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_003621 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 50 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "216.50635 m",
"B": "173.20508 m",
"C": "324.75953 m",
"D": "162.37976 m"
} | A | 216.50635 m | Range R=u²sin(2θ)/g. Substituting u=50, θ=60° and g=10 gives R=(50)²sin(120°)/10=216.50635 m. | {
"A": "Correct. The worked calculation gives 216.50635 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 216.50635 m, not 173.20508 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 216.50635 m, not 324.75953 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004869 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 10 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.925 A",
"B": "-2.925 A",
"C": "4.925 A",
"D": "3.925 A"
} | A | 2.925 A | Series branch resistance=9+7=16 Ω. Parallel equivalent R_eq=(16×10)/(16+10)=6.15385 Ω. Total current I=V/R_eq=18/6.15385=2.925 A. | {
"A": "Correct. The worked calculation gives 2.925 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.925 A, not -2.925 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.925 A, not 4.925 A.",
"D": "Incorrect. Substituting the stated v... | [
"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_006058 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 43 cm in front of a thin convex lens of focal length 9 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-1.73529",
"B": "2.26471",
"C": "0.26471",
"D": "0.13235"
} | C | 0.26471 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(43)(9)/(43−9)=11.38235 cm. Thus |m|=v/u=11.38235/43=0.26471. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.26471, not -1.73529.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.26471, not 2.26471.",
"C": "Correct. The worked calculation gives 0.26471.",
"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_003848 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 8 m s⁻¹. A constant net force does 27 N of work over 19 m in the direction of motion. Find its final kinetic energy. | {
"A": "739 J",
"B": "-737 J",
"C": "737 J",
"D": "738 J"
} | C | 737 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(8)²+(27)(19)=737 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 737 J, not 739 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 737 J, not -737 J.",
"C": "Correct. The worked calculation gives 737 J.",
"D": "Incorrect. Substituting the stated values into... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009115 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.21 V, transfers 3 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "4.2297 V",
"B": "0.2297 V",
"C": "2.4594 V",
"D": "1.2297 V"
} | D | 1.2297 V | Apply the Nernst equation: E=1.21−(0.0591/3)(-1)=1.2297 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.2297 V, not 4.2297 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.2297 V, not 0.2297 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2297 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_000954 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio -3. What is the sum of its first 9 terms? | {
"A": "41336.4",
"B": "34448",
"C": "34447",
"D": "3445.7"
} | C | 34447 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(-3^9−1)/(-3−1)=34447. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 34447, not 41336.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 34447, not 34448.",
"C": "Correct. The worked calculation gives 34447.",
"D": "Incorrect. Substituting the stated values int... | [
"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_006819 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 3 mol H₂ and 18 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "3 mol",
"B": "1 mol",
"C": "6 mol",
"D": "2.25 mol"
} | A | 3 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 3 mol H₂O; O₂ can produce 36 mol H₂O. The limiting condition is H₂; product=3 mol. | {
"A": "Correct. The worked calculation gives 3 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3 mol, not 1 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3 mol, not 6 mol.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_007223 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 12 mol of gas at 186 K and 2.78 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "131.76347 L",
"B": "32.94087 L",
"C": "65.88174 L",
"D": "-65.88174 L"
} | C | 65.88174 L | PV=nRT, so V=nRT/P=(12)(0.082057)(186)/(2.78)=65.88174 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 65.88174 L, not 131.76347 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 65.88174 L, not 32.94087 L.",
"C": "Correct. The worked calculation gives 65.88174 L.",
"D": "Incorrect. Substituti... | [
"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_006876 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 26 mol H₂ and 32 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "31.2 mol",
"B": "25 mol",
"C": "26 mol",
"D": "24 mol"
} | C | 26 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 26 mol H₂O; O₂ can produce 64 mol H₂O. The limiting condition is H₂; product=26 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 31.2 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 25 mol.",
"C": "Correct. The worked calculation gives 26 mol.",
"D": "Incorrect. Substituting the stated value... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006392 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 9 kg is attached to an ideal spring of force constant 1173 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.13139 s",
"B": "0.17519 s",
"C": "1.17519 s",
"D": "-0.17519 s"
} | B | 0.17519 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(9/1173)=0.17519 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.17519 s, not 0.13139 s.",
"B": "Correct. The worked calculation gives 0.17519 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.17519 s, not 1.17519 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004594 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 1 m is acted on by a constant torque of 50 N m about its central axis. Find its angular acceleration. | {
"A": "14.5 rad s⁻²",
"B": "9.375 rad s⁻²",
"C": "11.5 rad s⁻²",
"D": "12.5 rad s⁻²"
} | D | 12.5 rad s⁻² | For a solid disc, I=½MR²=½(8)(1)²=4 kg m². Using τ=Iα, α=50/4=12.5 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.5 rad s⁻², not 14.5 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.5 rad s⁻², not 9.375 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation giv... | [
"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_007500 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 52 mL of 0.10 M HCl is mixed with 63 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "11.98069",
"B": "8.98069",
"C": "14.98069",
"D": "10.98069"
} | A | 11.98069 | Excess OH⁻ moles=0.10×(63−52)/1000=0.001100 mol. Total volume=0.115 L, so [OH⁻]=0.009565 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=11.98069. | {
"A": "Correct. The worked calculation gives 11.98069.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.98069, not 8.98069.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.98069, not 14.98069.",
"D": "Incorrect. Substituting the state... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007052 | 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 356 K and 2.58 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "20.24841 L",
"B": "144.36307 L",
"C": "384.96819 L",
"D": "192.48409 L"
} | D | 192.48409 L | PV=nRT, so V=nRT/P=(17)(0.082057)(356)/(2.58)=192.48409 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 192.48409 L, not 20.24841 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 192.48409 L, not 144.36307 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 192... | [
"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_008352 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.33 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.33792 K",
"B": "1.03379 K",
"C": "-0.33792 K",
"D": "1.33792 K"
} | A | 0.33792 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×0.33=0.33792 K. | {
"A": "Correct. The worked calculation gives 0.33792 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33792 K, not 1.03379 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33792 K, not -0.33792 K.",
"D": "Incorrect. Substituting th... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007635 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 54 mL of 0.10 M HCl is mixed with 11 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "0.17944",
"B": "3.17944",
"C": "-1.82056",
"D": "1.17944"
} | D | 1.17944 | Excess H⁺ moles=0.10×(54−11)/1000=0.004300 mol. Total volume=0.065 L, so [H⁺]=0.066154 M and pH=−log₁₀[H⁺]=1.17944. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.17944, not 0.17944.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.17944, not 3.17944.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.17944, not -1.82... | [
"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_005986 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.7 atm at 202 K. What is its pressure at 464 K? | {
"A": "-1.39208 atm",
"B": "0.80396 atm",
"C": "1.60792 atm",
"D": "1.16079 atm"
} | C | 1.60792 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.7)(464)/(202)=1.60792 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.60792 atm, not -1.39208 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.60792 atm, not 0.80396 atm.",
"C": "Correct. The worked calculation gives 1.60792 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007293 | 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 256 K and 1.67 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "12.5788 L",
"B": "6.2894 L",
"C": "11.5788 L",
"D": "25.1576 L"
} | A | 12.5788 L | PV=nRT, so V=nRT/P=(1)(0.082057)(256)/(1.67)=12.5788 L. | {
"A": "Correct. The worked calculation gives 12.5788 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.5788 L, not 6.2894 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.5788 L, not 11.5788 L.",
"D": "Incorrect. Substituting the ... | [
"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_006633 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 23 kg is attached to an ideal spring of force constant 490 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.43331 s",
"B": "0.43331 s",
"C": "1.04333 s",
"D": "2.43331 s"
} | B | 0.43331 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(23/490)=0.43331 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.43331 s, not 1.43331 s.",
"B": "Correct. The worked calculation gives 0.43331 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.43331 s, not 1.04333 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009365 | 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_14H_0X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "9.75",
"B": "11",
"C": "26",
"D": "13"
} | D | 13 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×14+2+0−0−4)/2=13. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13, not 9.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13, not 11.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13, not 26.",
"D": "Correct. The w... | [
"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_007154 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 9 mol of gas at 380 K and 2.78 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "100.94782 L",
"B": "102.94782 L",
"C": "11.09478 L",
"D": "201.89564 L"
} | A | 100.94782 L | PV=nRT, so V=nRT/P=(9)(0.082057)(380)/(2.78)=100.94782 L. | {
"A": "Correct. The worked calculation gives 100.94782 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 100.94782 L, not 102.94782 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 100.94782 L, not 11.09478 L.",
"D": "Incorrect. Substit... | [
"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_006915 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 37 mol H₂ and 28 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "35 mol",
"B": "27.75 mol",
"C": "55.5 mol",
"D": "37 mol"
} | D | 37 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 37 mol H₂O; O₂ can produce 56 mol H₂O. The limiting condition is H₂; product=37 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 37 mol, not 35 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 37 mol, not 27.75 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 37 mol, not 55.5 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_000752 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio -3. What is the sum of its first 11 terms? | {
"A": "365367.75",
"B": "584588.4",
"C": "487155",
"D": "487157"
} | D | 487157 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(-3^11−1)/(-3−1)=487157. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 487157, not 365367.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 487157, not 584588.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 487157, not 48715... | [
"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_000022 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 -16x +5=0, let its roots be α and β. What is α²+β²? | {
"A": "16.48",
"B": "5.24",
"C": "6.18",
"D": "8.24"
} | D | 8.24 | By Vieta's relations, α+β = 16/5 and αβ = 5/5. Then α²+β²=(α+β)²−2αβ = (16/5)²−2(5/5) = 8.24. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.24, not 16.48.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.24, not 5.24.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.24, not 6.18.",
"D": "Cor... | [
"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_009716 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(CN)_4]^+0, each CN ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "6",
"B": "4",
"C": "3",
"D": "-4"
} | B | 4 | Let the formal oxidation state of Mn be x. Charge balance gives x+(4)(−1)=+0; hence x=0+4=+4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 6.",
"B": "Correct. The worked calculation gives 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 3.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009654 | 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_17H_18X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "10.5",
"B": "7",
"C": "5.25",
"D": "8"
} | B | 7 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×17+2+0−18−4)/2=7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 10.5.",
"B": "Correct. The worked calculation gives 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 5.25.",
"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_009972 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(OH)_6]^-3, each OH ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "3",
"B": "1",
"C": "5",
"D": "4"
} | A | 3 | Let the formal oxidation state of Cu be x. Charge balance gives x+(6)(−1)=-3; hence x=-3+6=+3. | {
"A": "Correct. The worked calculation gives 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 5.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006112 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 20 cm in front of a thin convex lens of focal length 9 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "2.81818",
"B": "0.81818",
"C": "-0.18182",
"D": "-0.81818"
} | B | 0.81818 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(20)(9)/(20−9)=16.36364 cm. Thus |m|=v/u=16.36364/20=0.81818. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.81818, not 2.81818.",
"B": "Correct. The worked calculation gives 0.81818.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.81818, not -0.18182.",
"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_007442 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 55 mL of 0.10 M HCl is mixed with 77 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.22185",
"B": "6.11092",
"C": "13.22185",
"D": "2.22218"
} | A | 12.22185 | Excess OH⁻ moles=0.10×(77−55)/1000=0.002200 mol. Total volume=0.132 L, so [OH⁻]=0.016667 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.22185. | {
"A": "Correct. The worked calculation gives 12.22185.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.22185, not 6.11092.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.22185, not 13.22185.",
"D": "Incorrect. Substituting the state... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006902 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 38 mol H₂ and 32 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "19 mol",
"B": "4.8 mol",
"C": "30.4 mol",
"D": "38 mol"
} | D | 38 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 38 mol H₂O; O₂ can produce 64 mol H₂O. The limiting condition is H₂; product=38 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 38 mol, not 19 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 38 mol, not 4.8 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 38 mol, not 30.4 mol.... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008324 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 4 A for 9824 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": "12.92899 g",
"B": "-12.92899 g",
"C": "14.92899 g",
"D": "13.92899 g"
} | A | 12.92899 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×9824/(2×96500)=12.92899 g. | {
"A": "Correct. The worked calculation gives 12.92899 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.92899 g, not -12.92899 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.92899 g, not 14.92899 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002300 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 8 blue and 9 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.62108",
"B": "3.31054",
"C": "-0.68946",
"D": "0.31054"
} | D | 0.31054 | Favourable pairs = C(10,2)+C(8,2)+C(9,2)=109. Total pairs=C(27,2)=351. Therefore P=109/351=0.31054. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31054, not 0.62108.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31054, not 3.31054.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31054, not -0.68... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003157 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-14+7i)/(8+12i). What is Re(z), the real part of z? | {
"A": "-1.13462",
"B": "0.13462",
"C": "-0.13462",
"D": "2.86538"
} | C | -0.13462 | Multiply numerator and denominator by the conjugate (8-12i). Then Re(z)=(ac+bd)/(c²+d²)=((-14)(8)+(7)(12))/(8²+(12)²)=-0.13462. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.13462, not -1.13462.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.13462, not 0.13462.",
"C": "Correct. The worked calculation gives -0.13462.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009177 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.19 V, transfers 3 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.1112 V",
"B": "-1.8888 V",
"C": "-1.1112 V",
"D": "2.1112 V"
} | A | 1.1112 V | Apply the Nernst equation: E=1.19−(0.0591/3)(4)=1.1112 V. | {
"A": "Correct. The worked calculation gives 1.1112 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1112 V, not -1.8888 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1112 V, not -1.1112 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_004188 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.20. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "22 N",
"B": "44 N",
"C": "33 N",
"D": "-44 N"
} | B | 44 N | Net force=mg(sinθ−μcosθ)=10×10×(0.6−0.20×0.8)=44 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 44 N, not 22 N.",
"B": "Correct. The worked calculation gives 44 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 44 N, not 33 N.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_003567 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 113 m s⁻¹ at 35° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "2399.78701 m",
"B": "1439.87221 m",
"C": "1799.84026 m",
"D": "1199.89351 m"
} | D | 1199.89351 m | Range R=u²sin(2θ)/g. Substituting u=113, θ=35° and g=10 gives R=(113)²sin(70°)/10=1199.89351 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1199.89351 m, not 2399.78701 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1199.89351 m, not 1439.87221 m.",
"C": "Incorrect. Substituting the stated values into the governing relation give... | [
"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_005608 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 74 μF capacitor is charged to a potential difference of 23 V. Calculate the energy stored, expressed in μJ. | {
"A": "19574 μJ",
"B": "19573 μJ",
"C": "1958.3 μJ",
"D": "15658.4 μJ"
} | B | 19573 μJ | U=½CV². Since C=74 μF, U in μJ is ½×74×(23)²=19573 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19573 μJ, not 19574 μJ.",
"B": "Correct. The worked calculation gives 19573 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19573 μJ, not 1958.3 μJ.",
"D": "Incorrect. Substituting the sta... | [
"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_004705 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 3 Ω are connected in series; this combination is connected in parallel with a 10 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.925 A",
"B": "1.4625 A",
"C": "1.95 A",
"D": "-1.95 A"
} | C | 1.95 A | Series branch resistance=13+3=16 Ω. Parallel equivalent R_eq=(16×10)/(16+10)=6.15385 Ω. Total current I=V/R_eq=12/6.15385=1.95 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.95 A, not 2.925 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.95 A, not 1.4625 A.",
"C": "Correct. The worked calculation gives 1.95 A.",
"D": "Incorrect. Substituting the stated valu... | [
"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_001390 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (-2x² +2x -1) dx. | {
"A": "-570.66667",
"B": "-285.33333",
"C": "-228.26667",
"D": "-342.4"
} | B | -285.33333 | An antiderivative is (-2/3)x³+(2/2)x²+(-1)x. Evaluating between 0 and 8 gives (-2/3)(8)³+(2/2)(8)²+(-1)(8)=-285.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -285.33333, not -570.66667.",
"B": "Correct. The worked calculation gives -285.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -285.33333, not -228.26667.",
"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_007287 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 14 mol of gas at 216 K and 1.33 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "188.57171 L",
"B": "139.92878 L",
"C": "186.57171 L",
"D": "184.57171 L"
} | C | 186.57171 L | PV=nRT, so V=nRT/P=(14)(0.082057)(216)/(1.33)=186.57171 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 186.57171 L, not 188.57171 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 186.57171 L, not 139.92878 L.",
"C": "Correct. The worked calculation gives 186.57171 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_002805 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, -5, 2) and v=(6, 7, -7), calculate u·v. | {
"A": "-44",
"B": "-43",
"C": "-42",
"D": "-86"
} | B | -43 | The dot product is the sum of corresponding component products: (1)(6)+(-5)(7)+(2)(-7)=-43. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -43, not -44.",
"B": "Correct. The worked calculation gives -43.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -43, not -42.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001507 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (-2x² +8x -5) dx. | {
"A": "-8.33333",
"B": "-16.66667",
"C": "-10.33333",
"D": "-5.33333"
} | A | -8.33333 | An antiderivative is (-2/3)x³+(8/2)x²+(-5)x. Evaluating between 0 and 5 gives (-2/3)(5)³+(8/2)(5)²+(-5)(5)=-8.33333. | {
"A": "Correct. The worked calculation gives -8.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -8.33333, not -16.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -8.33333, not -10.33333.",
"D": "Incorrect. Substituting the st... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002649 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, 0], [1, -6]]. | {
"A": "-4.4",
"B": "-64.8",
"C": "-54",
"D": "54"
} | C | -54 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(-6)−(0)(1)=-54. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -54, not -4.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -54, not -64.8.",
"C": "Correct. The worked calculation gives -54.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_009059 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.79 V, transfers 1 electrons, and has reaction quotient Q=10^2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.6718 V",
"B": "0.6718 V",
"C": "1.6718 V",
"D": "0.3359 V"
} | B | 0.6718 V | Apply the Nernst equation: E=0.79−(0.0591/1)(2)=0.6718 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6718 V, not 2.6718 V.",
"B": "Correct. The worked calculation gives 0.6718 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.6718 V, not 1.6718 V.",
"D": "Incorrect. Substituting the stat... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002933 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(3, -2, 0) and v=(7, 7, 8), calculate u·v. | {
"A": "8",
"B": "4",
"C": "7",
"D": "-7"
} | C | 7 | The dot product is the sum of corresponding component products: (3)(7)+(-2)(7)+(0)(8)=7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 4.",
"C": "Correct. The worked calculation gives 7.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_006166 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 37 cm in front of a thin convex lens of focal length 9 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.32143",
"B": "-1.67857",
"C": "2.32143",
"D": "1.32143"
} | A | 0.32143 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(37)(9)/(37−9)=11.89286 cm. Thus |m|=v/u=11.89286/37=0.32143. | {
"A": "Correct. The worked calculation gives 0.32143.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32143, not -1.67857.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32143, not 2.32143.",
"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_001436 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (3x² +0x +2) dx. | {
"A": "357",
"B": "714",
"C": "428.4",
"D": "355"
} | A | 357 | An antiderivative is (3/3)x³+(0/2)x²+(2)x. Evaluating between 0 and 7 gives (3/3)(7)³+(0/2)(7)²+(2)(7)=357. | {
"A": "Correct. The worked calculation gives 357.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 357, not 714.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 357, not 428.4.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003071 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-13+14i)/(2+6i). What is Re(z), the real part of z? | {
"A": "0.45",
"B": "1.45",
"C": "-1.45",
"D": "3.45"
} | B | 1.45 | Multiply numerator and denominator by the conjugate (2-6i). Then Re(z)=(ac+bd)/(c²+d²)=((-13)(2)+(14)(6))/(2²+(6)²)=1.45. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.45, not 0.45.",
"B": "Correct. The worked calculation gives 1.45.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.45, not -1.45.",
"D": "Incorrect. Substituting the stated values into the ... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000838 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio -3. What is the sum of its first 11 terms? | {
"A": "221434",
"B": "221435",
"C": "332152.5",
"D": "110717.5"
} | B | 221435 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(-3^11−1)/(-3−1)=221435. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 221435, not 221434.",
"B": "Correct. The worked calculation gives 221435.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 221435, not 332152.5.",
"D": "Incorrect. Substituting the stated value... | [
"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_008579 | 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 1.91 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "5.82 K",
"B": "3.82 K",
"C": "2.82 K",
"D": "4.82 K"
} | B | 3.82 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×1.91=3.82 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.82 K, not 5.82 K.",
"B": "Correct. The worked calculation gives 3.82 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.82 K, not 2.82 K.",
"D": "Incorrect. Substituting the stated values ... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007061 | 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 199 K and 1.56 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "15.70129 L",
"B": "5.23376 L",
"C": "13.46753 L",
"D": "10.46753 L"
} | D | 10.46753 L | PV=nRT, so V=nRT/P=(1)(0.082057)(199)/(1.56)=10.46753 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.46753 L, not 15.70129 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.46753 L, not 5.23376 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10.4675... | [
"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_006836 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 33 mol H₂ and 12 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "24 mol",
"B": "28.8 mol",
"C": "12 mol",
"D": "26 mol"
} | A | 24 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 33 mol H₂O; O₂ can produce 24 mol H₂O. The limiting condition is O₂; product=24 mol. | {
"A": "Correct. The worked calculation gives 24 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24 mol, not 28.8 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24 mol, not 12 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_008273 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 14 A for 28748 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": "198.62932 g",
"B": "132.41954 g",
"C": "131.41954 g",
"D": "66.20977 g"
} | B | 132.41954 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×28748/(2×96500)=132.41954 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 132.41954 g, not 198.62932 g.",
"B": "Correct. The worked calculation gives 132.41954 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 132.41954 g, not 131.41954 g.",
"D": "Incorrect. Substi... | [
"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_005163 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +9 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "3.67769 N",
"B": "-26.77686 N",
"C": "26.77686 N",
"D": "32.13223 N"
} | C | 26.77686 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(9×10⁻⁶)/(11×10⁻²)²=26.77686 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26.77686 N, not 3.67769 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26.77686 N, not -26.77686 N.",
"C": "Correct. The worked calculation gives 26.77686 N.",
"D": "Incorrect. Substitutin... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007430 | 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 71 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "6.33322",
"B": "11.66644",
"C": "13.66644",
"D": "12.66644"
} | D | 12.66644 | Excess OH⁻ moles=0.10×(71−26)/1000=0.004500 mol. Total volume=0.097 L, so [OH⁻]=0.046392 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.66644. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.66644, not 6.33322.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.66644, not 11.66644.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.66644, not 1... | [
"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_000358 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -2 and common difference 13. Find the sum of its first 9 terms. | {
"A": "450",
"B": "675",
"C": "448",
"D": "360"
} | A | 450 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-2, d=13, n=9: Sₙ=9/2[2(-2)+(9−1)(13)]=450. | {
"A": "Correct. The worked calculation gives 450.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 450, not 675.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 450, not 448.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004531 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 12 kg and radius 3 m is acted on by a constant torque of 78 N m about its central axis. Find its angular acceleration. | {
"A": "-0.55556 rad s⁻²",
"B": "1.44444 rad s⁻²",
"C": "2.88889 rad s⁻²",
"D": "1.08333 rad s⁻²"
} | B | 1.44444 rad s⁻² | For a solid disc, I=½MR²=½(12)(3)²=54 kg m². Using τ=Iα, α=78/54=1.44444 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.44444 rad s⁻², not -0.55556 rad s⁻².",
"B": "Correct. The worked calculation gives 1.44444 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.44444 rad s⁻², not 2.88889 rad s⁻².",
"D... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005779 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.5 atm at 404 K. What is its pressure at 716 K? | {
"A": "2.43069 atm",
"B": "7.43069 atm",
"C": "4.43069 atm",
"D": "6.64604 atm"
} | C | 4.43069 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.5)(716)/(404)=4.43069 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.43069 atm, not 2.43069 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.43069 atm, not 7.43069 atm.",
"C": "Correct. The worked calculation gives 4.43069 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_001487 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (6x² +0x +7) dx. | {
"A": "75",
"B": "77",
"C": "56.25",
"D": "74"
} | A | 75 | An antiderivative is (6/3)x³+(0/2)x²+(7)x. Evaluating between 0 and 3 gives (6/3)(3)³+(0/2)(3)²+(7)(3)=75. | {
"A": "Correct. The worked calculation gives 75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 75, not 77.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 75, not 56.25.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_003573 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 109 m s⁻¹ at 18° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "349.17383 m",
"B": "558.67813 m",
"C": "696.34766 m",
"D": "698.34766 m"
} | D | 698.34766 m | Range R=u²sin(2θ)/g. Substituting u=109, θ=18° and g=10 gives R=(109)²sin(36°)/10=698.34766 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 698.34766 m, not 349.17383 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 698.34766 m, not 558.67813 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 69... | [
"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_002206 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 8 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.66304",
"B": "0.16848",
"C": "2.33696",
"D": "0.33696"
} | D | 0.33696 | Favourable pairs = C(5,2)+C(8,2)+C(11,2)=93. Total pairs=C(24,2)=276. Therefore P=93/276=0.33696. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33696, not -0.66304.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33696, not 0.16848.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33696, not 2.33... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002788 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-5, 6, -7) and v=(1, 4, 7), calculate u·v. | {
"A": "-15",
"B": "-30",
"C": "-31",
"D": "-29"
} | B | -30 | The dot product is the sum of corresponding component products: (-5)(1)+(6)(4)+(-7)(7)=-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 -31.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004111 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.34. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "49.2 N",
"B": "59.04 N",
"C": "48.2 N",
"D": "73.8 N"
} | A | 49.2 N | Net force=mg(sinθ−μcosθ)=15×10×(0.6−0.34×0.8)=49.2 N. | {
"A": "Correct. The worked calculation gives 49.2 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 49.2 N, not 59.04 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 49.2 N, not 48.2 N.",
"D": "Incorrect. Substituting the stated values... | [
"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_001629 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (1x² +8x +3) dx. | {
"A": "49.33333",
"B": "24.66667",
"C": "26.66667",
"D": "12.33333"
} | B | 24.66667 | An antiderivative is (1/3)x³+(8/2)x²+(3)x. Evaluating between 0 and 2 gives (1/3)(2)³+(8/2)(2)²+(3)(2)=24.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24.66667, not 49.33333.",
"B": "Correct. The worked calculation gives 24.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24.66667, not 26.66667.",
"D": "Incorrect. Substituting the stat... | [
"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_009865 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(CN)_4]^-3, each CN ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "0.75",
"B": "1.1",
"C": "1",
"D": "-1"
} | C | 1 | Let the formal oxidation state of Mn be x. Charge balance gives x+(4)(−1)=-3; hence x=-3+4=+1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.1.",
"C": "Correct. The worked calculation gives 1.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_000558 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 0 and common difference 14. Find the sum of its first 13 terms. | {
"A": "873.6",
"B": "1092",
"C": "1310.4",
"D": "546"
} | B | 1092 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=0, d=14, n=13: Sₙ=13/2[2(0)+(13−1)(14)]=1092. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1092, not 873.6.",
"B": "Correct. The worked calculation gives 1092.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1092, not 1310.4.",
"D": "Incorrect. Substituting the stated values into th... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007374 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 24 mL of 0.10 M HCl is mixed with 33 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "14.19837",
"B": "12.19837",
"C": "24.39674",
"D": "15.19837"
} | B | 12.19837 | Excess OH⁻ moles=0.10×(33−24)/1000=0.000900 mol. Total volume=0.057 L, so [OH⁻]=0.015789 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.19837. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.19837, not 14.19837.",
"B": "Correct. The worked calculation gives 12.19837.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.19837, not 24.39674.",
"D": "Incorrect. Substituting the stat... | [
"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_004096 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.45. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "34 N",
"B": "36 N",
"C": "72 N",
"D": "37 N"
} | B | 36 N | Net force=mg(sinθ−μcosθ)=15×10×(0.6−0.45×0.8)=36 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 36 N, not 34 N.",
"B": "Correct. The worked calculation gives 36 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 36 N, not 72 N.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_009598 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_6H_1N_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "8",
"B": "5",
"C": "-8",
"D": "6"
} | A | 8 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+3−1−0)/2=8. | {
"A": "Correct. The worked calculation gives 8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not -8.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_007294 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 12 mol of gas at 195 K and 0.8 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "238.01673 L",
"B": "241.01673 L",
"C": "240.01673 L",
"D": "239.01673 L"
} | C | 240.01673 L | PV=nRT, so V=nRT/P=(12)(0.082057)(195)/(0.8)=240.01673 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 240.01673 L, not 238.01673 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 240.01673 L, not 241.01673 L.",
"C": "Correct. The worked calculation gives 240.01673 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_000731 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 3 and common ratio 2. What is the sum of its first 7 terms? | {
"A": "382",
"B": "571.5",
"C": "381",
"D": "380"
} | C | 381 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=3(2^7−1)/(2−1)=381. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 381, not 382.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 381, not 571.5.",
"C": "Correct. The worked calculation gives 381.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003259 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-6+0i)/(3+3i). What is Re(z), the real part of z? | {
"A": "2",
"B": "-3",
"C": "-1",
"D": "-2"
} | C | -1 | Multiply numerator and denominator by the conjugate (3-3i). Then Re(z)=(ac+bd)/(c²+d²)=((-6)(3)+(0)(3))/(3²+(3)²)=-1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1, not -3.",
"C": "Correct. The worked calculation gives -1.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_002580 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -7], [8, 5]]. | {
"A": "121.5",
"B": "81",
"C": "79",
"D": "-81"
} | B | 81 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(5)−(-7)(8)=81. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 81, not 121.5.",
"B": "Correct. The worked calculation gives 81.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 81, not 79.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_006276 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 120 cm in front of a thin convex lens of focal length 28 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.30435",
"B": "-2.69565",
"C": "1.30435",
"D": "0.30435"
} | D | 0.30435 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(120)(28)/(120−28)=36.52174 cm. Thus |m|=v/u=36.52174/120=0.30435. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30435, not -0.30435.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30435, not -2.69565.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30435, not 1.3... | [
"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_009152 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.65 V, transfers 3 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-2.2515 V",
"B": "0.7485 V",
"C": "-1.2515 V",
"D": "3.7485 V"
} | B | 0.7485 V | Apply the Nernst equation: E=0.65−(0.0591/3)(-5)=0.7485 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7485 V, not -2.2515 V.",
"B": "Correct. The worked calculation gives 0.7485 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7485 V, not -1.2515 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_006670 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 16 kg is attached to an ideal spring of force constant 930 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.52466 s",
"B": "0.26233 s",
"C": "-1.73767 s",
"D": "1.26233 s"
} | B | 0.26233 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(16/930)=0.26233 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.26233 s, not 0.52466 s.",
"B": "Correct. The worked calculation gives 0.26233 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.26233 s, not -1.73767 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009290 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.17 V, transfers 2 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "4.02225 V",
"B": "0.76669 V",
"C": "1.02225 V",
"D": "0.02225 V"
} | C | 1.02225 V | Apply the Nernst equation: E=1.17−(0.0591/2)(5)=1.02225 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.02225 V, not 4.02225 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.02225 V, not 0.76669 V.",
"C": "Correct. The worked calculation gives 1.02225 V.",
"D": "Incorrect. Substituting the... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006212 | 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 18 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.4",
"B": "0.2",
"C": "-2.6",
"D": "-0.6"
} | A | 0.4 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(63)(18)/(63−18)=25.2 cm. Thus |m|=v/u=25.2/63=0.4. | {
"A": "Correct. The worked calculation gives 0.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.4, not 0.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.4, not -2.6.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_008373 | 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 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.18 K",
"B": "-0.2 K",
"C": "1.8 K",
"D": "1.35 K"
} | C | 1.8 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.6×1=1.8 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.8 K, not 1.18 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.8 K, not -0.2 K.",
"C": "Correct. The worked calculation gives 1.8 K.",
"D": "Incorrect. Substituting the stated values int... | [
"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_001188 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=1x³ +9x² -12x+7. Evaluate f′(-4). | {
"A": "-72",
"B": "-36",
"C": "36",
"D": "-27"
} | B | -36 | Differentiate: f′(x)=3(1)x²+2(9)x+(-12). At x=-4, f′(-4)=3(1)(-4)²+2(9)(-4)+(-12)=-36. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -36, not -72.",
"B": "Correct. The worked calculation gives -36.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -36, not 36.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_003734 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 3 m s⁻¹. A constant net force does 7 N of work over 14 m in the direction of motion. Find its final kinetic energy. | {
"A": "147.5 J",
"B": "221.25 J",
"C": "110.625 J",
"D": "146.5 J"
} | A | 147.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(3)²+(7)(14)=147.5 J. | {
"A": "Correct. The worked calculation gives 147.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 147.5 J, not 221.25 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 147.5 J, not 110.625 J.",
"D": "Incorrect. Substituting the stated... | [
"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_009903 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(Cl)_5]^-3, each Cl ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "2",
"B": "3",
"C": "1",
"D": "1.5"
} | A | 2 | Let the formal oxidation state of Cu be x. Charge balance gives x+(5)(−1)=-3; hence x=-3+5=+2. | {
"A": "Correct. The worked calculation gives 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006828 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 31 mol H₂ and 10 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "40 mol",
"B": "15 mol",
"C": "20 mol",
"D": "-20 mol"
} | C | 20 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 31 mol H₂O; O₂ can produce 20 mol H₂O. The limiting condition is O₂; product=20 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20 mol, not 40 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20 mol, not 15 mol.",
"C": "Correct. The worked calculation gives 20 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_001424 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (1x² +8x -2) dx. | {
"A": "-77.33333",
"B": "78.33333",
"C": "38.66667",
"D": "77.33333"
} | D | 77.33333 | An antiderivative is (1/3)x³+(8/2)x²+(-2)x. Evaluating between 0 and 4 gives (1/3)(4)³+(8/2)(4)²+(-2)(4)=77.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 77.33333, not -77.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 77.33333, not 78.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 77.33333, 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_007190 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 11 mol of gas at 510 K and 2.26 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "244.4282 L",
"B": "-203.69016 L",
"C": "205.69016 L",
"D": "203.69016 L"
} | D | 203.69016 L | PV=nRT, so V=nRT/P=(11)(0.082057)(510)/(2.26)=203.69016 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 203.69016 L, not 244.4282 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 203.69016 L, not -203.69016 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20... | [
"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_005916 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.1 atm at 397 K. What is its pressure at 649 K? | {
"A": "5.1495 atm",
"B": "3.433 atm",
"C": "4.433 atm",
"D": "1.433 atm"
} | B | 3.433 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.1)(649)/(397)=3.433 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.433 atm, not 5.1495 atm.",
"B": "Correct. The worked calculation gives 3.433 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.433 atm, not 4.433 atm.",
"D": "Incorrect. Substituting th... | [
"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_005694 | 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 1.4 atm at 222 K. What is its pressure at 764 K? | {
"A": "4.81802 atm",
"B": "1.4818 atm",
"C": "9.63604 atm",
"D": "5.81802 atm"
} | A | 4.81802 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.4)(764)/(222)=4.81802 atm. | {
"A": "Correct. The worked calculation gives 4.81802 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.81802 atm, not 1.4818 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.81802 atm, not 9.63604 atm.",
"D": "Incorrect. Substit... | [
"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_002237 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 4 blue and 8 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.35238",
"B": "1.35238",
"C": "-2.64762",
"D": "0.52857"
} | A | 0.35238 | Favourable pairs = C(3,2)+C(4,2)+C(8,2)=37. Total pairs=C(15,2)=105. Therefore P=37/105=0.35238. | {
"A": "Correct. The worked calculation gives 0.35238.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35238, not 1.35238.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35238, not -2.64762.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000586 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -7 and common difference 3. Find the sum of its first 28 terms. | {
"A": "937",
"B": "939",
"C": "-938",
"D": "938"
} | D | 938 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-7, d=3, n=28: Sₙ=28/2[2(-7)+(28−1)(3)]=938. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 938, not 937.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 938, not 939.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 938, not -938.",
"D": "Correct. ... | [
"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_003517 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 111 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "868.34646 m",
"B": "1155.79528 m",
"C": "1157.79528 m",
"D": "-1157.79528 m"
} | C | 1157.79528 m | Range R=u²sin(2θ)/g. Substituting u=111, θ=55° and g=10 gives R=(111)²sin(110°)/10=1157.79528 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1157.79528 m, not 868.34646 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1157.79528 m, not 1155.79528 m.",
"C": "Correct. The worked calculation gives 1157.79528 m.",
"D": "Incorrect. Su... | [
"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_006407 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 14 kg is attached to an ideal spring of force constant 687 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.57101 s",
"B": "-1.71449 s",
"C": "1.28551 s",
"D": "0.28551 s"
} | D | 0.28551 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(14/687)=0.28551 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.28551 s, not 0.57101 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.28551 s, not -1.71449 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.28551 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002931 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(6, -3, 4) and v=(-4, 7, 2), calculate u·v. | {
"A": "-27.75",
"B": "-35",
"C": "-36",
"D": "-37"
} | D | -37 | The dot product is the sum of corresponding component products: (6)(-4)+(-3)(7)+(4)(2)=-37. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -37, not -27.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -37, not -35.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -37, not -36.",
"D": "Correct... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009030 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.65 V, transfers 1 electrons, and has reaction quotient Q=10^3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.35452 V",
"B": "1.04727 V",
"C": "2.4727 V",
"D": "0.4727 V"
} | D | 0.4727 V | Apply the Nernst equation: E=0.65−(0.0591/1)(3)=0.4727 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.4727 V, not 0.35452 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.4727 V, not 1.04727 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.4727 V, no... | [
"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_009782 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(CN)_4]^-2, each CN ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "-2",
"B": "3",
"C": "2",
"D": "1.2"
} | C | 2 | Let the formal oxidation state of Cr be x. Charge balance gives x+(4)(−1)=-2; hence x=-2+4=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"C": "Correct. The worked calculation gives 2.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009169 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.36 V, transfers 1 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.7146 V",
"B": "-1.2854 V",
"C": "0.7146 V",
"D": "0.8573 V"
} | A | 1.7146 V | Apply the Nernst equation: E=1.36−(0.0591/1)(-6)=1.7146 V. | {
"A": "Correct. The worked calculation gives 1.7146 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.7146 V, not -1.2854 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.7146 V, not 0.7146 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001624 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (3x² +1x +7) dx. | {
"A": "129.375",
"B": "345",
"C": "207",
"D": "172.5"
} | D | 172.5 | An antiderivative is (3/3)x³+(1/2)x²+(7)x. Evaluating between 0 and 5 gives (3/3)(5)³+(1/2)(5)²+(7)(5)=172.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 172.5, not 129.375.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 172.5, not 345.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 172.5, not 207.",
"D": "... | [
"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_006236 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 41 cm in front of a thin convex lens of focal length 20 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "3.95238",
"B": "0.95238",
"C": "0.71429",
"D": "-1.04762"
} | B | 0.95238 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(41)(20)/(41−20)=39.04762 cm. Thus |m|=v/u=39.04762/41=0.95238. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.95238, not 3.95238.",
"B": "Correct. The worked calculation gives 0.95238.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.95238, not 0.71429.",
"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_001309 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ -5x² +6x+7. Evaluate f′(1). | {
"A": "16",
"B": "6",
"C": "8",
"D": "5"
} | C | 8 | Differentiate: f′(x)=3(4)x²+2(-5)x+(6). At x=1, f′(1)=3(4)(1)²+2(-5)(1)+(6)=8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 16.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 6.",
"C": "Correct. The worked calculation gives 8.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_004566 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 5 m is acted on by a constant torque of 66 N m about its central axis. Find its angular acceleration. | {
"A": "0.33 rad s⁻²",
"B": "0.66 rad s⁻²",
"C": "1.66 rad s⁻²",
"D": "0.495 rad s⁻²"
} | B | 0.66 rad s⁻² | For a solid disc, I=½MR²=½(8)(5)²=100 kg m². Using τ=Iα, α=66/100=0.66 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.66 rad s⁻², not 0.33 rad s⁻².",
"B": "Correct. The worked calculation gives 0.66 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.66 rad s⁻², not 1.66 rad s⁻².",
"D": "Incorrect. S... | [
"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_001585 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (-3x² -6x -1) dx. | {
"A": "-59",
"B": "-42.75",
"C": "-68.4",
"D": "-57"
} | D | -57 | An antiderivative is (-3/3)x³+(-6/2)x²+(-1)x. Evaluating between 0 and 3 gives (-3/3)(3)³+(-6/2)(3)²+(-1)(3)=-57. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -57, not -59.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -57, not -42.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -57, not -68.4.",
"D": "Corre... | [
"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_007032 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 2 mol of gas at 609 K and 1.78 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "56.14912 L",
"B": "58.14912 L",
"C": "44.91929 L",
"D": "42.11184 L"
} | A | 56.14912 L | PV=nRT, so V=nRT/P=(2)(0.082057)(609)/(1.78)=56.14912 L. | {
"A": "Correct. The worked calculation gives 56.14912 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 56.14912 L, not 58.14912 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 56.14912 L, not 44.91929 L.",
"D": "Incorrect. Substitutin... | [
"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 |
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