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_002334 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 11 red, 4 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.39181",
"B": "1.03918",
"C": "-0.60819",
"D": "-1.60819"
} | A | 0.39181 | Favourable pairs = C(11,2)+C(4,2)+C(4,2)=67. Total pairs=C(19,2)=171. Therefore P=67/171=0.39181. | {
"A": "Correct. The worked calculation gives 0.39181.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.39181, not 1.03918.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.39181, not -0.60819.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009986 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(Cl)_5]^-1, each Cl ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "4",
"B": "2",
"C": "-4",
"D": "3"
} | A | 4 | Let the formal oxidation state of Cu be x. Charge balance gives x+(5)(−1)=-1; hence x=-1+5=+4. | {
"A": "Correct. The worked calculation gives 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not -4.",
"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_005609 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 71 μF capacitor is charged to a potential difference of 33 V. Calculate the energy stored, expressed in μJ. | {
"A": "19329.75 μJ",
"B": "3866.95 μJ",
"C": "57989.25 μJ",
"D": "38659.5 μJ"
} | D | 38659.5 μJ | U=½CV². Since C=71 μF, U in μJ is ½×71×(33)²=38659.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 38659.5 μJ, not 19329.75 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 38659.5 μJ, not 3866.95 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 38659... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005516 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 65 μF capacitor is charged to a potential difference of 12 V. Calculate the energy stored, expressed in μJ. | {
"A": "9360 μJ",
"B": "4678 μJ",
"C": "5616 μJ",
"D": "4680 μJ"
} | D | 4680 μJ | U=½CV². Since C=65 μF, U in μJ is ½×65×(12)²=4680 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4680 μJ, not 9360 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4680 μJ, not 4678 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4680 μJ, not 5616 ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007451 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 80 mL of 0.10 M HCl is mixed with 65 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.97792",
"B": "1.48896",
"C": "4.98528",
"D": "1.98528"
} | D | 1.98528 | Excess H⁺ moles=0.10×(80−65)/1000=0.001500 mol. Total volume=0.145 L, so [H⁺]=0.010345 M and pH=−log₁₀[H⁺]=1.98528. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.98528, not 2.97792.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.98528, not 1.48896.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.98528, not 4.985... | [
"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_006786 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 38 mol H₂ and 16 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "24 mol",
"B": "34 mol",
"C": "30 mol",
"D": "32 mol"
} | D | 32 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 38 mol H₂O; O₂ can produce 32 mol H₂O. The limiting condition is O₂; product=32 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 32 mol, not 24 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 32 mol, not 34 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 32 mol, not 30 mol.",
... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002232 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 7 red, 6 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": "-0.69935",
"B": "-1.69935",
"C": "0.30065",
"D": "-0.30065"
} | C | 0.30065 | Favourable pairs = C(7,2)+C(6,2)+C(5,2)=46. Total pairs=C(18,2)=153. Therefore P=46/153=0.30065. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30065, not -0.69935.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30065, not -1.69935.",
"C": "Correct. The worked calculation gives 0.30065.",
"D": "Incorrect. Substituting the stated ... | [
"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_007684 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 95 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "5.9375 mmol L⁻¹",
"B": "6.9375 mmol L⁻¹",
"C": "11.875 mmol L⁻¹",
"D": "8.9375 mmol L⁻¹"
} | A | 5.9375 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=95/2^4=5.9375 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 5.9375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.9375 mmol L⁻¹, not 6.9375 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.9375 mmol L⁻¹, not 11.875 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_004048 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 44 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.17. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "204.16 N",
"B": "21.416 N",
"C": "306.24 N",
"D": "205.16 N"
} | A | 204.16 N | Net force=mg(sinθ−μcosθ)=44×10×(0.6−0.17×0.8)=204.16 N. | {
"A": "Correct. The worked calculation gives 204.16 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 204.16 N, not 21.416 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 204.16 N, not 306.24 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_006130 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 39 cm in front of a thin convex lens of focal length 9 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.03",
"B": "-2.7",
"C": "3.3",
"D": "0.3"
} | D | 0.3 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(39)(9)/(39−9)=11.7 cm. Thus |m|=v/u=11.7/39=0.3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3, not 1.03.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3, not -2.7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3, not 3.3.",
"D": "Correct.... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006624 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 12 kg is attached to an ideal spring of force constant 479 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "2.31656 s",
"B": "1.31656 s",
"C": "0.31656 s",
"D": "-1.68344 s"
} | C | 0.31656 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(12/479)=0.31656 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31656 s, not 2.31656 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31656 s, not 1.31656 s.",
"C": "Correct. The worked calculation gives 0.31656 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_003345 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 85 m s⁻¹ at 15° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "359.25 m",
"B": "37.125 m",
"C": "361.25 m",
"D": "362.25 m"
} | C | 361.25 m | Range R=u²sin(2θ)/g. Substituting u=85, θ=15° and g=10 gives R=(85)²sin(30°)/10=361.25 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 361.25 m, not 359.25 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 361.25 m, not 37.125 m.",
"C": "Correct. The worked calculation gives 361.25 m.",
"D": "Incorrect. Substituting the stat... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008627 | 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 0.33 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.165 K",
"B": "3.33 K",
"C": "0.33 K",
"D": "0.495 K"
} | C | 0.33 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×1.0×0.33=0.33 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33 K, not 0.165 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33 K, not 3.33 K.",
"C": "Correct. The worked calculation gives 0.33 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003741 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 10 m s⁻¹. A constant net force does 24 N of work over 7 m in the direction of motion. Find its final kinetic energy. | {
"A": "276 J",
"B": "368 J",
"C": "367 J",
"D": "37.8 J"
} | B | 368 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(10)²+(24)(7)=368 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 368 J, not 276 J.",
"B": "Correct. The worked calculation gives 368 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 368 J, not 367 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_003425 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 94 m s⁻¹ at 75° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "443.8 m",
"B": "441.8 m",
"C": "530.16 m",
"D": "45.18 m"
} | B | 441.8 m | Range R=u²sin(2θ)/g. Substituting u=94, θ=75° and g=10 gives R=(94)²sin(150°)/10=441.8 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 441.8 m, not 443.8 m.",
"B": "Correct. The worked calculation gives 441.8 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 441.8 m, not 530.16 m.",
"D": "Incorrect. Substituting the stated v... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002277 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 11 red, 4 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": "0.36182",
"B": "-0.63818",
"C": "0.72365",
"D": "1.03618"
} | A | 0.36182 | Favourable pairs = C(11,2)+C(4,2)+C(12,2)=127. Total pairs=C(27,2)=351. Therefore P=127/351=0.36182. | {
"A": "Correct. The worked calculation gives 0.36182.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36182, not -0.63818.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.36182, not 0.72365.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009045 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.78 V, transfers 3 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.7997 V",
"B": "-2.2003 V",
"C": "-0.7997 V",
"D": "1.07997 V"
} | A | 0.7997 V | Apply the Nernst equation: E=0.78−(0.0591/3)(-1)=0.7997 V. | {
"A": "Correct. The worked calculation gives 0.7997 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7997 V, not -2.2003 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7997 V, not -0.7997 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_006672 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 5 mol H₂ and 10 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "10 mol",
"B": "1.5 mol",
"C": "5 mol",
"D": "-5 mol"
} | C | 5 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 5 mol H₂O; O₂ can produce 20 mol H₂O. The limiting condition is H₂; product=5 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5 mol, not 10 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5 mol, not 1.5 mol.",
"C": "Correct. The worked calculation gives 5 mol.",
"D": "Incorrect. Substituting the stated values in... | [
"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_003006 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, -6, 2) and v=(6, 2, -1), calculate u·v. | {
"A": "10",
"B": "15",
"C": "20",
"D": "13"
} | A | 10 | The dot product is the sum of corresponding component products: (4)(6)+(-6)(2)+(2)(-1)=10. | {
"A": "Correct. The worked calculation gives 10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 15.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 20.",
"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_005959 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.3 atm at 397 K. What is its pressure at 569 K? | {
"A": "6.16297 atm",
"B": "7.16297 atm",
"C": "3.08149 atm",
"D": "1.6163 atm"
} | A | 6.16297 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.3)(569)/(397)=6.16297 atm. | {
"A": "Correct. The worked calculation gives 6.16297 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.16297 atm, not 7.16297 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.16297 atm, not 3.08149 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_002828 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(9, 0, 7) and v=(2, 3, 6), calculate u·v. | {
"A": "120",
"B": "60",
"C": "-60",
"D": "72"
} | B | 60 | The dot product is the sum of corresponding component products: (9)(2)+(0)(3)+(7)(6)=60. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 60, not 120.",
"B": "Correct. The worked calculation gives 60.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 60, not -60.",
"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_002241 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 7 blue and 7 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.225",
"B": "2.3",
"C": "1.03",
"D": "0.3"
} | D | 0.3 | Favourable pairs = C(6,2)+C(7,2)+C(7,2)=57. Total pairs=C(20,2)=190. Therefore P=57/190=0.3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3, not 0.225.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3, not 2.3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3, not 1.03.",
"D": "Correct... | [
"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_004739 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 15 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 10 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "-0.1931 A",
"B": "1.61379 A",
"C": "0.8069 A",
"D": "-1.1931 A"
} | C | 0.8069 A | Series branch resistance=15+14=29 Ω. Parallel equivalent R_eq=(29×10)/(29+10)=7.4359 Ω. Total current I=V/R_eq=6/7.4359=0.8069 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8069 A, not -0.1931 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8069 A, not 1.61379 A.",
"C": "Correct. The worked calculation gives 0.8069 A.",
"D": "Incorrect. Substituting the st... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005361 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 3 μF capacitor is charged to a potential difference of 15 V. Calculate the energy stored, expressed in μJ. | {
"A": "339.5 μJ",
"B": "337.5 μJ",
"C": "336.5 μJ",
"D": "168.75 μJ"
} | B | 337.5 μJ | U=½CV². Since C=3 μF, U in μJ is ½×3×(15)²=337.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 337.5 μJ, not 339.5 μJ.",
"B": "Correct. The worked calculation gives 337.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 337.5 μJ, not 336.5 μJ.",
"D": "Incorrect. Substituting the stat... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005548 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 34 μF capacitor is charged to a potential difference of 33 V. Calculate the energy stored, expressed in μJ. | {
"A": "9256.5 μJ",
"B": "18515 μJ",
"C": "27769.5 μJ",
"D": "18513 μJ"
} | D | 18513 μJ | U=½CV². Since C=34 μF, U in μJ is ½×34×(33)²=18513 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18513 μJ, not 9256.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18513 μJ, not 18515 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18513 μJ, not... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001473 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (-1x² -4x +5) dx. | {
"A": "-24",
"B": "-14",
"C": "-18",
"D": "-12"
} | D | -12 | An antiderivative is (-1/3)x³+(-4/2)x²+(5)x. Evaluating between 0 and 3 gives (-1/3)(3)³+(-4/2)(3)²+(5)(3)=-12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -12, not -24.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -12, not -14.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -12, not -18.",
"D": "Correct. T... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006622 | 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 923 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.8528 s",
"B": "1.01472 s",
"C": "0.2944 s",
"D": "0.1472 s"
} | D | 0.1472 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(5/923)=0.1472 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.1472 s, not -0.8528 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.1472 s, not 1.01472 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.1472 s, no... | [
"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_004504 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 9 kg and radius 4 m is acted on by a constant torque of 45 N m about its central axis. Find its angular acceleration. | {
"A": "0.46875 rad s⁻²",
"B": "0.625 rad s⁻²",
"C": "0.9375 rad s⁻²",
"D": "0.3125 rad s⁻²"
} | B | 0.625 rad s⁻² | For a solid disc, I=½MR²=½(9)(4)²=72 kg m². Using τ=Iα, α=45/72=0.625 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.625 rad s⁻², not 0.46875 rad s⁻².",
"B": "Correct. The worked calculation gives 0.625 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.625 rad s⁻², not 0.9375 rad s⁻².",
"D": "Inco... | [
"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_007055 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 6 mol of gas at 546 K and 0.96 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "280.01951 L",
"B": "281.01951 L",
"C": "282.01951 L",
"D": "420.02927 L"
} | A | 280.01951 L | PV=nRT, so V=nRT/P=(6)(0.082057)(546)/(0.96)=280.01951 L. | {
"A": "Correct. The worked calculation gives 280.01951 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 280.01951 L, not 281.01951 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 280.01951 L, not 282.01951 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_006483 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 20 kg is attached to an ideal spring of force constant 186 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.34417 s",
"B": "0.98374 s",
"C": "0.49187 s",
"D": "0.65583 s"
} | D | 0.65583 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(20/186)=0.65583 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.65583 s, not -2.34417 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.65583 s, not 0.98374 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.65583 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_008356 | 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 0.34 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-1.36 K",
"B": "1.02 K",
"C": "1.36 K",
"D": "1.136 K"
} | C | 1.36 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×1.0×0.34=1.36 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.36 K, not -1.36 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.36 K, not 1.02 K.",
"C": "Correct. The worked calculation gives 1.36 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002780 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, -2, -1) and v=(-2, 5, 2), calculate u·v. | {
"A": "-40",
"B": "-18",
"C": "-30",
"D": "-20"
} | D | -20 | The dot product is the sum of corresponding component products: (4)(-2)+(-2)(5)+(-1)(2)=-20. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -20, not -40.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -20, not -18.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -20, not -30.",
"D": "Correct. T... | [
"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_003540 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 74 m s⁻¹ at 50° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "540.28073 m",
"B": "269.64036 m",
"C": "541.28073 m",
"D": "539.28073 m"
} | D | 539.28073 m | Range R=u²sin(2θ)/g. Substituting u=74, θ=50° and g=10 gives R=(74)²sin(100°)/10=539.28073 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 539.28073 m, not 540.28073 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 539.28073 m, not 269.64036 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 53... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002328 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 4 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": "-0.5614",
"B": "0.4386",
"C": "1.4386",
"D": "0.87719"
} | B | 0.4386 | Favourable pairs = C(12,2)+C(4,2)+C(3,2)=75. Total pairs=C(19,2)=171. Therefore P=75/171=0.4386. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.4386, not -0.5614.",
"B": "Correct. The worked calculation gives 0.4386.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.4386, not 1.4386.",
"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_005003 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 3 Ω are connected in series; this combination is connected in parallel with a 20 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "-1.35 A",
"B": "0.35 A",
"C": "1.35 A",
"D": "0.675 A"
} | C | 1.35 A | Series branch resistance=7+3=10 Ω. Parallel equivalent R_eq=(10×20)/(10+20)=6.66667 Ω. Total current I=V/R_eq=9/6.66667=1.35 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.35 A, not -1.35 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.35 A, not 0.35 A.",
"C": "Correct. The worked calculation gives 1.35 A.",
"D": "Incorrect. Substituting the stated values... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006255 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 46 cm in front of a thin convex lens of focal length 21 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.84",
"B": "-0.16",
"C": "1.68",
"D": "-1.16"
} | A | 0.84 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(46)(21)/(46−21)=38.64 cm. Thus |m|=v/u=38.64/46=0.84. | {
"A": "Correct. The worked calculation gives 0.84.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.84, not -0.16.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.84, not 1.68.",
"D": "Incorrect. Substituting the stated values into the ... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005439 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 34 μF capacitor is charged to a potential difference of 13 V. Calculate the energy stored, expressed in μJ. | {
"A": "4309.5 μJ",
"B": "2875 μJ",
"C": "2873 μJ",
"D": "-2873 μJ"
} | C | 2873 μJ | U=½CV². Since C=34 μF, U in μJ is ½×34×(13)²=2873 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2873 μJ, not 4309.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2873 μJ, not 2875 μJ.",
"C": "Correct. The worked calculation gives 2873 μJ.",
"D": "Incorrect. Substituting the stated ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002186 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 11 blue and 5 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.03385",
"B": "0.50769",
"C": "0.33846",
"D": "-2.66154"
} | C | 0.33846 | Favourable pairs = C(10,2)+C(11,2)+C(5,2)=110. Total pairs=C(26,2)=325. Therefore P=110/325=0.33846. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33846, not 1.03385.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33846, not 0.50769.",
"C": "Correct. The worked calculation gives 0.33846.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003149 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(6+3i)/(7+8i). What is Re(z), the real part of z? | {
"A": "-0.41593",
"B": "-2.41593",
"C": "-0.58407",
"D": "0.58407"
} | D | 0.58407 | Multiply numerator and denominator by the conjugate (7-8i). Then Re(z)=(ac+bd)/(c²+d²)=((6)(7)+(3)(8))/(7²+(8)²)=0.58407. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.58407, not -0.41593.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.58407, not -2.41593.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.58407, not -0.... | [
"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_008725 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.19 mol L⁻¹ and initially B is absent. At equilibrium, 80% of A has dissociated at constant volume. Find K_c. | {
"A": "22.848",
"B": "15.232",
"C": "2.5232",
"D": "30.464"
} | B | 15.232 | Let α=0.8. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.19)(0.8)²/(1−0.8)=15.232. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15.232, not 22.848.",
"B": "Correct. The worked calculation gives 15.232.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15.232, not 2.5232.",
"D": "Incorrect. Substituting the stated values ... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002490 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 0], [3, 7]]. | {
"A": "26",
"B": "28",
"C": "21",
"D": "56"
} | B | 28 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(7)−(0)(3)=28. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28, not 26.",
"B": "Correct. The worked calculation gives 28.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28, not 21.",
"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_000126 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 +17x +2=0, let its roots be α and β. What is α²+β²? | {
"A": "105.375",
"B": "35.125",
"C": "70.25",
"D": "71.25"
} | C | 70.25 | By Vieta's relations, α+β = -17/2 and αβ = 2/2. Then α²+β²=(α+β)²−2αβ = (-17/2)²−2(2/2) = 70.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 70.25, not 105.375.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 70.25, not 35.125.",
"C": "Correct. The worked calculation gives 70.25.",
"D": "Incorrect. Substituting the stated values in... | [
"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_004303 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 39 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.31. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "109.824 N",
"B": "137.28 N",
"C": "139.28 N",
"D": "68.64 N"
} | B | 137.28 N | Net force=mg(sinθ−μcosθ)=39×10×(0.6−0.31×0.8)=137.28 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 137.28 N, not 109.824 N.",
"B": "Correct. The worked calculation gives 137.28 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 137.28 N, not 139.28 N.",
"D": "Incorrect. Substituting the sta... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009449 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_12H_9N_2X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "13.5",
"B": "6.75",
"C": "8",
"D": "9"
} | D | 9 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×12+2+2−9−1)/2=9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9, not 13.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9, not 6.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9, not 8.",
"D": "Correct. The wor... | [
"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_006375 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 22 kg is attached to an ideal spring of force constant 1117 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "2.28068 s",
"B": "3.28068 s",
"C": "0.28068 s",
"D": "0.42102 s"
} | C | 0.28068 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(22/1117)=0.28068 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.28068 s, not 2.28068 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.28068 s, not 3.28068 s.",
"C": "Correct. The worked calculation gives 0.28068 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_008056 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 10 A for 23296 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": "153.29492 g",
"B": "-76.64746 g",
"C": "38.32373 g",
"D": "76.64746 g"
} | D | 76.64746 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×10×23296/(2×96500)=76.64746 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 76.64746 g, not 153.29492 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 76.64746 g, not -76.64746 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 76.6... | [
"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_005296 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +8 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "88.16327 N",
"B": "58.77551 N",
"C": "56.77551 N",
"D": "6.87755 N"
} | B | 58.77551 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(8×10⁻⁶)/(7×10⁻²)²=58.77551 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 58.77551 N, not 88.16327 N.",
"B": "Correct. The worked calculation gives 58.77551 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 58.77551 N, not 56.77551 N.",
"D": "Incorrect. Substitutin... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004714 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 11 Ω and 5 Ω are connected in series; this combination is connected in parallel with a 7 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.08036 A",
"B": "6.16071 A",
"C": "9.24107 A",
"D": "5.16071 A"
} | B | 6.16071 A | Series branch resistance=11+5=16 Ω. Parallel equivalent R_eq=(16×7)/(16+7)=4.86957 Ω. Total current I=V/R_eq=30/4.86957=6.16071 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.16071 A, not 3.08036 A.",
"B": "Correct. The worked calculation gives 6.16071 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.16071 A, not 9.24107 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005994 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.7 atm at 396 K. What is its pressure at 646 K? | {
"A": "-0.22677 atm",
"B": "2.77323 atm",
"C": "4.15985 atm",
"D": "5.77323 atm"
} | B | 2.77323 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.7)(646)/(396)=2.77323 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.77323 atm, not -0.22677 atm.",
"B": "Correct. The worked calculation gives 2.77323 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.77323 atm, not 4.15985 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004937 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 11 Ω are connected in series; this combination is connected in parallel with a 17 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.50155 A",
"B": "1.0031 A",
"C": "2.00619 A",
"D": "3.0031 A"
} | B | 1.0031 A | Series branch resistance=8+11=19 Ω. Parallel equivalent R_eq=(19×17)/(19+17)=8.97222 Ω. Total current I=V/R_eq=9/8.97222=1.0031 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0031 A, not 0.50155 A.",
"B": "Correct. The worked calculation gives 1.0031 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0031 A, not 2.00619 A.",
"D": "Incorrect. Substituting the st... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007518 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 30 mL of 0.10 M HCl is mixed with 75 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.63202",
"B": "6.31601",
"C": "9.63202",
"D": "14.63202"
} | A | 12.63202 | Excess OH⁻ moles=0.10×(75−30)/1000=0.004500 mol. Total volume=0.105 L, so [OH⁻]=0.042857 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.63202. | {
"A": "Correct. The worked calculation gives 12.63202.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.63202, not 6.31601.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.63202, not 9.63202.",
"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_003490 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 86 m s⁻¹ at 35° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "694.99666 m",
"B": "1042.49499 m",
"C": "693.99666 m",
"D": "70.49967 m"
} | A | 694.99666 m | Range R=u²sin(2θ)/g. Substituting u=86, θ=35° and g=10 gives R=(86)²sin(70°)/10=694.99666 m. | {
"A": "Correct. The worked calculation gives 694.99666 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 694.99666 m, not 1042.49499 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 694.99666 m, not 693.99666 m.",
"D": "Incorrect. Subst... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003005 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-1, 8, -3) and v=(2, 6, 1), calculate u·v. | {
"A": "43",
"B": "21.5",
"C": "51.6",
"D": "41"
} | A | 43 | The dot product is the sum of corresponding component products: (-1)(2)+(8)(6)+(-3)(1)=43. | {
"A": "Correct. The worked calculation gives 43.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 43, not 21.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 43, not 51.6.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_000140 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +2x +6=0, let its roots be α and β. What is α²+β²? | {
"A": "-0.55556",
"B": "0.64444",
"C": "-4.55556",
"D": "-3.55556"
} | D | -3.55556 | By Vieta's relations, α+β = -2/3 and αβ = 6/3. Then α²+β²=(α+β)²−2αβ = (-2/3)²−2(6/3) = -3.55556. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -3.55556, not -0.55556.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -3.55556, not 0.64444.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -3.55556, not -... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003351 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 73 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "369.20395 m",
"B": "463.50494 m",
"C": "692.25741 m",
"D": "461.50494 m"
} | D | 461.50494 m | Range R=u²sin(2θ)/g. Substituting u=73, θ=60° and g=10 gives R=(73)²sin(120°)/10=461.50494 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 461.50494 m, not 369.20395 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 461.50494 m, not 463.50494 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 46... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001777 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 9 elements can be selected from a set of 77 distinct elements? | {
"A": "161322559473",
"B": "161322559477",
"C": "161322559475",
"D": "16132255948.5"
} | C | 161322559475 | Order does not matter, so the count is C(77,9)=77!/[9!(68)!]=161322559475. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 161322559475, not 161322559473.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 161322559475, not 161322559477.",
"C": "Correct. The worked calculation gives 161322559475.",
"D": "Incorrect. S... | [
"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_005536 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 22 μF capacitor is charged to a potential difference of 6 V. Calculate the energy stored, expressed in μJ. | {
"A": "475.2 μJ",
"B": "396 μJ",
"C": "316.8 μJ",
"D": "-396 μJ"
} | B | 396 μJ | U=½CV². Since C=22 μF, U in μJ is ½×22×(6)²=396 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 396 μJ, not 475.2 μJ.",
"B": "Correct. The worked calculation gives 396 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 396 μJ, not 316.8 μJ.",
"D": "Incorrect. Substituting the stated val... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003919 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 12 m s⁻¹. A constant net force does 30 N of work over 16 m in the direction of motion. Find its final kinetic energy. | {
"A": "135.4 J",
"B": "1344 J",
"C": "1343 J",
"D": "1345 J"
} | B | 1344 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(12)²+(30)(16)=1344 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1344 J, not 135.4 J.",
"B": "Correct. The worked calculation gives 1344 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1344 J, not 1343 J.",
"D": "Incorrect. Substituting the stated values... | [
"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_002119 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 7 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.032",
"B": "0.24",
"C": "0.32",
"D": "-0.32"
} | C | 0.32 | Favourable pairs = C(8,2)+C(7,2)+C(11,2)=104. Total pairs=C(26,2)=325. Therefore P=104/325=0.32. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32, not 1.032.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32, not 0.24.",
"C": "Correct. The worked calculation gives 0.32.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_008202 | 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 6 A for 14186 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": "33.60538 g",
"B": "28.00449 g",
"C": "29.00449 g",
"D": "27.00449 g"
} | B | 28.00449 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×6×14186/(2×96500)=28.00449 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28.00449 g, not 33.60538 g.",
"B": "Correct. The worked calculation gives 28.00449 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28.00449 g, not 29.00449 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_008907 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.87 mol L⁻¹ and initially B is absent. At equilibrium, 69% of A has dissociated at constant volume. Find K_c. | {
"A": "14.48783",
"B": "12.48783",
"C": "11.48783",
"D": "13.48783"
} | C | 11.48783 | Let α=0.69. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.87)(0.69)²/(1−0.69)=11.48783. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.48783, not 14.48783.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.48783, not 12.48783.",
"C": "Correct. The worked calculation gives 11.48783.",
"D": "Incorrect. Substituting the stat... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009195 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.73 V, transfers 3 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-2.2306 V",
"B": "3.7694 V",
"C": "-0.7694 V",
"D": "0.7694 V"
} | D | 0.7694 V | Apply the Nernst equation: E=0.73−(0.0591/3)(-2)=0.7694 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7694 V, not -2.2306 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7694 V, not 3.7694 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7694 V, not... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000174 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 +9x +6=0, let its roots be α and β. What is α²+β²? | {
"A": "0.1875",
"B": "0.125",
"C": "2.25",
"D": "0.25"
} | D | 0.25 | By Vieta's relations, α+β = -9/6 and αβ = 6/6. Then α²+β²=(α+β)²−2αβ = (-9/6)²−2(6/6) = 0.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25, not 0.1875.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25, not 0.125.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25, not 2.25.",
"D": "C... | [
"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_005709 | 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 1.3 atm at 183 K. What is its pressure at 269 K? | {
"A": "-1.91093 atm",
"B": "-0.08907 atm",
"C": "0.95546 atm",
"D": "1.91093 atm"
} | D | 1.91093 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.3)(269)/(183)=1.91093 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.91093 atm, not -1.91093 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.91093 atm, not -0.08907 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives ... | [
"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_004333 | 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 0.18. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "446.88 N",
"B": "268.128 N",
"C": "224.44 N",
"D": "223.44 N"
} | D | 223.44 N | Net force=mg(sinθ−μcosθ)=49×10×(0.6−0.18×0.8)=223.44 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 223.44 N, not 446.88 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 223.44 N, not 268.128 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 223.44 N, not... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007836 | 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 45 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "1.14062 mmol L⁻¹",
"B": "1.40625 mmol L⁻¹",
"C": "-1.40625 mmol L⁻¹",
"D": "-1.59375 mmol L⁻¹"
} | B | 1.40625 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=45/2^5=1.40625 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.40625 mmol L⁻¹, not 1.14062 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 1.40625 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.40625 mmol L⁻¹, not -1.40625 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_007690 | 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 22 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "2.375 mmol L⁻¹",
"B": "0.6875 mmol L⁻¹",
"C": "2.75 mmol L⁻¹",
"D": "1.375 mmol L⁻¹"
} | D | 1.375 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=22/2^4=1.375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.375 mmol L⁻¹, not 2.375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.375 mmol L⁻¹, not 0.6875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing rela... | [
"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_001055 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=2x³ -9x² -4x+7. Evaluate f′(2). | {
"A": "-16",
"B": "-14",
"C": "-12",
"D": "-15"
} | A | -16 | Differentiate: f′(x)=3(2)x²+2(-9)x+(-4). At x=2, f′(2)=3(2)(2)²+2(-9)(2)+(-4)=-16. | {
"A": "Correct. The worked calculation gives -16.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -16, not -14.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -16, not -12.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005891 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.9 atm at 269 K. What is its pressure at 734 K? | {
"A": "9.91301 atm",
"B": "7.91301 atm",
"C": "6.91301 atm",
"D": "1.7913 atm"
} | B | 7.91301 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.9)(734)/(269)=7.91301 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.91301 atm, not 9.91301 atm.",
"B": "Correct. The worked calculation gives 7.91301 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.91301 atm, not 6.91301 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_006597 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 8 kg is attached to an ideal spring of force constant 654 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.7788 s",
"B": "0.4424 s",
"C": "0.2212 s",
"D": "1.2212 s"
} | C | 0.2212 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(8/654)=0.2212 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.2212 s, not -1.7788 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.2212 s, not 0.4424 s.",
"C": "Correct. The worked calculation gives 0.2212 s.",
"D": "Incorrect. Substituting the sta... | [
"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_003443 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 21 m s⁻¹ at 50° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "34.74402 m",
"B": "42.43002 m",
"C": "44.43002 m",
"D": "43.43002 m"
} | D | 43.43002 m | Range R=u²sin(2θ)/g. Substituting u=21, θ=50° and g=10 gives R=(21)²sin(100°)/10=43.43002 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 43.43002 m, not 34.74402 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 43.43002 m, not 42.43002 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 43.430... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009231 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.74 V, transfers 2 electrons, and has reaction quotient Q=10^2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-2.3191 V",
"B": "2.6809 V",
"C": "0.6809 V",
"D": "1.6809 V"
} | C | 0.6809 V | Apply the Nernst equation: E=0.74−(0.0591/2)(2)=0.6809 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6809 V, not -2.3191 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6809 V, not 2.6809 V.",
"C": "Correct. The worked calculation gives 0.6809 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_005488 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 23 μF capacitor is charged to a potential difference of 25 V. Calculate the energy stored, expressed in μJ. | {
"A": "5750 μJ",
"B": "-7187.5 μJ",
"C": "7187.5 μJ",
"D": "14375 μJ"
} | C | 7187.5 μJ | U=½CV². Since C=23 μF, U in μJ is ½×23×(25)²=7187.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7187.5 μJ, not 5750 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7187.5 μJ, not -7187.5 μJ.",
"C": "Correct. The worked calculation gives 7187.5 μJ.",
"D": "Incorrect. Substituting the ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005659 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 75 μF capacitor is charged to a potential difference of 12 V. Calculate the energy stored, expressed in μJ. | {
"A": "2700 μJ",
"B": "6480 μJ",
"C": "5400 μJ",
"D": "10800 μJ"
} | C | 5400 μJ | U=½CV². Since C=75 μF, U in μJ is ½×75×(12)²=5400 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5400 μJ, not 2700 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5400 μJ, not 6480 μJ.",
"C": "Correct. The worked calculation gives 5400 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002030 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 3 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": "0.83158",
"B": "-1.58421",
"C": "0.41579",
"D": "2.41579"
} | C | 0.41579 | Favourable pairs = C(5,2)+C(3,2)+C(12,2)=79. Total pairs=C(20,2)=190. Therefore P=79/190=0.41579. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.41579, not 0.83158.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.41579, not -1.58421.",
"C": "Correct. The worked calculation gives 0.41579.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002711 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, 2, -2) and v=(-2, 6, -3), calculate u·v. | {
"A": "-16",
"B": "14",
"C": "16",
"D": "15"
} | C | 16 | The dot product is the sum of corresponding component products: (1)(-2)+(2)(6)+(-2)(-3)=16. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16, not -16.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16, not 14.",
"C": "Correct. The worked calculation gives 16.",
"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_008118 | 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 13 A for 19172 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": "164.00504 g",
"B": "82.00252 g",
"C": "83.00252 g",
"D": "84.00252 g"
} | B | 82.00252 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×19172/(2×96500)=82.00252 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 82.00252 g, not 164.00504 g.",
"B": "Correct. The worked calculation gives 82.00252 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 82.00252 g, not 83.00252 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_008989 | 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 0.28 mol L⁻¹ and initially B is absent. At equilibrium, 36% of A has dissociated at constant volume. Find K_c. | {
"A": "2.2268",
"B": "0.2268",
"C": "1.2268",
"D": "1.02268"
} | B | 0.2268 | Let α=0.36. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.28)(0.36)²/(1−0.36)=0.2268. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.2268, not 2.2268.",
"B": "Correct. The worked calculation gives 0.2268.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.2268, not 1.2268.",
"D": "Incorrect. Substituting the stated values ... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007693 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 95 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "0.74219 mmol L⁻¹",
"B": "-1.48438 mmol L⁻¹",
"C": "-1.51562 mmol L⁻¹",
"D": "1.48438 mmol L⁻¹"
} | D | 1.48438 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=95/2^6=1.48438 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.48438 mmol L⁻¹, not 0.74219 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.48438 mmol L⁻¹, not -1.48438 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the govern... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007049 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 5 mol of gas at 213 K and 0.15 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "873.90705 L",
"B": "466.08376 L",
"C": "582.6047 L",
"D": "-582.6047 L"
} | C | 582.6047 L | PV=nRT, so V=nRT/P=(5)(0.082057)(213)/(0.15)=582.6047 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 582.6047 L, not 873.90705 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 582.6047 L, not 466.08376 L.",
"C": "Correct. The worked calculation gives 582.6047 L.",
"D": "Incorrect. Substitut... | [
"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_008818 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.62 mol L⁻¹ and initially B is absent. At equilibrium, 15% of A has dissociated at constant volume. Find K_c. | {
"A": "0.34306",
"B": "0.12865",
"C": "-0.82847",
"D": "0.17153"
} | D | 0.17153 | Let α=0.15. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.62)(0.15)²/(1−0.15)=0.17153. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.17153, not 0.34306.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.17153, not 0.12865.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.17153, not -0.82... | [
"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_007132 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 5 mol of gas at 410 K and 0.07 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "2883.71743 L",
"B": "2402.09786 L",
"C": "2401.09786 L",
"D": "2403.09786 L"
} | D | 2403.09786 L | PV=nRT, so V=nRT/P=(5)(0.082057)(410)/(0.07)=2403.09786 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2403.09786 L, not 2883.71743 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2403.09786 L, not 2402.09786 L.",
"C": "Incorrect. Substituting the stated values into the governing relation give... | [
"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_001838 | 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 58 distinct elements? | {
"A": "1916797309",
"B": "191679732.1",
"C": "1916797311",
"D": "2300156773.2"
} | C | 1916797311 | Order does not matter, so the count is C(58,8)=58!/[8!(50)!]=1916797311. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1916797311, not 1916797309.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1916797311, not 191679732.1.",
"C": "Correct. The worked calculation gives 1916797311.",
"D": "Incorrect. Substituti... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001595 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (4x² -7x +6) dx. | {
"A": "327.83333",
"B": "491.75",
"C": "163.91667",
"D": "325.83333"
} | A | 327.83333 | An antiderivative is (4/3)x³+(-7/2)x²+(6)x. Evaluating between 0 and 7 gives (4/3)(7)³+(-7/2)(7)²+(6)(7)=327.83333. | {
"A": "Correct. The worked calculation gives 327.83333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 327.83333, not 491.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 327.83333, not 163.91667.",
"D": "Incorrect. Substituting the st... | [
"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_004666 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 15 kg and radius 2 m is acted on by a constant torque of 91 N m about its central axis. Find its angular acceleration. | {
"A": "1.03333 rad s⁻²",
"B": "1.30333 rad s⁻²",
"C": "6.06667 rad s⁻²",
"D": "3.03333 rad s⁻²"
} | D | 3.03333 rad s⁻² | For a solid disc, I=½MR²=½(15)(2)²=30 kg m². Using τ=Iα, α=91/30=3.03333 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.03333 rad s⁻², not 1.03333 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.03333 rad s⁻², not 1.30333 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing r... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003135 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-10-9i)/(11+2i). What is Re(z), the real part of z? | {
"A": "0.976",
"B": "-4.024",
"C": "-1.024",
"D": "-2.048"
} | C | -1.024 | Multiply numerator and denominator by the conjugate (11-2i). Then Re(z)=(ac+bd)/(c²+d²)=((-10)(11)+(-9)(2))/(11²+(2)²)=-1.024. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.024, not 0.976.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.024, not -4.024.",
"C": "Correct. The worked calculation gives -1.024.",
"D": "Incorrect. Substituting the stated values i... | [
"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_009833 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(CN)_3]^+0, each CN ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "4.5",
"B": "1.3",
"C": "3",
"D": "2"
} | C | 3 | Let the formal oxidation state of Co be x. Charge balance gives x+(3)(−1)=+0; hence x=0+3=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"C": "Correct. The worked calculation gives 3.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002998 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, -4, -6) and v=(-3, 5, 4), calculate u·v. | {
"A": "-46",
"B": "-94",
"C": "-70.5",
"D": "-47"
} | D | -47 | The dot product is the sum of corresponding component products: (1)(-3)+(-4)(5)+(-6)(4)=-47. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -47, not -46.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -47, not -94.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -47, not -70.5.",
"D": "Correct.... | [
"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_003993 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block initially moves at 8 m s⁻¹. A constant net force does 5 N of work over 18 m in the direction of motion. Find its final kinetic energy. | {
"A": "308 J",
"B": "115.5 J",
"C": "77 J",
"D": "154 J"
} | D | 154 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(2)(8)²+(5)(18)=154 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 154 J, not 308 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 154 J, not 115.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 154 J, not 77 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_000369 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 14 and common difference 4. Find the sum of its first 10 terms. | {
"A": "480",
"B": "384",
"C": "320",
"D": "256"
} | C | 320 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=14, d=4, n=10: Sₙ=10/2[2(14)+(10−1)(4)]=320. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 320, not 480.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 320, not 384.",
"C": "Correct. The worked calculation gives 320.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_006193 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 62 cm in front of a thin convex lens of focal length 17 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.28333",
"B": "0.37778",
"C": "3.37778",
"D": "2.37778"
} | B | 0.37778 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(62)(17)/(62−17)=23.42222 cm. Thus |m|=v/u=23.42222/62=0.37778. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.37778, not 0.28333.",
"B": "Correct. The worked calculation gives 0.37778.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.37778, not 3.37778.",
"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_009891 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(OH)_5]^-2, each OH ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "2",
"B": "1.5",
"C": "3",
"D": "1.3"
} | C | 3 | Let the formal oxidation state of Pt be x. Charge balance gives x+(5)(−1)=-2; hence x=-2+5=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.5.",
"C": "Correct. The worked calculation gives 3.",
"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_006892 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 17 mol H₂ and 5 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "2 mol",
"B": "7.5 mol",
"C": "10 mol",
"D": "20 mol"
} | C | 10 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 17 mol H₂O; O₂ can produce 10 mol H₂O. The limiting condition is O₂; product=10 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 2 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 7.5 mol.",
"C": "Correct. The worked calculation gives 10 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001107 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=2x³ +1x² +9x+7. Evaluate f′(2). | {
"A": "35",
"B": "37",
"C": "-37",
"D": "44.4"
} | B | 37 | Differentiate: f′(x)=3(2)x²+2(1)x+(9). At x=2, f′(2)=3(2)(2)²+2(1)(2)+(9)=37. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 37, not 35.",
"B": "Correct. The worked calculation gives 37.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 37, not -37.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003609 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 52 m s⁻¹ at 75° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "108.16 m",
"B": "135.2 m",
"C": "-135.2 m",
"D": "67.6 m"
} | B | 135.2 m | Range R=u²sin(2θ)/g. Substituting u=52, θ=75° and g=10 gives R=(52)²sin(150°)/10=135.2 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 135.2 m, not 108.16 m.",
"B": "Correct. The worked calculation gives 135.2 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 135.2 m, not -135.2 m.",
"D": "Incorrect. Substituting the stated ... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000974 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 12 and common ratio 5. What is the sum of its first 6 terms? | {
"A": "70308",
"B": "4688.2",
"C": "46872",
"D": "35154"
} | C | 46872 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=12(5^6−1)/(5−1)=46872. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 46872, not 70308.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 46872, not 4688.2.",
"C": "Correct. The worked calculation gives 46872.",
"D": "Incorrect. Substituting the stated values into... | [
"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_002865 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(9, 2, -6) and v=(-1, -5, 8), calculate u·v. | {
"A": "-65",
"B": "-67",
"C": "-69",
"D": "-5.7"
} | B | -67 | The dot product is the sum of corresponding component products: (9)(-1)+(2)(-5)+(-6)(8)=-67. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -67, not -65.",
"B": "Correct. The worked calculation gives -67.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -67, not -69.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006966 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 26 mol H₂ and 13 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "26 mol",
"B": "19.5 mol",
"C": "3.6 mol",
"D": "24 mol"
} | A | 26 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 26 mol H₂O; O₂ can produce 26 mol H₂O. The limiting condition is neither; stoichiometric; product=26 mol. | {
"A": "Correct. The worked calculation gives 26 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 19.5 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 3.6 mol.",
"D": "Incorrect. Substituting the stated valu... | [
"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_002732 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(9, -7, -1) and v=(5, -5, 4), calculate u·v. | {
"A": "60.8",
"B": "8.6",
"C": "38",
"D": "76"
} | D | 76 | The dot product is the sum of corresponding component products: (9)(5)+(-7)(-5)+(-1)(4)=76. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 76, not 60.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 76, not 8.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 76, not 38.",
"D": "Correct. The ... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003810 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 1 m s⁻¹. A constant net force does 19 N of work over 19 m in the direction of motion. Find its final kinetic energy. | {
"A": "367.5 J",
"B": "366.5 J",
"C": "365.5 J",
"D": "37.55 J"
} | C | 365.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(1)²+(19)(19)=365.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 365.5 J, not 367.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 365.5 J, not 366.5 J.",
"C": "Correct. The worked calculation gives 365.5 J.",
"D": "Incorrect. Substituting the stated va... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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