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_007981 | 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 13 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "0.8125 mmol L⁻¹",
"B": "0.30469 mmol L⁻¹",
"C": "1.40625 mmol L⁻¹",
"D": "0.40625 mmol L⁻¹"
} | D | 0.40625 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=13/2^5=0.40625 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.40625 mmol L⁻¹, not 0.8125 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.40625 mmol L⁻¹, not 0.30469 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governin... | [
"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_006426 | 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 300 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.1633 s",
"B": "-1.8367 s",
"C": "0.08165 s",
"D": "3.1633 s"
} | A | 0.1633 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(2/300)=0.1633 s. | {
"A": "Correct. The worked calculation gives 0.1633 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.1633 s, not -1.8367 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.1633 s, not 0.08165 s.",
"D": "Incorrect. Substituting the st... | [
"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_007568 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 24 mL of 0.10 M HCl is mixed with 89 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "14.75983",
"B": "25.51967",
"C": "12.75983",
"D": "11.75983"
} | C | 12.75983 | Excess OH⁻ moles=0.10×(89−24)/1000=0.006500 mol. Total volume=0.113 L, so [OH⁻]=0.057522 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.75983. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.75983, not 14.75983.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.75983, not 25.51967.",
"C": "Correct. The worked calculation gives 12.75983.",
"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_007078 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 7 mol of gas at 404 K and 2.02 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "115.8798 L",
"B": "114.8798 L",
"C": "86.15985 L",
"D": "12.48798 L"
} | B | 114.8798 L | PV=nRT, so V=nRT/P=(7)(0.082057)(404)/(2.02)=114.8798 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 114.8798 L, not 115.8798 L.",
"B": "Correct. The worked calculation gives 114.8798 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 114.8798 L, not 86.15985 L.",
"D": "Incorrect. Substitutin... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007314 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 15 mol of gas at 643 K and 0.1 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "7914.39765 L",
"B": "7916.39765 L",
"C": "5935.79824 L",
"D": "11871.59647 L"
} | A | 7914.39765 L | PV=nRT, so V=nRT/P=(15)(0.082057)(643)/(0.1)=7914.39765 L. | {
"A": "Correct. The worked calculation gives 7914.39765 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7914.39765 L, not 7916.39765 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7914.39765 L, not 5935.79824 L.",
"D": "Incorrect. S... | [
"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_009221 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.47 V, transfers 1 electrons, and has reaction quotient Q=10^3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.64635 V",
"B": "1.2927 V",
"C": "1.12927 V",
"D": "2.2927 V"
} | B | 1.2927 V | Apply the Nernst equation: E=1.47−(0.0591/1)(3)=1.2927 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.2927 V, not 0.64635 V.",
"B": "Correct. The worked calculation gives 1.2927 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2927 V, not 1.12927 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_001156 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-1x³ -5x² -5x+7. Evaluate f′(2). | {
"A": "-38",
"B": "-37",
"C": "-35",
"D": "37"
} | B | -37 | Differentiate: f′(x)=3(-1)x²+2(-5)x+(-5). At x=2, f′(2)=3(-1)(2)²+2(-5)(2)+(-5)=-37. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -37, not -38.",
"B": "Correct. The worked calculation gives -37.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -37, not -35.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002053 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 6 blue and 7 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-2.675",
"B": "0.325",
"C": "0.4875",
"D": "-0.675"
} | B | 0.325 | Favourable pairs = C(3,2)+C(6,2)+C(7,2)=39. Total pairs=C(16,2)=120. Therefore P=39/120=0.325. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.325, not -2.675.",
"B": "Correct. The worked calculation gives 0.325.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.325, not 0.4875.",
"D": "Incorrect. Substituting the stated values int... | [
"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_000178 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 -4x +3=0, let its roots be α and β. What is α²+β²? | {
"A": "1.44444",
"B": "-0.83333",
"C": "-1.11111",
"D": "-0.55556"
} | D | -0.55556 | By Vieta's relations, α+β = 4/6 and αβ = 3/6. Then α²+β²=(α+β)²−2αβ = (4/6)²−2(3/6) = -0.55556. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.55556, not 1.44444.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.55556, not -0.83333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.55556, 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_006812 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 45 mol H₂ and 24 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "36 mol",
"B": "45 mol",
"C": "44 mol",
"D": "22.5 mol"
} | B | 45 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 45 mol H₂O; O₂ can produce 48 mol H₂O. The limiting condition is H₂; product=45 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45 mol, not 36 mol.",
"B": "Correct. The worked calculation gives 45 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 45 mol, not 44 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_001553 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (4x² +0x +3) dx. | {
"A": "306",
"B": "-306",
"C": "305",
"D": "367.2"
} | A | 306 | An antiderivative is (4/3)x³+(0/2)x²+(3)x. Evaluating between 0 and 6 gives (4/3)(6)³+(0/2)(6)²+(3)(6)=306. | {
"A": "Correct. The worked calculation gives 306.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 306, not -306.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 306, not 305.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_000724 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 5. What is the sum of its first 7 terms? | {
"A": "195310",
"B": "195312",
"C": "146482.5",
"D": "195309"
} | A | 195310 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(5^7−1)/(5−1)=195310. | {
"A": "Correct. The worked calculation gives 195310.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 195310, not 195312.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 195310, not 146482.5.",
"D": "Incorrect. Substituting the stated value... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004984 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 6 Ω and 10 Ω are connected in series; this combination is connected in parallel with a 18 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.0625 A",
"B": "-0.9375 A",
"C": "3.0625 A",
"D": "0.79688 A"
} | A | 1.0625 A | Series branch resistance=6+10=16 Ω. Parallel equivalent R_eq=(16×18)/(16+18)=8.47059 Ω. Total current I=V/R_eq=9/8.47059=1.0625 A. | {
"A": "Correct. The worked calculation gives 1.0625 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0625 A, not -0.9375 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0625 A, not 3.0625 A.",
"D": "Incorrect. Substituting the sta... | [
"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_008002 | 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 85 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "5.3125 mmol L⁻¹",
"B": "4.3125 mmol L⁻¹",
"C": "7.3125 mmol L⁻¹",
"D": "3.3125 mmol L⁻¹"
} | A | 5.3125 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=85/2^4=5.3125 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 5.3125 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.3125 mmol L⁻¹, not 4.3125 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.3125 mmol L⁻¹, not 7.3125 mmol L⁻¹.",
"D"... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001297 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-3x³ +5x² -8x+7. Evaluate f′(5). | {
"A": "-366",
"B": "-91.5",
"C": "-274.5",
"D": "-183"
} | D | -183 | Differentiate: f′(x)=3(-3)x²+2(5)x+(-8). At x=5, f′(5)=3(-3)(5)²+2(5)(5)+(-8)=-183. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -183, not -366.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -183, not -91.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -183, not -274.5.",
"D": "C... | [
"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_005415 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 17 μF capacitor is charged to a potential difference of 6 V. Calculate the energy stored, expressed in μJ. | {
"A": "304 μJ",
"B": "306 μJ",
"C": "305 μJ",
"D": "459 μJ"
} | B | 306 μJ | U=½CV². Since C=17 μF, U in μJ is ½×17×(6)²=306 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 306 μJ, not 304 μJ.",
"B": "Correct. The worked calculation gives 306 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 306 μJ, not 305 μJ.",
"D": "Incorrect. Substituting the stated values ... | [
"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_008196 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 11 A for 19440 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": "35.17834 g",
"B": "72.35668 g",
"C": "70.35668 g",
"D": "52.76751 g"
} | C | 70.35668 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×19440/(2×96500)=70.35668 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 70.35668 g, not 35.17834 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 70.35668 g, not 72.35668 g.",
"C": "Correct. The worked calculation gives 70.35668 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_005693 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.5 atm at 433 K. What is its pressure at 655 K? | {
"A": "-3.78176 atm",
"B": "3.78176 atm",
"C": "5.78176 atm",
"D": "2.78176 atm"
} | B | 3.78176 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.5)(655)/(433)=3.78176 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.78176 atm, not -3.78176 atm.",
"B": "Correct. The worked calculation gives 3.78176 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.78176 atm, not 5.78176 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002180 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 9 blue and 9 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.30952",
"B": "3.30952",
"C": "0.61905",
"D": "0.23214"
} | A | 0.30952 | Favourable pairs = C(10,2)+C(9,2)+C(9,2)=117. Total pairs=C(28,2)=378. Therefore P=117/378=0.30952. | {
"A": "Correct. The worked calculation gives 0.30952.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30952, not 3.30952.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30952, not 0.61905.",
"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_005545 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 54 μF capacitor is charged to a potential difference of 3 V. Calculate the energy stored, expressed in μJ. | {
"A": "243 μJ",
"B": "486 μJ",
"C": "245 μJ",
"D": "194.4 μJ"
} | A | 243 μJ | U=½CV². Since C=54 μF, U in μJ is ½×54×(3)²=243 μJ. | {
"A": "Correct. The worked calculation gives 243 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 243 μJ, not 486 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 243 μJ, not 245 μJ.",
"D": "Incorrect. Substituting the stated values ... | [
"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_007458 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 88 mL of 0.10 M HCl is mixed with 100 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "23.61005",
"B": "2.1805",
"C": "11.80502",
"D": "-11.80502"
} | C | 11.80502 | Excess OH⁻ moles=0.10×(100−88)/1000=0.001200 mol. Total volume=0.188 L, so [OH⁻]=0.006383 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=11.80502. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.80502, not 23.61005.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.80502, not 2.1805.",
"C": "Correct. The worked calculation gives 11.80502.",
"D": "Incorrect. Substituting the stated... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002650 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, 4], [5, 2]]. | {
"A": "-4.5",
"B": "-6",
"C": "-12",
"D": "-3"
} | B | -6 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(2)−(4)(5)=-6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -6, not -4.5.",
"B": "Correct. The worked calculation gives -6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -6, not -12.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008355 | 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 1.15 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": "1.38 K",
"B": "2.07 K",
"C": "4.38 K",
"D": "-1.62 K"
} | A | 1.38 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.6×1.15=1.38 K. | {
"A": "Correct. The worked calculation gives 1.38 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.38 K, not 2.07 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.38 K, not 4.38 K.",
"D": "Incorrect. Substituting the stated values ... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005717 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.2 atm at 336 K. What is its pressure at 472 K? | {
"A": "1.54524 atm",
"B": "3.09048 atm",
"C": "1.09048 atm",
"D": "1.30905 atm"
} | B | 3.09048 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.2)(472)/(336)=3.09048 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.09048 atm, not 1.54524 atm.",
"B": "Correct. The worked calculation gives 3.09048 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.09048 atm, not 1.09048 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_004710 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 2 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 11 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "14.54545 A",
"B": "10.27273 A",
"C": "7.27273 A",
"D": "1.72727 A"
} | C | 7.27273 A | Series branch resistance=2+7=9 Ω. Parallel equivalent R_eq=(9×11)/(9+11)=4.95 Ω. Total current I=V/R_eq=36/4.95=7.27273 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.27273 A, not 14.54545 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.27273 A, not 10.27273 A.",
"C": "Correct. The worked calculation gives 7.27273 A.",
"D": "Incorrect. Substituting t... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005787 | 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 426 K. What is its pressure at 797 K? | {
"A": "8.98685 atm",
"B": "-5.98685 atm",
"C": "5.98685 atm",
"D": "2.99343 atm"
} | C | 5.98685 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.2)(797)/(426)=5.98685 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.98685 atm, not 8.98685 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.98685 atm, not -5.98685 atm.",
"C": "Correct. The worked calculation gives 5.98685 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005227 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +9 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "60 N",
"B": "72 N",
"C": "7 N",
"D": "58 N"
} | A | 60 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(9×10⁻⁶)/(9×10⁻²)²=60 N. | {
"A": "Correct. The worked calculation gives 60 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 60 N, not 72 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 60 N, not 7 N.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_007134 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 10 mol of gas at 407 K and 1.99 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "251.73768 L",
"B": "168.82512 L",
"C": "125.86884 L",
"D": "167.82512 L"
} | D | 167.82512 L | PV=nRT, so V=nRT/P=(10)(0.082057)(407)/(1.99)=167.82512 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 167.82512 L, not 251.73768 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 167.82512 L, not 168.82512 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16... | [
"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_004766 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 5 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 11 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.00699 A",
"B": "-1.99301 A",
"C": "1.00699 A",
"D": "0.5035 A"
} | C | 1.00699 A | Series branch resistance=5+8=13 Ω. Parallel equivalent R_eq=(13×11)/(13+11)=5.95833 Ω. Total current I=V/R_eq=6/5.95833=1.00699 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.00699 A, not 4.00699 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.00699 A, not -1.99301 A.",
"C": "Correct. The worked calculation gives 1.00699 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_001497 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (4x² -2x +0) dx. | {
"A": "143.66667",
"B": "212.5",
"C": "113.33333",
"D": "141.66667"
} | D | 141.66667 | An antiderivative is (4/3)x³+(-2/2)x²+(0)x. Evaluating between 0 and 5 gives (4/3)(5)³+(-2/2)(5)²+(0)(5)=141.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 141.66667, not 143.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 141.66667, not 212.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 141.66667, not... | [
"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_000057 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 -2x -5=0, let its roots be α and β. What is α²+β²? | {
"A": "3.5102",
"B": "2.5102",
"C": "1.15102",
"D": "1.5102"
} | D | 1.5102 | By Vieta's relations, α+β = 2/7 and αβ = -5/7. Then α²+β²=(α+β)²−2αβ = (2/7)²−2(-5/7) = 1.5102. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.5102, not 3.5102.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.5102, not 2.5102.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.5102, not 1.15102.",... | [
"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_006104 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 50 cm in front of a thin convex lens of focal length 10 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.75",
"B": "1.25",
"C": "0.25",
"D": "0.375"
} | C | 0.25 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(50)(10)/(50−10)=12.5 cm. Thus |m|=v/u=12.5/50=0.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25, not -0.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25, not 1.25.",
"C": "Correct. The worked calculation gives 0.25.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_002917 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-1, 5, 0) and v=(-5, 4, -7), calculate u·v. | {
"A": "-25",
"B": "25",
"C": "24",
"D": "20"
} | B | 25 | The dot product is the sum of corresponding component products: (-1)(-5)+(5)(4)+(0)(-7)=25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 25, not -25.",
"B": "Correct. The worked calculation gives 25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 25, not 24.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006573 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 8 kg is attached to an ideal spring of force constant 313 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.47962 s",
"B": "1.31974 s",
"C": "0.31974 s",
"D": "-2.68026 s"
} | C | 0.31974 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(8/313)=0.31974 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31974 s, not 0.47962 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31974 s, not 1.31974 s.",
"C": "Correct. The worked calculation gives 0.31974 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_004171 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 22 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": "89.76 N",
"B": "71.808 N",
"C": "87.76 N",
"D": "-89.76 N"
} | A | 89.76 N | Net force=mg(sinθ−μcosθ)=22×10×(0.6−0.24×0.8)=89.76 N. | {
"A": "Correct. The worked calculation gives 89.76 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 89.76 N, not 71.808 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 89.76 N, not 87.76 N.",
"D": "Incorrect. Substituting the stated v... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002191 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 8 blue and 9 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.3202",
"B": "0.1601",
"C": "0.24015",
"D": "-0.3202"
} | A | 0.3202 | Favourable pairs = C(12,2)+C(8,2)+C(9,2)=130. Total pairs=C(29,2)=406. Therefore P=130/406=0.3202. | {
"A": "Correct. The worked calculation gives 0.3202.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3202, not 0.1601.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3202, not 0.24015.",
"D": "Incorrect. Substituting the stated values... | [
"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_000770 | 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 10 terms? | {
"A": "-17713.4",
"B": "-265716",
"C": "-177144",
"D": "-132858"
} | C | -177144 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=12(-3^10−1)/(-3−1)=-177144. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -177144, not -17713.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -177144, not -265716.",
"C": "Correct. The worked calculation gives -177144.",
"D": "Incorrect. Substituting the stated v... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000776 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio 4. What is the sum of its first 11 terms? | {
"A": "6710884.8",
"B": "559241.4",
"C": "5592404",
"D": "4473923.2"
} | C | 5592404 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(4^11−1)/(4−1)=5592404. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5592404, not 6710884.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5592404, not 559241.4.",
"C": "Correct. The worked calculation gives 5592404.",
"D": "Incorrect. Substituting the stated... | [
"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_007234 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 3 mol of gas at 462 K and 1.41 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "64.52823 L",
"B": "96.79234 L",
"C": "80.66029 L",
"D": "161.32057 L"
} | C | 80.66029 L | PV=nRT, so V=nRT/P=(3)(0.082057)(462)/(1.41)=80.66029 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 80.66029 L, not 64.52823 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 80.66029 L, not 96.79234 L.",
"C": "Correct. The worked calculation gives 80.66029 L.",
"D": "Incorrect. Substitutin... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001602 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (5x² +3x -2) dx. | {
"A": "504.93333",
"B": "631.16667",
"C": "757.4",
"D": "629.16667"
} | B | 631.16667 | An antiderivative is (5/3)x³+(3/2)x²+(-2)x. Evaluating between 0 and 7 gives (5/3)(7)³+(3/2)(7)²+(-2)(7)=631.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 631.16667, not 504.93333.",
"B": "Correct. The worked calculation gives 631.16667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 631.16667, not 757.4.",
"D": "Incorrect. Substituting the sta... | [
"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_001261 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ +3x² +3x+7. Evaluate f′(-4). | {
"A": "136.8",
"B": "173",
"C": "171",
"D": "169"
} | C | 171 | Differentiate: f′(x)=3(4)x²+2(3)x+(3). At x=-4, f′(-4)=3(4)(-4)²+2(3)(-4)+(3)=171. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 171, not 136.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 171, not 173.",
"C": "Correct. The worked calculation gives 171.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007872 | 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 38 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "-2.40625 mmol L⁻¹",
"B": "0.29688 mmol L⁻¹",
"C": "0.59375 mmol L⁻¹",
"D": "-1.40625 mmol L⁻¹"
} | C | 0.59375 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=38/2^6=0.59375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.59375 mmol L⁻¹, not -2.40625 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.59375 mmol L⁻¹, not 0.29688 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.59375 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_001242 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=3x³ -7x² -8x+7. Evaluate f′(-1). | {
"A": "15",
"B": "16",
"C": "30",
"D": "-15"
} | A | 15 | Differentiate: f′(x)=3(3)x²+2(-7)x+(-8). At x=-1, f′(-1)=3(3)(-1)²+2(-7)(-1)+(-8)=15. | {
"A": "Correct. The worked calculation gives 15.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15, not 16.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15, not 30.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003050 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(8-6i)/(6+9i). What is Re(z), the real part of z? | {
"A": "-1.05128",
"B": "-0.05128",
"C": "0.99487",
"D": "1.94872"
} | B | -0.05128 | Multiply numerator and denominator by the conjugate (6-9i). Then Re(z)=(ac+bd)/(c²+d²)=((8)(6)+(-6)(9))/(6²+(9)²)=-0.05128. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.05128, not -1.05128.",
"B": "Correct. The worked calculation gives -0.05128.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.05128, not 0.99487.",
"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_006750 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 11 mol H₂ and 3 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "6 mol",
"B": "4.5 mol",
"C": "4 mol",
"D": "8 mol"
} | A | 6 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 11 mol H₂O; O₂ can produce 6 mol H₂O. The limiting condition is O₂; product=6 mol. | {
"A": "Correct. The worked calculation gives 6 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 4.5 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 4 mol.",
"D": "Incorrect. Substituting the stated values int... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001853 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 2 elements can be selected from a set of 40 distinct elements? | {
"A": "936",
"B": "780",
"C": "1560",
"D": "624"
} | B | 780 | Order does not matter, so the count is C(40,2)=40!/[2!(38)!]=780. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 780, not 936.",
"B": "Correct. The worked calculation gives 780.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 780, not 1560.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_001590 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (-2x² -8x -1) dx. | {
"A": "-376.66667",
"B": "-188.33333",
"C": "-94.16667",
"D": "-189.33333"
} | B | -188.33333 | An antiderivative is (-2/3)x³+(-8/2)x²+(-1)x. Evaluating between 0 and 5 gives (-2/3)(5)³+(-8/2)(5)²+(-1)(5)=-188.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -188.33333, not -376.66667.",
"B": "Correct. The worked calculation gives -188.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -188.33333, not -94.16667.",
"D": "Incorrect. Substituting... | [
"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_006052 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 14 cm in front of a thin convex lens of focal length 8 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.33333",
"B": "1",
"C": "4.33333",
"D": "-1.33333"
} | A | 1.33333 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(14)(8)/(14−8)=18.66667 cm. Thus |m|=v/u=18.66667/14=1.33333. | {
"A": "Correct. The worked calculation gives 1.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.33333, not 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.33333, not 4.33333.",
"D": "Incorrect. Substituting the stated values i... | [
"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_001111 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ -4x² -8x+7. Evaluate f′(1). | {
"A": "-3",
"B": "-4",
"C": "-5",
"D": "-1"
} | B | -4 | Differentiate: f′(x)=3(4)x²+2(-4)x+(-8). At x=1, f′(1)=3(4)(1)²+2(-4)(1)+(-8)=-4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4, not -3.",
"B": "Correct. The worked calculation gives -4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -4, not -5.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006081 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 40 cm in front of a thin convex lens of focal length 10 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.33333",
"B": "0.5",
"C": "-0.33333",
"D": "0.33333"
} | D | 0.33333 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(40)(10)/(40−10)=13.33333 cm. Thus |m|=v/u=13.33333/40=0.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not 1.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not 0.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not -0.33333.... | [
"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_000881 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio -2. What is the sum of its first 9 terms? | {
"A": "598.5",
"B": "120.7",
"C": "957.6",
"D": "1197"
} | D | 1197 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(-2^9−1)/(-2−1)=1197. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1197, not 598.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1197, not 120.7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1197, not 957.6.",
"D": "C... | [
"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_000145 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -6x +10=0, let its roots be α and β. What is α²+β²? | {
"A": "-3",
"B": "-0.5",
"C": "-1",
"D": "1"
} | C | -1 | By Vieta's relations, α+β = 6/2 and αβ = 10/2. Then α²+β²=(α+β)²−2αβ = (6/2)²−2(10/2) = -1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1, not -3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1, not -0.5.",
"C": "Correct. The worked calculation gives -1.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"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_001400 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (4x² -1x +0) dx. | {
"A": "123.33333",
"B": "154.16667",
"C": "-154.16667",
"D": "231.25"
} | B | 154.16667 | An antiderivative is (4/3)x³+(-1/2)x²+(0)x. Evaluating between 0 and 5 gives (4/3)(5)³+(-1/2)(5)²+(0)(5)=154.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 154.16667, not 123.33333.",
"B": "Correct. The worked calculation gives 154.16667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 154.16667, not -154.16667.",
"D": "Incorrect. Substituting th... | [
"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_008439 | 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 1.72 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "3.096 K",
"B": "6.096 K",
"C": "1.096 K",
"D": "4.644 K"
} | A | 3.096 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.6×1.72=3.096 K. | {
"A": "Correct. The worked calculation gives 3.096 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.096 K, not 6.096 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.096 K, not 1.096 K.",
"D": "Incorrect. Substituting the stated va... | [
"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_000015 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 +6x -11=0, let its roots be α and β. What is α²+β²? | {
"A": "30",
"B": "20",
"C": "10",
"D": "24"
} | B | 20 | By Vieta's relations, α+β = -6/2 and αβ = -11/2. Then α²+β²=(α+β)²−2αβ = (-6/2)²−2(-11/2) = 20. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20, not 30.",
"B": "Correct. The worked calculation gives 20.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20, not 10.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000933 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 3 and common ratio 4. What is the sum of its first 12 terms? | {
"A": "16777215",
"B": "16777217",
"C": "12582911.25",
"D": "13421772"
} | A | 16777215 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=3(4^12−1)/(4−1)=16777215. | {
"A": "Correct. The worked calculation gives 16777215.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16777215, not 16777217.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16777215, not 12582911.25.",
"D": "Incorrect. Substituting the s... | [
"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_002195 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 9 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.31653",
"B": "0.15827",
"C": "-2.68347",
"D": "2.31653"
} | A | 0.31653 | Favourable pairs = C(12,2)+C(9,2)+C(11,2)=157. Total pairs=C(32,2)=496. Therefore P=157/496=0.31653. | {
"A": "Correct. The worked calculation gives 0.31653.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31653, not 0.15827.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31653, not -2.68347.",
"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_004924 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 15 Ω and 10 Ω are connected in series; this combination is connected in parallel with a 6 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.86 A",
"B": "1.395 A",
"C": "2.86 A",
"D": "-1.86 A"
} | A | 1.86 A | Series branch resistance=15+10=25 Ω. Parallel equivalent R_eq=(25×6)/(25+6)=4.83871 Ω. Total current I=V/R_eq=9/4.83871=1.86 A. | {
"A": "Correct. The worked calculation gives 1.86 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.86 A, not 1.395 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.86 A, not 2.86 A.",
"D": "Incorrect. Substituting the stated values... | [
"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_006642 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 15 kg is attached to an ideal spring of force constant 107 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.74883 s",
"B": "2.74883 s",
"C": "1.49766 s",
"D": "-0.25117 s"
} | A | 0.74883 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(15/107)=0.74883 s. | {
"A": "Correct. The worked calculation gives 0.74883 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.74883 s, not 2.74883 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.74883 s, not 1.49766 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_001746 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 35 distinct elements? | {
"A": "162316",
"B": "324632",
"C": "324633",
"D": "389558.4"
} | B | 324632 | Order does not matter, so the count is C(35,5)=35!/[5!(30)!]=324632. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 324632, not 162316.",
"B": "Correct. The worked calculation gives 324632.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 324632, not 324633.",
"D": "Incorrect. Substituting the stated values ... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009391 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_14H_17X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "1.5",
"B": "8",
"C": "-5",
"D": "5"
} | D | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×14+2+0−17−3)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not -5.",
"D": "Correct. The worked... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001165 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-3x³ +1x² +8x+7. Evaluate f′(-2). | {
"A": "-24",
"B": "-64",
"C": "-32",
"D": "-25.6"
} | C | -32 | Differentiate: f′(x)=3(-3)x²+2(1)x+(8). At x=-2, f′(-2)=3(-3)(-2)²+2(1)(-2)+(8)=-32. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -32, not -24.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -32, not -64.",
"C": "Correct. The worked calculation gives -32.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003225 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(13-8i)/(7+10i). What is Re(z), the real part of z? | {
"A": "0.05537",
"B": "-1.92617",
"C": "0.07383",
"D": "1.00738"
} | C | 0.07383 | Multiply numerator and denominator by the conjugate (7-10i). Then Re(z)=(ac+bd)/(c²+d²)=((13)(7)+(-8)(10))/(7²+(10)²)=0.07383. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.07383, not 0.05537.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.07383, not -1.92617.",
"C": "Correct. The worked calculation gives 0.07383.",
"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_003032 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(10+7i)/(2+8i). What is Re(z), the real part of z? | {
"A": "2.11765",
"B": "1.11765",
"C": "-1.88235",
"D": "-1.11765"
} | B | 1.11765 | Multiply numerator and denominator by the conjugate (2-8i). Then Re(z)=(ac+bd)/(c²+d²)=((10)(2)+(7)(8))/(2²+(8)²)=1.11765. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.11765, not 2.11765.",
"B": "Correct. The worked calculation gives 1.11765.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.11765, not -1.88235.",
"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_000020 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -3x +9=0, let its roots be α and β. What is α²+β²? | {
"A": "-6.75",
"B": "-10.125",
"C": "-8.75",
"D": "-13.5"
} | A | -6.75 | By Vieta's relations, α+β = 3/2 and αβ = 9/2. Then α²+β²=(α+β)²−2αβ = (3/2)²−2(9/2) = -6.75. | {
"A": "Correct. The worked calculation gives -6.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -6.75, not -10.125.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -6.75, not -8.75.",
"D": "Incorrect. Substituting the stated values int... | [
"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_008394 | 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 1.9 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "7.6 K",
"B": "-7.6 K",
"C": "10.6 K",
"D": "5.6 K"
} | A | 7.6 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×1.0×1.9=7.6 K. | {
"A": "Correct. The worked calculation gives 7.6 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.6 K, not -7.6 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.6 K, not 10.6 K.",
"D": "Incorrect. Substituting the stated values int... | [
"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_007659 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 47 mL of 0.10 M HCl is mixed with 34 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.79454",
"B": "0.89727",
"C": "1.17945",
"D": "3.58908"
} | A | 1.79454 | Excess H⁺ moles=0.10×(47−34)/1000=0.001300 mol. Total volume=0.081 L, so [H⁺]=0.016049 M and pH=−log₁₀[H⁺]=1.79454. | {
"A": "Correct. The worked calculation gives 1.79454.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.79454, not 0.89727.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.79454, not 1.17945.",
"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_008207 | 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 4 A for 19066 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": "27.09204 g",
"B": "26.09204 g",
"C": "50.18408 g",
"D": "25.09204 g"
} | D | 25.09204 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×19066/(2×96500)=25.09204 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 25.09204 g, not 27.09204 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 25.09204 g, not 26.09204 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 25.092... | [
"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_006144 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 28 cm in front of a thin convex lens of focal length 20 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "3.5",
"B": "5",
"C": "2.5",
"D": "1.875"
} | C | 2.5 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(28)(20)/(28−20)=70 cm. Thus |m|=v/u=70/28=2.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.5, not 3.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.5, not 5.",
"C": "Correct. The worked calculation gives 2.5.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_007139 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 11 mol of gas at 439 K and 0.75 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "527.33767 L",
"B": "-528.33767 L",
"C": "526.33767 L",
"D": "528.33767 L"
} | D | 528.33767 L | PV=nRT, so V=nRT/P=(11)(0.082057)(439)/(0.75)=528.33767 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 528.33767 L, not 527.33767 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 528.33767 L, not -528.33767 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5... | [
"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_006386 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 22 kg is attached to an ideal spring of force constant 751 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.68462 s",
"B": "-1.65769 s",
"C": "0.34231 s",
"D": "3.34231 s"
} | C | 0.34231 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(22/751)=0.34231 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34231 s, not 0.68462 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34231 s, not -1.65769 s.",
"C": "Correct. The worked calculation gives 0.34231 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_009310 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.23 V, transfers 3 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.5782 V",
"B": "1.93365 V",
"C": "0.64455 V",
"D": "1.2891 V"
} | D | 1.2891 V | Apply the Nernst equation: E=1.23−(0.0591/3)(-3)=1.2891 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.2891 V, not 2.5782 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.2891 V, not 1.93365 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2891 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_001282 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-2x³ +7x² -4x+7. Evaluate f′(-1). | {
"A": "-1.4",
"B": "-12",
"C": "-22",
"D": "-24"
} | D | -24 | Differentiate: f′(x)=3(-2)x²+2(7)x+(-4). At x=-1, f′(-1)=3(-2)(-1)²+2(7)(-1)+(-4)=-24. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -24, not -1.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -24, not -12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -24, not -22.",
"D": "Correct. ... | [
"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_001785 | 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 23 distinct elements? | {
"A": "1352077",
"B": "1014058.5",
"C": "1352078",
"D": "2704156"
} | C | 1352078 | Order does not matter, so the count is C(23,11)=23!/[11!(12)!]=1352078. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1352078, not 1352077.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1352078, not 1014058.5.",
"C": "Correct. The worked calculation gives 1352078.",
"D": "Incorrect. Substituting the stated ... | [
"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_009953 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(OH)_2]^-3, each OH ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "-1",
"B": "-0.5",
"C": "1",
"D": "-0.75"
} | A | -1 | Let the formal oxidation state of Cu be x. Charge balance gives x+(2)(−1)=-3; hence x=-3+2=-1. | {
"A": "Correct. The worked calculation gives -1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1, not -0.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1, not 1.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"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_002916 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, -2, 4) and v=(-4, -6, 0), calculate u·v. | {
"A": "5",
"B": "1.8",
"C": "6",
"D": "8"
} | D | 8 | The dot product is the sum of corresponding component products: (1)(-4)+(-2)(-6)+(4)(0)=8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 1.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 6.",
"D": "Correct. The worked ... | [
"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_003069 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-2+3i)/(9+9i). What is Re(z), the real part of z? | {
"A": "0.11111",
"B": "0.05556",
"C": "-0.94444",
"D": "1.00556"
} | B | 0.05556 | Multiply numerator and denominator by the conjugate (9-9i). Then Re(z)=(ac+bd)/(c²+d²)=((-2)(9)+(3)(9))/(9²+(9)²)=0.05556. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.05556, not 0.11111.",
"B": "Correct. The worked calculation gives 0.05556.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.05556, not -0.94444.",
"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_006363 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 13 kg is attached to an ideal spring of force constant 1170 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.78918 s",
"B": "0.42164 s",
"C": "0.21082 s",
"D": "-1.78918 s"
} | C | 0.21082 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(13/1170)=0.21082 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.21082 s, not -2.78918 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.21082 s, not 0.42164 s.",
"C": "Correct. The worked calculation gives 0.21082 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_009582 | 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_7H_7N_2X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "7",
"B": "2",
"C": "4",
"D": "6"
} | C | 4 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+2−7−3)/2=4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"C": "Correct. The worked calculation gives 4.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003078 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-8-4i)/(4+1i). What is Re(z), the real part of z? | {
"A": "-1.11765",
"B": "0.78824",
"C": "-2.11765",
"D": "-4.11765"
} | C | -2.11765 | Multiply numerator and denominator by the conjugate (4-1i). Then Re(z)=(ac+bd)/(c²+d²)=((-8)(4)+(-4)(1))/(4²+(1)²)=-2.11765. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2.11765, not -1.11765.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2.11765, not 0.78824.",
"C": "Correct. The worked calculation gives -2.11765.",
"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_009021 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.82 V, transfers 3 electrons, and has reaction quotient Q=10^-4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.8988 V",
"B": "1.7976 V",
"C": "-2.1012 V",
"D": "-1.1012 V"
} | A | 0.8988 V | Apply the Nernst equation: E=0.82−(0.0591/3)(-4)=0.8988 V. | {
"A": "Correct. The worked calculation gives 0.8988 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8988 V, not 1.7976 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8988 V, not -2.1012 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_003589 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 101 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1022.1 m",
"B": "1021.1 m",
"C": "1020.1 m",
"D": "1018.1 m"
} | C | 1020.1 m | Range R=u²sin(2θ)/g. Substituting u=101, θ=45° and g=10 gives R=(101)²sin(90°)/10=1020.1 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1020.1 m, not 1022.1 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1020.1 m, not 1021.1 m.",
"C": "Correct. The worked calculation gives 1020.1 m.",
"D": "Incorrect. Substituting the stat... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009650 | 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_34N_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "1.2",
"B": "2",
"C": "1",
"D": "3"
} | B | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×17+2+2−34−0)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.2.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009308 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.36 V, transfers 3 electrons, and has reaction quotient Q=10^-4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.5612 V",
"B": "3.4388 V",
"C": "1.4388 V",
"D": "2.8776 V"
} | C | 1.4388 V | Apply the Nernst equation: E=1.36−(0.0591/3)(-4)=1.4388 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.4388 V, not -1.5612 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4388 V, not 3.4388 V.",
"C": "Correct. The worked calculation gives 1.4388 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_007849 | 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 53 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "6.625 mmol L⁻¹",
"B": "3.3125 mmol L⁻¹",
"C": "4.96875 mmol L⁻¹",
"D": "9.9375 mmol L⁻¹"
} | A | 6.625 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=53/2^3=6.625 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 6.625 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.625 mmol L⁻¹, not 3.3125 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.625 mmol L⁻¹, not 4.96875 mmol L⁻¹.",
"D": ... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006289 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 124 cm in front of a thin convex lens of focal length 26 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.02653",
"B": "0.26531",
"C": "-0.26531",
"D": "0.39796"
} | B | 0.26531 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(124)(26)/(124−26)=32.89796 cm. Thus |m|=v/u=32.89796/124=0.26531. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.26531, not 1.02653.",
"B": "Correct. The worked calculation gives 0.26531.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.26531, not -0.26531.",
"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_003563 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 98 m s⁻¹ at 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "945.80937 m",
"B": "95.58094 m",
"C": "946.80937 m",
"D": "1134.97124 m"
} | A | 945.80937 m | Range R=u²sin(2θ)/g. Substituting u=98, θ=40° and g=10 gives R=(98)²sin(80°)/10=945.80937 m. | {
"A": "Correct. The worked calculation gives 945.80937 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 945.80937 m, not 95.58094 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 945.80937 m, not 946.80937 m.",
"D": "Incorrect. Substit... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000245 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +5x -3=0, let its roots be α and β. What is α²+β²? | {
"A": "-4.77778",
"B": "9.55556",
"C": "3.58333",
"D": "4.77778"
} | D | 4.77778 | By Vieta's relations, α+β = -5/3 and αβ = -3/3. Then α²+β²=(α+β)²−2αβ = (-5/3)²−2(-3/3) = 4.77778. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.77778, not -4.77778.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.77778, not 9.55556.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.77778, not 3.58... | [
"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_000820 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio 5. What is the sum of its first 12 terms? | {
"A": "274658202",
"B": "-549316404",
"C": "823974606",
"D": "549316404"
} | D | 549316404 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(5^12−1)/(5−1)=549316404. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 549316404, not 274658202.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 549316404, not -549316404.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 549316404... | [
"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_005136 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +9 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "87.59375 N",
"B": "9.85938 N",
"C": "132.89062 N",
"D": "88.59375 N"
} | D | 88.59375 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(9×10⁻⁶)/(8×10⁻²)²=88.59375 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 88.59375 N, not 87.59375 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 88.59375 N, not 9.85938 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 88.5937... | [
"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_002432 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, -2], [4, -2]]. | {
"A": "-8",
"B": "8",
"C": "-12",
"D": "-16"
} | A | -8 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(-2)−(-2)(4)=-8. | {
"A": "Correct. The worked calculation gives -8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -8, not 8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -8, not -12.",
"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_008405 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.07 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "3.1128 K",
"B": "0.5564 K",
"C": "0.1128 K",
"D": "1.1128 K"
} | D | 1.1128 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×1.07=1.1128 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.1128 K, not 3.1128 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1128 K, not 0.5564 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1128 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_000922 | 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 10 terms? | {
"A": "512.5",
"B": "5115",
"C": "4092",
"D": "6138"
} | B | 5115 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(2^10−1)/(2−1)=5115. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5115, not 512.5.",
"B": "Correct. The worked calculation gives 5115.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5115, not 4092.",
"D": "Incorrect. Substituting the stated values into the ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008080 | 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 12 A for 7434 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": "30.35082 g",
"B": "29.35082 g",
"C": "44.02623 g",
"D": "27.35082 g"
} | B | 29.35082 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×12×7434/(2×96500)=29.35082 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 29.35082 g, not 30.35082 g.",
"B": "Correct. The worked calculation gives 29.35082 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29.35082 g, not 44.02623 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_006679 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 27 mol H₂ and 32 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "32.4 mol",
"B": "25 mol",
"C": "27 mol",
"D": "28 mol"
} | C | 27 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 27 mol H₂O; O₂ can produce 64 mol H₂O. The limiting condition is H₂; product=27 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 27 mol, not 32.4 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 27 mol, not 25 mol.",
"C": "Correct. The worked calculation gives 27 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_001288 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-1x³ +7x² +11x+7. Evaluate f′(0). | {
"A": "11",
"B": "8.25",
"C": "22",
"D": "-11"
} | A | 11 | Differentiate: f′(x)=3(-1)x²+2(7)x+(11). At x=0, f′(0)=3(-1)(0)²+2(7)(0)+(11)=11. | {
"A": "Correct. The worked calculation gives 11.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11, not 8.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11, not 22.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003166 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(14-14i)/(2+12i). What is Re(z), the real part of z? | {
"A": "-3.94595",
"B": "-0.94595",
"C": "-0.70946",
"D": "0.05405"
} | B | -0.94595 | Multiply numerator and denominator by the conjugate (2-12i). Then Re(z)=(ac+bd)/(c²+d²)=((14)(2)+(-14)(12))/(2²+(12)²)=-0.94595. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.94595, not -3.94595.",
"B": "Correct. The worked calculation gives -0.94595.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.94595, not -0.70946.",
"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_008825 | 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 1.49 mol L⁻¹ and initially B is absent. At equilibrium, 73% of A has dissociated at constant volume. Find K_c. | {
"A": "11.76327",
"B": "13.76327",
"C": "10.76327",
"D": "9.76327"
} | A | 11.76327 | Let α=0.73. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.49)(0.73)²/(1−0.73)=11.76327. | {
"A": "Correct. The worked calculation gives 11.76327.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.76327, not 13.76327.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.76327, not 10.76327.",
"D": "Incorrect. Substituting the stat... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006176 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 47 cm in front of a thin convex lens of focal length 20 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-1.25926",
"B": "1.74074",
"C": "-0.25926",
"D": "0.74074"
} | D | 0.74074 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(47)(20)/(47−20)=34.81481 cm. Thus |m|=v/u=34.81481/47=0.74074. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.74074, not -1.25926.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.74074, not 1.74074.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.74074, not -0.2... | [
"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_003397 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 73 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "799.35 m",
"B": "426.32 m",
"C": "399.675 m",
"D": "532.9 m"
} | D | 532.9 m | Range R=u²sin(2θ)/g. Substituting u=73, θ=45° and g=10 gives R=(73)²sin(90°)/10=532.9 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 532.9 m, not 799.35 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 532.9 m, not 426.32 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 532.9 m, not 399... | [
"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 |
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