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_008157 | 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 22082 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": "29.06128 g",
"B": "-29.06128 g",
"C": "21.79596 g",
"D": "43.59193 g"
} | A | 29.06128 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×22082/(2×96500)=29.06128 g. | {
"A": "Correct. The worked calculation gives 29.06128 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 29.06128 g, not -29.06128 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29.06128 g, not 21.79596 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006399 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 4 kg is attached to an ideal spring of force constant 105 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.39036 s",
"B": "0.39036 s",
"C": "1.39036 s",
"D": "-2.60964 s"
} | B | 0.39036 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(4/105)=0.39036 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.39036 s, not -0.39036 s.",
"B": "Correct. The worked calculation gives 0.39036 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.39036 s, not 1.39036 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_008317 | 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 1 A for 14724 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": "4.84442 g",
"B": "6.84442 g",
"C": "5.84442 g",
"D": "3.63332 g"
} | A | 4.84442 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×1×14724/(2×96500)=4.84442 g. | {
"A": "Correct. The worked calculation gives 4.84442 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.84442 g, not 6.84442 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.84442 g, not 5.84442 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_007775 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 86 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "20.5 mmol L⁻¹",
"B": "22.5 mmol L⁻¹",
"C": "21.5 mmol L⁻¹",
"D": "19.5 mmol L⁻¹"
} | C | 21.5 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=86/2^2=21.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21.5 mmol L⁻¹, not 20.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21.5 mmol L⁻¹, not 22.5 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 21.5 mmol L⁻¹.",
"D": "Incorre... | [
"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_003807 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 6 m s⁻¹. A constant net force does 6 N of work over 9 m in the direction of motion. Find its final kinetic energy. | {
"A": "135 J",
"B": "179 J",
"C": "180 J",
"D": "144 J"
} | C | 180 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(6)²+(6)(9)=180 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 180 J, not 135 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 180 J, not 179 J.",
"C": "Correct. The worked calculation gives 180 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_007756 | 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 57 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "3.5625 mmol L⁻¹",
"B": "1.5625 mmol L⁻¹",
"C": "-3.5625 mmol L⁻¹",
"D": "4.5625 mmol L⁻¹"
} | A | 3.5625 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=57/2^4=3.5625 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 3.5625 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.5625 mmol L⁻¹, not 1.5625 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.5625 mmol L⁻¹, not -3.5625 mmol L⁻¹.",
"D... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001764 | 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 83 distinct elements? | {
"A": "47331872359.2",
"B": "39443226965",
"C": "39443226967",
"D": "39443226966"
} | D | 39443226966 | Order does not matter, so the count is C(83,8)=83!/[8!(75)!]=39443226966. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 39443226966, not 47331872359.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39443226966, not 39443226965.",
"C": "Incorrect. Substituting the stated values into the governing relation gives ... | [
"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_009297 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.94 V, transfers 3 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.08612 V",
"B": "0.4306 V",
"C": "0.8612 V",
"D": "3.8612 V"
} | C | 0.8612 V | Apply the Nernst equation: E=0.94−(0.0591/3)(4)=0.8612 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8612 V, not 1.08612 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8612 V, not 0.4306 V.",
"C": "Correct. The worked calculation gives 0.8612 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009867 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(Cl)_6]^+0, each Cl ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "3",
"B": "6",
"C": "5",
"D": "9"
} | B | 6 | Let the formal oxidation state of Co be x. Charge balance gives x+(6)(−1)=+0; hence x=0+6=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"B": "Correct. The worked calculation gives 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 5.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002167 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 7 red, 6 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.1625",
"B": "0.65",
"C": "2.325",
"D": "0.325"
} | D | 0.325 | Favourable pairs = C(7,2)+C(6,2)+C(3,2)=39. Total pairs=C(16,2)=120. Therefore P=39/120=0.325. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.325, not 0.1625.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.325, not 0.65.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.325, not 2.325.",
"D":... | [
"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_009077 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.68 V, transfers 1 electrons, and has reaction quotient Q=10^2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.5618 V",
"B": "1.05618 V",
"C": "0.42135 V",
"D": "3.5618 V"
} | A | 0.5618 V | Apply the Nernst equation: E=0.68−(0.0591/1)(2)=0.5618 V. | {
"A": "Correct. The worked calculation gives 0.5618 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.5618 V, not 1.05618 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5618 V, not 0.42135 V.",
"D": "Incorrect. Substituting the st... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006411 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 5 kg is attached to an ideal spring of force constant 690 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.82975 s",
"B": "0.25538 s",
"C": "0.17025 s",
"D": "0.3405 s"
} | C | 0.17025 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(5/690)=0.17025 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.17025 s, not -1.82975 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.17025 s, not 0.25538 s.",
"C": "Correct. The worked calculation gives 0.17025 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_003222 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(12+1i)/(2+6i). What is Re(z), the real part of z? | {
"A": "0.75",
"B": "-1.25",
"C": "-0.75",
"D": "-0.25"
} | A | 0.75 | Multiply numerator and denominator by the conjugate (2-6i). Then Re(z)=(ac+bd)/(c²+d²)=((12)(2)+(1)(6))/(2²+(6)²)=0.75. | {
"A": "Correct. The worked calculation gives 0.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.75, not -1.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.75, not -0.75.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_007604 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 70 mL of 0.10 M HCl is mixed with 90 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.09691",
"B": "13.09691",
"C": "2.20969",
"D": "15.09691"
} | A | 12.09691 | Excess OH⁻ moles=0.10×(90−70)/1000=0.002000 mol. Total volume=0.160 L, so [OH⁻]=0.012500 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.09691. | {
"A": "Correct. The worked calculation gives 12.09691.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.09691, not 13.09691.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.09691, not 2.20969.",
"D": "Incorrect. Substituting the state... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007673 | 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 46 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "4.75 mmol L⁻¹",
"B": "5.75 mmol L⁻¹",
"C": "6.75 mmol L⁻¹",
"D": "7.75 mmol L⁻¹"
} | B | 5.75 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=46/2^3=5.75 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.75 mmol L⁻¹, not 4.75 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 5.75 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.75 mmol L⁻¹, not 6.75 mmol L⁻¹.",
"D": "Incorre... | [
"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_006065 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 17 cm in front of a thin convex lens of focal length 10 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.42857",
"B": "1.07143",
"C": "2.85714",
"D": "2.42857"
} | A | 1.42857 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(17)(10)/(17−10)=24.28571 cm. Thus |m|=v/u=24.28571/17=1.42857. | {
"A": "Correct. The worked calculation gives 1.42857.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.42857, not 1.07143.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.42857, not 2.85714.",
"D": "Incorrect. Substituting the stated va... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008133 | 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 11587 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": "15.24921 g",
"B": "12.19937 g",
"C": "11.43691 g",
"D": "2.52492 g"
} | A | 15.24921 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×11587/(2×96500)=15.24921 g. | {
"A": "Correct. The worked calculation gives 15.24921 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15.24921 g, not 12.19937 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15.24921 g, not 11.43691 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_002735 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(9, -1, -4) and v=(9, 6, 0), calculate u·v. | {
"A": "37.5",
"B": "-75",
"C": "75",
"D": "150"
} | C | 75 | The dot product is the sum of corresponding component products: (9)(9)+(-1)(6)+(-4)(0)=75. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 75, not 37.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 75, not -75.",
"C": "Correct. The worked calculation gives 75.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002209 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 8 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.3202",
"B": "0.4803",
"C": "0.1601",
"D": "-2.6798"
} | A | 0.3202 | Favourable pairs = C(9,2)+C(8,2)+C(12,2)=130. Total pairs=C(29,2)=406. Therefore P=130/406=0.3202. | {
"A": "Correct. The worked calculation gives 0.3202.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3202, not 0.4803.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3202, not 0.1601.",
"D": "Incorrect. Substituting the stated values ... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006001 | 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 337 K. What is its pressure at 655 K? | {
"A": "8.02522 atm",
"B": "6.02522 atm",
"C": "4.02522 atm",
"D": "9.02522 atm"
} | B | 6.02522 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.1)(655)/(337)=6.02522 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.02522 atm, not 8.02522 atm.",
"B": "Correct. The worked calculation gives 6.02522 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.02522 atm, not 4.02522 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_007703 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 66 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "0.38672 mmol L⁻¹",
"B": "0.25781 mmol L⁻¹",
"C": "1.25781 mmol L⁻¹",
"D": "-0.74219 mmol L⁻¹"
} | B | 0.25781 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=66/2^8=0.25781 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25781 mmol L⁻¹, not 0.38672 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.25781 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25781 mmol L⁻¹, not 1.25781 mmol L⁻¹.",
... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000110 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -6x -12=0, let its roots be α and β. What is α²+β²? | {
"A": "19",
"B": "25.2",
"C": "21",
"D": "42"
} | C | 21 | By Vieta's relations, α+β = 6/2 and αβ = -12/2. Then α²+β²=(α+β)²−2αβ = (6/2)²−2(-12/2) = 21. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21, not 19.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21, not 25.2.",
"C": "Correct. The worked calculation gives 21.",
"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_006249 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 70 cm in front of a thin convex lens of focal length 29 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.70732",
"B": "-0.70732",
"C": "-1.29268",
"D": "1.41463"
} | A | 0.70732 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(70)(29)/(70−29)=49.5122 cm. Thus |m|=v/u=49.5122/70=0.70732. | {
"A": "Correct. The worked calculation gives 0.70732.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.70732, not -0.70732.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.70732, not -1.29268.",
"D": "Incorrect. Substituting the stated ... | [
"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_002333 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 12 blue and 5 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.17333",
"B": "-1.65333",
"C": "0.69333",
"D": "0.34667"
} | D | 0.34667 | Favourable pairs = C(8,2)+C(12,2)+C(5,2)=104. Total pairs=C(25,2)=300. Therefore P=104/300=0.34667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34667, not 0.17333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34667, not -1.65333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34667, not 0.69... | [
"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_001394 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (2x² +0x +2) dx. | {
"A": "154",
"B": "156",
"C": "234",
"D": "16.6"
} | B | 156 | An antiderivative is (2/3)x³+(0/2)x²+(2)x. Evaluating between 0 and 6 gives (2/3)(6)³+(0/2)(6)²+(2)(6)=156. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 156, not 154.",
"B": "Correct. The worked calculation gives 156.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 156, not 234.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006752 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 27 mol H₂ and 29 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "40.5 mol",
"B": "27 mol",
"C": "26 mol",
"D": "25 mol"
} | B | 27 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 27 mol H₂O; O₂ can produce 58 mol H₂O. The limiting condition is H₂; product=27 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 27 mol, not 40.5 mol.",
"B": "Correct. The worked calculation gives 27 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 27 mol, not 26 mol.",
"D": "Incorrect. Substituting the stated value... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007760 | 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 35 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "2.1875 mmol L⁻¹",
"B": "5.1875 mmol L⁻¹",
"C": "3.1875 mmol L⁻¹",
"D": "-0.8125 mmol L⁻¹"
} | A | 2.1875 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=35/2^4=2.1875 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 2.1875 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.1875 mmol L⁻¹, not 5.1875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.1875 mmol L⁻¹, not 3.1875 mmol L⁻¹.",
"D"... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003760 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 12 m s⁻¹. A constant net force does 18 N of work over 20 m in the direction of motion. Find its final kinetic energy. | {
"A": "432 J",
"B": "862 J",
"C": "648 J",
"D": "864 J"
} | D | 864 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(12)²+(18)(20)=864 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 864 J, not 432 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 864 J, not 862 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 864 J, not 648 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_006413 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 5 kg is attached to an ideal spring of force constant 1000 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.07071 s",
"B": "0.14142 s",
"C": "0.28284 s",
"D": "2.14142 s"
} | B | 0.14142 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(5/1000)=0.14142 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.14142 s, not 0.07071 s.",
"B": "Correct. The worked calculation gives 0.14142 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.14142 s, not 0.28284 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_008711 | 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, 26% of A has dissociated at constant volume. Find K_c. | {
"A": "0.59196",
"B": "-2.70402",
"C": "0.44397",
"D": "0.29598"
} | D | 0.29598 | Let α=0.26. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.81)(0.26)²/(1−0.26)=0.29598. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29598, not 0.59196.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29598, not -2.70402.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29598, not 0.44... | [
"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_008688 | 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 0.3 mol L⁻¹ and initially B is absent. At equilibrium, 17% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.95822",
"B": "-2.95822",
"C": "0.04178",
"D": "0.08357"
} | C | 0.04178 | Let α=0.17. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.3)(0.17)²/(1−0.17)=0.04178. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.04178, not -0.95822.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.04178, not -2.95822.",
"C": "Correct. The worked calculation gives 0.04178.",
"D": "Incorrect. Substituting the stated ... | [
"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_004567 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 12 kg and radius 3 m is acted on by a constant torque of 89 N m about its central axis. Find its angular acceleration. | {
"A": "1.16481 rad s⁻²",
"B": "1.64815 rad s⁻²",
"C": "-0.35185 rad s⁻²",
"D": "2.64815 rad s⁻²"
} | B | 1.64815 rad s⁻² | For a solid disc, I=½MR²=½(12)(3)²=54 kg m². Using τ=Iα, α=89/54=1.64815 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.64815 rad s⁻², not 1.16481 rad s⁻².",
"B": "Correct. The worked calculation gives 1.64815 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.64815 rad s⁻², not -0.35185 rad s⁻².",
"D... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006508 | 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 633 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.58415 s",
"B": "-2.61057 s",
"C": "3.38943 s",
"D": "0.38943 s"
} | D | 0.38943 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(24/633)=0.38943 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.38943 s, not 0.58415 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.38943 s, not -2.61057 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.38943 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_001110 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ +6x² -1x+7. Evaluate f′(0). | {
"A": "-1",
"B": "-3",
"C": "1",
"D": "-2"
} | A | -1 | Differentiate: f′(x)=3(6)x²+2(6)x+(-1). At x=0, f′(0)=3(6)(0)²+2(6)(0)+(-1)=-1. | {
"A": "Correct. The worked calculation gives -1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1, not -3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1, not 1.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002551 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, -1], [3, 6]]. | {
"A": "21",
"B": "19",
"C": "10.5",
"D": "42"
} | A | 21 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(6)−(-1)(3)=21. | {
"A": "Correct. The worked calculation gives 21.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21, not 19.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21, not 10.5.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"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_009037 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.23 V, transfers 2 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.08225 V",
"B": "4.08225 V",
"C": "3.08225 V",
"D": "0.54112 V"
} | A | 1.08225 V | Apply the Nernst equation: E=1.23−(0.0591/2)(5)=1.08225 V. | {
"A": "Correct. The worked calculation gives 1.08225 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.08225 V, not 4.08225 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.08225 V, not 3.08225 V.",
"D": "Incorrect. Substituting the... | [
"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_009595 | 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_9N_2X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "1",
"B": "-1",
"C": "0.5",
"D": "0"
} | A | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×5+2+2−9−3)/2=1. | {
"A": "Correct. The worked calculation gives 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not -1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.5.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007453 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 63 mL of 0.10 M HCl is mixed with 66 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "9.36653",
"B": "8.36653",
"C": "11.36653",
"D": "-11.36653"
} | C | 11.36653 | Excess OH⁻ moles=0.10×(66−63)/1000=0.000300 mol. Total volume=0.129 L, so [OH⁻]=0.002326 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=11.36653. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.36653, not 9.36653.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.36653, not 8.36653.",
"C": "Correct. The worked calculation gives 11.36653.",
"D": "Incorrect. Substituting the stated... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009729 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(Cl)_3]^+2, each Cl ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "-5",
"B": "7.5",
"C": "3",
"D": "5"
} | D | 5 | Let the formal oxidation state of Pt be x. Charge balance gives x+(3)(−1)=+2; hence x=2+3=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not -5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.",
"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_004159 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 49 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": "168.56 N",
"B": "84.28 N",
"C": "-168.56 N",
"D": "337.12 N"
} | A | 168.56 N | Net force=mg(sinθ−μcosθ)=49×10×(0.6−0.32×0.8)=168.56 N. | {
"A": "Correct. The worked calculation gives 168.56 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 168.56 N, not 84.28 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 168.56 N, not -168.56 N.",
"D": "Incorrect. Substituting the stat... | [
"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_002868 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(2, 2, 5) and v=(4, -7, 5), calculate u·v. | {
"A": "19",
"B": "9.5",
"C": "28.5",
"D": "-19"
} | A | 19 | The dot product is the sum of corresponding component products: (2)(4)+(2)(-7)+(5)(5)=19. | {
"A": "Correct. The worked calculation gives 19.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19, not 9.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19, not 28.5.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001617 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (-3x² +0x +3) dx. | {
"A": "-53",
"B": "-52",
"C": "-41.6",
"D": "-78"
} | B | -52 | An antiderivative is (-3/3)x³+(0/2)x²+(3)x. Evaluating between 0 and 4 gives (-3/3)(4)³+(0/2)(4)²+(3)(4)=-52. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -52, not -53.",
"B": "Correct. The worked calculation gives -52.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -52, not -41.6.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_000666 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -2 and common difference 15. Find the sum of its first 22 terms. | {
"A": "-3421",
"B": "343.1",
"C": "3421",
"D": "1710.5"
} | C | 3421 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-2, d=15, n=22: Sₙ=22/2[2(-2)+(22−1)(15)]=3421. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3421, not -3421.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3421, not 343.1.",
"C": "Correct. The worked calculation gives 3421.",
"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_003219 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-6+4i)/(12+1i). What is Re(z), the real part of z? | {
"A": "-0.46897",
"B": "-3.46897",
"C": "0.53103",
"D": "0.46897"
} | A | -0.46897 | Multiply numerator and denominator by the conjugate (12-1i). Then Re(z)=(ac+bd)/(c²+d²)=((-6)(12)+(4)(1))/(12²+(1)²)=-0.46897. | {
"A": "Correct. The worked calculation gives -0.46897.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.46897, not -3.46897.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.46897, not 0.53103.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001162 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ +1x² +12x+7. Evaluate f′(1). | {
"A": "24",
"B": "3.6",
"C": "27",
"D": "26"
} | D | 26 | Differentiate: f′(x)=3(4)x²+2(1)x+(12). At x=1, f′(1)=3(4)(1)²+2(1)(1)+(12)=26. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26, not 24.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26, not 3.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26, not 27.",
"D": "Correct. The wo... | [
"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_000580 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 30 and common difference 8. Find the sum of its first 16 terms. | {
"A": "720",
"B": "1440",
"C": "1152",
"D": "1441"
} | B | 1440 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=30, d=8, n=16: Sₙ=16/2[2(30)+(16−1)(8)]=1440. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1440, not 720.",
"B": "Correct. The worked calculation gives 1440.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1440, not 1152.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_001456 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (-1x² +2x -1) dx. | {
"A": "72.33333",
"B": "-72.33333",
"C": "-108.5",
"D": "-73.33333"
} | B | -72.33333 | An antiderivative is (-1/3)x³+(2/2)x²+(-1)x. Evaluating between 0 and 7 gives (-1/3)(7)³+(2/2)(7)²+(-1)(7)=-72.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -72.33333, not 72.33333.",
"B": "Correct. The worked calculation gives -72.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -72.33333, not -108.5.",
"D": "Incorrect. Substituting the sta... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002806 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(0, 5, -6) and v=(0, 0, -5), calculate u·v. | {
"A": "30",
"B": "36",
"C": "15",
"D": "60"
} | A | 30 | The dot product is the sum of corresponding component products: (0)(0)+(5)(0)+(-6)(-5)=30. | {
"A": "Correct. The worked calculation gives 30.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30, not 36.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30, not 15.",
"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_009772 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(CN)_3]^+2, each CN ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "7.5",
"B": "5",
"C": "4",
"D": "6"
} | B | 5 | Let the formal oxidation state of Co be x. Charge balance gives x+(3)(−1)=+2; hence x=2+3=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.5.",
"B": "Correct. The worked calculation gives 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 4.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007779 | 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 79 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "39.5 mmol L⁻¹",
"B": "40.5 mmol L⁻¹",
"C": "19.75 mmol L⁻¹",
"D": "31.6 mmol L⁻¹"
} | A | 39.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=79/2^1=39.5 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 39.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39.5 mmol L⁻¹, not 40.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39.5 mmol L⁻¹, not 19.75 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_000102 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 -8x -8=0, let its roots be α and β. What is α²+β²? | {
"A": "0.59184",
"B": "7.18367",
"C": "3.59184",
"D": "5.59184"
} | C | 3.59184 | By Vieta's relations, α+β = 8/7 and αβ = -8/7. Then α²+β²=(α+β)²−2αβ = (8/7)²−2(-8/7) = 3.59184. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.59184, not 0.59184.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.59184, not 7.18367.",
"C": "Correct. The worked calculation gives 3.59184.",
"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_007281 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 3 mol of gas at 348 K and 0.47 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "145.81703 L",
"B": "364.54259 L",
"C": "181.27129 L",
"D": "182.27129 L"
} | D | 182.27129 L | PV=nRT, so V=nRT/P=(3)(0.082057)(348)/(0.47)=182.27129 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 182.27129 L, not 145.81703 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 182.27129 L, not 364.54259 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18... | [
"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_004225 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 29 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.44. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "57.536 N",
"B": "143.84 N",
"C": "69.92 N",
"D": "71.92 N"
} | D | 71.92 N | Net force=mg(sinθ−μcosθ)=29×10×(0.6−0.44×0.8)=71.92 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 71.92 N, not 57.536 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 71.92 N, not 143.84 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 71.92 N, not 69.... | [
"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_002474 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, -7], [4, 6]]. | {
"A": "39",
"B": "52",
"C": "51",
"D": "104"
} | B | 52 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(6)−(-7)(4)=52. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 52, not 39.",
"B": "Correct. The worked calculation gives 52.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 52, not 51.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009020 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.23 V, transfers 2 electrons, and has reaction quotient Q=10^0. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.77 V",
"B": "2.23 V",
"C": "1.23 V",
"D": "1.845 V"
} | C | 1.23 V | Apply the Nernst equation: E=1.23−(0.0591/2)(0)=1.23 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.23 V, not -0.77 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.23 V, not 2.23 V.",
"C": "Correct. The worked calculation gives 1.23 V.",
"D": "Incorrect. Substituting the stated values... | [
"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_003249 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(15+13i)/(5+9i). What is Re(z), the real part of z? | {
"A": "-0.18868",
"B": "2.71698",
"C": "1.81132",
"D": "2.81132"
} | C | 1.81132 | Multiply numerator and denominator by the conjugate (5-9i). Then Re(z)=(ac+bd)/(c²+d²)=((15)(5)+(13)(9))/(5²+(9)²)=1.81132. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.81132, not -0.18868.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.81132, not 2.71698.",
"C": "Correct. The worked calculation gives 1.81132.",
"D": "Incorrect. Substituting the stated v... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009094 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.35 V, transfers 3 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.4682 V",
"B": "1.4682 V",
"C": "4.4682 V",
"D": "2.4682 V"
} | B | 1.4682 V | Apply the Nernst equation: E=1.35−(0.0591/3)(-6)=1.4682 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.4682 V, not -1.4682 V.",
"B": "Correct. The worked calculation gives 1.4682 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.4682 V, not 4.4682 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000164 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 +0x -1=0, let its roots be α and β. What is α²+β²? | {
"A": "1",
"B": "0.5",
"C": "2.5",
"D": "1.05"
} | B | 0.5 | By Vieta's relations, α+β = 0/4 and αβ = -1/4. Then α²+β²=(α+β)²−2αβ = (0/4)²−2(-1/4) = 0.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5, not 1.",
"B": "Correct. The worked calculation gives 0.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5, not 2.5.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_005032 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +8 μC and +8 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "142.22222 N",
"B": "53.33333 N",
"C": "73.11111 N",
"D": "71.11111 N"
} | D | 71.11111 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(8×10⁻⁶)(8×10⁻⁶)/(9×10⁻²)²=71.11111 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 71.11111 N, not 142.22222 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 71.11111 N, not 53.33333 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 71.11... | [
"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_001755 | 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 33 distinct elements? | {
"A": "4272050",
"B": "3204036",
"C": "4272049",
"D": "4272048"
} | D | 4272048 | Order does not matter, so the count is C(33,7)=33!/[7!(26)!]=4272048. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4272048, not 4272050.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4272048, not 3204036.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4272048, not 42720... | [
"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_003241 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-14+11i)/(1+11i). What is Re(z), the real part of z? | {
"A": "3.87705",
"B": "0.43852",
"C": "0.87705",
"D": "1.7541"
} | C | 0.87705 | Multiply numerator and denominator by the conjugate (1-11i). Then Re(z)=(ac+bd)/(c²+d²)=((-14)(1)+(11)(11))/(1²+(11)²)=0.87705. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.87705, not 3.87705.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.87705, not 0.43852.",
"C": "Correct. The worked calculation gives 0.87705.",
"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_008628 | 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 0.65 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.1664 K",
"B": "2.3328 K",
"C": "0.6656 K",
"D": "0.3328 K"
} | D | 0.3328 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.512×0.65=0.3328 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3328 K, not 0.1664 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3328 K, not 2.3328 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3328 K, not ... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003217 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(6-1i)/(1+4i). What is Re(z), the real part of z? | {
"A": "0.11765",
"B": "0.08824",
"C": "2.11765",
"D": "3.11765"
} | A | 0.11765 | Multiply numerator and denominator by the conjugate (1-4i). Then Re(z)=(ac+bd)/(c²+d²)=((6)(1)+(-1)(4))/(1²+(4)²)=0.11765. | {
"A": "Correct. The worked calculation gives 0.11765.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.11765, not 0.08824.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.11765, not 2.11765.",
"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_000762 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio 2. What is the sum of its first 10 terms? | {
"A": "6137",
"B": "6138",
"C": "7365.6",
"D": "6140"
} | B | 6138 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(2^10−1)/(2−1)=6138. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6138, not 6137.",
"B": "Correct. The worked calculation gives 6138.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6138, not 7365.6.",
"D": "Incorrect. Substituting the stated values into the... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003251 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(10+4i)/(7+6i). What is Re(z), the real part of z? | {
"A": "-0.89412",
"B": "-1.89412",
"C": "-1.10588",
"D": "1.10588"
} | D | 1.10588 | Multiply numerator and denominator by the conjugate (7-6i). Then Re(z)=(ac+bd)/(c²+d²)=((10)(7)+(4)(6))/(7²+(6)²)=1.10588. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.10588, not -0.89412.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.10588, not -1.89412.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.10588, not -1.... | [
"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_000383 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 11 and common difference 13. Find the sum of its first 20 terms. | {
"A": "5380",
"B": "2690",
"C": "2152",
"D": "-2690"
} | B | 2690 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=11, d=13, n=20: Sₙ=20/2[2(11)+(20−1)(13)]=2690. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2690, not 5380.",
"B": "Correct. The worked calculation gives 2690.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2690, not 2152.",
"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_008875 | 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 0.09 mol L⁻¹ and initially B is absent. At equilibrium, 27% of A has dissociated at constant volume. Find K_c. | {
"A": "2.03595",
"B": "-2.96405",
"C": "0.03595",
"D": "0.05393"
} | C | 0.03595 | Let α=0.27. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.09)(0.27)²/(1−0.27)=0.03595. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.03595, not 2.03595.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.03595, not -2.96405.",
"C": "Correct. The worked calculation gives 0.03595.",
"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_009586 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_9H_22N_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "2",
"B": "3",
"C": "1",
"D": "0"
} | D | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×9+2+2−22−0)/2=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"D": "Correct. The worked ca... | [
"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_002901 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-6, -7, 1) and v=(-6, 3, 7), calculate u·v. | {
"A": "-22",
"B": "22",
"C": "11",
"D": "24"
} | B | 22 | The dot product is the sum of corresponding component products: (-6)(-6)+(-7)(3)+(1)(7)=22. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22, not -22.",
"B": "Correct. The worked calculation gives 22.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22, not 11.",
"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_005914 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.1 atm at 196 K. What is its pressure at 376 K? | {
"A": "-2.1102 atm",
"B": "2.1102 atm",
"C": "3.16531 atm",
"D": "4.22041 atm"
} | B | 2.1102 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.1)(376)/(196)=2.1102 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.1102 atm, not -2.1102 atm.",
"B": "Correct. The worked calculation gives 2.1102 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.1102 atm, not 3.16531 atm.",
"D": "Incorrect. Substitut... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008781 | 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 0.94 mol L⁻¹ and initially B is absent. At equilibrium, 70% of A has dissociated at constant volume. Find K_c. | {
"A": "8.14133",
"B": "4.606",
"C": "6.14133",
"D": "9.212"
} | C | 6.14133 | Let α=0.7. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.94)(0.7)²/(1−0.7)=6.14133. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.14133, not 8.14133.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.14133, not 4.606.",
"C": "Correct. The worked calculation gives 6.14133.",
"D": "Incorrect. Substituting the stated valu... | [
"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_009302 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.92 V, transfers 2 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.15838 V",
"B": "1.07723 V",
"C": "3.77225 V",
"D": "0.77225 V"
} | D | 0.77225 V | Apply the Nernst equation: E=0.92−(0.0591/2)(5)=0.77225 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.77225 V, not 1.15838 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.77225 V, not 1.07723 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.77225 V,... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003323 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(8-3i)/(3+10i). What is Re(z), the real part of z? | {
"A": "0.9945",
"B": "-0.05505",
"C": "0.94495",
"D": "-1.05505"
} | B | -0.05505 | Multiply numerator and denominator by the conjugate (3-10i). Then Re(z)=(ac+bd)/(c²+d²)=((8)(3)+(-3)(10))/(3²+(10)²)=-0.05505. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.05505, not 0.9945.",
"B": "Correct. The worked calculation gives -0.05505.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.05505, not 0.94495.",
"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_002452 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, -4], [2, 1]]. | {
"A": "14",
"B": "11",
"C": "16.5",
"D": "12"
} | B | 11 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(1)−(-4)(2)=11. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11, not 14.",
"B": "Correct. The worked calculation gives 11.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11, not 16.5.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"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_008374 | 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 0.44 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": "-1.5424 K",
"B": "0.6864 K",
"C": "-0.4576 K",
"D": "0.4576 K"
} | D | 0.4576 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×0.44=0.4576 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.4576 K, not -1.5424 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.4576 K, not 0.6864 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.4576 K, not... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007582 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 88 mL of 0.10 M HCl is mixed with 78 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "5.22011",
"B": "2.22011",
"C": "0.22011",
"D": "1.11005"
} | B | 2.22011 | Excess H⁺ moles=0.10×(88−78)/1000=0.001000 mol. Total volume=0.166 L, so [H⁺]=0.006024 M and pH=−log₁₀[H⁺]=2.22011. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.22011, not 5.22011.",
"B": "Correct. The worked calculation gives 2.22011.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.22011, not 0.22011.",
"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_000645 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 24 and common difference 2. Find the sum of its first 30 terms. | {
"A": "1588",
"B": "1592",
"C": "1272",
"D": "1590"
} | D | 1590 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=24, d=2, n=30: Sₙ=30/2[2(24)+(30−1)(2)]=1590. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1590, not 1588.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1590, not 1592.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1590, not 1272.",
"D": "Corr... | [
"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_009740 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(CN)_2]^+0, each CN ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "3",
"B": "1",
"C": "5",
"D": "2"
} | D | 2 | Let the formal oxidation state of Fe be x. Charge balance gives x+(2)(−1)=+0; hence x=0+2=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 5.",
"D": "Correct. The worked ca... | [
"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_009480 | 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_6H_1N_3X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "9",
"B": "7",
"C": "6",
"D": "14"
} | B | 7 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+3−1−2)/2=7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 9.",
"B": "Correct. The worked calculation gives 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 6.",
"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_006603 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 23 kg is attached to an ideal spring of force constant 863 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.65301 s",
"B": "0.3265 s",
"C": "0.48976 s",
"D": "-2.6735 s"
} | B | 0.3265 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(23/863)=0.3265 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3265 s, not 0.65301 s.",
"B": "Correct. The worked calculation gives 0.3265 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3265 s, not 0.48976 s.",
"D": "Incorrect. Substituting the st... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006887 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 44 mol H₂ and 8 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "8 mol",
"B": "14 mol",
"C": "32 mol",
"D": "16 mol"
} | D | 16 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 44 mol H₂O; O₂ can produce 16 mol H₂O. The limiting condition is O₂; product=16 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 8 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 14 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 32 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_009838 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(CN)_4]^-4, each CN ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "1",
"B": "-3",
"C": "0",
"D": "3"
} | C | 0 | Let the formal oxidation state of Ni be x. Charge balance gives x+(4)(−1)=-4; hence x=-4+4=+0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"C": "Correct. The worked calculation gives 0.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006351 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 2 kg is attached to an ideal spring of force constant 696 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "2.10721 s",
"B": "-0.89279 s",
"C": "0.10721 s",
"D": "0.16082 s"
} | C | 0.10721 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(2/696)=0.10721 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.10721 s, not 2.10721 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.10721 s, not -0.89279 s.",
"C": "Correct. The worked calculation gives 0.10721 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_007249 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 11 mol of gas at 525 K and 0.98 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "386.84014 L",
"B": "483.55018 L",
"C": "362.66263 L",
"D": "485.55018 L"
} | B | 483.55018 L | PV=nRT, so V=nRT/P=(11)(0.082057)(525)/(0.98)=483.55018 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 483.55018 L, not 386.84014 L.",
"B": "Correct. The worked calculation gives 483.55018 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 483.55018 L, not 362.66263 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004525 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 9 kg and radius 3 m is acted on by a constant torque of 11 N m about its central axis. Find its angular acceleration. | {
"A": "3.2716 rad s⁻²",
"B": "0.2716 rad s⁻²",
"C": "0.40741 rad s⁻²",
"D": "-1.7284 rad s⁻²"
} | B | 0.2716 rad s⁻² | For a solid disc, I=½MR²=½(9)(3)²=40.5 kg m². Using τ=Iα, α=11/40.5=0.2716 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.2716 rad s⁻², not 3.2716 rad s⁻².",
"B": "Correct. The worked calculation gives 0.2716 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.2716 rad s⁻², not 0.40741 rad s⁻².",
"D": "I... | [
"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_007123 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 20 mol of gas at 291 K and 0.78 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "489.81717 L",
"B": "610.27146 L",
"C": "612.27146 L",
"D": "1224.54292 L"
} | C | 612.27146 L | PV=nRT, so V=nRT/P=(20)(0.082057)(291)/(0.78)=612.27146 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 612.27146 L, not 489.81717 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 612.27146 L, not 610.27146 L.",
"C": "Correct. The worked calculation gives 612.27146 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009791 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(Cl)_6]^-4, each Cl ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "2",
"B": "3",
"C": "4",
"D": "-1"
} | A | 2 | Let the formal oxidation state of Mn be x. Charge balance gives x+(6)(−1)=-4; hence x=-4+6=+2. | {
"A": "Correct. The worked calculation gives 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 4.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009149 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.06 V, transfers 3 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.1782 V",
"B": "4.1782 V",
"C": "1.7673 V",
"D": "2.1782 V"
} | A | 1.1782 V | Apply the Nernst equation: E=1.06−(0.0591/3)(-6)=1.1782 V. | {
"A": "Correct. The worked calculation gives 1.1782 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1782 V, not 4.1782 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1782 V, not 1.7673 V.",
"D": "Incorrect. Substituting the stat... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001406 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (6x² +5x -2) dx. | {
"A": "33",
"B": "22",
"C": "16.5",
"D": "-22"
} | B | 22 | An antiderivative is (6/3)x³+(5/2)x²+(-2)x. Evaluating between 0 and 2 gives (6/3)(2)³+(5/2)(2)²+(-2)(2)=22. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22, not 33.",
"B": "Correct. The worked calculation gives 22.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22, not 16.5.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"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_006049 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 83 cm in front of a thin convex lens of focal length 17 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.12879",
"B": "0.25758",
"C": "1.25758",
"D": "2.25758"
} | B | 0.25758 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(83)(17)/(83−17)=21.37879 cm. Thus |m|=v/u=21.37879/83=0.25758. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25758, not 0.12879.",
"B": "Correct. The worked calculation gives 0.25758.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25758, not 1.25758.",
"D": "Incorrect. Substituting the stated va... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003839 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block initially moves at 11 m s⁻¹. A constant net force does 13 N of work over 5 m in the direction of motion. Find its final kinetic energy. | {
"A": "684 J",
"B": "912 J",
"C": "911 J",
"D": "913 J"
} | B | 912 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(14)(11)²+(13)(5)=912 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 912 J, not 684 J.",
"B": "Correct. The worked calculation gives 912 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 912 J, not 911 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_004204 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 38 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.27. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "15.592 N",
"B": "145.92 N",
"C": "147.92 N",
"D": "146.92 N"
} | B | 145.92 N | Net force=mg(sinθ−μcosθ)=38×10×(0.6−0.27×0.8)=145.92 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 145.92 N, not 15.592 N.",
"B": "Correct. The worked calculation gives 145.92 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 145.92 N, not 147.92 N.",
"D": "Incorrect. Substituting the stat... | [
"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_003105 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(1+6i)/(5+9i). What is Re(z), the real part of z? | {
"A": "-0.5566",
"B": "0.5566",
"C": "1.5566",
"D": "0.2783"
} | B | 0.5566 | Multiply numerator and denominator by the conjugate (5-9i). Then Re(z)=(ac+bd)/(c²+d²)=((1)(5)+(6)(9))/(5²+(9)²)=0.5566. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5566, not -0.5566.",
"B": "Correct. The worked calculation gives 0.5566.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5566, not 1.5566.",
"D": "Incorrect. Substituting the stated values... | [
"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_005337 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +1 μC are separated by 12 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "0.9375 N",
"B": "1.875 N",
"C": "2.875 N",
"D": "1.40625 N"
} | B | 1.875 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(1×10⁻⁶)/(12×10⁻²)²=1.875 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.875 N, not 0.9375 N.",
"B": "Correct. The worked calculation gives 1.875 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.875 N, not 2.875 N.",
"D": "Incorrect. Substituting the stated v... | [
"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_002696 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(2, 3, 4) and v=(3, -2, -7), calculate u·v. | {
"A": "-22.4",
"B": "-28",
"C": "-30",
"D": "-27"
} | B | -28 | The dot product is the sum of corresponding component products: (2)(3)+(3)(-2)+(4)(-7)=-28. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -28, not -22.4.",
"B": "Correct. The worked calculation gives -28.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -28, not -30.",
"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_008615 | 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 0.63 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.29024 K",
"B": "1.93536 K",
"C": "0.29024 K",
"D": "0.96768 K"
} | A | 1.29024 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.512×0.63=1.29024 K. | {
"A": "Correct. The worked calculation gives 1.29024 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.29024 K, not 1.93536 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.29024 K, not 0.29024 K.",
"D": "Incorrect. Substituting the... | [
"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_000529 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -20 and common difference 15. Find the sum of its first 23 terms. | {
"A": "6670",
"B": "3333",
"C": "5002.5",
"D": "3335"
} | D | 3335 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-20, d=15, n=23: Sₙ=23/2[2(-20)+(23−1)(15)]=3335. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3335, not 6670.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3335, not 3333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3335, not 5002.5.",
"D": "Co... | [
"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_000585 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 13 and common difference 15. Find the sum of its first 11 terms. | {
"A": "970",
"B": "1161.6",
"C": "968",
"D": "-968"
} | C | 968 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=13, d=15, n=11: Sₙ=11/2[2(13)+(11−1)(15)]=968. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 968, not 970.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 968, not 1161.6.",
"C": "Correct. The worked calculation gives 968.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_002263 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 7 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "2.30882",
"B": "1.03088",
"C": "-1.69118",
"D": "0.30882"
} | D | 0.30882 | Favourable pairs = C(4,2)+C(7,2)+C(6,2)=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 2.30882.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30882, not 1.03088.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30882, not -1.69... | [
"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_008047 | 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 8 A for 9203 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": "24.22344 g",
"B": "36.33516 g",
"C": "48.44688 g",
"D": "19.37875 g"
} | A | 24.22344 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×8×9203/(2×96500)=24.22344 g. | {
"A": "Correct. The worked calculation gives 24.22344 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24.22344 g, not 36.33516 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24.22344 g, not 48.44688 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 |
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