Datasets:
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_004106 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 24 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.19. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "107.52 N",
"B": "11.752 N",
"C": "105.52 N",
"D": "129.024 N"
} | A | 107.52 N | Net force=mg(sinθ−μcosθ)=24×10×(0.6−0.19×0.8)=107.52 N. | {
"A": "Correct. The worked calculation gives 107.52 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 107.52 N, not 11.752 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 107.52 N, not 105.52 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_003879 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block initially moves at 11 m s⁻¹. A constant net force does 25 N of work over 7 m in the direction of motion. Find its final kinetic energy. | {
"A": "645.6 J",
"B": "538 J",
"C": "807 J",
"D": "54.8 J"
} | B | 538 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(6)(11)²+(25)(7)=538 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 538 J, not 645.6 J.",
"B": "Correct. The worked calculation gives 538 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 538 J, not 807 J.",
"D": "Incorrect. Substituting the stated values int... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003591 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 110 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "-1047.89074 m",
"B": "785.91805 m",
"C": "1047.89074 m",
"D": "1046.89074 m"
} | C | 1047.89074 m | Range R=u²sin(2θ)/g. Substituting u=110, θ=60° and g=10 gives R=(110)²sin(120°)/10=1047.89074 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1047.89074 m, not -1047.89074 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1047.89074 m, not 785.91805 m.",
"C": "Correct. The worked calculation gives 1047.89074 m.",
"D": "Incorrect. S... | [
"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_009637 | 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_16H_15N_3X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "12",
"B": "10",
"C": "7.5",
"D": "20"
} | B | 10 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×16+2+3−15−2)/2=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 12.",
"B": "Correct. The worked calculation gives 10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 7.5.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"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_007667 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 26 mL of 0.10 M HCl is mixed with 24 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.39794",
"B": "1.23979",
"C": "3.39794",
"D": "1.19897"
} | A | 2.39794 | Excess H⁺ moles=0.10×(26−24)/1000=0.000200 mol. Total volume=0.050 L, so [H⁺]=0.004000 M and pH=−log₁₀[H⁺]=2.39794. | {
"A": "Correct. The worked calculation gives 2.39794.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.39794, not 1.23979.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.39794, not 3.39794.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001721 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 3 elements can be selected from a set of 77 distinct elements? | {
"A": "73150",
"B": "7316",
"C": "73151",
"D": "87780"
} | A | 73150 | Order does not matter, so the count is C(77,3)=77!/[3!(74)!]=73150. | {
"A": "Correct. The worked calculation gives 73150.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 73150, not 7316.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 73150, not 73151.",
"D": "Incorrect. Substituting the stated values into t... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007861 | 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 44 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "0.34375 mmol L⁻¹",
"B": "3.34375 mmol L⁻¹",
"C": "0.51562 mmol L⁻¹",
"D": "-2.65625 mmol L⁻¹"
} | A | 0.34375 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=44/2^7=0.34375 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 0.34375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34375 mmol L⁻¹, not 3.34375 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34375 mmol L⁻¹, not 0.51562 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_008648 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.48 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.2304 K",
"B": "0.7696 K",
"C": "1.07696 K",
"D": "0.3848 K"
} | B | 0.7696 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.52×1.48=0.7696 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7696 K, not -0.2304 K.",
"B": "Correct. The worked calculation gives 0.7696 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7696 K, not 1.07696 K.",
"D": "Incorrect. Substituting the st... | [
"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_001065 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-2x³ -1x² +11x+7. Evaluate f′(5). | {
"A": "-147",
"B": "-119.2",
"C": "-149",
"D": "-148"
} | C | -149 | Differentiate: f′(x)=3(-2)x²+2(-1)x+(11). At x=5, f′(5)=3(-2)(5)²+2(-1)(5)+(11)=-149. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -149, not -147.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -149, not -119.2.",
"C": "Correct. The worked calculation gives -149.",
"D": "Incorrect. Substituting the stated values into the... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004669 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 5 m is acted on by a constant torque of 29 N m about its central axis. Find its angular acceleration. | {
"A": "0.232 rad s⁻²",
"B": "3.464 rad s⁻²",
"C": "-0.536 rad s⁻²",
"D": "0.464 rad s⁻²"
} | D | 0.464 rad s⁻² | For a solid disc, I=½MR²=½(5)(5)²=62.5 kg m². Using τ=Iα, α=29/62.5=0.464 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.464 rad s⁻², not 0.232 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.464 rad s⁻², not 3.464 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation ... | [
"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_002935 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(7, 7, 9) and v=(-3, -2, -2), calculate u·v. | {
"A": "-4.3",
"B": "-52",
"C": "-53",
"D": "-79.5"
} | C | -53 | The dot product is the sum of corresponding component products: (7)(-3)+(7)(-2)+(9)(-2)=-53. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -53, not -4.3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -53, not -52.",
"C": "Correct. The worked calculation gives -53.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_003195 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(4+14i)/(4+4i). What is Re(z), the real part of z? | {
"A": "2.25",
"B": "0.25",
"C": "3.25",
"D": "5.25"
} | A | 2.25 | Multiply numerator and denominator by the conjugate (4-4i). Then Re(z)=(ac+bd)/(c²+d²)=((4)(4)+(14)(4))/(4²+(4)²)=2.25. | {
"A": "Correct. The worked calculation gives 2.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.25, not 0.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.25, not 3.25.",
"D": "Incorrect. Substituting the stated values into the g... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004920 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 2 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 17 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.03922 A",
"B": "-2.03922 A",
"C": "2.03922 A",
"D": "3.03922 A"
} | C | 2.03922 A | Series branch resistance=2+7=9 Ω. Parallel equivalent R_eq=(9×17)/(9+17)=5.88462 Ω. Total current I=V/R_eq=12/5.88462=2.03922 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.03922 A, not 1.03922 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.03922 A, not -2.03922 A.",
"C": "Correct. The worked calculation gives 2.03922 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007545 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 98 mL of 0.10 M HCl is mixed with 36 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "0.33471",
"B": "1.33471",
"C": "-0.66529",
"D": "-1.66529"
} | B | 1.33471 | Excess H⁺ moles=0.10×(98−36)/1000=0.006200 mol. Total volume=0.134 L, so [H⁺]=0.046269 M and pH=−log₁₀[H⁺]=1.33471. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.33471, not 0.33471.",
"B": "Correct. The worked calculation gives 1.33471.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.33471, not -0.66529.",
"D": "Incorrect. Substituting the stated v... | [
"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_004849 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 13 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.08361 A",
"B": "0.08361 A",
"C": "2.16722 A",
"D": "3.08361 A"
} | A | 1.08361 A | Series branch resistance=9+14=23 Ω. Parallel equivalent R_eq=(23×13)/(23+13)=8.30556 Ω. Total current I=V/R_eq=9/8.30556=1.08361 A. | {
"A": "Correct. The worked calculation gives 1.08361 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.08361 A, not 0.08361 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.08361 A, not 2.16722 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_004944 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 12 Ω and 13 Ω are connected in series; this combination is connected in parallel with a 3 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.24 A",
"B": "1.12 A",
"C": "3.36 A",
"D": "-0.76 A"
} | A | 2.24 A | Series branch resistance=12+13=25 Ω. Parallel equivalent R_eq=(25×3)/(25+3)=2.67857 Ω. Total current I=V/R_eq=6/2.67857=2.24 A. | {
"A": "Correct. The worked calculation gives 2.24 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.24 A, not 1.12 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.24 A, not 3.36 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_003546 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 102 m s⁻¹ at 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "2049.18797 m",
"B": "1024.59399 m",
"C": "1536.89098 m",
"D": "1022.59399 m"
} | B | 1024.59399 m | Range R=u²sin(2θ)/g. Substituting u=102, θ=40° and g=10 gives R=(102)²sin(80°)/10=1024.59399 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1024.59399 m, not 2049.18797 m.",
"B": "Correct. The worked calculation gives 1024.59399 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1024.59399 m, not 1536.89098 m.",
"D": "Incorrect. S... | [
"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_006871 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 16 mol H₂ and 21 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "8 mol",
"B": "12.8 mol",
"C": "16 mol",
"D": "12 mol"
} | C | 16 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 16 mol H₂O; O₂ can produce 42 mol H₂O. The limiting condition is H₂; product=16 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 8 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 12.8 mol.",
"C": "Correct. The worked calculation gives 16 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_009263 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.13 V, transfers 3 electrons, and has reaction quotient Q=10^1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "3.1103 V",
"B": "2.1103 V",
"C": "0.83272 V",
"D": "1.1103 V"
} | D | 1.1103 V | Apply the Nernst equation: E=1.13−(0.0591/3)(1)=1.1103 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.1103 V, not 3.1103 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1103 V, not 2.1103 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1103 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_007182 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 1 mol of gas at 615 K and 1.76 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "-28.67333 L",
"B": "3.86733 L",
"C": "21.505 L",
"D": "28.67333 L"
} | D | 28.67333 L | PV=nRT, so V=nRT/P=(1)(0.082057)(615)/(1.76)=28.67333 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28.67333 L, not -28.67333 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28.67333 L, not 3.86733 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28.673... | [
"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_002481 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, -1], [6, 8]]. | {
"A": "46.5",
"B": "-62",
"C": "7.2",
"D": "62"
} | D | 62 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(8)−(-1)(6)=62. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 62, not 46.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 62, not -62.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 62, not 7.2.",
"D": "Correct. The... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003923 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 3 kg block initially moves at 10 m s⁻¹. A constant net force does 29 N of work over 2 m in the direction of motion. Find its final kinetic energy. | {
"A": "206 J",
"B": "166.4 J",
"C": "209 J",
"D": "208 J"
} | D | 208 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(3)(10)²+(29)(2)=208 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 208 J, not 206 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 208 J, not 166.4 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 208 J, not 209 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_007782 | 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 48 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "0.5625 mmol L⁻¹",
"B": "0.75 mmol L⁻¹",
"C": "1.5 mmol L⁻¹",
"D": "0.375 mmol L⁻¹"
} | B | 0.75 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=48/2^6=0.75 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.75 mmol L⁻¹, not 0.5625 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.75 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.75 mmol L⁻¹, not 1.5 mmol L⁻¹.",
"D": "Incorr... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001482 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (-2x² -3x +4) dx. | {
"A": "-275.16667",
"B": "-274.16667",
"C": "-219.33333",
"D": "274.16667"
} | B | -274.16667 | An antiderivative is (-2/3)x³+(-3/2)x²+(4)x. Evaluating between 0 and 7 gives (-2/3)(7)³+(-3/2)(7)²+(4)(7)=-274.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -274.16667, not -275.16667.",
"B": "Correct. The worked calculation gives -274.16667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -274.16667, not -219.33333.",
"D": "Incorrect. Substitutin... | [
"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_000562 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -10 and common difference 4. Find the sum of its first 8 terms. | {
"A": "48",
"B": "25.6",
"C": "32",
"D": "31"
} | C | 32 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-10, d=4, n=8: Sₙ=8/2[2(-10)+(8−1)(4)]=32. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 32, not 48.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 32, not 25.6.",
"C": "Correct. The worked calculation gives 32.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"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_001063 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-3x³ +3x² +9x+7. Evaluate f′(2). | {
"A": "-11.25",
"B": "-15",
"C": "-16",
"D": "15"
} | B | -15 | Differentiate: f′(x)=3(-3)x²+2(3)x+(9). At x=2, f′(2)=3(-3)(2)²+2(3)(2)+(9)=-15. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -15, not -11.25.",
"B": "Correct. The worked calculation gives -15.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -15, not -16.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_007135 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 17 mol of gas at 299 K and 2.57 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "162.29406 L",
"B": "324.58812 L",
"C": "160.29406 L",
"D": "129.83525 L"
} | A | 162.29406 L | PV=nRT, so V=nRT/P=(17)(0.082057)(299)/(2.57)=162.29406 L. | {
"A": "Correct. The worked calculation gives 162.29406 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 162.29406 L, not 324.58812 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 162.29406 L, not 160.29406 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_007753 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 52 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "0.30469 mmol L⁻¹",
"B": "0.40625 mmol L⁻¹",
"C": "-2.59375 mmol L⁻¹",
"D": "-1.59375 mmol L⁻¹"
} | B | 0.40625 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=52/2^7=0.40625 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.40625 mmol L⁻¹, not 0.30469 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.40625 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.40625 mmol L⁻¹, not -2.59375 mmol L⁻¹.",... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004003 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block initially moves at 2 m s⁻¹. A constant net force does 15 N of work over 3 m in the direction of motion. Find its final kinetic energy. | {
"A": "39.2 J",
"B": "50 J",
"C": "5.9 J",
"D": "49 J"
} | D | 49 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(2)(2)²+(15)(3)=49 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 49 J, not 39.2 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 49 J, not 50 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 49 J, not 5.9 J.",
"D": "C... | [
"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_008630 | 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 0.85 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.884 K",
"B": "-1.116 K",
"C": "-0.116 K",
"D": "0.884 K"
} | D | 0.884 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×0.85=0.884 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.884 K, not -0.884 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.884 K, not -1.116 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.884 K, not -0.... | [
"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_008158 | 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 8801 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": "17.37399 g",
"B": "18.37399 g",
"C": "13.8992 g",
"D": "15.37399 g"
} | A | 17.37399 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×6×8801/(2×96500)=17.37399 g. | {
"A": "Correct. The worked calculation gives 17.37399 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17.37399 g, not 18.37399 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17.37399 g, not 13.8992 g.",
"D": "Incorrect. Substituting... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005556 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 59 μF capacitor is charged to a potential difference of 12 V. Calculate the energy stored, expressed in μJ. | {
"A": "4248 μJ",
"B": "4250 μJ",
"C": "-4248 μJ",
"D": "4247 μJ"
} | A | 4248 μJ | U=½CV². Since C=59 μF, U in μJ is ½×59×(12)²=4248 μJ. | {
"A": "Correct. The worked calculation gives 4248 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4248 μJ, not 4250 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4248 μJ, not -4248 μJ.",
"D": "Incorrect. Substituting the stated v... | [
"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_001695 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 56 distinct elements? | {
"A": "35607051479",
"B": "35607051480",
"C": "17803525740",
"D": "26705288610"
} | B | 35607051480 | Order does not matter, so the count is C(56,10)=56!/[10!(46)!]=35607051480. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 35607051480, not 35607051479.",
"B": "Correct. The worked calculation gives 35607051480.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 35607051480, not 17803525740.",
"D": "Incorrect. Substi... | [
"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_002552 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 2], [9, -1]]. | {
"A": "-42",
"B": "-21",
"C": "-10.5",
"D": "-1.1"
} | B | -21 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(-1)−(2)(9)=-21. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -21, not -42.",
"B": "Correct. The worked calculation gives -21.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -21, not -10.5.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_000460 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 7 and common difference 5. Find the sum of its first 18 terms. | {
"A": "1336.5",
"B": "892",
"C": "891",
"D": "445.5"
} | C | 891 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=7, d=5, n=18: Sₙ=18/2[2(7)+(18−1)(5)]=891. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 891, not 1336.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 891, not 892.",
"C": "Correct. The worked calculation gives 891.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000670 | 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 5 terms? | {
"A": "7029",
"B": "18744",
"C": "9372",
"D": "938.2"
} | C | 9372 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=12(5^5−1)/(5−1)=9372. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9372, not 7029.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9372, not 18744.",
"C": "Correct. The worked calculation gives 9372.",
"D": "Incorrect. Substituting the stated values into the ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005817 | 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 4.9 atm at 274 K. What is its pressure at 544 K? | {
"A": "6.72847 atm",
"B": "7.29635 atm",
"C": "9.72847 atm",
"D": "4.86423 atm"
} | C | 9.72847 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.9)(544)/(274)=9.72847 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.72847 atm, not 6.72847 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.72847 atm, not 7.29635 atm.",
"C": "Correct. The worked calculation gives 9.72847 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_005389 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 39 μF capacitor is charged to a potential difference of 18 V. Calculate the energy stored, expressed in μJ. | {
"A": "6318 μJ",
"B": "6316 μJ",
"C": "-6318 μJ",
"D": "5054.4 μJ"
} | A | 6318 μJ | U=½CV². Since C=39 μF, U in μJ is ½×39×(18)²=6318 μJ. | {
"A": "Correct. The worked calculation gives 6318 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6318 μJ, not 6316 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6318 μJ, not -6318 μJ.",
"D": "Incorrect. Substituting the stated v... | [
"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_004135 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 34 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.36. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "53.04 N",
"B": "106.08 N",
"C": "104.08 N",
"D": "212.16 N"
} | B | 106.08 N | Net force=mg(sinθ−μcosθ)=34×10×(0.6−0.36×0.8)=106.08 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 106.08 N, not 53.04 N.",
"B": "Correct. The worked calculation gives 106.08 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 106.08 N, not 104.08 N.",
"D": "Incorrect. Substituting the state... | [
"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_008967 | 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, 51% of A has dissociated at constant volume. Find K_c. | {
"A": "2.57977",
"B": "3.43969",
"C": "1.71984",
"D": "2.43969"
} | B | 3.43969 | Let α=0.51. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.62)(0.51)²/(1−0.51)=3.43969. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.43969, not 2.57977.",
"B": "Correct. The worked calculation gives 3.43969.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.43969, not 1.71984.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002431 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, -8], [2, 6]]. | {
"A": "57",
"B": "6.8",
"C": "56",
"D": "58"
} | D | 58 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(6)−(-8)(2)=58. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 58, not 57.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 58, not 6.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 58, not 56.",
"D": "Correct. The wo... | [
"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_003221 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-12+2i)/(12+5i). What is Re(z), the real part of z? | {
"A": "-0.7929",
"B": "-1.5858",
"C": "0.92071",
"D": "-1.18935"
} | A | -0.7929 | Multiply numerator and denominator by the conjugate (12-5i). Then Re(z)=(ac+bd)/(c²+d²)=((-12)(12)+(2)(5))/(12²+(5)²)=-0.7929. | {
"A": "Correct. The worked calculation gives -0.7929.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.7929, not -1.5858.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.7929, not 0.92071.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003132 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-5+5i)/(4+9i). What is Re(z), the real part of z? | {
"A": "1.25773",
"B": "0.25773",
"C": "2.25773",
"D": "1.02577"
} | B | 0.25773 | Multiply numerator and denominator by the conjugate (4-9i). Then Re(z)=(ac+bd)/(c²+d²)=((-5)(4)+(5)(9))/(4²+(9)²)=0.25773. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25773, not 1.25773.",
"B": "Correct. The worked calculation gives 0.25773.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25773, not 2.25773.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005539 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 35 μF capacitor is charged to a potential difference of 32 V. Calculate the energy stored, expressed in μJ. | {
"A": "17919 μJ",
"B": "35840 μJ",
"C": "17920 μJ",
"D": "1793 μJ"
} | C | 17920 μJ | U=½CV². Since C=35 μF, U in μJ is ½×35×(32)²=17920 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 17920 μJ, not 17919 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17920 μJ, not 35840 μJ.",
"C": "Correct. The worked calculation gives 17920 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_005794 | 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 4.4 atm at 231 K. What is its pressure at 778 K? | {
"A": "14.81905 atm",
"B": "29.6381 atm",
"C": "17.81905 atm",
"D": "-14.81905 atm"
} | A | 14.81905 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.4)(778)/(231)=14.81905 atm. | {
"A": "Correct. The worked calculation gives 14.81905 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14.81905 atm, not 29.6381 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14.81905 atm, not 17.81905 atm.",
"D": "Incorrect. Su... | [
"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_002400 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, -4], [8, 2]]. | {
"A": "18",
"B": "27",
"C": "36",
"D": "-36"
} | C | 36 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(2)−(-4)(8)=36. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 36, not 18.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 36, not 27.",
"C": "Correct. The worked calculation gives 36.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004896 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 5 Ω and 6 Ω are connected in series; this combination is connected in parallel with a 12 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "7.84091 A",
"B": "6.22727 A",
"C": "3.92045 A",
"D": "5.22727 A"
} | D | 5.22727 A | Series branch resistance=5+6=11 Ω. Parallel equivalent R_eq=(11×12)/(11+12)=5.73913 Ω. Total current I=V/R_eq=30/5.73913=5.22727 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.22727 A, not 7.84091 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.22727 A, not 6.22727 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.22727 A,... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005286 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +6 μC are separated by 12 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "4.75 N",
"B": "-3.75 N",
"C": "5.625 N",
"D": "3.75 N"
} | D | 3.75 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(6×10⁻⁶)/(12×10⁻²)²=3.75 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.75 N, not 4.75 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.75 N, not -3.75 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.75 N, not 5.625 N."... | [
"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_005885 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.2 atm at 291 K. What is its pressure at 641 K? | {
"A": "11.25155 atm",
"B": "10.25155 atm",
"C": "-9.25155 atm",
"D": "9.25155 atm"
} | D | 9.25155 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.2)(641)/(291)=9.25155 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.25155 atm, not 11.25155 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.25155 atm, not 10.25155 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_009495 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_6H_3N_1X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "1.5",
"B": "2.5",
"C": "7.5",
"D": "5"
} | D | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+1−3−2)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.5.",
"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_005129 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +8 μC are separated by 5 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "113.2 N",
"B": "115.2 N",
"C": "116.2 N",
"D": "230.4 N"
} | B | 115.2 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(8×10⁻⁶)/(5×10⁻²)²=115.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 115.2 N, not 113.2 N.",
"B": "Correct. The worked calculation gives 115.2 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 115.2 N, not 116.2 N.",
"D": "Incorrect. Substituting the stated va... | [
"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_003971 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 6 m s⁻¹. A constant net force does 30 N of work over 4 m in the direction of motion. Find its final kinetic energy. | {
"A": "31 J",
"B": "299 J",
"C": "300 J",
"D": "240 J"
} | C | 300 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(6)²+(30)(4)=300 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 300 J, not 31 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 300 J, not 299 J.",
"C": "Correct. The worked calculation gives 300 J.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_005206 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +8 μC and +3 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "133 N",
"B": "14.5 N",
"C": "136 N",
"D": "135 N"
} | D | 135 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(8×10⁻⁶)(3×10⁻⁶)/(4×10⁻²)²=135 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 135 N, not 133 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 135 N, not 14.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 135 N, not 136 N.",
"D"... | [
"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_009058 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.60 V, transfers 3 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.0424 V",
"B": "1.05212 V",
"C": "1.5212 V",
"D": "0.5212 V"
} | D | 0.5212 V | Apply the Nernst equation: E=0.60−(0.0591/3)(4)=0.5212 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5212 V, not 1.0424 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.5212 V, not 1.05212 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5212 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_003539 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 46 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "162.095 m",
"B": "163.095 m",
"C": "324.19001 m",
"D": "160.095 m"
} | A | 162.095 m | Range R=u²sin(2θ)/g. Substituting u=46, θ=25° and g=10 gives R=(46)²sin(50°)/10=162.095 m. | {
"A": "Correct. The worked calculation gives 162.095 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 162.095 m, not 163.095 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 162.095 m, not 324.19001 m.",
"D": "Incorrect. Substituting t... | [
"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_000794 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio -3. What is the sum of its first 8 terms? | {
"A": "-14760",
"B": "-11070",
"C": "14760",
"D": "-17712"
} | A | -14760 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(-3^8−1)/(-3−1)=-14760. | {
"A": "Correct. The worked calculation gives -14760.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -14760, not -11070.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -14760, not 14760.",
"D": "Incorrect. Substituting the stated values i... | [
"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_004469 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 6 kg and radius 4 m is acted on by a constant torque of 15 N m about its central axis. Find its angular acceleration. | {
"A": "3.3125 rad s⁻²",
"B": "0.15625 rad s⁻²",
"C": "0.3125 rad s⁻²",
"D": "-0.6875 rad s⁻²"
} | C | 0.3125 rad s⁻² | For a solid disc, I=½MR²=½(6)(4)²=48 kg m². Using τ=Iα, α=15/48=0.3125 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3125 rad s⁻², not 3.3125 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3125 rad s⁻², not 0.15625 rad s⁻².",
"C": "Correct. The worked calculation gives 0.3125 rad s⁻².",
"D": "I... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003446 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 117 m s⁻¹ at 18° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "402.30962 m",
"B": "81.46192 m",
"C": "804.61923 m",
"D": "802.61923 m"
} | C | 804.61923 m | Range R=u²sin(2θ)/g. Substituting u=117, θ=18° and g=10 gives R=(117)²sin(36°)/10=804.61923 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 804.61923 m, not 402.30962 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 804.61923 m, not 81.46192 m.",
"C": "Correct. The worked calculation gives 804.61923 m.",
"D": "Incorrect. Substit... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005152 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +3 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "10.125 N",
"B": "12.5 N",
"C": "14.5 N",
"D": "13.5 N"
} | D | 13.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(3×10⁻⁶)/(10×10⁻²)²=13.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13.5 N, not 10.125 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13.5 N, not 12.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13.5 N, not 14.5 N."... | [
"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_002985 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, 6, -7) and v=(5, 2, 1), calculate u·v. | {
"A": "13",
"B": "10",
"C": "7",
"D": "11"
} | B | 10 | The dot product is the sum of corresponding component products: (1)(5)+(6)(2)+(-7)(1)=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 13.",
"B": "Correct. The worked calculation gives 10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 7.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_009936 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(Cl)_2]^+1, each Cl ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "2.25",
"B": "1.5",
"C": "1",
"D": "3"
} | D | 3 | Let the formal oxidation state of Cr be x. Charge balance gives x+(2)(−1)=+1; hence x=1+2=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.",
"D": "Correct. The work... | [
"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_006715 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 36 mol H₂ and 33 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "28.8 mol",
"B": "72 mol",
"C": "36 mol",
"D": "43.2 mol"
} | C | 36 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 36 mol H₂O; O₂ can produce 66 mol H₂O. The limiting condition is H₂; product=36 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 36 mol, not 28.8 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 36 mol, not 72 mol.",
"C": "Correct. The worked calculation gives 36 mol.",
"D": "Incorrect. Substituting the stated value... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006138 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 49 cm in front of a thin convex lens of focal length 10 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.25641",
"B": "0.19231",
"C": "-0.25641",
"D": "2.25641"
} | A | 0.25641 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(49)(10)/(49−10)=12.5641 cm. Thus |m|=v/u=12.5641/49=0.25641. | {
"A": "Correct. The worked calculation gives 0.25641.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25641, not 0.19231.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25641, not -0.25641.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008130 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 9 A for 25499 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": "75.50611 g",
"B": "90.60733 g",
"C": "56.62958 g",
"D": "151.01221 g"
} | A | 75.50611 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×9×25499/(2×96500)=75.50611 g. | {
"A": "Correct. The worked calculation gives 75.50611 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 75.50611 g, not 90.60733 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 75.50611 g, not 56.62958 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_000800 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio 5. What is the sum of its first 5 terms? | {
"A": "8589",
"B": "8591",
"C": "10309.2",
"D": "8593"
} | B | 8591 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(5^5−1)/(5−1)=8591. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8591, not 8589.",
"B": "Correct. The worked calculation gives 8591.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8591, not 10309.2.",
"D": "Incorrect. Substituting the stated values into th... | [
"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_002416 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, -5], [2, 3]]. | {
"A": "14.25",
"B": "19",
"C": "15.2",
"D": "22.8"
} | B | 19 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(3)−(-5)(2)=19. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19, not 14.25.",
"B": "Correct. The worked calculation gives 19.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19, not 15.2.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_000650 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 5 and common difference 4. Find the sum of its first 13 terms. | {
"A": "377",
"B": "38.7",
"C": "188.5",
"D": "375"
} | A | 377 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=5, d=4, n=13: Sₙ=13/2[2(5)+(13−1)(4)]=377. | {
"A": "Correct. The worked calculation gives 377.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 377, not 38.7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 377, not 188.5.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006709 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 29 mol H₂ and 30 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "58 mol",
"B": "21.75 mol",
"C": "23.2 mol",
"D": "29 mol"
} | D | 29 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 29 mol H₂O; O₂ can produce 60 mol H₂O. The limiting condition is H₂; product=29 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 29 mol, not 58 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 29 mol, not 21.75 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29 mol, not 23.2 mo... | [
"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_005757 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.5 atm at 295 K. What is its pressure at 743 K? | {
"A": "14.3339 atm",
"B": "17.00085 atm",
"C": "10.3339 atm",
"D": "11.3339 atm"
} | D | 11.3339 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.5)(743)/(295)=11.3339 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.3339 atm, not 14.3339 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.3339 atm, not 17.00085 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1... | [
"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_007862 | 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 75 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "0.21973 mmol L⁻¹",
"B": "0.29297 mmol L⁻¹",
"C": "1.29297 mmol L⁻¹",
"D": "0.43945 mmol L⁻¹"
} | B | 0.29297 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=75/2^8=0.29297 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29297 mmol L⁻¹, not 0.21973 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.29297 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29297 mmol L⁻¹, not 1.29297 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_002810 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(0, 9, 8) and v=(-1, 2, -3), calculate u·v. | {
"A": "-6",
"B": "6",
"C": "-8",
"D": "-9"
} | A | -6 | The dot product is the sum of corresponding component products: (0)(-1)+(9)(2)+(8)(-3)=-6. | {
"A": "Correct. The worked calculation gives -6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -6, not 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -6, not -8.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_001290 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ -2x² -12x+7. Evaluate f′(4). | {
"A": "-270",
"B": "-268",
"C": "-25.8",
"D": "-214.4"
} | B | -268 | Differentiate: f′(x)=3(-5)x²+2(-2)x+(-12). At x=4, f′(4)=3(-5)(4)²+2(-2)(4)+(-12)=-268. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -268, not -270.",
"B": "Correct. The worked calculation gives -268.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -268, not -25.8.",
"D": "Incorrect. Substituting the stated values into the ... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005384 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 64 μF capacitor is charged to a potential difference of 17 V. Calculate the energy stored, expressed in μJ. | {
"A": "9249 μJ",
"B": "9247 μJ",
"C": "9248 μJ",
"D": "11097.6 μJ"
} | C | 9248 μJ | U=½CV². Since C=64 μF, U in μJ is ½×64×(17)²=9248 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9248 μJ, not 9249 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9248 μJ, not 9247 μJ.",
"C": "Correct. The worked calculation gives 9248 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_000764 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio 5. What is the sum of its first 12 terms? | {
"A": "213623046",
"B": "427246092",
"C": "341796873.6",
"D": "640869138"
} | B | 427246092 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(5^12−1)/(5−1)=427246092. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 427246092, not 213623046.",
"B": "Correct. The worked calculation gives 427246092.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 427246092, not 341796873.6.",
"D": "Incorrect. Substituting t... | [
"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_004964 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 14 Ω and 3 Ω are connected in series; this combination is connected in parallel with a 5 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.65882 A",
"B": "9.31765 A",
"C": "7.31765 A",
"D": "8.31765 A"
} | B | 9.31765 A | Series branch resistance=14+3=17 Ω. Parallel equivalent R_eq=(17×5)/(17+5)=3.86364 Ω. Total current I=V/R_eq=36/3.86364=9.31765 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.31765 A, not 4.65882 A.",
"B": "Correct. The worked calculation gives 9.31765 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.31765 A, not 7.31765 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_007283 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 8 mol of gas at 254 K and 1.18 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "141.30494 L",
"B": "113.04395 L",
"C": "143.30494 L",
"D": "15.13049 L"
} | A | 141.30494 L | PV=nRT, so V=nRT/P=(8)(0.082057)(254)/(1.18)=141.30494 L. | {
"A": "Correct. The worked calculation gives 141.30494 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 141.30494 L, not 113.04395 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 141.30494 L, not 143.30494 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_007899 | 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 27 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "1.6875 mmol L⁻¹",
"B": "0.6875 mmol L⁻¹",
"C": "-0.3125 mmol L⁻¹",
"D": "3.375 mmol L⁻¹"
} | A | 1.6875 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=27/2^4=1.6875 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 1.6875 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.6875 mmol L⁻¹, not 0.6875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.6875 mmol L⁻¹, not -0.3125 mmol L⁻¹.",
"D... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004658 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 2 m is acted on by a constant torque of 49 N m about its central axis. Find its angular acceleration. | {
"A": "6.125 rad s⁻²",
"B": "15.25 rad s⁻²",
"C": "12.25 rad s⁻²",
"D": "18.375 rad s⁻²"
} | C | 12.25 rad s⁻² | For a solid disc, I=½MR²=½(2)(2)²=4 kg m². Using τ=Iα, α=49/4=12.25 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.25 rad s⁻², not 6.125 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.25 rad s⁻², not 15.25 rad s⁻².",
"C": "Correct. The worked calculation gives 12.25 rad s⁻².",
"D": "Incorre... | [
"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_001519 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (4x² -7x +4) dx. | {
"A": "-99.16667",
"B": "49.58333",
"C": "97.16667",
"D": "99.16667"
} | D | 99.16667 | An antiderivative is (4/3)x³+(-7/2)x²+(4)x. Evaluating between 0 and 5 gives (4/3)(5)³+(-7/2)(5)²+(4)(5)=99.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 99.16667, not -99.16667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 99.16667, not 49.58333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 99.16667, not... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002512 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, 1], [5, 2]]. | {
"A": "10",
"B": "4",
"C": "-7",
"D": "7"
} | D | 7 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(2)−(1)(5)=7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not -7.",
"D": "Correct. The worked ... | [
"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_000124 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 -5x +12=0, let its roots be α and β. What is α²+β²? | {
"A": "0.70816",
"B": "-5.91837",
"C": "-2.91837",
"D": "-2.18878"
} | C | -2.91837 | By Vieta's relations, α+β = 5/7 and αβ = 12/7. Then α²+β²=(α+β)²−2αβ = (5/7)²−2(12/7) = -2.91837. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2.91837, not 0.70816.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2.91837, not -5.91837.",
"C": "Correct. The worked calculation gives -2.91837.",
"D": "Incorrect. Substituting the state... | [
"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_008901 | 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 0.89 mol L⁻¹ and initially B is absent. At equilibrium, 47% of A has dissociated at constant volume. Find K_c. | {
"A": "4.48378",
"B": "1.48378",
"C": "1.14838",
"D": "2.48378"
} | B | 1.48378 | Let α=0.47. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.89)(0.47)²/(1−0.47)=1.48378. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.48378, not 4.48378.",
"B": "Correct. The worked calculation gives 1.48378.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.48378, not 1.14838.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008786 | 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 1.75 mol L⁻¹ and initially B is absent. At equilibrium, 70% of A has dissociated at constant volume. Find K_c. | {
"A": "11.43333",
"B": "17.15",
"C": "5.71667",
"D": "22.86667"
} | A | 11.43333 | Let α=0.7. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.75)(0.7)²/(1−0.7)=11.43333. | {
"A": "Correct. The worked calculation gives 11.43333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.43333, not 17.15.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.43333, not 5.71667.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006216 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 63 cm in front of a thin convex lens of focal length 22 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.53659",
"B": "0.40244",
"C": "0.80488",
"D": "1.05366"
} | A | 0.53659 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(63)(22)/(63−22)=33.80488 cm. Thus |m|=v/u=33.80488/63=0.53659. | {
"A": "Correct. The worked calculation gives 0.53659.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.53659, not 0.40244.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.53659, not 0.80488.",
"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_006158 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 54 cm in front of a thin convex lens of focal length 11 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.25581",
"B": "0.25581",
"C": "0.38372",
"D": "-0.74419"
} | B | 0.25581 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(54)(11)/(54−11)=13.81395 cm. Thus |m|=v/u=13.81395/54=0.25581. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25581, not -0.25581.",
"B": "Correct. The worked calculation gives 0.25581.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25581, not 0.38372.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000278 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +11x -9=0, let its roots be α and β. What is α²+β²? | {
"A": "8.44",
"B": "6.44",
"C": "1.844",
"D": "-8.44"
} | A | 8.44 | By Vieta's relations, α+β = -11/5 and αβ = -9/5. Then α²+β²=(α+β)²−2αβ = (-11/5)²−2(-9/5) = 8.44. | {
"A": "Correct. The worked calculation gives 8.44.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.44, not 6.44.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.44, not 1.844.",
"D": "Incorrect. Substituting the stated values into the ... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008325 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 12 A for 7100 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": "42.04819 g",
"B": "29.03212 g",
"C": "28.03212 g",
"D": "-28.03212 g"
} | C | 28.03212 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×12×7100/(2×96500)=28.03212 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28.03212 g, not 42.04819 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28.03212 g, not 29.03212 g.",
"C": "Correct. The worked calculation gives 28.03212 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_005270 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +8 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "14.25 N",
"B": "16.875 N",
"C": "11.25 N",
"D": "22.5 N"
} | C | 11.25 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(8×10⁻⁶)/(8×10⁻²)²=11.25 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.25 N, not 14.25 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.25 N, not 16.875 N.",
"C": "Correct. The worked calculation gives 11.25 N.",
"D": "Incorrect. Substituting the stated v... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006779 | 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 25 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "5 mol",
"B": "7.5 mol",
"C": "3 mol",
"D": "6 mol"
} | A | 5 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 5 mol H₂O; O₂ can produce 50 mol H₂O. The limiting condition is H₂; product=5 mol. | {
"A": "Correct. The worked calculation gives 5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5 mol, not 7.5 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5 mol, not 3 mol.",
"D": "Incorrect. Substituting the stated values int... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008086 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 8 A for 22399 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "29.47848 g",
"B": "58.95695 g",
"C": "59.95695 g",
"D": "57.95695 g"
} | B | 58.95695 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×8×22399/(2×96500)=58.95695 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 58.95695 g, not 29.47848 g.",
"B": "Correct. The worked calculation gives 58.95695 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 58.95695 g, not 59.95695 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_003536 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 23 m s⁻¹ at 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "52.09633 m",
"B": "104.19266 m",
"C": "53.09633 m",
"D": "50.09633 m"
} | A | 52.09633 m | Range R=u²sin(2θ)/g. Substituting u=23, θ=40° and g=10 gives R=(23)²sin(80°)/10=52.09633 m. | {
"A": "Correct. The worked calculation gives 52.09633 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 52.09633 m, not 104.19266 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 52.09633 m, not 53.09633 m.",
"D": "Incorrect. Substituti... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002644 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, 4], [4, -7]]. | {
"A": "-15",
"B": "-30",
"C": "-36",
"D": "30"
} | B | -30 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(-7)−(4)(4)=-30. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -30, not -15.",
"B": "Correct. The worked calculation gives -30.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -30, not -36.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_008430 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.7 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.8704 K",
"B": "1.3056 K",
"C": "-0.1296 K",
"D": "3.8704 K"
} | A | 0.8704 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.512×1.7=0.8704 K. | {
"A": "Correct. The worked calculation gives 0.8704 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8704 K, not 1.3056 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8704 K, not -0.1296 K.",
"D": "Incorrect. Substituting the sta... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009614 | 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_8H_0N_3X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "-10",
"B": "10",
"C": "8",
"D": "2"
} | B | 10 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×8+2+3−0−1)/2=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not -10.",
"B": "Correct. The worked calculation gives 10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 8.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001383 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (6x² +3x -5) dx. | {
"A": "50.5",
"B": "52.5",
"C": "-52.5",
"D": "26.25"
} | B | 52.5 | An antiderivative is (6/3)x³+(3/2)x²+(-5)x. Evaluating between 0 and 3 gives (6/3)(3)³+(3/2)(3)²+(-5)(3)=52.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 52.5, not 50.5.",
"B": "Correct. The worked calculation gives 52.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 52.5, not -52.5.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_000464 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 16 and common difference 3. Find the sum of its first 34 terms. | {
"A": "-2227",
"B": "2229",
"C": "2227",
"D": "223.7"
} | C | 2227 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=16, d=3, n=34: Sₙ=34/2[2(16)+(34−1)(3)]=2227. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2227, not -2227.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2227, not 2229.",
"C": "Correct. The worked calculation gives 2227.",
"D": "Incorrect. Substituting the stated values into the ... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005823 | 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 1.9 atm at 185 K. What is its pressure at 722 K? | {
"A": "9.41514 atm",
"B": "5.56135 atm",
"C": "1.74151 atm",
"D": "7.41514 atm"
} | D | 7.41514 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.9)(722)/(185)=7.41514 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.41514 atm, not 9.41514 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.41514 atm, not 5.56135 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.... | [
"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_006145 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 78 cm in front of a thin convex lens of focal length 26 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.5",
"B": "1",
"C": "2.5",
"D": "3.5"
} | A | 0.5 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(78)(26)/(78−26)=39 cm. Thus |m|=v/u=39/78=0.5. | {
"A": "Correct. The worked calculation gives 0.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.5, not 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5, not 2.5.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_009160 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.95 V, transfers 1 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.6545 V",
"B": "0.98175 V",
"C": "-0.6545 V",
"D": "-2.3455 V"
} | A | 0.6545 V | Apply the Nernst equation: E=0.95−(0.0591/1)(5)=0.6545 V. | {
"A": "Correct. The worked calculation gives 0.6545 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6545 V, not 0.98175 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.6545 V, not -0.6545 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_001086 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-2x³ +0x² +9x+7. Evaluate f′(-3). | {
"A": "-45",
"B": "-3.5",
"C": "-33.75",
"D": "-44"
} | A | -45 | Differentiate: f′(x)=3(-2)x²+2(0)x+(9). At x=-3, f′(-3)=3(-2)(-3)²+2(0)(-3)+(9)=-45. | {
"A": "Correct. The worked calculation gives -45.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -45, not -3.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -45, not -33.75.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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 |
End of preview. Expand in Data Studio
OpenSTEM-QA
10,000 original, synthetic STEM multiple-choice QA records by Axilo Labz.
Hugging Face target repository: Axilo67/openstem-qa
Release contents
- 10,000 unique question records.
- Exactly four options (A–D) per question.
- One designated answer option.
- A worked numerical solution.
- An explanation field for each option.
- 3,340 mathematics, 3,330 physics and 3,330 chemistry questions.
train(9,000),validation(500) andtest(500) JSONL splits.- A combined JSONL file containing all records.
Subject and topic coverage
Mathematics
Quadratic-root identities, arithmetic and geometric progressions, polynomial differentiation, polynomial definite integrals, combinations, probability without replacement, determinants, vector dot products, and complex-number division.
Physics
Projectile motion, work–energy, friction on an inclined plane, rotational dynamics, series-parallel circuits, Coulomb's law, capacitor energy, isochoric ideal-gas processes, thin-lens magnification, and mass–spring simple harmonic motion.
Chemistry
Limiting reagents, ideal gases, strong-acid/strong-base mixtures, first-order kinetics, electrolysis, colligative properties, chemical equilibrium, the Nernst equation, degree of unsaturation, and formal oxidation-state charge balance in hypothetical coordination ions.
Generation method
This release was generated with deterministic Python templates and randomized numerical parameters. It was not generated by zai-org/GLM-5.3-Flash. The hosted GLM model was not run because the available Hugging Face remote-compute route returned 402 Payment Required.
The questions are newly worded and parameterized. They are inspired by the subject matter and calculation style of Indian JEE preparation, but they are not official JEE questions and do not reproduce past-paper questions.
Record schema
Each JSONL object contains:
| Field | Meaning |
|---|---|
id |
Unique record identifier |
subject, topic, subtopic |
Curriculum labels |
difficulty |
Provisional hard or very_hard label |
difficulty_labeling_method, difficulty_note |
Explain the provisional label |
question_type |
single_correct_mcq |
question |
Question statement |
options |
Exactly four choices keyed A–D |
correct_answer |
Correct option label |
correct_answer_value |
Numeric answer with units where applicable |
solution |
Worked calculation |
option_explanations |
Explanation for all four choices |
concepts_required |
Concept tags |
reasoning_steps |
Template-declared step count |
answer_type, language |
Answer format and language |
origin, source_type |
Synthetic-data provenance |
generator, generator_template_id |
Generator and question family |
verification_status, verification_note, answer_validation |
Validation provenance and limitations |
Validation performed
The generated release passed these structural checks:
- Exactly 10,000 rows.
- 10,000 unique IDs.
- 10,000 unique question strings after basic punctuation/case normalization.
- Exactly four option keys per record (A, B, C, D).
- Four distinct option strings per record.
- The
correct_answerlabel points to the option that matchescorrect_answer_value. - A non-empty question and worked solution.
- An explanation field for every option.
- Exact split sizes: 9,000 / 500 / 500.
- Balanced subject representation across splits.
The validation report is included as quality_report.json.
Important limitations
- Not expert-reviewed: Structural checks confirm schema and answer-key consistency. They do not replace an independent subject-matter solution review.
- Difficulty is provisional: This release labels records
hardorvery_hardby question-template family. It does not claim examiner-calibrated JEE Advanced difficulty. No records are labeledultra_hardin v0.1 because the current template set does not justify that claim. - Parameterized families: The 10,000 rows come from 30 underlying templates. Values and wording vary, but solution structures repeat. This is not equivalent to 10,000 independently authored problems.
- Evaluation leakage: The same template families appear in train, validation and test. The validation/test splits are useful for basic pipeline checks, but should not be treated as template-generalization benchmarks.
- Numeric emphasis: Most questions are calculation-based. Proof-based mathematics, multi-select questions, assertion-reason questions, qualitative chemistry, organic reaction mechanisms, and experimental-data interpretation are limited or absent.
- Distractors: Incorrect numerical options are distinct alternatives. Their explanations generally identify the computed value rather than diagnosing a specific misconception.
- Licensing: No separate reuse license is asserted in this seed release. A formal license should be selected before third-party redistribution or commercial use.
Loading
from datasets import load_dataset
ds = load_dataset(
"json",
data_files={
"train": "data/train.jsonl",
"validation": "data/validation.jsonl",
"test": "data/test.jsonl",
},
)
print(ds)
To use a single combined file:
from datasets import load_dataset
ds = load_dataset("json", data_files="openstem_qa_v0.1.jsonl", split="train")
Intended use
Useful for experiments in STEM question answering, numeric MCQ supervision, answer extraction and worked-solution training. Independently review examples before using them in high-stakes educational settings.
Axilo Labz — Exploring Intelligence. Engineering Possibilities.
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