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_000103 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 -2x +4=0, let its roots be α and β. What is α²+β²? | {
"A": "-3",
"B": "-4",
"C": "-1",
"D": "0.6"
} | B | -4 | By Vieta's relations, α+β = 2/1 and αβ = 4/1. Then α²+β²=(α+β)²−2αβ = (2/1)²−2(4/1) = -4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4, not -3.",
"B": "Correct. The worked calculation gives -4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -4, not -1.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_003487 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 34 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "89.55474 m",
"B": "132.83211 m",
"C": "88.55474 m",
"D": "-88.55474 m"
} | C | 88.55474 m | Range R=u²sin(2θ)/g. Substituting u=34, θ=25° and g=10 gives R=(34)²sin(50°)/10=88.55474 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 88.55474 m, not 89.55474 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 88.55474 m, not 132.83211 m.",
"C": "Correct. The worked calculation gives 88.55474 m.",
"D": "Incorrect. Substituti... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004124 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 37 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.17. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "128.76 N",
"B": "171.68 N",
"C": "206.016 N",
"D": "257.52 N"
} | B | 171.68 N | Net force=mg(sinθ−μcosθ)=37×10×(0.6−0.17×0.8)=171.68 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 171.68 N, not 128.76 N.",
"B": "Correct. The worked calculation gives 171.68 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 171.68 N, not 206.016 N.",
"D": "Incorrect. Substituting the sta... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003266 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(2-14i)/(10+2i). What is Re(z), the real part of z? | {
"A": "-0.07692",
"B": "0.92308",
"C": "-0.03846",
"D": "-3.07692"
} | A | -0.07692 | Multiply numerator and denominator by the conjugate (10-2i). Then Re(z)=(ac+bd)/(c²+d²)=((2)(10)+(-14)(2))/(10²+(2)²)=-0.07692. | {
"A": "Correct. The worked calculation gives -0.07692.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.07692, not 0.92308.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.07692, not -0.03846.",
"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_003731 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block initially moves at 6 m s⁻¹. A constant net force does 21 N of work over 18 m in the direction of motion. Find its final kinetic energy. | {
"A": "485 J",
"B": "486 J",
"C": "-486 J",
"D": "49.6 J"
} | B | 486 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(6)(6)²+(21)(18)=486 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 486 J, not 485 J.",
"B": "Correct. The worked calculation gives 486 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 486 J, not -486 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_000201 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 -15x +6=0, let its roots be α and β. What is α²+β²? | {
"A": "8.6",
"B": "4.6",
"C": "6.6",
"D": "3.6"
} | C | 6.6 | By Vieta's relations, α+β = 15/5 and αβ = 6/5. Then α²+β²=(α+β)²−2αβ = (15/5)²−2(6/5) = 6.6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.6, not 8.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.6, not 4.6.",
"C": "Correct. The worked calculation gives 6.6.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_006631 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 20 kg is attached to an ideal spring of force constant 467 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.58611 s",
"B": "3.41389 s",
"C": "1.04139 s",
"D": "0.41389 s"
} | D | 0.41389 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(20/467)=0.41389 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.41389 s, not -1.58611 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.41389 s, not 3.41389 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.41389 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_002090 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 10 blue and 10 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "2.33333",
"B": "0.33333",
"C": "-0.66667",
"D": "1.03333"
} | B | 0.33333 | Favourable pairs = C(5,2)+C(10,2)+C(10,2)=100. Total pairs=C(25,2)=300. Therefore P=100/300=0.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not 2.33333.",
"B": "Correct. The worked calculation gives 0.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not -0.66667.",
"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_007623 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 77 mL of 0.10 M HCl is mixed with 70 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.16111",
"B": "2.32222",
"C": "1.74166",
"D": "-0.67778"
} | B | 2.32222 | Excess H⁺ moles=0.10×(77−70)/1000=0.000700 mol. Total volume=0.147 L, so [H⁺]=0.004762 M and pH=−log₁₀[H⁺]=2.32222. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.32222, not 1.16111.",
"B": "Correct. The worked calculation gives 2.32222.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.32222, not 1.74166.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006856 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 18 mol H₂ and 26 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "17 mol",
"B": "13.5 mol",
"C": "27 mol",
"D": "18 mol"
} | D | 18 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 18 mol H₂O; O₂ can produce 52 mol H₂O. The limiting condition is H₂; product=18 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18 mol, not 17 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18 mol, not 13.5 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18 mol, not 27 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_001314 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=7x³ +9x² -5x+7. Evaluate f′(3). | {
"A": "-238",
"B": "357",
"C": "285.6",
"D": "238"
} | D | 238 | Differentiate: f′(x)=3(7)x²+2(9)x+(-5). At x=3, f′(3)=3(7)(3)²+2(9)(3)+(-5)=238. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 238, not -238.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 238, not 357.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 238, not 285.6.",
"D": "Correct... | [
"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_003088 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(6+7i)/(12+11i). What is Re(z), the real part of z? | {
"A": "1.12453",
"B": "0.56226",
"C": "1.56226",
"D": "-1.43774"
} | B | 0.56226 | Multiply numerator and denominator by the conjugate (12-11i). Then Re(z)=(ac+bd)/(c²+d²)=((6)(12)+(7)(11))/(12²+(11)²)=0.56226. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.56226, not 1.12453.",
"B": "Correct. The worked calculation gives 0.56226.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.56226, not 1.56226.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005613 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 78 μF capacitor is charged to a potential difference of 10 V. Calculate the energy stored, expressed in μJ. | {
"A": "3900 μJ",
"B": "3120 μJ",
"C": "3899 μJ",
"D": "1950 μJ"
} | A | 3900 μJ | U=½CV². Since C=78 μF, U in μJ is ½×78×(10)²=3900 μJ. | {
"A": "Correct. The worked calculation gives 3900 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3900 μJ, not 3120 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3900 μJ, not 3899 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006142 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 102 cm in front of a thin convex lens of focal length 24 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.46154",
"B": "-2.69231",
"C": "3.30769",
"D": "0.30769"
} | D | 0.30769 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(102)(24)/(102−24)=31.38462 cm. Thus |m|=v/u=31.38462/102=0.30769. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not 0.46154.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not -2.69231.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not 3.30... | [
"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_005707 | 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 396 K. What is its pressure at 543 K? | {
"A": "5.14205 atm",
"B": "3.42803 atm",
"C": "0.42803 atm",
"D": "6.42803 atm"
} | B | 3.42803 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.5)(543)/(396)=3.42803 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.42803 atm, not 5.14205 atm.",
"B": "Correct. The worked calculation gives 3.42803 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.42803 atm, not 0.42803 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_005977 | 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 1.8 atm at 188 K. What is its pressure at 326 K? | {
"A": "1.31213 atm",
"B": "2.34096 atm",
"C": "1.12128 atm",
"D": "3.12128 atm"
} | D | 3.12128 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.8)(326)/(188)=3.12128 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.12128 atm, not 1.31213 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.12128 atm, not 2.34096 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.... | [
"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_006096 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 36 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": "0.25",
"B": "0.9375",
"C": "2.5",
"D": "1.25"
} | D | 1.25 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(36)(20)/(36−20)=45 cm. Thus |m|=v/u=45/36=1.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.25, not 0.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.25, not 0.9375.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.25, not 2.5.",
"D": "Cor... | [
"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_003344 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 96 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "691.2 m",
"B": "460.8 m",
"C": "93.16 m",
"D": "921.6 m"
} | D | 921.6 m | Range R=u²sin(2θ)/g. Substituting u=96, θ=45° and g=10 gives R=(96)²sin(90°)/10=921.6 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 921.6 m, not 691.2 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 921.6 m, not 460.8 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 921.6 m, not 93.16... | [
"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_006762 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 36 mol H₂ and 18 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "34 mol",
"B": "54 mol",
"C": "36 mol",
"D": "37 mol"
} | C | 36 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 36 mol H₂O; O₂ can produce 36 mol H₂O. The limiting condition is neither; stoichiometric; product=36 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 36 mol, not 34 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 36 mol, not 54 mol.",
"C": "Correct. The worked calculation gives 36 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_008023 | 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 3 A for 14605 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": "28.83163 g",
"B": "7.20791 g",
"C": "14.41582 g",
"D": "10.81186 g"
} | C | 14.41582 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×3×14605/(2×96500)=14.41582 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14.41582 g, not 28.83163 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14.41582 g, not 7.20791 g.",
"C": "Correct. The worked calculation gives 14.41582 g.",
"D": "Incorrect. Substituting... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008651 | 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 0.73 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.7592 K",
"B": "-1.2408 K",
"C": "-0.7592 K",
"D": "-2.2408 K"
} | A | 0.7592 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×0.73=0.7592 K. | {
"A": "Correct. The worked calculation gives 0.7592 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7592 K, not -1.2408 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7592 K, not -0.7592 K.",
"D": "Incorrect. Substituting the st... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006270 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 50 cm in front of a thin convex lens of focal length 16 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.47059",
"B": "-0.47059",
"C": "1.47059",
"D": "-0.52941"
} | A | 0.47059 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(50)(16)/(50−16)=23.52941 cm. Thus |m|=v/u=23.52941/50=0.47059. | {
"A": "Correct. The worked calculation gives 0.47059.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.47059, not -0.47059.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.47059, not 1.47059.",
"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_008010 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 10 A for 18852 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": "62.02601 g",
"B": "63.02601 g",
"C": "31.01301 g",
"D": "7.2026 g"
} | A | 62.02601 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×10×18852/(2×96500)=62.02601 g. | {
"A": "Correct. The worked calculation gives 62.02601 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 62.02601 g, not 63.02601 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 62.02601 g, not 31.01301 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004379 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 12 kg and radius 1 m is acted on by a constant torque of 37 N m about its central axis. Find its angular acceleration. | {
"A": "3.16667 rad s⁻²",
"B": "5.16667 rad s⁻²",
"C": "6.16667 rad s⁻²",
"D": "12.33333 rad s⁻²"
} | C | 6.16667 rad s⁻² | For a solid disc, I=½MR²=½(12)(1)²=6 kg m². Using τ=Iα, α=37/6=6.16667 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.16667 rad s⁻², not 3.16667 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.16667 rad s⁻², not 5.16667 rad s⁻².",
"C": "Correct. The worked calculation gives 6.16667 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_007010 | 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 382 K and 0.57 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "604.91845 L",
"B": "605.91845 L",
"C": "606.91845 L",
"D": "453.68883 L"
} | A | 604.91845 L | PV=nRT, so V=nRT/P=(11)(0.082057)(382)/(0.57)=604.91845 L. | {
"A": "Correct. The worked calculation gives 604.91845 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 604.91845 L, not 605.91845 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 604.91845 L, not 606.91845 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_001793 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 38 distinct elements? | {
"A": "236366878",
"B": "472733758",
"C": "472733756",
"D": "-472733756"
} | C | 472733756 | Order does not matter, so the count is C(38,10)=38!/[10!(28)!]=472733756. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 472733756, not 236366878.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 472733756, not 472733758.",
"C": "Correct. The worked calculation gives 472733756.",
"D": "Incorrect. Substituting the... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005330 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +3 μC are separated by 5 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "8.56 N",
"B": "73.6 N",
"C": "74.6 N",
"D": "75.6 N"
} | D | 75.6 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(3×10⁻⁶)/(5×10⁻²)²=75.6 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 75.6 N, not 8.56 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 75.6 N, not 73.6 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 75.6 N, not 74.6 N.",
... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002506 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, 4], [6, 1]]. | {
"A": "-20",
"B": "-0.9",
"C": "-21",
"D": "-19"
} | D | -19 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(1)−(4)(6)=-19. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -19, not -20.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -19, not -0.9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -19, not -21.",
"D": "Correct. ... | [
"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_002853 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(0, 2, 7) and v=(6, -2, 9), calculate u·v. | {
"A": "57",
"B": "88.5",
"C": "59",
"D": "-59"
} | C | 59 | The dot product is the sum of corresponding component products: (0)(6)+(2)(-2)+(7)(9)=59. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 59, not 57.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 59, not 88.5.",
"C": "Correct. The worked calculation gives 59.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000466 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 20 and common difference 8. Find the sum of its first 13 terms. | {
"A": "884",
"B": "1060.8",
"C": "883",
"D": "885"
} | A | 884 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=20, d=8, n=13: Sₙ=13/2[2(20)+(13−1)(8)]=884. | {
"A": "Correct. The worked calculation gives 884.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 884, not 1060.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 884, not 883.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001909 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 6 elements can be selected from a set of 24 distinct elements? | {
"A": "161515.2",
"B": "134596",
"C": "134597",
"D": "-134596"
} | B | 134596 | Order does not matter, so the count is C(24,6)=24!/[6!(18)!]=134596. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 134596, not 161515.2.",
"B": "Correct. The worked calculation gives 134596.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 134596, not 134597.",
"D": "Incorrect. Substituting the stated value... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002371 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 6], [3, 0]]. | {
"A": "-18",
"B": "-14.4",
"C": "-19",
"D": "18"
} | A | -18 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(0)−(6)(3)=-18. | {
"A": "Correct. The worked calculation gives -18.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -18, not -14.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -18, not -19.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002541 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 3], [1, 7]]. | {
"A": "20",
"B": "16",
"C": "17",
"D": "18"
} | D | 18 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(7)−(3)(1)=18. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18, not 20.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18, not 16.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18, not 17.",
"D": "Correct. The wor... | [
"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_004542 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 10 kg and radius 5 m is acted on by a constant torque of 23 N m about its central axis. Find its angular acceleration. | {
"A": "0.184 rad s⁻²",
"B": "3.184 rad s⁻²",
"C": "-0.816 rad s⁻²",
"D": "-2.816 rad s⁻²"
} | A | 0.184 rad s⁻² | For a solid disc, I=½MR²=½(10)(5)²=125 kg m². Using τ=Iα, α=23/125=0.184 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.184 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.184 rad s⁻², not 3.184 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.184 rad s⁻², not -0.816 rad s⁻².",
"D": "Incorr... | [
"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_007546 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 21 mL of 0.10 M HCl is mixed with 80 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "15.76653",
"B": "14.76653",
"C": "9.5749",
"D": "12.76653"
} | D | 12.76653 | Excess OH⁻ moles=0.10×(80−21)/1000=0.005900 mol. Total volume=0.101 L, so [OH⁻]=0.058416 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.76653. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.76653, not 15.76653.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.76653, not 14.76653.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.76653, not ... | [
"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_007432 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 51 mL of 0.10 M HCl is mixed with 15 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.26324",
"B": "2.52648",
"C": "0.63162",
"D": "4.26324"
} | A | 1.26324 | Excess H⁺ moles=0.10×(51−15)/1000=0.003600 mol. Total volume=0.066 L, so [H⁺]=0.054545 M and pH=−log₁₀[H⁺]=1.26324. | {
"A": "Correct. The worked calculation gives 1.26324.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.26324, not 2.52648.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.26324, not 0.63162.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005681 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.8 atm at 332 K. What is its pressure at 470 K? | {
"A": "4.79518 atm",
"B": "6.79518 atm",
"C": "3.79518 atm",
"D": "8.79518 atm"
} | B | 6.79518 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.8)(470)/(332)=6.79518 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.79518 atm, not 4.79518 atm.",
"B": "Correct. The worked calculation gives 6.79518 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.79518 atm, not 3.79518 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_009028 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.98 V, transfers 3 electrons, and has reaction quotient Q=10^-4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.0588 V",
"B": "1.10588 V",
"C": "1.5882 V",
"D": "2.0588 V"
} | A | 1.0588 V | Apply the Nernst equation: E=0.98−(0.0591/3)(-4)=1.0588 V. | {
"A": "Correct. The worked calculation gives 1.0588 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0588 V, not 1.10588 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0588 V, not 1.5882 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_004318 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 27 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.41. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "73.44 N",
"B": "-73.44 N",
"C": "72.44 N",
"D": "55.08 N"
} | A | 73.44 N | Net force=mg(sinθ−μcosθ)=27×10×(0.6−0.41×0.8)=73.44 N. | {
"A": "Correct. The worked calculation gives 73.44 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 73.44 N, not -73.44 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 73.44 N, not 72.44 N.",
"D": "Incorrect. Substituting the stated v... | [
"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_009173 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.82 V, transfers 2 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.52635 V",
"B": "-0.7018 V",
"C": "0.7018 V",
"D": "1.0527 V"
} | C | 0.7018 V | Apply the Nernst equation: E=0.82−(0.0591/2)(4)=0.7018 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7018 V, not 0.52635 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7018 V, not -0.7018 V.",
"C": "Correct. The worked calculation gives 0.7018 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_002197 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 7 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": "0.30435",
"B": "0.45652",
"C": "3.30435",
"D": "1.03043"
} | A | 0.30435 | Favourable pairs = C(8,2)+C(7,2)+C(8,2)=77. Total pairs=C(23,2)=253. Therefore P=77/253=0.30435. | {
"A": "Correct. The worked calculation gives 0.30435.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30435, not 0.45652.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30435, not 3.30435.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002436 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, 7], [9, 4]]. | {
"A": "-26.25",
"B": "-35",
"C": "-37",
"D": "-17.5"
} | B | -35 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(4)−(7)(9)=-35. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -35, not -26.25.",
"B": "Correct. The worked calculation gives -35.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -35, not -37.",
"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_001775 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 3 elements can be selected from a set of 70 distinct elements? | {
"A": "82110",
"B": "54740",
"C": "41055",
"D": "109480"
} | B | 54740 | Order does not matter, so the count is C(70,3)=70!/[3!(67)!]=54740. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 54740, not 82110.",
"B": "Correct. The worked calculation gives 54740.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 54740, not 41055.",
"D": "Incorrect. Substituting the stated values into ... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007702 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 96 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "3.5 mmol L⁻¹",
"B": "0.5 mmol L⁻¹",
"C": "1.5 mmol L⁻¹",
"D": "2.25 mmol L⁻¹"
} | C | 1.5 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=96/2^6=1.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.5 mmol L⁻¹, not 3.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.5 mmol L⁻¹, not 0.5 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 1.5 mmol L⁻¹.",
"D": "Incorrect. S... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009652 | 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_18H_33N_2X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "2",
"B": "-2",
"C": "1",
"D": "1.2"
} | A | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+2−33−3)/2=2. | {
"A": "Correct. The worked calculation gives 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"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_006141 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 19 cm in front of a thin convex lens of focal length 5 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.35714",
"B": "-2.64286",
"C": "0.17857",
"D": "1.35714"
} | A | 0.35714 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(19)(5)/(19−5)=6.78571 cm. Thus |m|=v/u=6.78571/19=0.35714. | {
"A": "Correct. The worked calculation gives 0.35714.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35714, not -2.64286.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35714, not 0.17857.",
"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_003836 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block initially moves at 7 m s⁻¹. A constant net force does 15 N of work over 12 m in the direction of motion. Find its final kinetic energy. | {
"A": "-547.5 J",
"B": "657 J",
"C": "547.5 J",
"D": "821.25 J"
} | C | 547.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(15)(7)²+(15)(12)=547.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 547.5 J, not -547.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 547.5 J, not 657 J.",
"C": "Correct. The worked calculation gives 547.5 J.",
"D": "Incorrect. Substituting the stated val... | [
"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_006431 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 25 kg is attached to an ideal spring of force constant 219 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.35147 s",
"B": "0.5068 s",
"C": "-2.32426 s",
"D": "0.67574 s"
} | D | 0.67574 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(25/219)=0.67574 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.67574 s, not 1.35147 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.67574 s, not 0.5068 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.67574 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_000123 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 +1x +4=0, let its roots be α and β. What is α²+β²? | {
"A": "0.3",
"B": "-8",
"C": "7",
"D": "-7"
} | D | -7 | By Vieta's relations, α+β = -1/1 and αβ = 4/1. Then α²+β²=(α+β)²−2αβ = (-1/1)²−2(4/1) = -7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -7, not 0.3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -7, not -8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -7, not 7.",
"D": "Correct. The wor... | [
"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_005903 | 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 0.4 atm at 448 K. What is its pressure at 485 K? | {
"A": "-0.56696 atm",
"B": "0.86607 atm",
"C": "1.0433 atm",
"D": "0.43304 atm"
} | D | 0.43304 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.4)(485)/(448)=0.43304 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.43304 atm, not -0.56696 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.43304 atm, not 0.86607 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0... | [
"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_006590 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 25 kg is attached to an ideal spring of force constant 1070 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.03057 s",
"B": "0.30571 s",
"C": "-0.69429 s",
"D": "0.22928 s"
} | B | 0.30571 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(25/1070)=0.30571 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30571 s, not 1.03057 s.",
"B": "Correct. The worked calculation gives 0.30571 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30571 s, not -0.69429 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_005563 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 50 μF capacitor is charged to a potential difference of 16 V. Calculate the energy stored, expressed in μJ. | {
"A": "6400 μJ",
"B": "3200 μJ",
"C": "5120 μJ",
"D": "4800 μJ"
} | A | 6400 μJ | U=½CV². Since C=50 μF, U in μJ is ½×50×(16)²=6400 μJ. | {
"A": "Correct. The worked calculation gives 6400 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6400 μJ, not 3200 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6400 μJ, not 5120 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004194 | 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 0.44. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "44.64 N",
"B": "55.8 N",
"C": "37.2 N",
"D": "4.72 N"
} | C | 37.2 N | Net force=mg(sinθ−μcosθ)=15×10×(0.6−0.44×0.8)=37.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 37.2 N, not 44.64 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 37.2 N, not 55.8 N.",
"C": "Correct. The worked calculation gives 37.2 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_002984 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-6, 7, 8) and v=(4, -6, -5), calculate u·v. | {
"A": "-107",
"B": "-212",
"C": "106",
"D": "-106"
} | D | -106 | The dot product is the sum of corresponding component products: (-6)(4)+(7)(-6)+(8)(-5)=-106. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -106, not -107.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -106, not -212.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -106, not 106.",
"D": "Corre... | [
"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_000833 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio -2. What is the sum of its first 5 terms? | {
"A": "109",
"B": "82.5",
"C": "110",
"D": "-110"
} | C | 110 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(-2^5−1)/(-2−1)=110. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 110, not 109.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 110, not 82.5.",
"C": "Correct. The worked calculation gives 110.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_001596 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (-2x² -3x +4) dx. | {
"A": "-1.33333",
"B": "-3.33333",
"C": "-1.66667",
"D": "-4.33333"
} | B | -3.33333 | An antiderivative is (-2/3)x³+(-3/2)x²+(4)x. Evaluating between 0 and 2 gives (-2/3)(2)³+(-3/2)(2)²+(4)(2)=-3.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -3.33333, not -1.33333.",
"B": "Correct. The worked calculation gives -3.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -3.33333, not -1.66667.",
"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_004253 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 36 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.37. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "-109.44 N",
"B": "111.44 N",
"C": "109.44 N",
"D": "87.552 N"
} | C | 109.44 N | Net force=mg(sinθ−μcosθ)=36×10×(0.6−0.37×0.8)=109.44 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 109.44 N, not -109.44 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 109.44 N, not 111.44 N.",
"C": "Correct. The worked calculation gives 109.44 N.",
"D": "Incorrect. Substituting the sta... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006753 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 45 mol H₂ and 35 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "44 mol",
"B": "45 mol",
"C": "5.5 mol",
"D": "46 mol"
} | B | 45 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 45 mol H₂O; O₂ can produce 70 mol H₂O. The limiting condition is H₂; product=45 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45 mol, not 44 mol.",
"B": "Correct. The worked calculation gives 45 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 45 mol, not 5.5 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_006646 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 1 kg is attached to an ideal spring of force constant 428 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.14501 s",
"B": "0.04834 s",
"C": "0.07251 s",
"D": "0.09667 s"
} | D | 0.09667 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(1/428)=0.09667 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.09667 s, not 0.14501 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.09667 s, not 0.04834 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.09667 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_005764 | 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 376 K. What is its pressure at 673 K? | {
"A": "0.62646 atm",
"B": "2.25293 atm",
"C": "3.25293 atm",
"D": "1.25293 atm"
} | D | 1.25293 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.7)(673)/(376)=1.25293 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.25293 atm, not 0.62646 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.25293 atm, not 2.25293 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006994 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 11 mol H₂ and 25 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "12 mol",
"B": "9 mol",
"C": "10 mol",
"D": "11 mol"
} | D | 11 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 11 mol H₂O; O₂ can produce 50 mol H₂O. The limiting condition is H₂; product=11 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11 mol, not 12 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11 mol, not 9 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11 mol, not 10 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_007807 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 25 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "15.5 mmol L⁻¹",
"B": "12.5 mmol L⁻¹",
"C": "25 mmol L⁻¹",
"D": "9.375 mmol L⁻¹"
} | B | 12.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=25/2^1=12.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.5 mmol L⁻¹, not 15.5 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 12.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.5 mmol L⁻¹, not 25 mmol L⁻¹.",
"D": "Incorrect... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009063 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.87 V, transfers 1 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.9882 V",
"B": "1.9882 V",
"C": "0.74115 V",
"D": "-1.0118 V"
} | A | 0.9882 V | Apply the Nernst equation: E=0.87−(0.0591/1)(-2)=0.9882 V. | {
"A": "Correct. The worked calculation gives 0.9882 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9882 V, not 1.9882 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9882 V, not 0.74115 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_003010 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-1-6i)/(9+10i). What is Re(z), the real part of z? | {
"A": "2.61878",
"B": "-0.38122",
"C": "-0.57182",
"D": "-1.38122"
} | B | -0.38122 | Multiply numerator and denominator by the conjugate (9-10i). Then Re(z)=(ac+bd)/(c²+d²)=((-1)(9)+(-6)(10))/(9²+(10)²)=-0.38122. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.38122, not 2.61878.",
"B": "Correct. The worked calculation gives -0.38122.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.38122, not -0.57182.",
"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_004569 | 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 32 N m about its central axis. Find its angular acceleration. | {
"A": "0.44444 rad s⁻²",
"B": "0.59259 rad s⁻²",
"C": "1.18519 rad s⁻²",
"D": "-1.40741 rad s⁻²"
} | B | 0.59259 rad s⁻² | For a solid disc, I=½MR²=½(12)(3)²=54 kg m². Using τ=Iα, α=32/54=0.59259 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.59259 rad s⁻², not 0.44444 rad s⁻².",
"B": "Correct. The worked calculation gives 0.59259 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.59259 rad s⁻², not 1.18519 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_004799 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 11 Ω are connected in series; this combination is connected in parallel with a 11 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "5.07273 A",
"B": "7.60909 A",
"C": "3.80455 A",
"D": "4.07273 A"
} | A | 5.07273 A | Series branch resistance=9+11=20 Ω. Parallel equivalent R_eq=(20×11)/(20+11)=7.09677 Ω. Total current I=V/R_eq=36/7.09677=5.07273 A. | {
"A": "Correct. The worked calculation gives 5.07273 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.07273 A, not 7.60909 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.07273 A, not 3.80455 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002011 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 3 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": "1.33824",
"B": "0.33824",
"C": "-0.33824",
"D": "-1.66176"
} | B | 0.33824 | Favourable pairs = C(6,2)+C(3,2)+C(8,2)=46. Total pairs=C(17,2)=136. Therefore P=46/136=0.33824. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33824, not 1.33824.",
"B": "Correct. The worked calculation gives 0.33824.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33824, not -0.33824.",
"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_005844 | 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 1.2 atm at 351 K. What is its pressure at 683 K? | {
"A": "-0.66496 atm",
"B": "0.33504 atm",
"C": "2.33504 atm",
"D": "1.16752 atm"
} | C | 2.33504 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.2)(683)/(351)=2.33504 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.33504 atm, not -0.66496 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.33504 atm, not 0.33504 atm.",
"C": "Correct. The worked calculation gives 2.33504 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_006064 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 44 cm in front of a thin convex lens of focal length 10 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.29412",
"B": "0.22059",
"C": "0.14706",
"D": "0.29412"
} | D | 0.29412 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(44)(10)/(44−10)=12.94118 cm. Thus |m|=v/u=12.94118/44=0.29412. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29412, not 1.29412.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29412, not 0.22059.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29412, not 0.147... | [
"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_003890 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 13 kg block initially moves at 2 m s⁻¹. A constant net force does 25 N of work over 13 m in the direction of motion. Find its final kinetic energy. | {
"A": "351 J",
"B": "280.8 J",
"C": "353 J",
"D": "349 J"
} | A | 351 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(13)(2)²+(25)(13)=351 J. | {
"A": "Correct. The worked calculation gives 351 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 351 J, not 280.8 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 351 J, not 353 J.",
"D": "Incorrect. Substituting the stated values int... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003240 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-13+7i)/(7+5i). What is Re(z), the real part of z? | {
"A": "2.24324",
"B": "-3.75676",
"C": "-0.75676",
"D": "0.24324"
} | C | -0.75676 | Multiply numerator and denominator by the conjugate (7-5i). Then Re(z)=(ac+bd)/(c²+d²)=((-13)(7)+(7)(5))/(7²+(5)²)=-0.75676. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.75676, not 2.24324.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.75676, not -3.75676.",
"C": "Correct. The worked calculation gives -0.75676.",
"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_002427 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, -6], [1, 5]]. | {
"A": "32.8",
"B": "39",
"C": "41",
"D": "42"
} | C | 41 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(5)−(-6)(1)=41. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 41, not 32.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 41, not 39.",
"C": "Correct. The worked calculation gives 41.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005793 | 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 1.2 atm at 346 K. What is its pressure at 373 K? | {
"A": "1.12936 atm",
"B": "-1.29364 atm",
"C": "-0.70636 atm",
"D": "1.29364 atm"
} | D | 1.29364 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.2)(373)/(346)=1.29364 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.29364 atm, not 1.12936 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.29364 atm, not -1.29364 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001657 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (-4x² +4x +6) dx. | {
"A": "-508.66667",
"B": "-506.66667",
"C": "-507.66667",
"D": "-405.33333"
} | B | -506.66667 | An antiderivative is (-4/3)x³+(4/2)x²+(6)x. Evaluating between 0 and 8 gives (-4/3)(8)³+(4/2)(8)²+(6)(8)=-506.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -506.66667, not -508.66667.",
"B": "Correct. The worked calculation gives -506.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -506.66667, not -507.66667.",
"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_003541 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 99 m s⁻¹ at 70° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "629.99614 m",
"B": "1259.99227 m",
"C": "630.99614 m",
"D": "-629.99614 m"
} | A | 629.99614 m | Range R=u²sin(2θ)/g. Substituting u=99, θ=70° and g=10 gives R=(99)²sin(140°)/10=629.99614 m. | {
"A": "Correct. The worked calculation gives 629.99614 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 629.99614 m, not 1259.99227 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 629.99614 m, not 630.99614 m.",
"D": "Incorrect. Subst... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004122 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 47 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.30. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "203.04 N",
"B": "169.2 N",
"C": "-169.2 N",
"D": "167.2 N"
} | B | 169.2 N | Net force=mg(sinθ−μcosθ)=47×10×(0.6−0.30×0.8)=169.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 169.2 N, not 203.04 N.",
"B": "Correct. The worked calculation gives 169.2 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 169.2 N, not -169.2 N.",
"D": "Incorrect. Substituting the stated ... | [
"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_007960 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 26 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "4.25 mmol L⁻¹",
"B": "1.625 mmol L⁻¹",
"C": "-3.25 mmol L⁻¹",
"D": "3.25 mmol L⁻¹"
} | D | 3.25 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=26/2^3=3.25 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.25 mmol L⁻¹, not 4.25 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.25 mmol L⁻¹, not 1.625 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007616 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 100 mL of 0.10 M HCl is mixed with 36 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.13274",
"B": "1.32736",
"C": "0.66368",
"D": "1.99104"
} | B | 1.32736 | Excess H⁺ moles=0.10×(100−36)/1000=0.006400 mol. Total volume=0.136 L, so [H⁺]=0.047059 M and pH=−log₁₀[H⁺]=1.32736. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.32736, not 1.13274.",
"B": "Correct. The worked calculation gives 1.32736.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.32736, not 0.66368.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009776 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(OH)_4]^+2, each OH ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "6",
"B": "8",
"C": "4",
"D": "-6"
} | A | 6 | Let the formal oxidation state of Pd be x. Charge balance gives x+(4)(−1)=+2; hence x=2+4=+6. | {
"A": "Correct. The worked calculation gives 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001246 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=3x³ -5x² -5x+7. Evaluate f′(-4). | {
"A": "178",
"B": "18.9",
"C": "179",
"D": "177"
} | C | 179 | Differentiate: f′(x)=3(3)x²+2(-5)x+(-5). At x=-4, f′(-4)=3(3)(-4)²+2(-5)(-4)+(-5)=179. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 179, not 178.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 179, not 18.9.",
"C": "Correct. The worked calculation gives 179.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_007662 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 36 mL of 0.10 M HCl is mixed with 18 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "4.47712",
"B": "1.47712",
"C": "1.10784",
"D": "2.47712"
} | B | 1.47712 | Excess H⁺ moles=0.10×(36−18)/1000=0.001800 mol. Total volume=0.054 L, so [H⁺]=0.033333 M and pH=−log₁₀[H⁺]=1.47712. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.47712, not 4.47712.",
"B": "Correct. The worked calculation gives 1.47712.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.47712, not 1.10784.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007708 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 81 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "1.26562 mmol L⁻¹",
"B": "4.26562 mmol L⁻¹",
"C": "-0.73438 mmol L⁻¹",
"D": "1.89844 mmol L⁻¹"
} | A | 1.26562 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=81/2^6=1.26562 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 1.26562 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.26562 mmol L⁻¹, not 4.26562 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.26562 mmol L⁻¹, not -0.73438 mmol L⁻¹.",... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004862 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 3 Ω and 10 Ω are connected in series; this combination is connected in parallel with a 7 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.31868 A",
"B": "5.27473 A",
"C": "2.63736 A",
"D": "1.97802 A"
} | C | 2.63736 A | Series branch resistance=3+10=13 Ω. Parallel equivalent R_eq=(13×7)/(13+7)=4.55 Ω. Total current I=V/R_eq=12/4.55=2.63736 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.63736 A, not 1.31868 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.63736 A, not 5.27473 A.",
"C": "Correct. The worked calculation gives 2.63736 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000824 | 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 12 terms? | {
"A": "-146145",
"B": "-1461460",
"C": "-730730",
"D": "-1096095"
} | B | -1461460 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(-3^12−1)/(-3−1)=-1461460. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1461460, not -146145.",
"B": "Correct. The worked calculation gives -1461460.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1461460, not -730730.",
"D": "Incorrect. Substituting the stated... | [
"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_007031 | 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 180 K and 1.12 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "160.25279 L",
"B": "79.12639 L",
"C": "158.25279 L",
"D": "316.50557 L"
} | C | 158.25279 L | PV=nRT, so V=nRT/P=(12)(0.082057)(180)/(1.12)=158.25279 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 158.25279 L, not 160.25279 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 158.25279 L, not 79.12639 L.",
"C": "Correct. The worked calculation gives 158.25279 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_007164 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 7 mol of gas at 353 K and 2.63 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "8.70961 L",
"B": "77.09614 L",
"C": "79.09614 L",
"D": "75.09614 L"
} | B | 77.09614 L | PV=nRT, so V=nRT/P=(7)(0.082057)(353)/(2.63)=77.09614 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 77.09614 L, not 8.70961 L.",
"B": "Correct. The worked calculation gives 77.09614 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 77.09614 L, not 79.09614 L.",
"D": "Incorrect. Substituting... | [
"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_006232 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 19 cm in front of a thin convex lens of focal length 6 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.04615",
"B": "0.46154",
"C": "0.92308",
"D": "-2.53846"
} | B | 0.46154 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(19)(6)/(19−6)=8.76923 cm. Thus |m|=v/u=8.76923/19=0.46154. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.46154, not 1.04615.",
"B": "Correct. The worked calculation gives 0.46154.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.46154, not 0.92308.",
"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_002841 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-1, 6, -1) and v=(7, 1, 2), calculate u·v. | {
"A": "0.7",
"B": "-6",
"C": "-3",
"D": "-1.5"
} | C | -3 | The dot product is the sum of corresponding component products: (-1)(7)+(6)(1)+(-1)(2)=-3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -3, not 0.7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -3, not -6.",
"C": "Correct. The worked calculation gives -3.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000747 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio -3. What is the sum of its first 5 terms? | {
"A": "610",
"B": "915",
"C": "62",
"D": "611"
} | A | 610 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(-3^5−1)/(-3−1)=610. | {
"A": "Correct. The worked calculation gives 610.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 610, not 915.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 610, not 62.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_000416 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 16 and common difference 4. Find the sum of its first 17 terms. | {
"A": "814",
"B": "82.6",
"C": "816",
"D": "818"
} | C | 816 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=16, d=4, n=17: Sₙ=17/2[2(16)+(17−1)(4)]=816. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 816, not 814.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 816, not 82.6.",
"C": "Correct. The worked calculation gives 816.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_003237 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-13+8i)/(8+10i). What is Re(z), the real part of z? | {
"A": "-0.14634",
"B": "-2.14634",
"C": "1.85366",
"D": "0.14634"
} | A | -0.14634 | Multiply numerator and denominator by the conjugate (8-10i). Then Re(z)=(ac+bd)/(c²+d²)=((-13)(8)+(8)(10))/(8²+(10)²)=-0.14634. | {
"A": "Correct. The worked calculation gives -0.14634.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.14634, not -2.14634.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.14634, not 1.85366.",
"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_002666 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, 2], [5, 2]]. | {
"A": "-8",
"B": "-5",
"C": "8",
"D": "-12"
} | A | -8 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(2)−(2)(5)=-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 re... | [
"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_009234 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.82 V, transfers 3 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "3.8791 V",
"B": "0.8791 V",
"C": "-0.1209 V",
"D": "-2.1209 V"
} | B | 0.8791 V | Apply the Nernst equation: E=0.82−(0.0591/3)(-3)=0.8791 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8791 V, not 3.8791 V.",
"B": "Correct. The worked calculation gives 0.8791 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8791 V, not -0.1209 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_003967 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 8 m s⁻¹. A constant net force does 5 N of work over 12 m in the direction of motion. Find its final kinetic energy. | {
"A": "225.6 J",
"B": "19.8 J",
"C": "141 J",
"D": "188 J"
} | D | 188 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(8)²+(5)(12)=188 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 188 J, not 225.6 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 188 J, not 19.8 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 188 J, not 141 J.",
"... | [
"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_003193 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-12-3i)/(12+1i). What is Re(z), the real part of z? | {
"A": "0.89862",
"B": "-3.01379",
"C": "-1.01379",
"D": "-2.01379"
} | C | -1.01379 | Multiply numerator and denominator by the conjugate (12-1i). Then Re(z)=(ac+bd)/(c²+d²)=((-12)(12)+(-3)(1))/(12²+(1)²)=-1.01379. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.01379, not 0.89862.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.01379, not -3.01379.",
"C": "Correct. The worked calculation gives -1.01379.",
"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_008359 | 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 0.2 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.312 K",
"B": "0.312 K",
"C": "-2.688 K",
"D": "0.234 K"
} | B | 0.312 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.52×0.2=0.312 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.312 K, not -0.312 K.",
"B": "Correct. The worked calculation gives 0.312 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.312 K, not -2.688 K.",
"D": "Incorrect. Substituting the stated ... | [
"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_000490 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -12 and common difference 4. Find the sum of its first 33 terms. | {
"A": "1718",
"B": "2574",
"C": "172.6",
"D": "1716"
} | D | 1716 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-12, d=4, n=33: Sₙ=33/2[2(-12)+(33−1)(4)]=1716. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1716, not 1718.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1716, not 2574.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1716, not 172.6.",
"D": "Cor... | [
"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_002105 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 7 red, 7 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.03309",
"B": "-2.66912",
"C": "3.33088",
"D": "0.33088"
} | D | 0.33088 | Favourable pairs = C(7,2)+C(7,2)+C(3,2)=45. Total pairs=C(17,2)=136. Therefore P=45/136=0.33088. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33088, not 1.03309.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33088, not -2.66912.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33088, not 3.33... | [
"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_007119 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 6 mol of gas at 583 K and 1.04 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "275.99556 L",
"B": "206.99667 L",
"C": "277.99556 L",
"D": "274.99556 L"
} | A | 275.99556 L | PV=nRT, so V=nRT/P=(6)(0.082057)(583)/(1.04)=275.99556 L. | {
"A": "Correct. The worked calculation gives 275.99556 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 275.99556 L, not 206.99667 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 275.99556 L, not 277.99556 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_007893 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 35 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "6.5625 mmol L⁻¹",
"B": "11.75 mmol L⁻¹",
"C": "8.75 mmol L⁻¹",
"D": "5.75 mmol L⁻¹"
} | C | 8.75 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=35/2^2=8.75 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.75 mmol L⁻¹, not 6.5625 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.75 mmol L⁻¹, not 11.75 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 8.75 mmol L⁻¹.",
"D": "Inco... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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