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_003256 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(8+4i)/(5+2i). What is Re(z), the real part of z? | {
"A": "1.65517",
"B": "4.65517",
"C": "3.31034",
"D": "-0.34483"
} | A | 1.65517 | Multiply numerator and denominator by the conjugate (5-2i). Then Re(z)=(ac+bd)/(c²+d²)=((8)(5)+(4)(2))/(5²+(2)²)=1.65517. | {
"A": "Correct. The worked calculation gives 1.65517.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.65517, not 4.65517.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.65517, not 3.31034.",
"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_004547 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 5 m is acted on by a constant torque of 45 N m about its central axis. Find its angular acceleration. | {
"A": "1.8 rad s⁻²",
"B": "1.35 rad s⁻²",
"C": "4.8 rad s⁻²",
"D": "3.6 rad s⁻²"
} | A | 1.8 rad s⁻² | For a solid disc, I=½MR²=½(2)(5)²=25 kg m². Using τ=Iα, α=45/25=1.8 rad s⁻². | {
"A": "Correct. The worked calculation gives 1.8 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.8 rad s⁻², not 1.35 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.8 rad s⁻², not 4.8 rad s⁻².",
"D": "Incorrect. Subst... | [
"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_005898 | 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 1.7 atm at 263 K. What is its pressure at 360 K? | {
"A": "-0.673 atm",
"B": "2.327 atm",
"C": "4.327 atm",
"D": "3.49049 atm"
} | B | 2.327 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.7)(360)/(263)=2.327 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.327 atm, not -0.673 atm.",
"B": "Correct. The worked calculation gives 2.327 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.327 atm, not 4.327 atm.",
"D": "Incorrect. Substituting th... | [
"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_005219 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +9 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "19.08264 N",
"B": "18.08264 N",
"C": "20.08264 N",
"D": "3.00826 N"
} | C | 20.08264 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(9×10⁻⁶)/(11×10⁻²)²=20.08264 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20.08264 N, not 19.08264 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20.08264 N, not 18.08264 N.",
"C": "Correct. The worked calculation gives 20.08264 N.",
"D": "Incorrect. Substitutin... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001832 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 2 elements can be selected from a set of 23 distinct elements? | {
"A": "253",
"B": "251",
"C": "189.75",
"D": "255"
} | A | 253 | Order does not matter, so the count is C(23,2)=23!/[2!(21)!]=253. | {
"A": "Correct. The worked calculation gives 253.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 253, not 251.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 253, not 189.75.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_003991 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 6 m s⁻¹. A constant net force does 25 N of work over 19 m in the direction of motion. Find its final kinetic energy. | {
"A": "672 J",
"B": "673 J",
"C": "671 J",
"D": "68.3 J"
} | B | 673 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(6)²+(25)(19)=673 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 673 J, not 672 J.",
"B": "Correct. The worked calculation gives 673 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 673 J, not 671 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_004628 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 6 m is acted on by a constant torque of 8 N m about its central axis. Find its angular acceleration. | {
"A": "-0.06349 rad s⁻²",
"B": "-0.93651 rad s⁻²",
"C": "0.06349 rad s⁻²",
"D": "0.04762 rad s⁻²"
} | C | 0.06349 rad s⁻² | For a solid disc, I=½MR²=½(7)(6)²=126 kg m². Using τ=Iα, α=8/126=0.06349 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.06349 rad s⁻², not -0.06349 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.06349 rad s⁻², not -0.93651 rad s⁻².",
"C": "Correct. The worked calculation gives 0.06349 rad s⁻².",
"... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006537 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 10 kg is attached to an ideal spring of force constant 637 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "3.25059 s",
"B": "-0.74941 s",
"C": "0.37588 s",
"D": "0.25059 s"
} | D | 0.25059 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(10/637)=0.25059 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25059 s, not 3.25059 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25059 s, not -0.74941 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25059 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009959 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(OH)_6]^-1, each OH ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "7",
"B": "5",
"C": "3",
"D": "7.5"
} | B | 5 | Let the formal oxidation state of Cr be x. Charge balance gives x+(6)(−1)=-1; hence x=-1+6=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.",
"B": "Correct. The worked calculation gives 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.",
"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_000523 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 5 and common difference 14. Find the sum of its first 9 terms. | {
"A": "658.8",
"B": "411.75",
"C": "547",
"D": "549"
} | D | 549 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=5, d=14, n=9: Sₙ=9/2[2(5)+(9−1)(14)]=549. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 549, not 658.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 549, not 411.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 549, not 547.",
"D": "Corre... | [
"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_003872 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 3 m s⁻¹. A constant net force does 19 N of work over 14 m in the direction of motion. Find its final kinetic energy. | {
"A": "313.5 J",
"B": "315.5 J",
"C": "316.5 J",
"D": "252.4 J"
} | B | 315.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(3)²+(19)(14)=315.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 315.5 J, not 313.5 J.",
"B": "Correct. The worked calculation gives 315.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 315.5 J, not 316.5 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_007589 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 54 mL of 0.10 M HCl is mixed with 83 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.32568",
"B": "18.48852",
"C": "11.32568",
"D": "24.65135"
} | A | 12.32568 | Excess OH⁻ moles=0.10×(83−54)/1000=0.002900 mol. Total volume=0.137 L, so [OH⁻]=0.021168 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.32568. | {
"A": "Correct. The worked calculation gives 12.32568.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.32568, not 18.48852.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.32568, not 11.32568.",
"D": "Incorrect. Substituting the stat... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002752 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-6, -4, 1) and v=(-7, 4, 5), calculate u·v. | {
"A": "15.5",
"B": "31",
"C": "32",
"D": "-31"
} | B | 31 | The dot product is the sum of corresponding component products: (-6)(-7)+(-4)(4)+(1)(5)=31. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 31, not 15.5.",
"B": "Correct. The worked calculation gives 31.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 31, not 32.",
"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_001960 | 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 79 distinct elements? | {
"A": "1502499",
"B": "1502501",
"C": "150251.1",
"D": "1502500"
} | B | 1502501 | Order does not matter, so the count is C(79,4)=79!/[4!(75)!]=1502501. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1502501, not 1502499.",
"B": "Correct. The worked calculation gives 1502501.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1502501, not 150251.1.",
"D": "Incorrect. Substituting the stated v... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002739 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, -1, -2) and v=(3, 2, 8), calculate u·v. | {
"A": "-3",
"B": "-5",
"C": "6",
"D": "-6"
} | D | -6 | The dot product is the sum of corresponding component products: (4)(3)+(-1)(2)+(-2)(8)=-6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -6, not -3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -6, not -5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -6, not 6.",
"D": "Correct. The work... | [
"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_006906 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 37 mol H₂ and 34 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "18.5 mol",
"B": "27.75 mol",
"C": "37 mol",
"D": "-37 mol"
} | C | 37 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 37 mol H₂O; O₂ can produce 68 mol H₂O. The limiting condition is H₂; product=37 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 37 mol, not 18.5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 37 mol, not 27.75 mol.",
"C": "Correct. The worked calculation gives 37 mol.",
"D": "Incorrect. Substituting the stated va... | [
"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_003604 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 28 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "67.89639 m",
"B": "65.89639 m",
"C": "68.89639 m",
"D": "66.89639 m"
} | A | 67.89639 m | Range R=u²sin(2θ)/g. Substituting u=28, θ=60° and g=10 gives R=(28)²sin(120°)/10=67.89639 m. | {
"A": "Correct. The worked calculation gives 67.89639 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 67.89639 m, not 65.89639 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 67.89639 m, not 68.89639 m.",
"D": "Incorrect. Substitutin... | [
"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_001366 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (-3x² -5x +6) dx. | {
"A": "-3",
"B": "-12",
"C": "-5",
"D": "-6"
} | D | -6 | An antiderivative is (-3/3)x³+(-5/2)x²+(6)x. Evaluating between 0 and 2 gives (-3/3)(2)³+(-5/2)(2)²+(6)(2)=-6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -6, not -3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -6, not -12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -6, not -5.",
"D": "Correct. The wo... | [
"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_005461 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 47 μF capacitor is charged to a potential difference of 19 V. Calculate the energy stored, expressed in μJ. | {
"A": "8483.5 μJ",
"B": "12725.25 μJ",
"C": "849.35 μJ",
"D": "16967 μJ"
} | A | 8483.5 μJ | U=½CV². Since C=47 μF, U in μJ is ½×47×(19)²=8483.5 μJ. | {
"A": "Correct. The worked calculation gives 8483.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8483.5 μJ, not 12725.25 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8483.5 μJ, not 849.35 μJ.",
"D": "Incorrect. Substituting t... | [
"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_002199 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 7 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.26316",
"B": "0.17544",
"C": "1.03509",
"D": "0.35088"
} | D | 0.35088 | Favourable pairs = C(9,2)+C(7,2)+C(3,2)=60. Total pairs=C(19,2)=171. Therefore P=60/171=0.35088. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35088, not 0.26316.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35088, not 0.17544.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35088, not 1.035... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007335 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 17 mol of gas at 327 K and 0.71 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "513.97731 L",
"B": "641.47164 L",
"C": "1284.94328 L",
"D": "642.47164 L"
} | D | 642.47164 L | PV=nRT, so V=nRT/P=(17)(0.082057)(327)/(0.71)=642.47164 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 642.47164 L, not 513.97731 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 642.47164 L, not 641.47164 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 64... | [
"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_000385 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 29 and common difference 10. Find the sum of its first 15 terms. | {
"A": "1483",
"B": "1485",
"C": "1782",
"D": "1113.75"
} | B | 1485 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=29, d=10, n=15: Sₙ=15/2[2(29)+(15−1)(10)]=1485. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1485, not 1483.",
"B": "Correct. The worked calculation gives 1485.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1485, not 1782.",
"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_007906 | 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 66 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "13.2 mmol L⁻¹",
"B": "16.5 mmol L⁻¹",
"C": "12.375 mmol L⁻¹",
"D": "33 mmol L⁻¹"
} | B | 16.5 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=66/2^2=16.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16.5 mmol L⁻¹, not 13.2 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 16.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16.5 mmol L⁻¹, not 12.375 mmol L⁻¹.",
"D": "Incor... | [
"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_001531 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (-3x² +2x +0) dx. | {
"A": "-296",
"B": "294",
"C": "-352.8",
"D": "-294"
} | D | -294 | An antiderivative is (-3/3)x³+(2/2)x²+(0)x. Evaluating between 0 and 7 gives (-3/3)(7)³+(2/2)(7)²+(0)(7)=-294. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -294, not -296.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -294, not 294.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -294, not -352.8.",
"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_004420 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 5 m is acted on by a constant torque of 29 N m about its central axis. Find its angular acceleration. | {
"A": "0.29 rad s⁻²",
"B": "0.435 rad s⁻²",
"C": "-0.29 rad s⁻²",
"D": "2.29 rad s⁻²"
} | A | 0.29 rad s⁻² | For a solid disc, I=½MR²=½(8)(5)²=100 kg m². Using τ=Iα, α=29/100=0.29 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.29 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29 rad s⁻², not 0.435 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29 rad s⁻², not -0.29 rad s⁻².",
"D": "Incorrect.... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006275 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 68 cm in front of a thin convex lens of focal length 24 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.54545",
"B": "0.27273",
"C": "-0.54545",
"D": "3.54545"
} | A | 0.54545 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(68)(24)/(68−24)=37.09091 cm. Thus |m|=v/u=37.09091/68=0.54545. | {
"A": "Correct. The worked calculation gives 0.54545.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.54545, not 0.27273.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.54545, not -0.54545.",
"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_000539 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -16 and common difference 7. Find the sum of its first 9 terms. | {
"A": "108",
"B": "86.4",
"C": "-108",
"D": "11.8"
} | A | 108 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-16, d=7, n=9: Sₙ=9/2[2(-16)+(9−1)(7)]=108. | {
"A": "Correct. The worked calculation gives 108.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 108, not 86.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 108, not -108.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009103 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.39 V, transfers 2 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.5673 V",
"B": "2.35095 V",
"C": "1.5673 V",
"D": "3.5673 V"
} | C | 1.5673 V | Apply the Nernst equation: E=1.39−(0.0591/2)(-6)=1.5673 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.5673 V, not 0.5673 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.5673 V, not 2.35095 V.",
"C": "Correct. The worked calculation gives 1.5673 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_001656 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (-3x² -6x +4) dx. | {
"A": "-95",
"B": "-115.2",
"C": "-144",
"D": "-96"
} | D | -96 | An antiderivative is (-3/3)x³+(-6/2)x²+(4)x. Evaluating between 0 and 4 gives (-3/3)(4)³+(-6/2)(4)²+(4)(4)=-96. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -96, not -95.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -96, not -115.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -96, not -144.",
"D": "Correc... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000890 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 5. What is the sum of its first 6 terms? | {
"A": "3907",
"B": "39061",
"C": "29295",
"D": "39060"
} | D | 39060 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(5^6−1)/(5−1)=39060. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 39060, not 3907.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39060, not 39061.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39060, not 29295.",
"D": ... | [
"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_007375 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 13 mL of 0.10 M HCl is mixed with 31 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "25.22364",
"B": "6.30591",
"C": "12.61182",
"D": "13.61182"
} | C | 12.61182 | Excess OH⁻ moles=0.10×(31−13)/1000=0.001800 mol. Total volume=0.044 L, so [OH⁻]=0.040909 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.61182. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.61182, not 25.22364.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.61182, not 6.30591.",
"C": "Correct. The worked calculation gives 12.61182.",
"D": "Incorrect. Substituting the state... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001575 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (5x² -4x -1) dx. | {
"A": "0.66667",
"B": "-0.66667",
"C": "-1.33333",
"D": "-2.33333"
} | C | -1.33333 | An antiderivative is (5/3)x³+(-4/2)x²+(-1)x. Evaluating between 0 and 1 gives (5/3)(1)³+(-4/2)(1)²+(-1)(1)=-1.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.33333, not 0.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.33333, not -0.66667.",
"C": "Correct. The worked calculation gives -1.33333.",
"D": "Incorrect. Substituting the state... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009874 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(Cl)_4]^+3, each Cl ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "9",
"B": "10.5",
"C": "7",
"D": "-7"
} | C | 7 | Let the formal oxidation state of Ni be x. Charge balance gives x+(4)(−1)=+3; hence x=3+4=+7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 10.5.",
"C": "Correct. The worked calculation gives 7.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004367 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 13 kg and radius 5 m is acted on by a constant torque of 12 N m about its central axis. Find its angular acceleration. | {
"A": "-0.07385 rad s⁻²",
"B": "0.05538 rad s⁻²",
"C": "0.07385 rad s⁻²",
"D": "0.03692 rad s⁻²"
} | C | 0.07385 rad s⁻² | For a solid disc, I=½MR²=½(13)(5)²=162.5 kg m². Using τ=Iα, α=12/162.5=0.07385 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.07385 rad s⁻², not -0.07385 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.07385 rad s⁻², not 0.05538 rad s⁻².",
"C": "Correct. The worked calculation gives 0.07385 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_008185 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 11 A for 20121 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "74.82134 g",
"B": "71.82134 g",
"C": "72.82134 g",
"D": "73.82134 g"
} | C | 72.82134 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×20121/(2×96500)=72.82134 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 72.82134 g, not 74.82134 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 72.82134 g, not 71.82134 g.",
"C": "Correct. The worked calculation gives 72.82134 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006514 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 17 kg is attached to an ideal spring of force constant 254 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.48259 s",
"B": "0.51741 s",
"C": "-0.51741 s",
"D": "0.25871 s"
} | B | 0.51741 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(17/254)=0.51741 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.51741 s, not -0.48259 s.",
"B": "Correct. The worked calculation gives 0.51741 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.51741 s, not -0.51741 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_005324 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +7 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "42 N",
"B": "-52.5 N",
"C": "26.25 N",
"D": "52.5 N"
} | D | 52.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(7×10⁻⁶)/(6×10⁻²)²=52.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 52.5 N, not 42 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 52.5 N, not -52.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 52.5 N, not 26.25 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_005466 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 50 μF capacitor is charged to a potential difference of 30 V. Calculate the energy stored, expressed in μJ. | {
"A": "22502 μJ",
"B": "11250 μJ",
"C": "33750 μJ",
"D": "22500 μJ"
} | D | 22500 μJ | U=½CV². Since C=50 μF, U in μJ is ½×50×(30)²=22500 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22500 μJ, not 22502 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22500 μJ, not 11250 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22500 μJ, not ... | [
"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_005640 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 62 μF capacitor is charged to a potential difference of 8 V. Calculate the energy stored, expressed in μJ. | {
"A": "1587.2 μJ",
"B": "1984 μJ",
"C": "2976 μJ",
"D": "3968 μJ"
} | B | 1984 μJ | U=½CV². Since C=62 μF, U in μJ is ½×62×(8)²=1984 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1984 μJ, not 1587.2 μJ.",
"B": "Correct. The worked calculation gives 1984 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1984 μJ, not 2976 μJ.",
"D": "Incorrect. Substituting the stated ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001501 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (1x² +4x +3) dx. | {
"A": "33.33333",
"B": "14.66667",
"C": "16.66667",
"D": "12.5"
} | C | 16.66667 | An antiderivative is (1/3)x³+(4/2)x²+(3)x. Evaluating between 0 and 2 gives (1/3)(2)³+(4/2)(2)²+(3)(2)=16.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16.66667, not 33.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16.66667, not 14.66667.",
"C": "Correct. The worked calculation gives 16.66667.",
"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_005527 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 60 μF capacitor is charged to a potential difference of 5 V. Calculate the energy stored, expressed in μJ. | {
"A": "562.5 μJ",
"B": "750 μJ",
"C": "752 μJ",
"D": "751 μJ"
} | B | 750 μJ | U=½CV². Since C=60 μF, U in μJ is ½×60×(5)²=750 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 750 μJ, not 562.5 μJ.",
"B": "Correct. The worked calculation gives 750 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 750 μJ, not 752 μJ.",
"D": "Incorrect. Substituting the stated value... | [
"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_009638 | 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_12. Treat X as the total number of monovalent halogen atoms. | {
"A": "13",
"B": "19.5",
"C": "26",
"D": "2.3"
} | A | 13 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+0−12−0)/2=13. | {
"A": "Correct. The worked calculation gives 13.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13, not 19.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13, not 26.",
"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_004104 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 36 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": "155.52 N",
"B": "-155.52 N",
"C": "311.04 N",
"D": "156.52 N"
} | A | 155.52 N | Net force=mg(sinθ−μcosθ)=36×10×(0.6−0.21×0.8)=155.52 N. | {
"A": "Correct. The worked calculation gives 155.52 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 155.52 N, not -155.52 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 155.52 N, not 311.04 N.",
"D": "Incorrect. Substituting the sta... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009555 | 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_12H_5X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "11",
"B": "1.9",
"C": "10",
"D": "9"
} | D | 9 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×12+2+0−5−3)/2=9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9, not 11.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9, not 1.9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9, not 10.",
"D": "Correct. The worke... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003180 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(8+10i)/(2+11i). What is Re(z), the real part of z? | {
"A": "-1.008",
"B": "1.512",
"C": "1.008",
"D": "2.008"
} | C | 1.008 | Multiply numerator and denominator by the conjugate (2-11i). Then Re(z)=(ac+bd)/(c²+d²)=((8)(2)+(10)(11))/(2²+(11)²)=1.008. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.008, not -1.008.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.008, not 1.512.",
"C": "Correct. The worked calculation gives 1.008.",
"D": "Incorrect. Substituting the stated values into... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006947 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 35 mol H₂ and 12 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "18 mol",
"B": "24 mol",
"C": "25 mol",
"D": "26 mol"
} | B | 24 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 35 mol H₂O; O₂ can produce 24 mol H₂O. The limiting condition is O₂; product=24 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24 mol, not 18 mol.",
"B": "Correct. The worked calculation gives 24 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24 mol, not 25 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007473 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 55 mL of 0.10 M HCl is mixed with 54 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "4.03743",
"B": "3.03743",
"C": "2.27807",
"D": "1.03743"
} | B | 3.03743 | Excess H⁺ moles=0.10×(55−54)/1000=0.000100 mol. Total volume=0.109 L, so [H⁺]=0.000917 M and pH=−log₁₀[H⁺]=3.03743. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.03743, not 4.03743.",
"B": "Correct. The worked calculation gives 3.03743.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.03743, not 2.27807.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003234 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(13+8i)/(2+9i). What is Re(z), the real part of z? | {
"A": "0.86471",
"B": "2.30588",
"C": "1.11529",
"D": "1.15294"
} | D | 1.15294 | Multiply numerator and denominator by the conjugate (2-9i). Then Re(z)=(ac+bd)/(c²+d²)=((13)(2)+(8)(9))/(2²+(9)²)=1.15294. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.15294, not 0.86471.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.15294, not 2.30588.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.15294, not 1.115... | [
"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_008160 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 3 A for 19487 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": "18.23458 g",
"B": "19.23458 g",
"C": "14.42593 g",
"D": "20.23458 g"
} | B | 19.23458 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×3×19487/(2×96500)=19.23458 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19.23458 g, not 18.23458 g.",
"B": "Correct. The worked calculation gives 19.23458 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19.23458 g, not 14.42593 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009146 | 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 3 electrons, and has reaction quotient Q=10^1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.6503 V",
"B": "0.6503 V",
"C": "2.6503 V",
"D": "0.32515 V"
} | B | 0.6503 V | Apply the Nernst equation: E=0.67−(0.0591/3)(1)=0.6503 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6503 V, not -0.6503 V.",
"B": "Correct. The worked calculation gives 0.6503 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.6503 V, not 2.6503 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_003136 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(8+10i)/(1+11i). What is Re(z), the real part of z? | {
"A": "1.09672",
"B": "1.93443",
"C": "3.96721",
"D": "0.96721"
} | D | 0.96721 | Multiply numerator and denominator by the conjugate (1-11i). Then Re(z)=(ac+bd)/(c²+d²)=((8)(1)+(10)(11))/(1²+(11)²)=0.96721. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.96721, not 1.09672.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.96721, not 1.93443.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.96721, not 3.967... | [
"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_002816 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(7, 8, 4) and v=(-5, -7, 8), calculate u·v. | {
"A": "-4.9",
"B": "59",
"C": "-59",
"D": "-60"
} | C | -59 | The dot product is the sum of corresponding component products: (7)(-5)+(8)(-7)+(4)(8)=-59. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -59, not -4.9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -59, not 59.",
"C": "Correct. The worked calculation gives -59.",
"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_004731 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 2 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 4 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.5 A",
"B": "3.5 A",
"C": "-0.5 A",
"D": "3.75 A"
} | A | 2.5 A | Series branch resistance=2+4=6 Ω. Parallel equivalent R_eq=(6×4)/(6+4)=2.4 Ω. Total current I=V/R_eq=6/2.4=2.5 A. | {
"A": "Correct. The worked calculation gives 2.5 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.5 A, not 3.5 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.5 A, not -0.5 A.",
"D": "Incorrect. Substituting the stated values into... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001193 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=2x³ +8x² +10x+7. Evaluate f′(-2). | {
"A": "4",
"B": "0",
"C": "2",
"D": "1.5"
} | C | 2 | Differentiate: f′(x)=3(2)x²+2(8)x+(10). At x=-2, f′(-2)=3(2)(-2)²+2(8)(-2)+(10)=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 0.",
"C": "Correct. The worked calculation gives 2.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006228 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 55 cm in front of a thin convex lens of focal length 20 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.28571",
"B": "1.57143",
"C": "0.57143",
"D": "-2.42857"
} | C | 0.57143 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(55)(20)/(55−20)=31.42857 cm. Thus |m|=v/u=31.42857/55=0.57143. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.57143, not 0.28571.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.57143, not 1.57143.",
"C": "Correct. The worked calculation gives 0.57143.",
"D": "Incorrect. Substituting the stated va... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009006 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.53 V, transfers 3 electrons, and has reaction quotient Q=10^0. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.053 V",
"B": "1.53 V",
"C": "0.795 V",
"D": "0.53 V"
} | D | 0.53 V | Apply the Nernst equation: E=0.53−(0.0591/3)(0)=0.53 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.53 V, not 1.053 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.53 V, not 1.53 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.53 V, not 0.795 V."... | [
"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_006978 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 15 mol H₂ and 9 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "-15 mol",
"B": "15 mol",
"C": "14 mol",
"D": "13 mol"
} | B | 15 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 15 mol H₂O; O₂ can produce 18 mol H₂O. The limiting condition is H₂; product=15 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15 mol, not -15 mol.",
"B": "Correct. The worked calculation gives 15 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15 mol, not 14 mol.",
"D": "Incorrect. Substituting the stated values... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007046 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 5 mol of gas at 221 K and 1.28 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "70.83827 L",
"B": "68.83827 L",
"C": "71.83827 L",
"D": "53.1287 L"
} | A | 70.83827 L | PV=nRT, so V=nRT/P=(5)(0.082057)(221)/(1.28)=70.83827 L. | {
"A": "Correct. The worked calculation gives 70.83827 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 70.83827 L, not 68.83827 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 70.83827 L, not 71.83827 L.",
"D": "Incorrect. Substitutin... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007109 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 6 mol of gas at 357 K and 0.45 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "585.88698 L",
"B": "389.59132 L",
"C": "391.59132 L",
"D": "390.59132 L"
} | D | 390.59132 L | PV=nRT, so V=nRT/P=(6)(0.082057)(357)/(0.45)=390.59132 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 390.59132 L, not 585.88698 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 390.59132 L, not 389.59132 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39... | [
"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_000089 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 -8x -5=0, let its roots be α and β. What is α²+β²? | {
"A": "13",
"B": "9.75",
"C": "4.875",
"D": "6.5"
} | D | 6.5 | By Vieta's relations, α+β = 8/4 and αβ = -5/4. Then α²+β²=(α+β)²−2αβ = (8/4)²−2(-5/4) = 6.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.5, not 13.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.5, not 9.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.5, not 4.875.",
"D": "Correct.... | [
"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_001374 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (6x² -3x +3) dx. | {
"A": "227.5",
"B": "341.25",
"C": "182",
"D": "225.5"
} | A | 227.5 | An antiderivative is (6/3)x³+(-3/2)x²+(3)x. Evaluating between 0 and 5 gives (6/3)(5)³+(-3/2)(5)²+(3)(5)=227.5. | {
"A": "Correct. The worked calculation gives 227.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 227.5, not 341.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 227.5, not 182.",
"D": "Incorrect. Substituting the stated values into 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_001533 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (6x² +2x -4) dx. | {
"A": "888",
"B": "444",
"C": "446",
"D": "45.4"
} | B | 444 | An antiderivative is (6/3)x³+(2/2)x²+(-4)x. Evaluating between 0 and 6 gives (6/3)(6)³+(2/2)(6)²+(-4)(6)=444. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 444, not 888.",
"B": "Correct. The worked calculation gives 444.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 444, not 446.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006265 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 44 cm in front of a thin convex lens of focal length 14 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.46667",
"B": "-2.53333",
"C": "2.46667",
"D": "3.46667"
} | A | 0.46667 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(44)(14)/(44−14)=20.53333 cm. Thus |m|=v/u=20.53333/44=0.46667. | {
"A": "Correct. The worked calculation gives 0.46667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.46667, not -2.53333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.46667, not 2.46667.",
"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_007268 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 7 mol of gas at 321 K and 0.69 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "265.2204 L",
"B": "268.2204 L",
"C": "267.2204 L",
"D": "213.77632 L"
} | C | 267.2204 L | PV=nRT, so V=nRT/P=(7)(0.082057)(321)/(0.69)=267.2204 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 267.2204 L, not 265.2204 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 267.2204 L, not 268.2204 L.",
"C": "Correct. The worked calculation gives 267.2204 L.",
"D": "Incorrect. Substitutin... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009336 | 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_13H_20N_3X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "7.5",
"B": "3",
"C": "6",
"D": "5"
} | D | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×13+2+3−20−1)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 6.",
"D": "Correct. The worked ... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003465 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 118 m s⁻¹ at 50° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "685.62316 m",
"B": "1370.24632 m",
"C": "1096.99705 m",
"D": "1371.24632 m"
} | D | 1371.24632 m | Range R=u²sin(2θ)/g. Substituting u=118, θ=50° and g=10 gives R=(118)²sin(100°)/10=1371.24632 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1371.24632 m, not 685.62316 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1371.24632 m, not 1370.24632 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives... | [
"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_003755 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 7 m s⁻¹. A constant net force does 20 N of work over 19 m in the direction of motion. Find its final kinetic energy. | {
"A": "500 J",
"B": "627 J",
"C": "625 J",
"D": "468.75 J"
} | C | 625 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(7)²+(20)(19)=625 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 625 J, not 500 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 625 J, not 627 J.",
"C": "Correct. The worked calculation gives 625 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_009885 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(CN)_3]^-3, each CN ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "3",
"B": "-2",
"C": "1",
"D": "0"
} | D | 0 | Let the formal oxidation state of Mn be x. Charge balance gives x+(3)(−1)=-3; hence x=-3+3=+0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"D": "Correct. The worked c... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000194 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 -6x +3=0, let its roots be α and β. What is α²+β²? | {
"A": "30",
"B": "24",
"C": "29",
"D": "32"
} | A | 30 | By Vieta's relations, α+β = 6/1 and αβ = 3/1. Then α²+β²=(α+β)²−2αβ = (6/1)²−2(3/1) = 30. | {
"A": "Correct. The worked calculation gives 30.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30, not 24.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30, not 29.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001191 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=3x³ -8x² -2x+7. Evaluate f′(-3). | {
"A": "127",
"B": "152.4",
"C": "125",
"D": "128"
} | A | 127 | Differentiate: f′(x)=3(3)x²+2(-8)x+(-2). At x=-3, f′(-3)=3(3)(-3)²+2(-8)(-3)+(-2)=127. | {
"A": "Correct. The worked calculation gives 127.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 127, not 152.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 127, not 125.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_003656 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 117 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1284.34523 m",
"B": "643.17261 m",
"C": "1286.34523 m",
"D": "129.63452 m"
} | C | 1286.34523 m | Range R=u²sin(2θ)/g. Substituting u=117, θ=55° and g=10 gives R=(117)²sin(110°)/10=1286.34523 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1286.34523 m, not 1284.34523 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1286.34523 m, not 643.17261 m.",
"C": "Correct. The worked calculation gives 1286.34523 m.",
"D": "Incorrect. Su... | [
"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_005237 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +3 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "68.5 N",
"B": "54 N",
"C": "-67.5 N",
"D": "67.5 N"
} | D | 67.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(3×10⁻⁶)/(2×10⁻²)²=67.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 67.5 N, not 68.5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 67.5 N, not 54 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 67.5 N, not -67.5 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_008176 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 3 A for 1035 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": "0.5108 g",
"B": "0.76619 g",
"C": "1.02159 g",
"D": "-1.02159 g"
} | C | 1.02159 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×3×1035/(2×96500)=1.02159 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.02159 g, not 0.5108 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.02159 g, not 0.76619 g.",
"C": "Correct. The worked calculation gives 1.02159 g.",
"D": "Incorrect. Substituting the ... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007898 | 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 32 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "8 mmol L⁻¹",
"B": "7 mmol L⁻¹",
"C": "1.8 mmol L⁻¹",
"D": "16 mmol L⁻¹"
} | A | 8 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=32/2^2=8 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 8 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8 mmol L⁻¹, not 7 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8 mmol L⁻¹, not 1.8 mmol L⁻¹.",
"D": "Incorrect. Substitut... | [
"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_009275 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.25 V, transfers 3 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.1318 V",
"B": "3.1318 V",
"C": "1.11318 V",
"D": "1.1318 V"
} | D | 1.1318 V | Apply the Nernst equation: E=1.25−(0.0591/3)(6)=1.1318 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.1318 V, not 0.1318 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1318 V, not 3.1318 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1318 V, not ... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000044 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 +10x -11=0, let its roots be α and β. What is α²+β²? | {
"A": "122",
"B": "146.4",
"C": "244",
"D": "124"
} | A | 122 | By Vieta's relations, α+β = -10/1 and αβ = -11/1. Then α²+β²=(α+β)²−2αβ = (-10/1)²−2(-11/1) = 122. | {
"A": "Correct. The worked calculation gives 122.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 122, not 146.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 122, not 244.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007581 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 11 mL of 0.10 M HCl is mixed with 20 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "14.46288",
"B": "-12.46288",
"C": "12.46288",
"D": "15.46288"
} | C | 12.46288 | Excess OH⁻ moles=0.10×(20−11)/1000=0.000900 mol. Total volume=0.031 L, so [OH⁻]=0.029032 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.46288. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.46288, not 14.46288.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.46288, not -12.46288.",
"C": "Correct. The worked calculation gives 12.46288.",
"D": "Incorrect. Substituting the sta... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009775 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(CN)_4]^+1, each CN ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "-5",
"B": "4",
"C": "6",
"D": "5"
} | D | 5 | Let the formal oxidation state of Cu be x. Charge balance gives x+(4)(−1)=+1; hence x=1+4=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not -5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 6.",
"D": "Correct. The worked c... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001963 | 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 24 distinct elements? | {
"A": "2024",
"B": "203.4",
"C": "2025",
"D": "2428.8"
} | A | 2024 | Order does not matter, so the count is C(24,3)=24!/[3!(21)!]=2024. | {
"A": "Correct. The worked calculation gives 2024.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2024, not 203.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2024, not 2025.",
"D": "Incorrect. Substituting the stated values into the ... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005107 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +3 μC are separated by 5 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "10.8 N",
"B": "16.2 N",
"C": "8.1 N",
"D": "2.08 N"
} | A | 10.8 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(3×10⁻⁶)/(5×10⁻²)²=10.8 N. | {
"A": "Correct. The worked calculation gives 10.8 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.8 N, not 16.2 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10.8 N, not 8.1 N.",
"D": "Incorrect. Substituting the stated values i... | [
"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_004066 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.45. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "31.68 N",
"B": "19.8 N",
"C": "39.6 N",
"D": "26.4 N"
} | D | 26.4 N | Net force=mg(sinθ−μcosθ)=11×10×(0.6−0.45×0.8)=26.4 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26.4 N, not 31.68 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26.4 N, not 19.8 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26.4 N, not 39.6 N.",... | [
"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_007495 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 86 mL of 0.10 M HCl is mixed with 35 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.37522",
"B": "2.06282",
"C": "-0.62478",
"D": "2.37522"
} | A | 1.37522 | Excess H⁺ moles=0.10×(86−35)/1000=0.005100 mol. Total volume=0.121 L, so [H⁺]=0.042149 M and pH=−log₁₀[H⁺]=1.37522. | {
"A": "Correct. The worked calculation gives 1.37522.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.37522, not 2.06282.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.37522, not -0.62478.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009283 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.13 V, transfers 2 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "4.27775 V",
"B": "0.63887 V",
"C": "1.91662 V",
"D": "1.27775 V"
} | D | 1.27775 V | Apply the Nernst equation: E=1.13−(0.0591/2)(-5)=1.27775 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.27775 V, not 4.27775 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.27775 V, not 0.63887 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.27775 V,... | [
"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_009376 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_11H_17N_1X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "0",
"B": "-3",
"C": "3",
"D": "1.3"
} | C | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+1−17−2)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not -3.",
"C": "Correct. The worked calculation gives 3.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003529 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 76 m s⁻¹ at 65° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "443.46727 m",
"B": "-442.46727 m",
"C": "884.93454 m",
"D": "442.46727 m"
} | D | 442.46727 m | Range R=u²sin(2θ)/g. Substituting u=76, θ=65° and g=10 gives R=(76)²sin(130°)/10=442.46727 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 442.46727 m, not 443.46727 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 442.46727 m, not -442.46727 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006286 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 93 cm in front of a thin convex lens of focal length 19 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.25676",
"B": "-0.74324",
"C": "0.51351",
"D": "1.25676"
} | A | 0.25676 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(93)(19)/(93−19)=23.87838 cm. Thus |m|=v/u=23.87838/93=0.25676. | {
"A": "Correct. The worked calculation gives 0.25676.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25676, not -0.74324.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25676, not 0.51351.",
"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_008852 | 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 0.27 mol L⁻¹ and initially B is absent. At equilibrium, 43% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.64966",
"B": "2.35034",
"C": "0.35034",
"D": "0.70067"
} | C | 0.35034 | Let α=0.43. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.27)(0.43)²/(1−0.43)=0.35034. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35034, not -0.64966.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35034, not 2.35034.",
"C": "Correct. The worked calculation gives 0.35034.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005896 | 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 atm at 288 K. What is its pressure at 411 K? | {
"A": "1.42708 atm",
"B": "2.85417 atm",
"C": "-1.42708 atm",
"D": "3.42708 atm"
} | A | 1.42708 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1)(411)/(288)=1.42708 atm. | {
"A": "Correct. The worked calculation gives 1.42708 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.42708 atm, not 2.85417 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.42708 atm, not -1.42708 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_005617 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 71 μF capacitor is charged to a potential difference of 25 V. Calculate the energy stored, expressed in μJ. | {
"A": "11093.75 μJ",
"B": "22186.5 μJ",
"C": "22187.5 μJ",
"D": "16640.625 μJ"
} | C | 22187.5 μJ | U=½CV². Since C=71 μF, U in μJ is ½×71×(25)²=22187.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22187.5 μJ, not 11093.75 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22187.5 μJ, not 22186.5 μJ.",
"C": "Correct. The worked calculation gives 22187.5 μJ.",
"D": "Incorrect. Substituti... | [
"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_007016 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 14 mol of gas at 310 K and 0.28 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "1526.2602 L",
"B": "1271.8835 L",
"C": "1017.5068 L",
"D": "2543.767 L"
} | B | 1271.8835 L | PV=nRT, so V=nRT/P=(14)(0.082057)(310)/(0.28)=1271.8835 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1271.8835 L, not 1526.2602 L.",
"B": "Correct. The worked calculation gives 1271.8835 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1271.8835 L, not 1017.5068 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_004012 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 24 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.37. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "73.96 N",
"B": "72.96 N",
"C": "58.368 N",
"D": "-72.96 N"
} | B | 72.96 N | Net force=mg(sinθ−μcosθ)=24×10×(0.6−0.37×0.8)=72.96 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 72.96 N, not 73.96 N.",
"B": "Correct. The worked calculation gives 72.96 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 72.96 N, not 58.368 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_001373 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (-3x² +8x -4) dx. | {
"A": "-96",
"B": "-115.2",
"C": "-95",
"D": "-98"
} | A | -96 | An antiderivative is (-3/3)x³+(8/2)x²+(-4)x. Evaluating between 0 and 6 gives (-3/3)(6)³+(8/2)(6)²+(-4)(6)=-96. | {
"A": "Correct. The worked calculation gives -96.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -96, not -115.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -96, not -95.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_007167 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 12 mol of gas at 233 K and 1.39 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "330.11708 L",
"B": "164.05854 L",
"C": "165.05854 L",
"D": "82.52927 L"
} | C | 165.05854 L | PV=nRT, so V=nRT/P=(12)(0.082057)(233)/(1.39)=165.05854 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 165.05854 L, not 330.11708 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 165.05854 L, not 164.05854 L.",
"C": "Correct. The worked calculation gives 165.05854 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_009565 | 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_13H_25N_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "2",
"C": "0",
"D": "6"
} | A | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×13+2+3−25−0)/2=3. | {
"A": "Correct. The worked calculation gives 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 0.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006330 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 28 cm in front of a thin convex lens of focal length 6 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-1.72727",
"B": "0.27273",
"C": "0.40909",
"D": "3.27273"
} | B | 0.27273 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(28)(6)/(28−6)=7.63636 cm. Thus |m|=v/u=7.63636/28=0.27273. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.27273, not -1.72727.",
"B": "Correct. The worked calculation gives 0.27273.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.27273, not 0.40909.",
"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_008948 | 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 1.3 mol L⁻¹ and initially B is absent. At equilibrium, 56% of A has dissociated at constant volume. Find K_c. | {
"A": "3.70618",
"B": "2.70618",
"C": "-3.70618",
"D": "5.55927"
} | A | 3.70618 | Let α=0.56. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.3)(0.56)²/(1−0.56)=3.70618. | {
"A": "Correct. The worked calculation gives 3.70618.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.70618, not 2.70618.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.70618, not -3.70618.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009526 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_4H_1X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "4",
"B": "0",
"C": "3",
"D": "-3"
} | C | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×4+2+0−1−3)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 0.",
"C": "Correct. The worked calculation gives 3.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006998 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 30 mol H₂ and 27 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "30 mol",
"B": "32 mol",
"C": "31 mol",
"D": "45 mol"
} | A | 30 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 30 mol H₂O; O₂ can produce 54 mol H₂O. The limiting condition is H₂; product=30 mol. | {
"A": "Correct. The worked calculation gives 30 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30 mol, not 32 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30 mol, not 31 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000026 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 +10x -6=0, let its roots be α and β. What is α²+β²? | {
"A": "84",
"B": "111",
"C": "110",
"D": "112"
} | D | 112 | By Vieta's relations, α+β = -10/1 and αβ = -6/1. Then α²+β²=(α+β)²−2αβ = (-10/1)²−2(-6/1) = 112. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 112, not 84.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 112, not 111.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 112, not 110.",
"D": "Correct. Th... | [
"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_003985 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block initially moves at 5 m s⁻¹. A constant net force does 14 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "183.2 J",
"B": "458 J",
"C": "229 J",
"D": "114.5 J"
} | C | 229 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(6)(5)²+(14)(11)=229 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 229 J, not 183.2 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 229 J, not 458 J.",
"C": "Correct. The worked calculation gives 229 J.",
"D": "Incorrect. Substituting the stated values int... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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