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_007027 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 19 mol of gas at 535 K and 0.94 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "887.35043 L",
"B": "886.35043 L",
"C": "709.88034 L",
"D": "89.73504 L"
} | A | 887.35043 L | PV=nRT, so V=nRT/P=(19)(0.082057)(535)/(0.94)=887.35043 L. | {
"A": "Correct. The worked calculation gives 887.35043 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 887.35043 L, not 886.35043 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 887.35043 L, not 709.88034 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_007738 | 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 49 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "3.45 mmol L⁻¹",
"B": "18.375 mmol L⁻¹",
"C": "36.75 mmol L⁻¹",
"D": "24.5 mmol L⁻¹"
} | D | 24.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=49/2^1=24.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24.5 mmol L⁻¹, not 3.45 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24.5 mmol L⁻¹, not 18.375 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relatio... | [
"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_006918 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 41 mol H₂ and 14 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "28 mol",
"B": "56 mol",
"C": "33.6 mol",
"D": "14 mol"
} | A | 28 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 41 mol H₂O; O₂ can produce 28 mol H₂O. The limiting condition is O₂; product=28 mol. | {
"A": "Correct. The worked calculation gives 28 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28 mol, not 56 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28 mol, not 33.6 mol.",
"D": "Incorrect. Substituting the stated value... | [
"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_007718 | 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 62 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "-1.03125 mmol L⁻¹",
"B": "1.96875 mmol L⁻¹",
"C": "1.9375 mmol L⁻¹",
"D": "0.96875 mmol L⁻¹"
} | D | 0.96875 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=62/2^6=0.96875 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.96875 mmol L⁻¹, not -1.03125 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.96875 mmol L⁻¹, not 1.96875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the govern... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009042 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.08 V, transfers 1 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.7845 V",
"B": "-1.2155 V",
"C": "1.07845 V",
"D": "1.569 V"
} | A | 0.7845 V | Apply the Nernst equation: E=1.08−(0.0591/1)(5)=0.7845 V. | {
"A": "Correct. The worked calculation gives 0.7845 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7845 V, not -1.2155 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7845 V, not 1.07845 V.",
"D": "Incorrect. Substituting the st... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005481 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 21 μF capacitor is charged to a potential difference of 26 V. Calculate the energy stored, expressed in μJ. | {
"A": "5678.4 μJ",
"B": "7097 μJ",
"C": "7098 μJ",
"D": "7099 μJ"
} | C | 7098 μJ | U=½CV². Since C=21 μF, U in μJ is ½×21×(26)²=7098 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7098 μJ, not 5678.4 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7098 μJ, not 7097 μJ.",
"C": "Correct. The worked calculation gives 7098 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_008555 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.55 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "3.5872 K",
"B": "3.1744 K",
"C": "1.15872 K",
"D": "1.5872 K"
} | D | 1.5872 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×1.55=1.5872 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.5872 K, not 3.5872 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.5872 K, not 3.1744 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.5872 K, not ... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003593 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 108 m s⁻¹ at 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "918.94381 m",
"B": "1378.41572 m",
"C": "1723.01964 m",
"D": "1148.67976 m"
} | D | 1148.67976 m | Range R=u²sin(2θ)/g. Substituting u=108, θ=40° and g=10 gives R=(108)²sin(80°)/10=1148.67976 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1148.67976 m, not 918.94381 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1148.67976 m, not 1378.41572 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_001135 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=2x³ -5x² +1x+7. Evaluate f′(0). | {
"A": "1",
"B": "1.1",
"C": "0.5",
"D": "0.75"
} | A | 1 | Differentiate: f′(x)=3(2)x²+2(-5)x+(1). At x=0, f′(0)=3(2)(0)²+2(-5)(0)+(1)=1. | {
"A": "Correct. The worked calculation gives 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.5.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001264 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ -3x² +4x+7. Evaluate f′(-1). | {
"A": "-4",
"B": "1",
"C": "-1",
"D": "-2"
} | D | -2 | Differentiate: f′(x)=3(-4)x²+2(-3)x+(4). At x=-1, f′(-1)=3(-4)(-1)²+2(-3)(-1)+(4)=-2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2, not -4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2, not 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2, not -1.",
"D": "Correct. The work... | [
"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_003080 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(4+0i)/(8+2i). What is Re(z), the real part of z? | {
"A": "3.47059",
"B": "0.47059",
"C": "1.47059",
"D": "-2.52941"
} | B | 0.47059 | Multiply numerator and denominator by the conjugate (8-2i). Then Re(z)=(ac+bd)/(c²+d²)=((4)(8)+(0)(2))/(8²+(2)²)=0.47059. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.47059, not 3.47059.",
"B": "Correct. The worked calculation gives 0.47059.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.47059, not 1.47059.",
"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_003660 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 93 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "331.27592 m",
"B": "530.04147 m",
"C": "67.25518 m",
"D": "662.55184 m"
} | D | 662.55184 m | Range R=u²sin(2θ)/g. Substituting u=93, θ=25° and g=10 gives R=(93)²sin(50°)/10=662.55184 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 662.55184 m, not 331.27592 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 662.55184 m, not 530.04147 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 66... | [
"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_000701 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio 4. What is the sum of its first 12 terms? | {
"A": "25165822.5",
"B": "33554430",
"C": "3355444",
"D": "26843544"
} | B | 33554430 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(4^12−1)/(4−1)=33554430. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33554430, not 25165822.5.",
"B": "Correct. The worked calculation gives 33554430.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 33554430, not 3355444.",
"D": "Incorrect. Substituting the sta... | [
"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_002278 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 11 blue and 5 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.39766",
"B": "0.29825",
"C": "0.59649",
"D": "3.39766"
} | A | 0.39766 | Favourable pairs = C(3,2)+C(11,2)+C(5,2)=68. Total pairs=C(19,2)=171. Therefore P=68/171=0.39766. | {
"A": "Correct. The worked calculation gives 0.39766.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.39766, not 0.29825.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.39766, not 0.59649.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009796 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(OH)_2]^+3, each OH ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "3",
"B": "7.5",
"C": "5",
"D": "4"
} | C | 5 | Let the formal oxidation state of Fe be x. Charge balance gives x+(2)(−1)=+3; hence x=3+2=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.5.",
"C": "Correct. The worked calculation gives 5.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005837 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.2 atm at 362 K. What is its pressure at 622 K? | {
"A": "8.24751 atm",
"B": "5.49834 atm",
"C": "3.49834 atm",
"D": "-5.49834 atm"
} | B | 5.49834 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.2)(622)/(362)=5.49834 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.49834 atm, not 8.24751 atm.",
"B": "Correct. The worked calculation gives 5.49834 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.49834 atm, not 3.49834 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005810 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.5 atm at 406 K. What is its pressure at 663 K? | {
"A": "6.34852 atm",
"B": "7.34852 atm",
"C": "5.51139 atm",
"D": "1.73485 atm"
} | B | 7.34852 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.5)(663)/(406)=7.34852 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.34852 atm, not 6.34852 atm.",
"B": "Correct. The worked calculation gives 7.34852 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.34852 atm, not 5.51139 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004354 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 1 m is acted on by a constant torque of 12 N m about its central axis. Find its angular acceleration. | {
"A": "5.14286 rad s⁻²",
"B": "3.42857 rad s⁻²",
"C": "2.57143 rad s⁻²",
"D": "4.42857 rad s⁻²"
} | B | 3.42857 rad s⁻² | For a solid disc, I=½MR²=½(7)(1)²=3.5 kg m². Using τ=Iα, α=12/3.5=3.42857 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.42857 rad s⁻², not 5.14286 rad s⁻².",
"B": "Correct. The worked calculation gives 3.42857 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.42857 rad s⁻², not 2.57143 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_000325 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 +11x +3=0, let its roots be α and β. What is α²+β²? | {
"A": "57.5",
"B": "115",
"C": "12.5",
"D": "116"
} | B | 115 | By Vieta's relations, α+β = -11/1 and αβ = 3/1. Then α²+β²=(α+β)²−2αβ = (-11/1)²−2(3/1) = 115. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 115, not 57.5.",
"B": "Correct. The worked calculation gives 115.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 115, not 12.5.",
"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_003098 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-12+1i)/(8+11i). What is Re(z), the real part of z? | {
"A": "-0.45946",
"B": "-1.45946",
"C": "-0.68919",
"D": "2.54054"
} | A | -0.45946 | Multiply numerator and denominator by the conjugate (8-11i). Then Re(z)=(ac+bd)/(c²+d²)=((-12)(8)+(1)(11))/(8²+(11)²)=-0.45946. | {
"A": "Correct. The worked calculation gives -0.45946.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.45946, not -1.45946.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.45946, not -0.68919.",
"D": "Incorrect. Substituting the stat... | [
"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_000723 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 12 and common ratio -3. What is the sum of its first 8 terms? | {
"A": "-19678",
"B": "-19680",
"C": "-29520",
"D": "-15744"
} | B | -19680 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=12(-3^8−1)/(-3−1)=-19680. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -19680, not -19678.",
"B": "Correct. The worked calculation gives -19680.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -19680, not -29520.",
"D": "Incorrect. Substituting the stated values ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006830 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 47 mol H₂ and 30 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "94 mol",
"B": "47 mol",
"C": "5.7 mol",
"D": "23.5 mol"
} | B | 47 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 47 mol H₂O; O₂ can produce 60 mol H₂O. The limiting condition is H₂; product=47 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 47 mol, not 94 mol.",
"B": "Correct. The worked calculation gives 47 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 47 mol, not 5.7 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_000234 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 -5x +12=0, let its roots be α and β. What is α²+β²? | {
"A": "-2.47917",
"B": "-4.95833",
"C": "0.66944",
"D": "-3.30556"
} | D | -3.30556 | By Vieta's relations, α+β = 5/6 and αβ = 12/6. Then α²+β²=(α+β)²−2αβ = (5/6)²−2(12/6) = -3.30556. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -3.30556, not -2.47917.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -3.30556, not -4.95833.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -3.30556, not ... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009918 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(CN)_3]^+1, each CN ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "1.4",
"B": "7",
"C": "5",
"D": "4"
} | D | 4 | Let the formal oxidation state of Mn be x. Charge balance gives x+(3)(−1)=+1; hence x=1+3=+4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 5.",
"D": "Correct. The worked ... | [
"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_007828 | 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 42 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "9.5 mmol L⁻¹",
"B": "2.05 mmol L⁻¹",
"C": "10.5 mmol L⁻¹",
"D": "-10.5 mmol L⁻¹"
} | C | 10.5 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=42/2^2=10.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.5 mmol L⁻¹, not 9.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.5 mmol L⁻¹, not 2.05 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 10.5 mmol L⁻¹.",
"D": "Incorrec... | [
"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_003816 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block initially moves at 10 m s⁻¹. A constant net force does 6 N of work over 4 m in the direction of motion. Find its final kinetic energy. | {
"A": "13.4 J",
"B": "93 J",
"C": "186 J",
"D": "124 J"
} | D | 124 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(2)(10)²+(6)(4)=124 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 124 J, not 13.4 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 124 J, not 93 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 124 J, not 186 J.",
"D":... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007133 | 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 501 K and 1.64 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "428.14602 L",
"B": "426.14602 L",
"C": "424.14602 L",
"D": "639.21903 L"
} | B | 426.14602 L | PV=nRT, so V=nRT/P=(17)(0.082057)(501)/(1.64)=426.14602 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 426.14602 L, not 428.14602 L.",
"B": "Correct. The worked calculation gives 426.14602 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 426.14602 L, not 424.14602 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_007140 | 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 589 K and 1.66 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "406.61568 L",
"B": "611.42351 L",
"C": "407.61568 L",
"D": "326.09254 L"
} | C | 407.61568 L | PV=nRT, so V=nRT/P=(14)(0.082057)(589)/(1.66)=407.61568 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 407.61568 L, not 406.61568 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 407.61568 L, not 611.42351 L.",
"C": "Correct. The worked calculation gives 407.61568 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_003107 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-8+9i)/(4+3i). What is Re(z), the real part of z? | {
"A": "0.8",
"B": "-3.2",
"C": "-0.2",
"D": "0.2"
} | C | -0.2 | Multiply numerator and denominator by the conjugate (4-3i). Then Re(z)=(ac+bd)/(c²+d²)=((-8)(4)+(9)(3))/(4²+(3)²)=-0.2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.2, not 0.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.2, not -3.2.",
"C": "Correct. The worked calculation gives -0.2.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_001634 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (-4x² +7x -5) dx. | {
"A": "104.16667",
"B": "-156.25",
"C": "-208.33333",
"D": "-104.16667"
} | D | -104.16667 | An antiderivative is (-4/3)x³+(7/2)x²+(-5)x. Evaluating between 0 and 5 gives (-4/3)(5)³+(7/2)(5)²+(-5)(5)=-104.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -104.16667, not 104.16667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -104.16667, not -156.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -104.16667... | [
"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_005706 | 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 1.6 atm at 234 K. What is its pressure at 509 K? | {
"A": "4.48034 atm",
"B": "1.48034 atm",
"C": "5.22051 atm",
"D": "3.48034 atm"
} | D | 3.48034 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.6)(509)/(234)=3.48034 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.48034 atm, not 4.48034 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.48034 atm, not 1.48034 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.... | [
"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_003186 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-2-12i)/(7+6i). What is Re(z), the real part of z? | {
"A": "-4.01176",
"B": "-0.75882",
"C": "-1.01176",
"D": "-1.51765"
} | C | -1.01176 | Multiply numerator and denominator by the conjugate (7-6i). Then Re(z)=(ac+bd)/(c²+d²)=((-2)(7)+(-12)(6))/(7²+(6)²)=-1.01176. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.01176, not -4.01176.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.01176, not -0.75882.",
"C": "Correct. The worked calculation gives -1.01176.",
"D": "Incorrect. Substituting the stat... | [
"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_009680 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(OH)_2]^+1, each OH ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "2",
"B": "3",
"C": "6",
"D": "1"
} | B | 3 | Let the formal oxidation state of Cr be x. Charge balance gives x+(2)(−1)=+1; hence x=1+2=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004928 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 14 Ω and 13 Ω are connected in series; this combination is connected in parallel with a 9 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.13333 A",
"B": "2.33333 A",
"C": "0.33333 A",
"D": "1.33333 A"
} | D | 1.33333 A | Series branch resistance=14+13=27 Ω. Parallel equivalent R_eq=(27×9)/(27+9)=6.75 Ω. Total current I=V/R_eq=9/6.75=1.33333 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.33333 A, not 1.13333 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.33333 A, not 2.33333 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.33333 A,... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007924 | 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 88 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "22 mmol L⁻¹",
"B": "44 mmol L⁻¹",
"C": "35.2 mmol L⁻¹",
"D": "66 mmol L⁻¹"
} | B | 44 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=88/2^1=44 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 44 mmol L⁻¹, not 22 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 44 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 44 mmol L⁻¹, not 35.2 mmol L⁻¹.",
"D": "Incorrect. Subs... | [
"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_002681 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(9, -4, 2) and v=(-4, -7, 1), calculate u·v. | {
"A": "-12",
"B": "6",
"C": "-7",
"D": "-6"
} | D | -6 | The dot product is the sum of corresponding component products: (9)(-4)+(-4)(-7)+(2)(1)=-6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -6, not -12.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -6, not 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -6, not -7.",
"D": "Correct. The wor... | [
"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_006617 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 25 kg is attached to an ideal spring of force constant 624 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.40032 s",
"B": "-0.59968 s",
"C": "0.40032 s",
"D": "1.04003 s"
} | C | 0.40032 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(25/624)=0.40032 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.40032 s, not -0.40032 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.40032 s, not -0.59968 s.",
"C": "Correct. The worked calculation gives 0.40032 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_002439 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, -1], [1, 5]]. | {
"A": "72",
"B": "18",
"C": "36",
"D": "43.2"
} | C | 36 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(5)−(-1)(1)=36. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 36, not 72.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 36, not 18.",
"C": "Correct. The worked calculation gives 36.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006582 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 20 kg is attached to an ideal spring of force constant 510 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.79212 s",
"B": "-0.39606 s",
"C": "0.39606 s",
"D": "0.59409 s"
} | C | 0.39606 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(20/510)=0.39606 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.39606 s, not 0.79212 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.39606 s, not -0.39606 s.",
"C": "Correct. The worked calculation gives 0.39606 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005036 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +1 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "1.25 N",
"B": "2.5 N",
"C": "1.875 N",
"D": "5.5 N"
} | B | 2.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(1×10⁻⁶)/(6×10⁻²)²=2.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.5 N, not 1.25 N.",
"B": "Correct. The worked calculation gives 2.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.5 N, not 1.875 N.",
"D": "Incorrect. Substituting the stated values in... | [
"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_009809 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(Cl)_2]^-1, each Cl ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "0",
"B": "-1",
"C": "1.1",
"D": "1"
} | D | 1 | Let the formal oxidation state of Cu be x. Charge balance gives x+(2)(−1)=-1; hence x=-1+2=+1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not -1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.1.",
"D": "Correct. The worked... | [
"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_004895 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 3 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 10 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.18571 A",
"B": "3.27857 A",
"C": "-0.81429 A",
"D": "-2.18571 A"
} | A | 2.18571 A | Series branch resistance=3+4=7 Ω. Parallel equivalent R_eq=(7×10)/(7+10)=4.11765 Ω. Total current I=V/R_eq=9/4.11765=2.18571 A. | {
"A": "Correct. The worked calculation gives 2.18571 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.18571 A, not 3.27857 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.18571 A, not -0.81429 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005786 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.2 atm at 374 K. What is its pressure at 459 K? | {
"A": "5.15455 atm",
"B": "7.15455 atm",
"C": "8.15455 atm",
"D": "10.30909 atm"
} | A | 5.15455 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.2)(459)/(374)=5.15455 atm. | {
"A": "Correct. The worked calculation gives 5.15455 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.15455 atm, not 7.15455 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.15455 atm, not 8.15455 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008892 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.16 mol L⁻¹ and initially B is absent. At equilibrium, 72% of A has dissociated at constant volume. Find K_c. | {
"A": "9.59063",
"B": "8.59063",
"C": "7.59063",
"D": "12.88594"
} | B | 8.59063 | Let α=0.72. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.16)(0.72)²/(1−0.72)=8.59063. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.59063, not 9.59063.",
"B": "Correct. The worked calculation gives 8.59063.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.59063, not 7.59063.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007685 | 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 86 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "0.67188 mmol L⁻¹",
"B": "1.06719 mmol L⁻¹",
"C": "-0.67188 mmol L⁻¹",
"D": "0.50391 mmol L⁻¹"
} | A | 0.67188 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=86/2^7=0.67188 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 0.67188 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.67188 mmol L⁻¹, not 1.06719 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.67188 mmol L⁻¹, not -0.67188 mmol L⁻¹.",... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005090 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +7 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "88 N",
"B": "10 N",
"C": "90 N",
"D": "67.5 N"
} | C | 90 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(7×10⁻⁶)/(7×10⁻²)²=90 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 90 N, not 88 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 90 N, not 10 N.",
"C": "Correct. The worked calculation gives 90 N.",
"D": "Incorrect. Substituting the stated values into the g... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001940 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 9 elements can be selected from a set of 79 distinct elements? | {
"A": "20581151377.5",
"B": "205811513766",
"C": "205811513765",
"D": "205811513767"
} | C | 205811513765 | Order does not matter, so the count is C(79,9)=79!/[9!(70)!]=205811513765. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 205811513765, not 20581151377.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 205811513765, not 205811513766.",
"C": "Correct. The worked calculation gives 205811513765.",
"D": "Incorrect. ... | [
"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_005973 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.5 atm at 374 K. What is its pressure at 744 K? | {
"A": "6.96257 atm",
"B": "9.96257 atm",
"C": "7.96257 atm",
"D": "3.96257 atm"
} | A | 6.96257 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.5)(744)/(374)=6.96257 atm. | {
"A": "Correct. The worked calculation gives 6.96257 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.96257 atm, not 9.96257 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.96257 atm, not 7.96257 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000299 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 -6x -8=0, let its roots be α and β. What is α²+β²? | {
"A": "6.25",
"B": "1.625",
"C": "7.25",
"D": "5.25"
} | A | 6.25 | By Vieta's relations, α+β = 6/4 and αβ = -8/4. Then α²+β²=(α+β)²−2αβ = (6/4)²−2(-8/4) = 6.25. | {
"A": "Correct. The worked calculation gives 6.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.25, not 1.625.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.25, not 7.25.",
"D": "Incorrect. Substituting the stated values into the ... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001844 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 10 distinct elements? | {
"A": "67.5",
"B": "45",
"C": "44",
"D": "47"
} | B | 45 | Order does not matter, so the count is C(10,8)=10!/[8!(2)!]=45. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45, not 67.5.",
"B": "Correct. The worked calculation gives 45.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 45, not 44.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"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_001464 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (5x² -7x +4) dx. | {
"A": "321.125",
"B": "426.16667",
"C": "427.16667",
"D": "428.16667"
} | D | 428.16667 | An antiderivative is (5/3)x³+(-7/2)x²+(4)x. Evaluating between 0 and 7 gives (5/3)(7)³+(-7/2)(7)²+(4)(7)=428.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 428.16667, not 321.125.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 428.16667, not 426.16667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 428.16667, n... | [
"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_002108 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 4 blue and 5 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-1.64327",
"B": "0.35673",
"C": "0.17836",
"D": "-0.64327"
} | B | 0.35673 | Favourable pairs = C(10,2)+C(4,2)+C(5,2)=61. Total pairs=C(19,2)=171. Therefore P=61/171=0.35673. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35673, not -1.64327.",
"B": "Correct. The worked calculation gives 0.35673.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35673, not 0.17836.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001936 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 11 elements can be selected from a set of 87 distinct elements? | {
"A": "21003942987436.5",
"B": "56010514633164",
"C": "28005257316582",
"D": "14002628658291"
} | C | 28005257316582 | Order does not matter, so the count is C(87,11)=87!/[11!(76)!]=28005257316582. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28005257316582, not 21003942987436.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28005257316582, not 56010514633164.",
"C": "Correct. The worked calculation gives 28005257316582.",
"D": "... | [
"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_006581 | 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 1174 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.13844 s",
"B": "0.18458 s",
"C": "0.09229 s",
"D": "-0.81542 s"
} | B | 0.18458 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(10/1174)=0.18458 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.18458 s, not 0.13844 s.",
"B": "Correct. The worked calculation gives 0.18458 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.18458 s, not 0.09229 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009378 | 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_17H_17N_3X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "4.5",
"B": "7",
"C": "18",
"D": "9"
} | D | 9 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×17+2+3−17−4)/2=9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9, not 4.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9, not 18.",
"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_006074 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 62 cm in front of a thin convex lens of focal length 23 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "2.58974",
"B": "0.58974",
"C": "-0.41026",
"D": "0.44231"
} | B | 0.58974 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(62)(23)/(62−23)=36.5641 cm. Thus |m|=v/u=36.5641/62=0.58974. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.58974, not 2.58974.",
"B": "Correct. The worked calculation gives 0.58974.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.58974, not -0.41026.",
"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_007282 | 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 403 K and 2.16 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "91.85825 L",
"B": "183.71651 L",
"C": "92.85825 L",
"D": "137.78738 L"
} | A | 91.85825 L | PV=nRT, so V=nRT/P=(6)(0.082057)(403)/(2.16)=91.85825 L. | {
"A": "Correct. The worked calculation gives 91.85825 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 91.85825 L, not 183.71651 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 91.85825 L, not 92.85825 L.",
"D": "Incorrect. Substituti... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006799 | 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 19 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "15 mol",
"B": "2.5 mol",
"C": "14 mol",
"D": "12 mol"
} | A | 15 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 15 mol H₂O; O₂ can produce 38 mol H₂O. The limiting condition is H₂; product=15 mol. | {
"A": "Correct. The worked calculation gives 15 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15 mol, not 2.5 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_000787 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio 3. What is the sum of its first 5 terms? | {
"A": "724",
"B": "544.5",
"C": "363",
"D": "726"
} | D | 726 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(3^5−1)/(3−1)=726. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 726, not 724.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 726, not 544.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 726, not 363.",
"D": "Correct.... | [
"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_008626 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.11 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "2.5974 K",
"B": "1.2987 K",
"C": "0.7316 K",
"D": "1.7316 K"
} | D | 1.7316 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.52×1.11=1.7316 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.7316 K, not 2.5974 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.7316 K, not 1.2987 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.7316 K, not ... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000401 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 11 and common difference 12. Find the sum of its first 25 terms. | {
"A": "3875",
"B": "388.5",
"C": "3874",
"D": "3877"
} | A | 3875 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=11, d=12, n=25: Sₙ=25/2[2(11)+(25−1)(12)]=3875. | {
"A": "Correct. The worked calculation gives 3875.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3875, not 388.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3875, not 3874.",
"D": "Incorrect. Substituting the stated values into the ... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006175 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 33 cm in front of a thin convex lens of focal length 18 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.2",
"B": "1.12",
"C": "-1.8",
"D": "0.2"
} | A | 1.2 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(33)(18)/(33−18)=39.6 cm. Thus |m|=v/u=39.6/33=1.2. | {
"A": "Correct. The worked calculation gives 1.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.2, not 1.12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2, not -1.8.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_002425 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, 5], [9, -7]]. | {
"A": "-78",
"B": "-80",
"C": "-120",
"D": "80"
} | B | -80 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(-7)−(5)(9)=-80. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -80, not -78.",
"B": "Correct. The worked calculation gives -80.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -80, not -120.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005965 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.6 atm at 250 K. What is its pressure at 300 K? | {
"A": "-4.32 atm",
"B": "2.32 atm",
"C": "6.48 atm",
"D": "4.32 atm"
} | D | 4.32 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.6)(300)/(250)=4.32 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.32 atm, not -4.32 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.32 atm, not 2.32 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.32 atm, not... | [
"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_008369 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.38 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.8704 K",
"B": "-2.8704 K",
"C": "2.8704 K",
"D": "-0.1296 K"
} | C | 2.8704 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.52×1.38=2.8704 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.8704 K, not 1.8704 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.8704 K, not -2.8704 K.",
"C": "Correct. The worked calculation gives 2.8704 K.",
"D": "Incorrect. Substituting the sta... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003353 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 34 m s⁻¹ at 15° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "6.78 m",
"B": "57.8 m",
"C": "86.7 m",
"D": "58.8 m"
} | B | 57.8 m | Range R=u²sin(2θ)/g. Substituting u=34, θ=15° and g=10 gives R=(34)²sin(30°)/10=57.8 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 57.8 m, not 6.78 m.",
"B": "Correct. The worked calculation gives 57.8 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 57.8 m, not 86.7 m.",
"D": "Incorrect. Substituting the stated values ... | [
"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_005146 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +8 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "225 N",
"B": "224 N",
"C": "226 N",
"D": "180 N"
} | A | 225 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(8×10⁻⁶)/(4×10⁻²)²=225 N. | {
"A": "Correct. The worked calculation gives 225 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 225 N, not 224 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 225 N, not 226 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008992 | 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 1.23 mol L⁻¹ and initially B is absent. At equilibrium, 34% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.13825",
"B": "-2.13825",
"C": "0.64631",
"D": "0.86175"
} | D | 0.86175 | Let α=0.34. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.23)(0.34)²/(1−0.34)=0.86175. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.86175, not -0.13825.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.86175, not -2.13825.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.86175, not 0.6... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001710 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 66 distinct elements? | {
"A": "5743572120",
"B": "5743572122",
"C": "11487144240",
"D": "5743572119"
} | A | 5743572120 | Order does not matter, so the count is C(66,8)=66!/[8!(58)!]=5743572120. | {
"A": "Correct. The worked calculation gives 5743572120.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5743572120, not 5743572122.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5743572120, not 11487144240.",
"D": "Incorrect. Substituti... | [
"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_006930 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 48 mol H₂ and 19 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "45.6 mol",
"B": "76 mol",
"C": "57 mol",
"D": "38 mol"
} | D | 38 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 48 mol H₂O; O₂ can produce 38 mol H₂O. The limiting condition is O₂; product=38 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 38 mol, not 45.6 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 38 mol, not 76 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 38 mol, not 57 mol."... | [
"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_004205 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 50 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.24. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "204 N",
"B": "205 N",
"C": "306 N",
"D": "206 N"
} | A | 204 N | Net force=mg(sinθ−μcosθ)=50×10×(0.6−0.24×0.8)=204 N. | {
"A": "Correct. The worked calculation gives 204 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 204 N, not 205 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 204 N, not 306 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_008429 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.43 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.2236 K",
"B": "0.4472 K",
"C": "-2.7764 K",
"D": "0.3354 K"
} | A | 0.2236 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.52×0.43=0.2236 K. | {
"A": "Correct. The worked calculation gives 0.2236 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.2236 K, not 0.4472 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.2236 K, not -2.7764 K.",
"D": "Incorrect. Substituting the sta... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002387 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 7], [3, -7]]. | {
"A": "-39.2",
"B": "-36.75",
"C": "-50",
"D": "-49"
} | D | -49 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(-7)−(7)(3)=-49. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -49, not -39.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -49, not -36.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -49, not -50.",
"D": "Corre... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003257 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-13-5i)/(6+4i). What is Re(z), the real part of z? | {
"A": "-1.88462",
"B": "-0.88462",
"C": "-3.88462",
"D": "-2.82692"
} | A | -1.88462 | Multiply numerator and denominator by the conjugate (6-4i). Then Re(z)=(ac+bd)/(c²+d²)=((-13)(6)+(-5)(4))/(6²+(4)²)=-1.88462. | {
"A": "Correct. The worked calculation gives -1.88462.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.88462, not -0.88462.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.88462, not -3.88462.",
"D": "Incorrect. Substituting the stat... | [
"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_007961 | 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 95 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "1.07422 mmol L⁻¹",
"B": "1.48438 mmol L⁻¹",
"C": "0.74219 mmol L⁻¹",
"D": "-1.25781 mmol L⁻¹"
} | C | 0.74219 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=95/2^7=0.74219 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.74219 mmol L⁻¹, not 1.07422 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.74219 mmol L⁻¹, not 1.48438 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.74219 mmol L⁻¹.",
... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009239 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.98 V, transfers 3 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.0982 V",
"B": "-1.9018 V",
"C": "0.5491 V",
"D": "-0.9018 V"
} | A | 1.0982 V | Apply the Nernst equation: E=0.98−(0.0591/3)(-6)=1.0982 V. | {
"A": "Correct. The worked calculation gives 1.0982 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0982 V, not -1.9018 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0982 V, not 0.5491 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_009151 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.76 V, transfers 3 electrons, and has reaction quotient Q=10^3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.4018 V",
"B": "0.52568 V",
"C": "0.7009 V",
"D": "-1.2991 V"
} | C | 0.7009 V | Apply the Nernst equation: E=0.76−(0.0591/3)(3)=0.7009 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7009 V, not 1.4018 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7009 V, not 0.52568 V.",
"C": "Correct. The worked calculation gives 0.7009 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_007360 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 92 mL of 0.10 M HCl is mixed with 87 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "3.83082",
"B": "2.55388",
"C": "1.27694",
"D": "5.55388"
} | B | 2.55388 | Excess H⁺ moles=0.10×(92−87)/1000=0.000500 mol. Total volume=0.179 L, so [H⁺]=0.002793 M and pH=−log₁₀[H⁺]=2.55388. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.55388, not 3.83082.",
"B": "Correct. The worked calculation gives 2.55388.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.55388, not 1.27694.",
"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_009279 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.96 V, transfers 3 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.8812 V",
"B": "0.4406 V",
"C": "2.8812 V",
"D": "0.8812 V"
} | D | 0.8812 V | Apply the Nernst equation: E=0.96−(0.0591/3)(4)=0.8812 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8812 V, not 1.8812 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8812 V, not 0.4406 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8812 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_000878 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio 2. What is the sum of its first 7 terms? | {
"A": "635",
"B": "633",
"C": "762",
"D": "-635"
} | A | 635 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(2^7−1)/(2−1)=635. | {
"A": "Correct. The worked calculation gives 635.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 635, not 633.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 635, not 762.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008110 | 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 10 A for 14596 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "48.02311 g",
"B": "50.02311 g",
"C": "24.01155 g",
"D": "38.41849 g"
} | A | 48.02311 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×10×14596/(2×96500)=48.02311 g. | {
"A": "Correct. The worked calculation gives 48.02311 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 48.02311 g, not 50.02311 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 48.02311 g, not 24.01155 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_001235 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ +5x² -10x+7. Evaluate f′(-3). | {
"A": "-176",
"B": "-140",
"C": "-175",
"D": "-210"
} | C | -175 | Differentiate: f′(x)=3(-5)x²+2(5)x+(-10). At x=-3, f′(-3)=3(-5)(-3)²+2(5)(-3)+(-10)=-175. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -175, not -176.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -175, not -140.",
"C": "Correct. The worked calculation gives -175.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_005979 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.4 atm at 393 K. What is its pressure at 769 K? | {
"A": "13.30585 atm",
"B": "9.65293 atm",
"C": "9.97939 atm",
"D": "6.65293 atm"
} | D | 6.65293 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.4)(769)/(393)=6.65293 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.65293 atm, not 13.30585 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.65293 atm, not 9.65293 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6... | [
"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_001867 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 7 elements can be selected from a set of 30 distinct elements? | {
"A": "2035800",
"B": "3053700",
"C": "1526850",
"D": "1017900"
} | A | 2035800 | Order does not matter, so the count is C(30,7)=30!/[7!(23)!]=2035800. | {
"A": "Correct. The worked calculation gives 2035800.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2035800, not 3053700.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2035800, not 1526850.",
"D": "Incorrect. Substituting the stated va... | [
"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_004686 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 15 Ω and 13 Ω are connected in series; this combination is connected in parallel with a 5 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.24286 A",
"B": "5.24286 A",
"C": "-4.24286 A",
"D": "4.24286 A"
} | D | 4.24286 A | Series branch resistance=15+13=28 Ω. Parallel equivalent R_eq=(28×5)/(28+5)=4.24242 Ω. Total current I=V/R_eq=18/4.24242=4.24286 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.24286 A, not 1.24286 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.24286 A, not 5.24286 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.24286 A,... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003231 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-11+5i)/(6+7i). What is Re(z), the real part of z? | {
"A": "0.96353",
"B": "-1.36471",
"C": "-0.36471",
"D": "0.36471"
} | C | -0.36471 | Multiply numerator and denominator by the conjugate (6-7i). Then Re(z)=(ac+bd)/(c²+d²)=((-11)(6)+(5)(7))/(6²+(7)²)=-0.36471. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.36471, not 0.96353.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.36471, not -1.36471.",
"C": "Correct. The worked calculation gives -0.36471.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003104 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(6+5i)/(6+12i). What is Re(z), the real part of z? | {
"A": "0.53333",
"B": "3.53333",
"C": "-2.46667",
"D": "-1.46667"
} | A | 0.53333 | Multiply numerator and denominator by the conjugate (6-12i). Then Re(z)=(ac+bd)/(c²+d²)=((6)(6)+(5)(12))/(6²+(12)²)=0.53333. | {
"A": "Correct. The worked calculation gives 0.53333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.53333, not 3.53333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.53333, not -2.46667.",
"D": "Incorrect. Substituting the stated v... | [
"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_009137 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.60 V, transfers 1 electrons, and has reaction quotient Q=10^0. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-2.4 V",
"B": "0.9 V",
"C": "0.6 V",
"D": "1.6 V"
} | C | 0.6 V | Apply the Nernst equation: E=0.60−(0.0591/1)(0)=0.6 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6 V, not -2.4 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6 V, not 0.9 V.",
"C": "Correct. The worked calculation gives 0.6 V.",
"D": "Incorrect. Substituting the stated values into... | [
"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_009118 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.33 V, transfers 3 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.2512 V",
"B": "-1.2512 V",
"C": "0.9384 V",
"D": "0.6256 V"
} | A | 1.2512 V | Apply the Nernst equation: E=1.33−(0.0591/3)(4)=1.2512 V. | {
"A": "Correct. The worked calculation gives 1.2512 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.2512 V, not -1.2512 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2512 V, not 0.9384 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_005239 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +8 μC and +1 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "9 N",
"B": "-80 N",
"C": "120 N",
"D": "80 N"
} | D | 80 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(8×10⁻⁶)(1×10⁻⁶)/(3×10⁻²)²=80 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 80 N, not 9 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 80 N, not -80 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 80 N, not 120 N.",
"D": "Cor... | [
"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_006722 | 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 12 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "23 mol",
"B": "26 mol",
"C": "12 mol",
"D": "24 mol"
} | D | 24 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 37 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 23 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24 mol, not 26 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24 mol, not 12 mol.",
... | [
"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_006420 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 3 kg is attached to an ideal spring of force constant 812 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.87843 s",
"B": "0.06078 s",
"C": "0.12157 s",
"D": "0.18235 s"
} | C | 0.12157 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(3/812)=0.12157 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.12157 s, not -2.87843 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.12157 s, not 0.06078 s.",
"C": "Correct. The worked calculation gives 0.12157 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007533 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 32 mL of 0.10 M HCl is mixed with 87 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "15.66482",
"B": "13.66482",
"C": "12.66482",
"D": "2.26648"
} | C | 12.66482 | Excess OH⁻ moles=0.10×(87−32)/1000=0.005500 mol. Total volume=0.119 L, so [OH⁻]=0.046218 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.66482. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.66482, not 15.66482.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.66482, not 13.66482.",
"C": "Correct. The worked calculation gives 12.66482.",
"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_004678 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 11 Ω and 10 Ω are connected in series; this combination is connected in parallel with a 13 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.74725 A",
"B": "1.49451 A",
"C": "0.37363 A",
"D": "-1.25275 A"
} | A | 0.74725 A | Series branch resistance=11+10=21 Ω. Parallel equivalent R_eq=(21×13)/(21+13)=8.02941 Ω. Total current I=V/R_eq=6/8.02941=0.74725 A. | {
"A": "Correct. The worked calculation gives 0.74725 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.74725 A, not 1.49451 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.74725 A, not 0.37363 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006002 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.7 atm at 412 K. What is its pressure at 649 K? | {
"A": "2.8284 atm",
"B": "5.8284 atm",
"C": "1.58284 atm",
"D": "-5.8284 atm"
} | B | 5.8284 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.7)(649)/(412)=5.8284 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.8284 atm, not 2.8284 atm.",
"B": "Correct. The worked calculation gives 5.8284 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.8284 atm, not 1.58284 atm.",
"D": "Incorrect. Substituti... | [
"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_001783 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 11 elements can be selected from a set of 40 distinct elements? | {
"A": "2311801441",
"B": "3467702160",
"C": "2311801440",
"D": "2311801442"
} | C | 2311801440 | Order does not matter, so the count is C(40,11)=40!/[11!(29)!]=2311801440. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2311801440, not 2311801441.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2311801440, not 3467702160.",
"C": "Correct. The worked calculation gives 2311801440.",
"D": "Incorrect. Substitutin... | [
"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_004126 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 33 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.14. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "160.04 N",
"B": "193.248 N",
"C": "161.04 N",
"D": "17.104 N"
} | C | 161.04 N | Net force=mg(sinθ−μcosθ)=33×10×(0.6−0.14×0.8)=161.04 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 161.04 N, not 160.04 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 161.04 N, not 193.248 N.",
"C": "Correct. The worked calculation gives 161.04 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_004570 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 15 kg and radius 1 m is acted on by a constant torque of 75 N m about its central axis. Find its angular acceleration. | {
"A": "10 rad s⁻²",
"B": "15 rad s⁻²",
"C": "2 rad s⁻²",
"D": "9 rad s⁻²"
} | A | 10 rad s⁻² | For a solid disc, I=½MR²=½(15)(1)²=7.5 kg m². Using τ=Iα, α=75/7.5=10 rad s⁻². | {
"A": "Correct. The worked calculation gives 10 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10 rad s⁻², not 15 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10 rad s⁻², not 2 rad s⁻².",
"D": "Incorrect. Substituting... | [
"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_006447 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 2 kg is attached to an ideal spring of force constant 316 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "2.15911 s",
"B": "-1.84089 s",
"C": "0.11933 s",
"D": "0.15911 s"
} | D | 0.15911 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(2/316)=0.15911 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.15911 s, not 2.15911 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.15911 s, not -1.84089 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.15911 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_008658 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.46 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-1.248 K",
"B": "0.752 K",
"C": "1.752 K",
"D": "-0.248 K"
} | C | 1.752 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.6×1.46=1.752 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.752 K, not -1.248 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.752 K, not 0.752 K.",
"C": "Correct. The worked calculation gives 1.752 K.",
"D": "Incorrect. Substituting the stated v... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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