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_004690 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 11 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 10 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "6 A",
"B": "3 A",
"C": "4 A",
"D": "8 A"
} | C | 4 A | Series branch resistance=11+4=15 Ω. Parallel equivalent R_eq=(15×10)/(15+10)=6 Ω. Total current I=V/R_eq=24/6=4 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4 A, not 6 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4 A, not 3 A.",
"C": "Correct. The worked calculation gives 4 A.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_002131 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 7 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.15441",
"B": "0.30882",
"C": "-0.69118",
"D": "1.03088"
} | B | 0.30882 | Favourable pairs = C(6,2)+C(7,2)+C(4,2)=42. Total pairs=C(17,2)=136. Therefore P=42/136=0.30882. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30882, not 0.15441.",
"B": "Correct. The worked calculation gives 0.30882.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30882, not -0.69118.",
"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_000311 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +4x -4=0, let its roots be α and β. What is α²+β²? | {
"A": "8.88889",
"B": "4.44444",
"C": "1.44444",
"D": "3.44444"
} | B | 4.44444 | By Vieta's relations, α+β = -4/3 and αβ = -4/3. Then α²+β²=(α+β)²−2αβ = (-4/3)²−2(-4/3) = 4.44444. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.44444, not 8.88889.",
"B": "Correct. The worked calculation gives 4.44444.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.44444, not 1.44444.",
"D": "Incorrect. Substituting the stated va... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008263 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 3 A for 19751 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": "21.49516 g",
"B": "2.94952 g",
"C": "19.49516 g",
"D": "18.49516 g"
} | C | 19.49516 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×3×19751/(2×96500)=19.49516 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19.49516 g, not 21.49516 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19.49516 g, not 2.94952 g.",
"C": "Correct. The worked calculation gives 19.49516 g.",
"D": "Incorrect. Substituting... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007876 | 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 52 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "3.25 mmol L⁻¹",
"B": "5.25 mmol L⁻¹",
"C": "1.625 mmol L⁻¹",
"D": "4.25 mmol L⁻¹"
} | A | 3.25 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=52/2^4=3.25 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 3.25 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.25 mmol L⁻¹, not 5.25 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.25 mmol L⁻¹, not 1.625 mmol L⁻¹.",
"D": "Incorr... | [
"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_008423 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.62 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.95232 K",
"B": "3.95232 K",
"C": "-2.04768 K",
"D": "2.95232 K"
} | A | 0.95232 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.512×0.62=0.95232 K. | {
"A": "Correct. The worked calculation gives 0.95232 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.95232 K, not 3.95232 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.95232 K, not -2.04768 K.",
"D": "Incorrect. Substituting th... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006338 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 12 kg is attached to an ideal spring of force constant 205 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.72583 s",
"B": "0.48389 s",
"C": "-1.51611 s",
"D": "-0.51611 s"
} | B | 0.48389 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(12/205)=0.48389 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.48389 s, not 0.72583 s.",
"B": "Correct. The worked calculation gives 0.48389 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.48389 s, not -1.51611 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_008950 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.72 mol L⁻¹ and initially B is absent. At equilibrium, 59% of A has dissociated at constant volume. Find K_c. | {
"A": "2.44519",
"B": "1.44519",
"C": "0.44519",
"D": "1.2226"
} | A | 2.44519 | Let α=0.59. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.72)(0.59)²/(1−0.59)=2.44519. | {
"A": "Correct. The worked calculation gives 2.44519.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.44519, not 1.44519.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.44519, not 0.44519.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004998 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 6 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 12 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.4 A",
"B": "5.4 A",
"C": "-4.4 A",
"D": "1.44 A"
} | A | 4.4 A | Series branch resistance=6+4=10 Ω. Parallel equivalent R_eq=(10×12)/(10+12)=5.45455 Ω. Total current I=V/R_eq=24/5.45455=4.4 A. | {
"A": "Correct. The worked calculation gives 4.4 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.4 A, not 5.4 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.4 A, not -4.4 A.",
"D": "Incorrect. Substituting the stated values into... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003694 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 9 m s⁻¹. A constant net force does 25 N of work over 2 m in the direction of motion. Find its final kinetic energy. | {
"A": "169.6 J",
"B": "424 J",
"C": "214 J",
"D": "212 J"
} | D | 212 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(9)²+(25)(2)=212 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 212 J, not 169.6 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 212 J, not 424 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 212 J, not 214 J.",
"D... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005500 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 52 μF capacitor is charged to a potential difference of 5 V. Calculate the energy stored, expressed in μJ. | {
"A": "520 μJ",
"B": "650 μJ",
"C": "649 μJ",
"D": "1300 μJ"
} | B | 650 μJ | U=½CV². Since C=52 μF, U in μJ is ½×52×(5)²=650 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 650 μJ, not 520 μJ.",
"B": "Correct. The worked calculation gives 650 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 650 μJ, not 649 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_003680 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block initially moves at 6 m s⁻¹. A constant net force does 5 N of work over 5 m in the direction of motion. Find its final kinetic energy. | {
"A": "266 J",
"B": "99.75 J",
"C": "106.4 J",
"D": "133 J"
} | D | 133 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(6)(6)²+(5)(5)=133 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 133 J, not 266 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 133 J, not 99.75 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 133 J, not 106.4 J.",
... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000509 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 20 and common difference 4. Find the sum of its first 22 terms. | {
"A": "-1364",
"B": "1636.8",
"C": "1364",
"D": "2046"
} | C | 1364 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=20, d=4, n=22: Sₙ=22/2[2(20)+(22−1)(4)]=1364. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1364, not -1364.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1364, not 1636.8.",
"C": "Correct. The worked calculation gives 1364.",
"D": "Incorrect. Substituting the stated values into th... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001985 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 4 elements can be selected from a set of 51 distinct elements? | {
"A": "249899",
"B": "249900",
"C": "24991",
"D": "-249900"
} | B | 249900 | Order does not matter, so the count is C(51,4)=51!/[4!(47)!]=249900. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 249900, not 249899.",
"B": "Correct. The worked calculation gives 249900.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 249900, not 24991.",
"D": "Incorrect. Substituting the stated values i... | [
"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_005940 | 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 3.1 atm at 404 K. What is its pressure at 589 K? | {
"A": "9.03911 atm",
"B": "3.51955 atm",
"C": "4.51955 atm",
"D": "2.25978 atm"
} | C | 4.51955 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.1)(589)/(404)=4.51955 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.51955 atm, not 9.03911 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.51955 atm, not 3.51955 atm.",
"C": "Correct. The worked calculation gives 4.51955 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_001398 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (4x² +8x -4) dx. | {
"A": "2",
"B": "2.66667",
"C": "1.33333",
"D": "-1.33333"
} | C | 1.33333 | An antiderivative is (4/3)x³+(8/2)x²+(-4)x. Evaluating between 0 and 1 gives (4/3)(1)³+(8/2)(1)²+(-4)(1)=1.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.33333, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.33333, not 2.66667.",
"C": "Correct. The worked calculation gives 1.33333.",
"D": "Incorrect. Substituting the stated values i... | [
"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_009825 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(Cl)_4]^-1, each Cl ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "6",
"B": "2.25",
"C": "5",
"D": "3"
} | D | 3 | Let the formal oxidation state of Pd be x. Charge balance gives x+(4)(−1)=-1; hence x=-1+4=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 5.",
"D": "Correct. The worked... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009674 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(Cl)_2]^-4, each Cl ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "-2",
"B": "2",
"C": "-3",
"D": "-4"
} | A | -2 | Let the formal oxidation state of Pt be x. Charge balance gives x+(2)(−1)=-4; hence x=-4+2=-2. | {
"A": "Correct. The worked calculation gives -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2, not -3.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002503 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -3], [9, 6]]. | {
"A": "6.7",
"B": "28.5",
"C": "55",
"D": "57"
} | D | 57 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(6)−(-3)(9)=57. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 57, not 6.7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 57, not 28.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 57, not 55.",
"D": "Correct. The ... | [
"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_003899 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 8 m s⁻¹. A constant net force does 17 N of work over 7 m in the direction of motion. Find its final kinetic energy. | {
"A": "343 J",
"B": "35.3 J",
"C": "342 J",
"D": "171.5 J"
} | A | 343 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(8)²+(17)(7)=343 J. | {
"A": "Correct. The worked calculation gives 343 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 343 J, not 35.3 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 343 J, not 342 J.",
"D": "Incorrect. Substituting the stated values into... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008916 | 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, 12% of A has dissociated at constant volume. Find K_c. | {
"A": "0.09753",
"B": "-1.90247",
"C": "0.19505",
"D": "3.09753"
} | A | 0.09753 | Let α=0.12. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.49)(0.12)²/(1−0.12)=0.09753. | {
"A": "Correct. The worked calculation gives 0.09753.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.09753, not -1.90247.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.09753, not 0.19505.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003957 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 13 kg block initially moves at 10 m s⁻¹. A constant net force does 14 N of work over 16 m in the direction of motion. Find its final kinetic energy. | {
"A": "699.2 J",
"B": "876 J",
"C": "875 J",
"D": "874 J"
} | D | 874 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(13)(10)²+(14)(16)=874 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 874 J, not 699.2 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 874 J, not 876 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 874 J, not 875 J.",
"D... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008050 | 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 9 A for 23085 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": "51.26844 g",
"B": "82.0295 g",
"C": "68.35791 g",
"D": "66.35791 g"
} | C | 68.35791 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×9×23085/(2×96500)=68.35791 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 68.35791 g, not 51.26844 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 68.35791 g, not 82.0295 g.",
"C": "Correct. The worked calculation gives 68.35791 g.",
"D": "Incorrect. Substituting... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003013 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(10-12i)/(12+2i). What is Re(z), the real part of z? | {
"A": "0.32432",
"B": "3.64865",
"C": "-1.35135",
"D": "0.64865"
} | D | 0.64865 | Multiply numerator and denominator by the conjugate (12-2i). Then Re(z)=(ac+bd)/(c²+d²)=((10)(12)+(-12)(2))/(12²+(2)²)=0.64865. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.64865, not 0.32432.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.64865, not 3.64865.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.64865, not -1.35... | [
"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_001737 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 3 elements can be selected from a set of 65 distinct elements? | {
"A": "43680",
"B": "87360",
"C": "21840",
"D": "43681"
} | A | 43680 | Order does not matter, so the count is C(65,3)=65!/[3!(62)!]=43680. | {
"A": "Correct. The worked calculation gives 43680.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 43680, not 87360.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 43680, not 21840.",
"D": "Incorrect. Substituting the stated values into ... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006768 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 34 mol H₂ and 15 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "45 mol",
"B": "36 mol",
"C": "-30 mol",
"D": "30 mol"
} | D | 30 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 34 mol H₂O; O₂ can produce 30 mol H₂O. The limiting condition is O₂; product=30 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 30 mol, not 45 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30 mol, not 36 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30 mol, not -30 mol.",... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000672 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 3 and common ratio 2. What is the sum of its first 5 terms? | {
"A": "93",
"B": "94",
"C": "186",
"D": "74.4"
} | A | 93 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=3(2^5−1)/(2−1)=93. | {
"A": "Correct. The worked calculation gives 93.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 93, not 94.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 93, not 186.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"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_008427 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.97 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": "3.0088 K",
"B": "1.0088 K",
"C": "-1.9912 K",
"D": "1.5132 K"
} | B | 1.0088 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×0.97=1.0088 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0088 K, not 3.0088 K.",
"B": "Correct. The worked calculation gives 1.0088 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0088 K, not -1.9912 K.",
"D": "Incorrect. Substituting the sta... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007166 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 1 mol of gas at 646 K and 2.67 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "14.89012 L",
"B": "19.85349 L",
"C": "2.98535 L",
"D": "29.78024 L"
} | B | 19.85349 L | PV=nRT, so V=nRT/P=(1)(0.082057)(646)/(2.67)=19.85349 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19.85349 L, not 14.89012 L.",
"B": "Correct. The worked calculation gives 19.85349 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19.85349 L, not 2.98535 L.",
"D": "Incorrect. Substituting... | [
"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_004596 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 3 kg and radius 3 m is acted on by a constant torque of 52 N m about its central axis. Find its angular acceleration. | {
"A": "5.77778 rad s⁻²",
"B": "2.88889 rad s⁻²",
"C": "6.85185 rad s⁻²",
"D": "3.85185 rad s⁻²"
} | D | 3.85185 rad s⁻² | For a solid disc, I=½MR²=½(3)(3)²=13.5 kg m². Using τ=Iα, α=52/13.5=3.85185 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.85185 rad s⁻², not 5.77778 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.85185 rad s⁻², not 2.88889 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing r... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001029 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-1x³ +2x² -6x+7. Evaluate f′(2). | {
"A": "-7",
"B": "-12",
"C": "-9",
"D": "-10"
} | D | -10 | Differentiate: f′(x)=3(-1)x²+2(2)x+(-6). At x=2, f′(2)=3(-1)(2)²+2(2)(2)+(-6)=-10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -10, not -7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -10, not -12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -10, not -9.",
"D": "Correct. The... | [
"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_006070 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 25 cm in front of a thin convex lens of focal length 6 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.31579",
"B": "0.31579",
"C": "-0.68421",
"D": "0.63158"
} | B | 0.31579 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(25)(6)/(25−6)=7.89474 cm. Thus |m|=v/u=7.89474/25=0.31579. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31579, not 1.31579.",
"B": "Correct. The worked calculation gives 0.31579.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31579, not -0.68421.",
"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_003739 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 1 m s⁻¹. A constant net force does 13 N of work over 19 m in the direction of motion. Find its final kinetic energy. | {
"A": "251 J",
"B": "26.1 J",
"C": "301.2 J",
"D": "250 J"
} | A | 251 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(1)²+(13)(19)=251 J. | {
"A": "Correct. The worked calculation gives 251 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 251 J, not 26.1 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 251 J, not 301.2 J.",
"D": "Incorrect. Substituting the stated values in... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006393 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 24 kg is attached to an ideal spring of force constant 935 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.64086 s",
"B": "0.24032 s",
"C": "2.32043 s",
"D": "0.32043 s"
} | D | 0.32043 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(24/935)=0.32043 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32043 s, not 0.64086 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32043 s, not 0.24032 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32043 s,... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004817 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 12 Ω are connected in series; this combination is connected in parallel with a 12 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "6.5 A",
"B": "3.5 A",
"C": "2.625 A",
"D": "-3.5 A"
} | B | 3.5 A | Series branch resistance=4+12=16 Ω. Parallel equivalent R_eq=(16×12)/(16+12)=6.85714 Ω. Total current I=V/R_eq=24/6.85714=3.5 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.5 A, not 6.5 A.",
"B": "Correct. The worked calculation gives 3.5 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.5 A, not 2.625 A.",
"D": "Incorrect. Substituting the stated values int... | [
"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_008230 | 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 1071 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": "1.4095 g",
"B": "-1.5905 g",
"C": "-0.5905 g",
"D": "2.81901 g"
} | A | 1.4095 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×1071/(2×96500)=1.4095 g. | {
"A": "Correct. The worked calculation gives 1.4095 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4095 g, not -1.5905 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.4095 g, not -0.5905 g.",
"D": "Incorrect. Substituting the st... | [
"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_009517 | 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_6N_3X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "5",
"C": "7.5",
"D": "8"
} | B | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+3−6−3)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.",
"B": "Correct. The worked calculation gives 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.5.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_004349 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 6 m is acted on by a constant torque of 42 N m about its central axis. Find its angular acceleration. | {
"A": "-0.66667 rad s⁻²",
"B": "-0.33333 rad s⁻²",
"C": "1.33333 rad s⁻²",
"D": "0.33333 rad s⁻²"
} | D | 0.33333 rad s⁻² | For a solid disc, I=½MR²=½(7)(6)²=126 kg m². Using τ=Iα, α=42/126=0.33333 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33333 rad s⁻², not -0.66667 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33333 rad s⁻², not -0.33333 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003714 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 3 m s⁻¹. A constant net force does 22 N of work over 19 m in the direction of motion. Find its final kinetic energy. | {
"A": "452 J",
"B": "454 J",
"C": "46.4 J",
"D": "340.5 J"
} | B | 454 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(3)²+(22)(19)=454 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 454 J, not 452 J.",
"B": "Correct. The worked calculation gives 454 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 454 J, not 46.4 J.",
"D": "Incorrect. Substituting the stated values into... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003554 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 107 m s⁻¹ at 50° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "902.00512 m",
"B": "1125.5064 m",
"C": "1127.5064 m",
"D": "1126.5064 m"
} | C | 1127.5064 m | Range R=u²sin(2θ)/g. Substituting u=107, θ=50° and g=10 gives R=(107)²sin(100°)/10=1127.5064 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1127.5064 m, not 902.00512 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1127.5064 m, not 1125.5064 m.",
"C": "Correct. The worked calculation gives 1127.5064 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004245 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 13 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.23. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "52.08 N",
"B": "56.08 N",
"C": "27.04 N",
"D": "54.08 N"
} | D | 54.08 N | Net force=mg(sinθ−μcosθ)=13×10×(0.6−0.23×0.8)=54.08 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 54.08 N, not 52.08 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 54.08 N, not 56.08 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 54.08 N, not 27.04... | [
"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_009768 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(Cl)_6]^-4, each Cl ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "-2",
"B": "2",
"C": "1.2",
"D": "1"
} | B | 2 | Let the formal oxidation state of Cr be x. Charge balance gives x+(6)(−1)=-4; hence x=-4+6=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.2.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005151 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +9 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "23.3 N",
"B": "24.3 N",
"C": "36.45 N",
"D": "48.6 N"
} | B | 24.3 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(9×10⁻⁶)/(10×10⁻²)²=24.3 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24.3 N, not 23.3 N.",
"B": "Correct. The worked calculation gives 24.3 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24.3 N, not 36.45 N.",
"D": "Incorrect. Substituting the stated values... | [
"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_000611 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -14 and common difference 8. Find the sum of its first 22 terms. | {
"A": "1538",
"B": "1155",
"C": "1540",
"D": "2310"
} | C | 1540 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-14, d=8, n=22: Sₙ=22/2[2(-14)+(22−1)(8)]=1540. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1540, not 1538.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1540, not 1155.",
"C": "Correct. The worked calculation gives 1540.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003565 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 28 m s⁻¹ at 15° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "37.2 m",
"B": "47.04 m",
"C": "39.2 m",
"D": "4.92 m"
} | C | 39.2 m | Range R=u²sin(2θ)/g. Substituting u=28, θ=15° and g=10 gives R=(28)²sin(30°)/10=39.2 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 39.2 m, not 37.2 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39.2 m, not 47.04 m.",
"C": "Correct. The worked calculation gives 39.2 m.",
"D": "Incorrect. Substituting the stated values... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005812 | 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 0.3 atm at 379 K. What is its pressure at 724 K? | {
"A": "0.57309 atm",
"B": "0.42982 atm",
"C": "1.05731 atm",
"D": "0.28654 atm"
} | A | 0.57309 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.3)(724)/(379)=0.57309 atm. | {
"A": "Correct. The worked calculation gives 0.57309 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.57309 atm, not 0.42982 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.57309 atm, not 1.05731 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_009201 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.45 V, transfers 1 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "3.491 V",
"B": "1.7455 V",
"C": "0.7455 V",
"D": "-1.2545 V"
} | B | 1.7455 V | Apply the Nernst equation: E=1.45−(0.0591/1)(-5)=1.7455 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.7455 V, not 3.491 V.",
"B": "Correct. The worked calculation gives 1.7455 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.7455 V, not 0.7455 V.",
"D": "Incorrect. Substituting the state... | [
"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_009298 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.18 V, transfers 3 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.1997 V",
"B": "0.59985 V",
"C": "-0.8003 V",
"D": "1.1997 V"
} | D | 1.1997 V | Apply the Nernst equation: E=1.18−(0.0591/3)(-1)=1.1997 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.1997 V, not 2.1997 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1997 V, not 0.59985 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1997 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_008944 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.74 mol L⁻¹ and initially B is absent. At equilibrium, 34% of A has dissociated at constant volume. Find K_c. | {
"A": "1.51845",
"B": "1.05184",
"C": "-0.48155",
"D": "0.51845"
} | D | 0.51845 | Let α=0.34. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.74)(0.34)²/(1−0.34)=0.51845. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.51845, not 1.51845.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.51845, not 1.05184.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.51845, not -0.48... | [
"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_006378 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 10 kg is attached to an ideal spring of force constant 140 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "3.53452 s",
"B": "0.53452 s",
"C": "1.05345 s",
"D": "0.26726 s"
} | B | 0.53452 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(10/140)=0.53452 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.53452 s, not 3.53452 s.",
"B": "Correct. The worked calculation gives 0.53452 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.53452 s, not 1.05345 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_007931 | 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 26 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "1.8125 mmol L⁻¹",
"B": "2.8125 mmol L⁻¹",
"C": "1.21875 mmol L⁻¹",
"D": "0.8125 mmol L⁻¹"
} | D | 0.8125 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=26/2^5=0.8125 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8125 mmol L⁻¹, not 1.8125 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8125 mmol L⁻¹, not 2.8125 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing r... | [
"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_001945 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 80 distinct elements? | {
"A": "164649211013",
"B": "1646492110120",
"C": "1646492110119",
"D": "2469738165180"
} | B | 1646492110120 | Order does not matter, so the count is C(80,10)=80!/[10!(70)!]=1646492110120. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1646492110120, not 164649211013.",
"B": "Correct. The worked calculation gives 1646492110120.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1646492110120, not 1646492110119.",
"D": "Incorrec... | [
"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_008256 | 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 1499 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": "2.97278 g",
"B": "1.19728 g",
"C": "1.97278 g",
"D": "0.97278 g"
} | C | 1.97278 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×1499/(2×96500)=1.97278 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.97278 g, not 2.97278 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.97278 g, not 1.19728 g.",
"C": "Correct. The worked calculation gives 1.97278 g.",
"D": "Incorrect. Substituting the... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000572 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 14 and common difference 11. Find the sum of its first 34 terms. | {
"A": "9970.5",
"B": "6647",
"C": "6648",
"D": "6649"
} | B | 6647 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=14, d=11, n=34: Sₙ=34/2[2(14)+(34−1)(11)]=6647. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6647, not 9970.5.",
"B": "Correct. The worked calculation gives 6647.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6647, not 6648.",
"D": "Incorrect. Substituting the stated values into the... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000247 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +9x -2=0, let its roots be α and β. What is α²+β²? | {
"A": "-10.33333",
"B": "10.33333",
"C": "13.33333",
"D": "12.33333"
} | B | 10.33333 | By Vieta's relations, α+β = -9/3 and αβ = -2/3. Then α²+β²=(α+β)²−2αβ = (-9/3)²−2(-2/3) = 10.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.33333, not -10.33333.",
"B": "Correct. The worked calculation gives 10.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10.33333, not 13.33333.",
"D": "Incorrect. Substituting the sta... | [
"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_004366 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 1 m is acted on by a constant torque of 75 N m about its central axis. Find its angular acceleration. | {
"A": "21.42857 rad s⁻²",
"B": "20.42857 rad s⁻²",
"C": "-21.42857 rad s⁻²",
"D": "25.71429 rad s⁻²"
} | A | 21.42857 rad s⁻² | For a solid disc, I=½MR²=½(7)(1)²=3.5 kg m². Using τ=Iα, α=75/3.5=21.42857 rad s⁻². | {
"A": "Correct. The worked calculation gives 21.42857 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21.42857 rad s⁻², not 20.42857 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21.42857 rad s⁻², not -21.42857 rad s⁻².",... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003960 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 3 m s⁻¹. A constant net force does 8 N of work over 7 m in the direction of motion. Find its final kinetic energy. | {
"A": "121.2 J",
"B": "99 J",
"C": "101 J",
"D": "75.75 J"
} | C | 101 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(3)²+(8)(7)=101 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 101 J, not 121.2 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 101 J, not 99 J.",
"C": "Correct. The worked calculation gives 101 J.",
"D": "Incorrect. Substituting the stated values into... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009402 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_5H_8N_3X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "6",
"B": "0",
"C": "3",
"D": "2"
} | C | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×5+2+3−8−1)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 0.",
"C": "Correct. The worked calculation gives 3.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003286 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-3+11i)/(11+12i). What is Re(z), the real part of z? | {
"A": "1.03736",
"B": "0.37358",
"C": "0.56038",
"D": "3.37358"
} | B | 0.37358 | Multiply numerator and denominator by the conjugate (11-12i). Then Re(z)=(ac+bd)/(c²+d²)=((-3)(11)+(11)(12))/(11²+(12)²)=0.37358. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.37358, not 1.03736.",
"B": "Correct. The worked calculation gives 0.37358.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.37358, not 0.56038.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008294 | 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 14 A for 2922 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": "11.45937 g",
"B": "13.45937 g",
"C": "14.45937 g",
"D": "12.45937 g"
} | B | 13.45937 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×2922/(2×96500)=13.45937 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13.45937 g, not 11.45937 g.",
"B": "Correct. The worked calculation gives 13.45937 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13.45937 g, not 14.45937 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_007503 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 76 mL of 0.10 M HCl is mixed with 23 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.27136",
"B": "1.27136",
"C": "1.12714",
"D": "0.27136"
} | B | 1.27136 | Excess H⁺ moles=0.10×(76−23)/1000=0.005300 mol. Total volume=0.099 L, so [H⁺]=0.053535 M and pH=−log₁₀[H⁺]=1.27136. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.27136, not 2.27136.",
"B": "Correct. The worked calculation gives 1.27136.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.27136, not 1.12714.",
"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_009871 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(CN)_3]^+0, each CN ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "1.3",
"B": "2.25",
"C": "-3",
"D": "3"
} | D | 3 | Let the formal oxidation state of Ni be x. Charge balance gives x+(3)(−1)=+0; hence x=0+3=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not -3.",
"D": "Correct. The wor... | [
"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_004314 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.32. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "13.76 N",
"B": "28.52 N",
"C": "26.52 N",
"D": "27.52 N"
} | D | 27.52 N | Net force=mg(sinθ−μcosθ)=8×10×(0.6−0.32×0.8)=27.52 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 27.52 N, not 13.76 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 27.52 N, not 28.52 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 27.52 N, not 26.52... | [
"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_001187 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ -9x² -8x+7. Evaluate f′(2). | {
"A": "16",
"B": "32",
"C": "-16",
"D": "24"
} | A | 16 | Differentiate: f′(x)=3(5)x²+2(-9)x+(-8). At x=2, f′(2)=3(5)(2)²+2(-9)(2)+(-8)=16. | {
"A": "Correct. The worked calculation gives 16.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16, not 32.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16, not -16.",
"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_005038 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +5 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "32.47107 N",
"B": "31.47107 N",
"C": "33.47107 N",
"D": "34.47107 N"
} | C | 33.47107 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(5×10⁻⁶)/(11×10⁻²)²=33.47107 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33.47107 N, not 32.47107 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33.47107 N, not 31.47107 N.",
"C": "Correct. The worked calculation gives 33.47107 N.",
"D": "Incorrect. Substitutin... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003177 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-8+9i)/(7+3i). What is Re(z), the real part of z? | {
"A": "-0.75",
"B": "1.5",
"C": "-0.5",
"D": "-0.25"
} | C | -0.5 | Multiply numerator and denominator by the conjugate (7-3i). Then Re(z)=(ac+bd)/(c²+d²)=((-8)(7)+(9)(3))/(7²+(3)²)=-0.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.5, not -0.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.5, not 1.5.",
"C": "Correct. The worked calculation gives -0.5.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_004167 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 24 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.13. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "59.52 N",
"B": "89.28 N",
"C": "119.04 N",
"D": "121.04 N"
} | C | 119.04 N | Net force=mg(sinθ−μcosθ)=24×10×(0.6−0.13×0.8)=119.04 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 119.04 N, not 59.52 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 119.04 N, not 89.28 N.",
"C": "Correct. The worked calculation gives 119.04 N.",
"D": "Incorrect. Substituting the stated... | [
"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_000871 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio 3. What is the sum of its first 10 terms? | {
"A": "265717",
"B": "398574",
"C": "318859.2",
"D": "265716"
} | D | 265716 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(3^10−1)/(3−1)=265716. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 265716, not 265717.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 265716, not 398574.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 265716, not 318859.2."... | [
"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_003327 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-1+2i)/(12+11i). What is Re(z), the real part of z? | {
"A": "0.03774",
"B": "-1.96226",
"C": "-2.96226",
"D": "-0.96226"
} | A | 0.03774 | Multiply numerator and denominator by the conjugate (12-11i). Then Re(z)=(ac+bd)/(c²+d²)=((-1)(12)+(2)(11))/(12²+(11)²)=0.03774. | {
"A": "Correct. The worked calculation gives 0.03774.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.03774, not -1.96226.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.03774, not -2.96226.",
"D": "Incorrect. Substituting the stated ... | [
"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_004950 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 2 Ω and 6 Ω are connected in series; this combination is connected in parallel with a 17 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.10294 A",
"B": "1.10294 A",
"C": "3.10294 A",
"D": "-1.89706 A"
} | B | 1.10294 A | Series branch resistance=2+6=8 Ω. Parallel equivalent R_eq=(8×17)/(8+17)=5.44 Ω. Total current I=V/R_eq=6/5.44=1.10294 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.10294 A, not 0.10294 A.",
"B": "Correct. The worked calculation gives 1.10294 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.10294 A, not 3.10294 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002878 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(0, 9, 2) and v=(6, 4, -7), calculate u·v. | {
"A": "22",
"B": "11",
"C": "33",
"D": "16.5"
} | A | 22 | The dot product is the sum of corresponding component products: (0)(6)+(9)(4)+(2)(-7)=22. | {
"A": "Correct. The worked calculation gives 22.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22, not 11.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22, not 33.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_006596 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 14 kg is attached to an ideal spring of force constant 945 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.02434 s",
"B": "0.18257 s",
"C": "0.24343 s",
"D": "-2.75657 s"
} | C | 0.24343 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(14/945)=0.24343 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.24343 s, not 1.02434 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.24343 s, not 0.18257 s.",
"C": "Correct. The worked calculation gives 0.24343 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_006547 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 21 kg is attached to an ideal spring of force constant 652 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.5384 s",
"B": "3.35894 s",
"C": "1.35894 s",
"D": "0.35894 s"
} | D | 0.35894 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(21/652)=0.35894 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35894 s, not 0.5384 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35894 s, not 3.35894 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35894 s, ... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008807 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.81 mol L⁻¹ and initially B is absent. At equilibrium, 52% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.1748",
"B": "4.8252",
"C": "1.8252",
"D": "2.7378"
} | C | 1.8252 | Let α=0.52. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.81)(0.52)²/(1−0.52)=1.8252. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.8252, not -0.1748.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.8252, not 4.8252.",
"C": "Correct. The worked calculation gives 1.8252.",
"D": "Incorrect. Substituting the stated values... | [
"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_003662 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 71 m s⁻¹ at 70° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "326.02923 m",
"B": "259.22339 m",
"C": "324.02923 m",
"D": "648.05847 m"
} | C | 324.02923 m | Range R=u²sin(2θ)/g. Substituting u=71, θ=70° and g=10 gives R=(71)²sin(140°)/10=324.02923 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 324.02923 m, not 326.02923 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 324.02923 m, not 259.22339 m.",
"C": "Correct. The worked calculation gives 324.02923 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002721 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-7, -1, 4) and v=(-2, -7, 2), calculate u·v. | {
"A": "29",
"B": "28",
"C": "27",
"D": "31"
} | A | 29 | The dot product is the sum of corresponding component products: (-7)(-2)+(-1)(-7)+(4)(2)=29. | {
"A": "Correct. The worked calculation gives 29.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 29, not 28.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29, not 27.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_006308 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 23 cm in front of a thin convex lens of focal length 7 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.4375",
"B": "0.4375",
"C": "-1.5625",
"D": "0.875"
} | B | 0.4375 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(23)(7)/(23−7)=10.0625 cm. Thus |m|=v/u=10.0625/23=0.4375. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.4375, not -0.4375.",
"B": "Correct. The worked calculation gives 0.4375.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.4375, not -1.5625.",
"D": "Incorrect. Substituting the stated value... | [
"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_002958 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-2, 6, -4) and v=(-4, 7, 2), calculate u·v. | {
"A": "50.4",
"B": "5.2",
"C": "21",
"D": "42"
} | D | 42 | The dot product is the sum of corresponding component products: (-2)(-4)+(6)(7)+(-4)(2)=42. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 42, not 50.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 42, not 5.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 42, not 21.",
"D": "Correct. The ... | [
"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_009490 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_13H_5X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "7.5",
"B": "10",
"C": "5",
"D": "9"
} | B | 10 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×13+2+0−5−3)/2=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 7.5.",
"B": "Correct. The worked calculation gives 10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 5.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_000689 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 4. What is the sum of its first 5 terms? | {
"A": "4092",
"B": "3411",
"C": "1705",
"D": "3410"
} | D | 3410 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(4^5−1)/(4−1)=3410. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3410, not 4092.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3410, not 3411.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3410, not 1705.",
"D": "Corr... | [
"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_004207 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 44 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.28. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "198.528 N",
"B": "166.44 N",
"C": "167.44 N",
"D": "165.44 N"
} | D | 165.44 N | Net force=mg(sinθ−μcosθ)=44×10×(0.6−0.28×0.8)=165.44 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 165.44 N, not 198.528 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 165.44 N, not 166.44 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 165.44 N, not... | [
"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_002769 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(3, 1, -3) and v=(-5, 6, 7), calculate u·v. | {
"A": "-22.5",
"B": "-30",
"C": "-15",
"D": "-60"
} | B | -30 | The dot product is the sum of corresponding component products: (3)(-5)+(1)(6)+(-3)(7)=-30. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -30, not -22.5.",
"B": "Correct. The worked calculation gives -30.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -30, not -15.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008523 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.05 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": "2.06 K",
"B": "0.06 K",
"C": "-0.94 K",
"D": "1.06 K"
} | B | 0.06 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.6×0.05=0.06 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.06 K, not 2.06 K.",
"B": "Correct. The worked calculation gives 0.06 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.06 K, not -0.94 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_003444 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 113 m s⁻¹ at 70° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "820.7755 m",
"B": "821.7755 m",
"C": "615.58162 m",
"D": "818.7755 m"
} | A | 820.7755 m | Range R=u²sin(2θ)/g. Substituting u=113, θ=70° and g=10 gives R=(113)²sin(140°)/10=820.7755 m. | {
"A": "Correct. The worked calculation gives 820.7755 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 820.7755 m, not 821.7755 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 820.7755 m, not 615.58162 m.",
"D": "Incorrect. Substituti... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003248 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(5-12i)/(12+5i). What is Re(z), the real part of z? | {
"A": "1",
"B": "0",
"C": "3",
"D": "-3"
} | B | 0 | Multiply numerator and denominator by the conjugate (12-5i). Then Re(z)=(ac+bd)/(c²+d²)=((5)(12)+(-12)(5))/(12²+(5)²)=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"B": "Correct. The worked calculation gives 0.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 3.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_008664 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.86 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.936 K",
"B": "5.064 K",
"C": "4.128 K",
"D": "2.064 K"
} | D | 2.064 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.6×0.86=2.064 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.064 K, not -0.936 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.064 K, not 5.064 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.064 K, not 4.12... | [
"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_004939 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 3 Ω are connected in series; this combination is connected in parallel with a 9 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.91667 A",
"B": "8.83333 A",
"C": "6.83333 A",
"D": "5.83333 A"
} | D | 5.83333 A | Series branch resistance=9+3=12 Ω. Parallel equivalent R_eq=(12×9)/(12+9)=5.14286 Ω. Total current I=V/R_eq=30/5.14286=5.83333 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.83333 A, not 2.91667 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.83333 A, not 8.83333 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.83333 A,... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000320 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 -5x +3=0, let its roots be α and β. What is α²+β²? | {
"A": "-0.30556",
"B": "-0.61111",
"C": "-3.30556",
"D": "-0.15278"
} | A | -0.30556 | By Vieta's relations, α+β = 5/6 and αβ = 3/6. Then α²+β²=(α+β)²−2αβ = (5/6)²−2(3/6) = -0.30556. | {
"A": "Correct. The worked calculation gives -0.30556.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.30556, not -0.61111.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.30556, not -3.30556.",
"D": "Incorrect. Substituting the stat... | [
"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_001245 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=7x³ -1x² +3x+7. Evaluate f′(0). | {
"A": "4.5",
"B": "4",
"C": "3",
"D": "6"
} | C | 3 | Differentiate: f′(x)=3(7)x²+2(-1)x+(3). At x=0, f′(0)=3(7)(0)²+2(-1)(0)+(3)=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.",
"C": "Correct. The worked calculation gives 3.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_001978 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 44 distinct elements? | {
"A": "177232628",
"B": "265848940.5",
"C": "177232627",
"D": "177232629"
} | C | 177232627 | Order does not matter, so the count is C(44,8)=44!/[8!(36)!]=177232627. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 177232627, not 177232628.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 177232627, not 265848940.5.",
"C": "Correct. The worked calculation gives 177232627.",
"D": "Incorrect. Substituting t... | [
"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_006018 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 39 cm in front of a thin convex lens of focal length 24 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "3.2",
"B": "4.6",
"C": "-1.4",
"D": "1.6"
} | D | 1.6 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(39)(24)/(39−24)=62.4 cm. Thus |m|=v/u=62.4/39=1.6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.6, not 3.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.6, not 4.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.6, not -1.4.",
"D": "Correct. ... | [
"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_001983 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 7 elements can be selected from a set of 69 distinct elements? | {
"A": "1078897248",
"B": "1078897250",
"C": "2157794496",
"D": "539448624"
} | A | 1078897248 | Order does not matter, so the count is C(69,7)=69!/[7!(62)!]=1078897248. | {
"A": "Correct. The worked calculation gives 1078897248.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1078897248, not 1078897250.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1078897248, not 2157794496.",
"D": "Incorrect. Substitutin... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008536 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.07 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.07 K",
"B": "0.07 K",
"C": "-2.93 K",
"D": "0.0525 K"
} | B | 0.07 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×1.0×0.07=0.07 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.07 K, not -0.07 K.",
"B": "Correct. The worked calculation gives 0.07 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.07 K, not -2.93 K.",
"D": "Incorrect. Substituting the stated value... | [
"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_006587 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 12 kg is attached to an ideal spring of force constant 390 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.35082 s",
"B": "0.35082 s",
"C": "-2.64918 s",
"D": "-1.64918 s"
} | B | 0.35082 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(12/390)=0.35082 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35082 s, not 1.35082 s.",
"B": "Correct. The worked calculation gives 0.35082 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35082 s, not -2.64918 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_000248 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 +10x +1=0, let its roots be α and β. What is α²+β²? | {
"A": "98",
"B": "99",
"C": "147",
"D": "73.5"
} | A | 98 | By Vieta's relations, α+β = -10/1 and αβ = 1/1. Then α²+β²=(α+β)²−2αβ = (-10/1)²−2(1/1) = 98. | {
"A": "Correct. The worked calculation gives 98.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 98, not 99.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 98, not 147.",
"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_004058 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 37 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.32. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "127.28 N",
"B": "125.28 N",
"C": "-127.28 N",
"D": "13.728 N"
} | A | 127.28 N | Net force=mg(sinθ−μcosθ)=37×10×(0.6−0.32×0.8)=127.28 N. | {
"A": "Correct. The worked calculation gives 127.28 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 127.28 N, not 125.28 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 127.28 N, not -127.28 N.",
"D": "Incorrect. Substituting the sta... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003851 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 8 m s⁻¹. A constant net force does 21 N of work over 17 m in the direction of motion. Find its final kinetic energy. | {
"A": "871.5 J",
"B": "581 J",
"C": "579 J",
"D": "697.2 J"
} | B | 581 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(8)²+(21)(17)=581 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 581 J, not 871.5 J.",
"B": "Correct. The worked calculation gives 581 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 581 J, not 579 J.",
"D": "Incorrect. Substituting the stated values int... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002781 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(6, 0, 3) and v=(8, 8, -4), calculate u·v. | {
"A": "36",
"B": "-36",
"C": "37",
"D": "35"
} | A | 36 | The dot product is the sum of corresponding component products: (6)(8)+(0)(8)+(3)(-4)=36. | {
"A": "Correct. The worked calculation gives 36.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 36, not -36.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 36, not 37.",
"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_002896 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, 3, 6) and v=(1, 4, 8), calculate u·v. | {
"A": "64",
"B": "128",
"C": "-64",
"D": "62"
} | A | 64 | The dot product is the sum of corresponding component products: (4)(1)+(3)(4)+(6)(8)=64. | {
"A": "Correct. The worked calculation gives 64.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 64, not 128.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 64, not -64.",
"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_000943 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio 2. What is the sum of its first 5 terms? | {
"A": "341",
"B": "409.2",
"C": "340",
"D": "342"
} | A | 341 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(2^5−1)/(2−1)=341. | {
"A": "Correct. The worked calculation gives 341.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 341, not 409.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 341, not 340.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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 |
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