, 4, 1), calculate u·v. | {
"A": "14",
"B": "-14",
"C": "-10.5",
"D": "-0.4"
} | B | -14 | The dot product is the sum of corresponding component products: (1)(7)+(-6)(4)+(3)(1)=-14. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -14, not 14.",
"B": "Correct. The worked calculation gives -14.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -14, not -10.5.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002615 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 3], [9, 0]]. | {
"A": "-27",
"B": "-40.5",
"C": "-28",
"D": "-26"
} | A | -27 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(0)−(3)(9)=-27. | {
"A": "Correct. The worked calculation gives -27.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -27, not -40.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -27, not -28.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_009360 | 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_3H_5X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "1",
"B": "0",
"C": "-1",
"D": "3"
} | A | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×3+2+0−5−1)/2=1. | {
"A": "Correct. The worked calculation gives 1.",
"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.",
"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_005578 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 73 μF capacitor is charged to a potential difference of 36 V. Calculate the energy stored, expressed in μJ. | {
"A": "47304 μJ",
"B": "4731.4 μJ",
"C": "37843.2 μJ",
"D": "47306 μJ"
} | A | 47304 μJ | U=½CV². Since C=73 μF, U in μJ is ½×73×(36)²=47304 μJ. | {
"A": "Correct. The worked calculation gives 47304 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 47304 μJ, not 4731.4 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 47304 μJ, not 37843.2 μJ.",
"D": "Incorrect. Substituting the s... | [
"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_002005 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 7 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.24573",
"B": "3.32764",
"C": "2.32764",
"D": "0.32764"
} | D | 0.32764 | Favourable pairs = C(8,2)+C(7,2)+C(12,2)=115. Total pairs=C(27,2)=351. Therefore P=115/351=0.32764. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32764, not 0.24573.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32764, not 3.32764.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32764, not 2.327... | [
"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_001828 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 41 distinct elements? | {
"A": "749400",
"B": "749399",
"C": "-749398",
"D": "749398"
} | D | 749398 | Order does not matter, so the count is C(41,5)=41!/[5!(36)!]=749398. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 749398, not 749400.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 749398, not 749399.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 749398, not -749398.",... | [
"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_005863 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.8 atm at 411 K. What is its pressure at 494 K? | {
"A": "1.21635 atm",
"B": "4.32701 atm",
"C": "2.1635 atm",
"D": "1.1635 atm"
} | C | 2.1635 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.8)(494)/(411)=2.1635 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.1635 atm, not 1.21635 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.1635 atm, not 4.32701 atm.",
"C": "Correct. The worked calculation gives 2.1635 atm.",
"D": "Incorrect. Substitut... | [
"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_005850 | 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 3.2 atm at 370 K. What is its pressure at 642 K? | {
"A": "8.32865 atm",
"B": "3.55243 atm",
"C": "5.55243 atm",
"D": "-5.55243 atm"
} | C | 5.55243 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.2)(642)/(370)=5.55243 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.55243 atm, not 8.32865 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.55243 atm, not 3.55243 atm.",
"C": "Correct. The worked calculation gives 5.55243 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002565 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 1], [1, -1]]. | {
"A": "-1",
"B": "-4",
"C": "-2",
"D": "-3"
} | B | -4 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(-1)−(1)(1)=-4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4, not -1.",
"B": "Correct. The worked calculation gives -4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -4, not -2.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004315 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 19 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.38. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "56.24 N",
"B": "6.624 N",
"C": "57.24 N",
"D": "67.488 N"
} | A | 56.24 N | Net force=mg(sinθ−μcosθ)=19×10×(0.6−0.38×0.8)=56.24 N. | {
"A": "Correct. The worked calculation gives 56.24 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 56.24 N, not 6.624 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 56.24 N, not 57.24 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_008462 | 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 1.8 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.9216 K",
"B": "-0.0784 K",
"C": "0.9216 K",
"D": "1.8432 K"
} | C | 0.9216 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.512×1.8=0.9216 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9216 K, not -0.9216 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9216 K, not -0.0784 K.",
"C": "Correct. The worked calculation gives 0.9216 K.",
"D": "Incorrect. Substituting the st... | [
"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_006222 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 62 cm in front of a thin convex lens of focal length 18 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.81818",
"B": "3.40909",
"C": "-0.40909",
"D": "0.40909"
} | D | 0.40909 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(62)(18)/(62−18)=25.36364 cm. Thus |m|=v/u=25.36364/62=0.40909. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.40909, not 0.81818.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.40909, not 3.40909.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.40909, not -0.40... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003869 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 1 m s⁻¹. A constant net force does 8 N of work over 19 m in the direction of motion. Find its final kinetic energy. | {
"A": "16.55 J",
"B": "155.5 J",
"C": "311 J",
"D": "156.5 J"
} | B | 155.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(1)²+(8)(19)=155.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 155.5 J, not 16.55 J.",
"B": "Correct. The worked calculation gives 155.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 155.5 J, not 311 J.",
"D": "Incorrect. Substituting the stated valu... | [
"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_009854 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(CN)_4]^-3, each CN ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "1.5",
"B": "1",
"C": "1.1",
"D": "0"
} | B | 1 | Let the formal oxidation state of Cu be x. Charge balance gives x+(4)(−1)=-3; hence x=-3+4=+1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.5.",
"B": "Correct. The worked calculation gives 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.1.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_004217 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 13 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.21. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "56.16 N",
"B": "112.32 N",
"C": "55.16 N",
"D": "28.08 N"
} | A | 56.16 N | Net force=mg(sinθ−μcosθ)=13×10×(0.6−0.21×0.8)=56.16 N. | {
"A": "Correct. The worked calculation gives 56.16 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 56.16 N, not 112.32 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 56.16 N, not 55.16 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_002126 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 7 red, 12 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "3.32903",
"B": "2.32903",
"C": "0.32903",
"D": "0.16452"
} | C | 0.32903 | Favourable pairs = C(7,2)+C(12,2)+C(12,2)=153. Total pairs=C(31,2)=465. Therefore P=153/465=0.32903. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32903, not 3.32903.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32903, not 2.32903.",
"C": "Correct. The worked calculation gives 0.32903.",
"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_006079 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 38 cm in front of a thin convex lens of focal length 9 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.03103",
"B": "-2.68966",
"C": "3.31034",
"D": "0.31034"
} | D | 0.31034 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(38)(9)/(38−9)=11.7931 cm. Thus |m|=v/u=11.7931/38=0.31034. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31034, not 1.03103.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31034, not -2.68966.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31034, not 3.31... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005374 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 63 μF capacitor is charged to a potential difference of 24 V. Calculate the energy stored, expressed in μJ. | {
"A": "18146 μJ",
"B": "18142 μJ",
"C": "18144 μJ",
"D": "-18144 μJ"
} | C | 18144 μJ | U=½CV². Since C=63 μF, U in μJ is ½×63×(24)²=18144 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18144 μJ, not 18146 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18144 μJ, not 18142 μJ.",
"C": "Correct. The worked calculation gives 18144 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_009895 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(OH)_6]^+1, each OH ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "-7",
"B": "7",
"C": "5",
"D": "8"
} | B | 7 | Let the formal oxidation state of Co be x. Charge balance gives x+(6)(−1)=+1; hence x=1+6=+7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not -7.",
"B": "Correct. The worked calculation gives 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, 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_008712 | 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 0.4 mol L⁻¹ and initially B is absent. At equilibrium, 79% of A has dissociated at constant volume. Find K_c. | {
"A": "5.75505",
"B": "3.75505",
"C": "9.5101",
"D": "4.75505"
} | D | 4.75505 | Let α=0.79. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.4)(0.79)²/(1−0.79)=4.75505. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.75505, not 5.75505.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.75505, not 3.75505.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.75505, not 9.510... | [
"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_008171 | 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 6 A for 26339 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": "103.99128 g",
"B": "41.59651 g",
"C": "51.99564 g",
"D": "77.99346 g"
} | C | 51.99564 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×6×26339/(2×96500)=51.99564 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 51.99564 g, not 103.99128 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 51.99564 g, not 41.59651 g.",
"C": "Correct. The worked calculation gives 51.99564 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002068 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 12 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.15775",
"B": "3.31551",
"C": "0.31551",
"D": "1.31551"
} | C | 0.31551 | Favourable pairs = C(10,2)+C(12,2)+C(12,2)=177. Total pairs=C(34,2)=561. Therefore P=177/561=0.31551. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31551, not 0.15775.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31551, not 3.31551.",
"C": "Correct. The worked calculation gives 0.31551.",
"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_006804 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 34 mol H₂ and 3 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "5 mol",
"B": "8 mol",
"C": "7 mol",
"D": "6 mol"
} | D | 6 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 34 mol H₂O; O₂ can produce 6 mol H₂O. The limiting condition is O₂; product=6 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 8 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 7 mol.",
"D":... | [
"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_007957 | 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 98 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "-1.61719 mmol L⁻¹",
"B": "0.19141 mmol L⁻¹",
"C": "1.38281 mmol L⁻¹",
"D": "0.38281 mmol L⁻¹"
} | D | 0.38281 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=98/2^8=0.38281 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.38281 mmol L⁻¹, not -1.61719 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.38281 mmol L⁻¹, not 0.19141 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the govern... | [
"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_003400 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 17 m s⁻¹ at 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "26.46094 m",
"B": "14.23047 m",
"C": "34.15313 m",
"D": "28.46094 m"
} | D | 28.46094 m | Range R=u²sin(2θ)/g. Substituting u=17, θ=40° and g=10 gives R=(17)²sin(80°)/10=28.46094 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28.46094 m, not 26.46094 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28.46094 m, not 14.23047 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28.460... | [
"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_005517 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 62 μF capacitor is charged to a potential difference of 10 V. Calculate the energy stored, expressed in μJ. | {
"A": "3720 μJ",
"B": "3100 μJ",
"C": "2325 μJ",
"D": "6200 μJ"
} | B | 3100 μJ | U=½CV². Since C=62 μF, U in μJ is ½×62×(10)²=3100 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3100 μJ, not 3720 μJ.",
"B": "Correct. The worked calculation gives 3100 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3100 μJ, not 2325 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001688 | 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 61 distinct elements? | {
"A": "1472413882.5",
"B": "294482777.5",
"C": "2944827765",
"D": "5889655530"
} | C | 2944827765 | Order does not matter, so the count is C(61,8)=61!/[8!(53)!]=2944827765. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2944827765, not 1472413882.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2944827765, not 294482777.5.",
"C": "Correct. The worked calculation gives 2944827765.",
"D": "Incorrect. Substitu... | [
"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_008452 | 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 0.19 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.09728 K",
"B": "-0.90272 K",
"C": "1.09728 K",
"D": "-0.09728 K"
} | A | 0.09728 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.512×0.19=0.09728 K. | {
"A": "Correct. The worked calculation gives 0.09728 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.09728 K, not -0.90272 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.09728 K, not 1.09728 K.",
"D": "Incorrect. Substituting th... | [
"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_001941 | 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 80 distinct elements? | {
"A": "60246643120299",
"B": "6024664312031",
"C": "60246643120300",
"D": "72295971744360"
} | C | 60246643120300 | Order does not matter, so the count is C(80,12)=80!/[12!(68)!]=60246643120300. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 60246643120300, not 60246643120299.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 60246643120300, not 6024664312031.",
"C": "Correct. The worked calculation gives 60246643120300.",
"D": "Inc... | [
"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_006151 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 121 cm in front of a thin convex lens of focal length 28 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.30108",
"B": "0.30108",
"C": "3.30108",
"D": "0.22581"
} | B | 0.30108 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(121)(28)/(121−28)=36.43011 cm. Thus |m|=v/u=36.43011/121=0.30108. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30108, not -0.30108.",
"B": "Correct. The worked calculation gives 0.30108.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30108, not 3.30108.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005849 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.1 atm at 230 K. What is its pressure at 737 K? | {
"A": "1.76239 atm",
"B": "1.52478 atm",
"C": "3.52478 atm",
"D": "-3.52478 atm"
} | C | 3.52478 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.1)(737)/(230)=3.52478 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.52478 atm, not 1.76239 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.52478 atm, not 1.52478 atm.",
"C": "Correct. The worked calculation gives 3.52478 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003295 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-1+11i)/(3+5i). What is Re(z), the real part of z? | {
"A": "1.52941",
"B": "3.05882",
"C": "3.52941",
"D": "1.14706"
} | A | 1.52941 | Multiply numerator and denominator by the conjugate (3-5i). Then Re(z)=(ac+bd)/(c²+d²)=((-1)(3)+(11)(5))/(3²+(5)²)=1.52941. | {
"A": "Correct. The worked calculation gives 1.52941.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.52941, not 3.05882.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.52941, not 3.52941.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000808 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio 5. What is the sum of its first 9 terms? | {
"A": "2929684",
"B": "2929686",
"C": "-2929686",
"D": "5859372"
} | B | 2929686 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(5^9−1)/(5−1)=2929686. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2929686, not 2929684.",
"B": "Correct. The worked calculation gives 2929686.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2929686, not -2929686.",
"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_003988 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 10 m s⁻¹. A constant net force does 15 N of work over 19 m in the direction of motion. Find its final kinetic energy. | {
"A": "883 J",
"B": "887 J",
"C": "885 J",
"D": "663.75 J"
} | C | 885 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(10)²+(15)(19)=885 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 885 J, not 883 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 885 J, not 887 J.",
"C": "Correct. The worked calculation gives 885 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_004881 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 9 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.125 A",
"B": "0.125 A",
"C": "1.5625 A",
"D": "2.125 A"
} | A | 3.125 A | Series branch resistance=9+7=16 Ω. Parallel equivalent R_eq=(16×9)/(16+9)=5.76 Ω. Total current I=V/R_eq=18/5.76=3.125 A. | {
"A": "Correct. The worked calculation gives 3.125 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.125 A, not 0.125 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.125 A, not 1.5625 A.",
"D": "Incorrect. Substituting the stated v... | [
"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_005155 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +1 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "13.5 N",
"B": "-12.5 N",
"C": "9.375 N",
"D": "12.5 N"
} | D | 12.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(1×10⁻⁶)/(6×10⁻²)²=12.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.5 N, not 13.5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.5 N, not -12.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.5 N, not 9.375 N."... | [
"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_005705 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.9 atm at 403 K. What is its pressure at 503 K? | {
"A": "4.37146 atm",
"B": "2.37146 atm",
"C": "1.23715 atm",
"D": "1.37146 atm"
} | B | 2.37146 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.9)(503)/(403)=2.37146 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.37146 atm, not 4.37146 atm.",
"B": "Correct. The worked calculation gives 2.37146 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.37146 atm, not 1.23715 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007920 | 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 36 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "2.14062 mmol L⁻¹",
"B": "0.14062 mmol L⁻¹",
"C": "-0.85938 mmol L⁻¹",
"D": "0.10547 mmol L⁻¹"
} | B | 0.14062 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=36/2^8=0.14062 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.14062 mmol L⁻¹, not 2.14062 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.14062 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.14062 mmol L⁻¹, not -0.85938 mmol L⁻¹.",... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001426 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (-4x² +7x -5) dx. | {
"A": "192",
"B": "-193",
"C": "-153.6",
"D": "-192"
} | D | -192 | An antiderivative is (-4/3)x³+(7/2)x²+(-5)x. Evaluating between 0 and 6 gives (-4/3)(6)³+(7/2)(6)²+(-5)(6)=-192. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -192, not 192.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -192, not -193.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -192, not -153.6.",
"D": "Cor... | [
"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_008633 | 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 1.74 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "4.22 K",
"B": "5.22 K",
"C": "3.915 K",
"D": "7.83 K"
} | B | 5.22 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×1.0×1.74=5.22 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.22 K, not 4.22 K.",
"B": "Correct. The worked calculation gives 5.22 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.22 K, not 3.915 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005574 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 75 μF capacitor is charged to a potential difference of 7 V. Calculate the energy stored, expressed in μJ. | {
"A": "1837.5 μJ",
"B": "1378.125 μJ",
"C": "1470 μJ",
"D": "1835.5 μJ"
} | A | 1837.5 μJ | U=½CV². Since C=75 μF, U in μJ is ½×75×(7)²=1837.5 μJ. | {
"A": "Correct. The worked calculation gives 1837.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1837.5 μJ, not 1378.125 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1837.5 μJ, not 1470 μJ.",
"D": "Incorrect. Substituting the... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006746 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 48 mol H₂ and 1 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "0 mol",
"B": "1 mol",
"C": "2 mol",
"D": "1.5 mol"
} | C | 2 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 48 mol H₂O; O₂ can produce 2 mol H₂O. The limiting condition is O₂; product=2 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 0 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 1 mol.",
"C": "Correct. The worked calculation gives 2 mol.",
"D": "Incorrect. Substituting the stated values into ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002713 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(8, -3, -4) and v=(-3, -6, 9), calculate u·v. | {
"A": "-40",
"B": "-21",
"C": "-42",
"D": "42"
} | C | -42 | The dot product is the sum of corresponding component products: (8)(-3)+(-3)(-6)+(-4)(9)=-42. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -42, not -40.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -42, not -21.",
"C": "Correct. The worked calculation gives -42.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002962 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(9, -4, -6) and v=(2, -5, -4), calculate u·v. | {
"A": "74.4",
"B": "62",
"C": "124",
"D": "61"
} | B | 62 | The dot product is the sum of corresponding component products: (9)(2)+(-4)(-5)+(-6)(-4)=62. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 62, not 74.4.",
"B": "Correct. The worked calculation gives 62.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 62, not 124.",
"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_002172 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 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": "0.79412",
"B": "0.29779",
"C": "-2.60294",
"D": "0.39706"
} | D | 0.39706 | Favourable pairs = C(10,2)+C(4,2)+C(3,2)=54. Total pairs=C(17,2)=136. Therefore P=54/136=0.39706. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.39706, not 0.79412.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.39706, not 0.29779.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.39706, not -2.60... | [
"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_009074 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.87 V, transfers 1 electrons, and has reaction quotient Q=10^-4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.2128 V",
"B": "1.1064 V",
"C": "1.6596 V",
"D": "1.11064 V"
} | B | 1.1064 V | Apply the Nernst equation: E=0.87−(0.0591/1)(-4)=1.1064 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.1064 V, not 2.2128 V.",
"B": "Correct. The worked calculation gives 1.1064 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1064 V, not 1.6596 V.",
"D": "Incorrect. Substituting the stat... | [
"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_001888 | 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 25 distinct elements? | {
"A": "15180",
"B": "12649",
"C": "12650",
"D": "6325"
} | C | 12650 | Order does not matter, so the count is C(25,4)=25!/[4!(21)!]=12650. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12650, not 15180.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12650, not 12649.",
"C": "Correct. The worked calculation gives 12650.",
"D": "Incorrect. Substituting the stated values into ... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007081 | 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 193 K and 0.35 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "162.89487 L",
"B": "133.74572 L",
"C": "135.74572 L",
"D": "-135.74572 L"
} | C | 135.74572 L | PV=nRT, so V=nRT/P=(3)(0.082057)(193)/(0.35)=135.74572 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 135.74572 L, not 162.89487 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 135.74572 L, not 133.74572 L.",
"C": "Correct. The worked calculation gives 135.74572 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006522 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 1 kg is attached to an ideal spring of force constant 804 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.1058 s",
"B": "-2.92947 s",
"C": "0.07053 s",
"D": "0.03527 s"
} | C | 0.07053 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(1/804)=0.07053 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.07053 s, not 0.1058 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.07053 s, not -2.92947 s.",
"C": "Correct. The worked calculation gives 0.07053 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_001273 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=2x³ -8x² +2x+7. Evaluate f′(4). | {
"A": "34",
"B": "17",
"C": "33",
"D": "-34"
} | A | 34 | Differentiate: f′(x)=3(2)x²+2(-8)x+(2). At x=4, f′(4)=3(2)(4)²+2(-8)(4)+(2)=34. | {
"A": "Correct. The worked calculation gives 34.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 34, not 17.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 34, not 33.",
"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_001083 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-1x³ +8x² +6x+7. Evaluate f′(4). | {
"A": "22",
"B": "-22",
"C": "23",
"D": "17.6"
} | A | 22 | Differentiate: f′(x)=3(-1)x²+2(8)x+(6). At x=4, f′(4)=3(-1)(4)²+2(8)(4)+(6)=22. | {
"A": "Correct. The worked calculation gives 22.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22, not -22.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22, not 23.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007879 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 19 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "14.25 mmol L⁻¹",
"B": "19 mmol L⁻¹",
"C": "10.5 mmol L⁻¹",
"D": "9.5 mmol L⁻¹"
} | D | 9.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=19/2^1=9.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.5 mmol L⁻¹, not 14.25 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.5 mmol L⁻¹, not 19 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation giv... | [
"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_000961 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 12 and common ratio 3. What is the sum of its first 6 terms? | {
"A": "3276",
"B": "437.8",
"C": "-4368",
"D": "4368"
} | D | 4368 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=12(3^6−1)/(3−1)=4368. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4368, not 3276.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4368, not 437.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4368, not -4368.",
"D": "Co... | [
"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_002150 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 10 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.33333",
"B": "-1.66667",
"C": "0.16667",
"D": "-2.66667"
} | A | 0.33333 | Favourable pairs = C(5,2)+C(10,2)+C(6,2)=70. Total pairs=C(21,2)=210. Therefore P=70/210=0.33333. | {
"A": "Correct. The worked calculation gives 0.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not -1.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not 0.16667.",
"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_003958 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 6 m s⁻¹. A constant net force does 27 N of work over 14 m in the direction of motion. Find its final kinetic energy. | {
"A": "592 J",
"B": "712.8 J",
"C": "297 J",
"D": "594 J"
} | D | 594 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(6)²+(27)(14)=594 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 594 J, not 592 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 594 J, not 712.8 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 594 J, not 297 J.",
"D... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004549 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 1 m is acted on by a constant torque of 19 N m about its central axis. Find its angular acceleration. | {
"A": "2.71429 rad s⁻²",
"B": "5.42857 rad s⁻²",
"C": "1.54286 rad s⁻²",
"D": "8.42857 rad s⁻²"
} | B | 5.42857 rad s⁻² | For a solid disc, I=½MR²=½(7)(1)²=3.5 kg m². Using τ=Iα, α=19/3.5=5.42857 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.42857 rad s⁻², not 2.71429 rad s⁻².",
"B": "Correct. The worked calculation gives 5.42857 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.42857 rad s⁻², not 1.54286 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_000043 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 -17x +5=0, let its roots be α and β. What is α²+β²? | {
"A": "10.56",
"B": "9.56",
"C": "11.56",
"D": "14.34"
} | B | 9.56 | By Vieta's relations, α+β = 17/5 and αβ = 5/5. Then α²+β²=(α+β)²−2αβ = (17/5)²−2(5/5) = 9.56. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.56, not 10.56.",
"B": "Correct. The worked calculation gives 9.56.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.56, not 11.56.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_002600 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, 2], [4, 8]]. | {
"A": "48",
"B": "50",
"C": "49",
"D": "96"
} | A | 48 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(8)−(2)(4)=48. | {
"A": "Correct. The worked calculation gives 48.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 48, not 50.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 48, not 49.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000271 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 +7x -9=0, let its roots be α and β. What is α²+β²? | {
"A": "3.57143",
"B": "0.57143",
"C": "5.57143",
"D": "7.14286"
} | A | 3.57143 | By Vieta's relations, α+β = -7/7 and αβ = -9/7. Then α²+β²=(α+β)²−2αβ = (-7/7)²−2(-9/7) = 3.57143. | {
"A": "Correct. The worked calculation gives 3.57143.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.57143, not 0.57143.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.57143, not 5.57143.",
"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_007955 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 43 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "1.34375 mmol L⁻¹",
"B": "3.34375 mmol L⁻¹",
"C": "4.34375 mmol L⁻¹",
"D": "-0.65625 mmol L⁻¹"
} | A | 1.34375 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=43/2^5=1.34375 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 1.34375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.34375 mmol L⁻¹, not 3.34375 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.34375 mmol L⁻¹, not 4.34375 mmol L⁻¹.",
... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000827 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio -2. What is the sum of its first 9 terms? | {
"A": "684",
"B": "342",
"C": "513",
"D": "685"
} | A | 684 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(-2^9−1)/(-2−1)=684. | {
"A": "Correct. The worked calculation gives 684.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 684, not 342.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 684, not 513.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_007694 | 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 72 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "0.21094 mmol L⁻¹",
"B": "0.28125 mmol L⁻¹",
"C": "0.42188 mmol L⁻¹",
"D": "-0.71875 mmol L⁻¹"
} | B | 0.28125 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=72/2^8=0.28125 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.28125 mmol L⁻¹, not 0.21094 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.28125 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.28125 mmol L⁻¹, not 0.42188 mmol L⁻¹.",
... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009547 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_18H_5X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "16",
"B": "19.2",
"C": "18",
"D": "15"
} | A | 16 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+0−5−1)/2=16. | {
"A": "Correct. The worked calculation gives 16.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16, not 19.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16, not 18.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"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_001931 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 3 elements can be selected from a set of 10 distinct elements? | {
"A": "144",
"B": "120",
"C": "118",
"D": "180"
} | B | 120 | Order does not matter, so the count is C(10,3)=10!/[3!(7)!]=120. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 120, not 144.",
"B": "Correct. The worked calculation gives 120.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 120, not 118.",
"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_009881 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(Cl)_3]^-1, each Cl ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "-2",
"B": "4",
"C": "2",
"D": "-1"
} | C | 2 | Let the formal oxidation state of Ni be x. Charge balance gives x+(3)(−1)=-1; hence x=-1+3=+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 4.",
"C": "Correct. The worked calculation gives 2.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003022 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-1-4i)/(7+4i). What is Re(z), the real part of z? | {
"A": "2.64615",
"B": "-0.26538",
"C": "-0.35385",
"D": "-0.70769"
} | C | -0.35385 | Multiply numerator and denominator by the conjugate (7-4i). Then Re(z)=(ac+bd)/(c²+d²)=((-1)(7)+(-4)(4))/(7²+(4)²)=-0.35385. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.35385, not 2.64615.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.35385, not -0.26538.",
"C": "Correct. The worked calculation gives -0.35385.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003970 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block initially moves at 11 m s⁻¹. A constant net force does 18 N of work over 9 m in the direction of motion. Find its final kinetic energy. | {
"A": "47.45 J",
"B": "464.5 J",
"C": "462.5 J",
"D": "557.4 J"
} | B | 464.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(5)(11)²+(18)(9)=464.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 464.5 J, not 47.45 J.",
"B": "Correct. The worked calculation gives 464.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 464.5 J, not 462.5 J.",
"D": "Incorrect. Substituting the stated va... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006137 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 33 cm in front of a thin convex lens of focal length 12 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.14286",
"B": "0.57143",
"C": "-1.42857",
"D": "1.57143"
} | B | 0.57143 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(33)(12)/(33−12)=18.85714 cm. Thus |m|=v/u=18.85714/33=0.57143. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.57143, not 1.14286.",
"B": "Correct. The worked calculation gives 0.57143.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.57143, not -1.42857.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006591 | 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 1043 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.22754 s",
"B": "0.15169 s",
"C": "0.07585 s",
"D": "-2.84831 s"
} | B | 0.15169 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(6/1043)=0.15169 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.15169 s, not 0.22754 s.",
"B": "Correct. The worked calculation gives 0.15169 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.15169 s, not 0.07585 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_008860 | 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 1.16 mol L⁻¹ and initially B is absent. At equilibrium, 32% of A has dissociated at constant volume. Find K_c. | {
"A": "-1.30127",
"B": "0.34936",
"C": "-0.69873",
"D": "0.69873"
} | D | 0.69873 | Let α=0.32. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.16)(0.32)²/(1−0.32)=0.69873. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.69873, not -1.30127.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.69873, not 0.34936.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.69873, not -0.6... | [
"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_008966 | 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 1.33 mol L⁻¹ and initially B is absent. At equilibrium, 11% of A has dissociated at constant volume. Find K_c. | {
"A": "0.07233",
"B": "1.00723",
"C": "0.05425",
"D": "-2.92767"
} | A | 0.07233 | Let α=0.11. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.33)(0.11)²/(1−0.11)=0.07233. | {
"A": "Correct. The worked calculation gives 0.07233.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.07233, not 1.00723.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.07233, not 0.05425.",
"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_005937 | 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 3.5 atm at 330 K. What is its pressure at 552 K? | {
"A": "-5.85455 atm",
"B": "5.85455 atm",
"C": "3.85455 atm",
"D": "7.85455 atm"
} | B | 5.85455 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.5)(552)/(330)=5.85455 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.85455 atm, not -5.85455 atm.",
"B": "Correct. The worked calculation gives 5.85455 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.85455 atm, not 3.85455 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_001659 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (-3x² -7x -2) dx. | {
"A": "-13",
"B": "-1.6",
"C": "26",
"D": "-26"
} | D | -26 | An antiderivative is (-3/3)x³+(-7/2)x²+(-2)x. Evaluating between 0 and 2 gives (-3/3)(2)³+(-7/2)(2)²+(-2)(2)=-26. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -26, not -13.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -26, not -1.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -26, not 26.",
"D": "Correct. T... | [
"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_007146 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 2 mol of gas at 217 K and 2.67 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "20.00716 L",
"B": "-13.3381 L",
"C": "10.00358 L",
"D": "13.3381 L"
} | D | 13.3381 L | PV=nRT, so V=nRT/P=(2)(0.082057)(217)/(2.67)=13.3381 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13.3381 L, not 20.00716 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13.3381 L, not -13.3381 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13.3381 ... | [
"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_009003 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.04 V, transfers 3 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "4.0794 V",
"B": "2.1588 V",
"C": "1.0794 V",
"D": "2.0794 V"
} | C | 1.0794 V | Apply the Nernst equation: E=1.04−(0.0591/3)(-2)=1.0794 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0794 V, not 4.0794 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0794 V, not 2.1588 V.",
"C": "Correct. The worked calculation gives 1.0794 V.",
"D": "Incorrect. Substituting the stat... | [
"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_000602 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -15 and common difference 15. Find the sum of its first 32 terms. | {
"A": "5568",
"B": "6960",
"C": "6958",
"D": "6959"
} | B | 6960 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-15, d=15, n=32: Sₙ=32/2[2(-15)+(32−1)(15)]=6960. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6960, not 5568.",
"B": "Correct. The worked calculation gives 6960.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6960, not 6958.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009640 | 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_9H_13N_3X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "2.25",
"B": "3",
"C": "2",
"D": "1.5"
} | B | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×9+2+3−13−4)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"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 rel... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001138 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-2x³ -4x² +3x+7. Evaluate f′(5). | {
"A": "-187",
"B": "-280.5",
"C": "-224.4",
"D": "-17.7"
} | A | -187 | Differentiate: f′(x)=3(-2)x²+2(-4)x+(3). At x=5, f′(5)=3(-2)(5)²+2(-4)(5)+(3)=-187. | {
"A": "Correct. The worked calculation gives -187.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -187, not -280.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -187, not -224.4.",
"D": "Incorrect. Substituting the stated values into t... | [
"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 |
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