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 |
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