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_004726 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 3 Ω are connected in series; this combination is connected in parallel with a 2 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "-14.18182 A",
"B": "14.18182 A",
"C": "7.09091 A",
"D": "12.18182 A"
} | B | 14.18182 A | Series branch resistance=8+3=11 Ω. Parallel equivalent R_eq=(11×2)/(11+2)=1.69231 Ω. Total current I=V/R_eq=24/1.69231=14.18182 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14.18182 A, not -14.18182 A.",
"B": "Correct. The worked calculation gives 14.18182 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14.18182 A, not 7.09091 A.",
"D": "Incorrect. Substitutin... | [
"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_008865 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.42 mol L⁻¹ and initially B is absent. At equilibrium, 52% of A has dissociated at constant volume. Find K_c. | {
"A": "2.9464",
"B": "-1.0536",
"C": "-2.0536",
"D": "0.9464"
} | D | 0.9464 | Let α=0.52. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.42)(0.52)²/(1−0.52)=0.9464. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9464, not 2.9464.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9464, not -1.0536.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9464, not -2.0536."... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000072 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 +14x +10=0, let its roots be α and β. What is α²+β²? | {
"A": "-1.14286",
"B": "0.14286",
"C": "1.14286",
"D": "0.57143"
} | C | 1.14286 | By Vieta's relations, α+β = -14/7 and αβ = 10/7. Then α²+β²=(α+β)²−2αβ = (-14/7)²−2(10/7) = 1.14286. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.14286, not -1.14286.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.14286, not 0.14286.",
"C": "Correct. The worked calculation gives 1.14286.",
"D": "Incorrect. Substituting the stated v... | [
"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_004259 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 40 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.45. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "-96 N",
"B": "96 N",
"C": "192 N",
"D": "76.8 N"
} | B | 96 N | Net force=mg(sinθ−μcosθ)=40×10×(0.6−0.45×0.8)=96 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 96 N, not -96 N.",
"B": "Correct. The worked calculation gives 96 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 96 N, not 192 N.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_002669 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, -7], [1, 1]]. | {
"A": "14",
"B": "11",
"C": "12",
"D": "16.5"
} | B | 11 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(1)−(-7)(1)=11. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11, not 14.",
"B": "Correct. The worked calculation gives 11.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11, not 12.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008493 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.35 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.404 K",
"B": "2.808 K",
"C": "-0.192 K",
"D": "1.2808 K"
} | B | 2.808 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.52×1.35=2.808 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.808 K, not 1.404 K.",
"B": "Correct. The worked calculation gives 2.808 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.808 K, not -0.192 K.",
"D": "Incorrect. Substituting the stated v... | [
"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_000262 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 +2x -11=0, let its roots be α and β. What is α²+β²? | {
"A": "6.77778",
"B": "3.77778",
"C": "4.77778",
"D": "0.77778"
} | B | 3.77778 | By Vieta's relations, α+β = -2/6 and αβ = -11/6. Then α²+β²=(α+β)²−2αβ = (-2/6)²−2(-11/6) = 3.77778. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.77778, not 6.77778.",
"B": "Correct. The worked calculation gives 3.77778.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.77778, not 4.77778.",
"D": "Incorrect. Substituting the stated va... | [
"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_006954 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 47 mol H₂ and 10 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "20 mol",
"B": "19 mol",
"C": "22 mol",
"D": "10 mol"
} | A | 20 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 47 mol H₂O; O₂ can produce 20 mol H₂O. The limiting condition is O₂; product=20 mol. | {
"A": "Correct. The worked calculation gives 20 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20 mol, not 19 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20 mol, not 22 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_003576 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 87 m s⁻¹ at 20° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "389.22075 m",
"B": "-486.52594 m",
"C": "486.52594 m",
"D": "487.52594 m"
} | C | 486.52594 m | Range R=u²sin(2θ)/g. Substituting u=87, θ=20° and g=10 gives R=(87)²sin(40°)/10=486.52594 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 486.52594 m, not 389.22075 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 486.52594 m, not -486.52594 m.",
"C": "Correct. The worked calculation gives 486.52594 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_004806 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 15 Ω are connected in series; this combination is connected in parallel with a 20 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.1 A",
"B": "3.1 A",
"C": "1.65 A",
"D": "0.1 A"
} | A | 1.1 A | Series branch resistance=9+15=24 Ω. Parallel equivalent R_eq=(24×20)/(24+20)=10.90909 Ω. Total current I=V/R_eq=12/10.90909=1.1 A. | {
"A": "Correct. The worked calculation gives 1.1 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1 A, not 3.1 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1 A, not 1.65 A.",
"D": "Incorrect. Substituting the stated values into... | [
"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_004563 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 11 kg and radius 3 m is acted on by a constant torque of 54 N m about its central axis. Find its angular acceleration. | {
"A": "2.18182 rad s⁻²",
"B": "-1.90909 rad s⁻²",
"C": "1.09091 rad s⁻²",
"D": "2.09091 rad s⁻²"
} | C | 1.09091 rad s⁻² | For a solid disc, I=½MR²=½(11)(3)²=49.5 kg m². Using τ=Iα, α=54/49.5=1.09091 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.09091 rad s⁻², not 2.18182 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.09091 rad s⁻², not -1.90909 rad s⁻².",
"C": "Correct. The worked calculation gives 1.09091 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_005559 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 75 μF capacitor is charged to a potential difference of 33 V. Calculate the energy stored, expressed in μJ. | {
"A": "40835.5 μJ",
"B": "20418.75 μJ",
"C": "40837.5 μJ",
"D": "40836.5 μJ"
} | C | 40837.5 μJ | U=½CV². Since C=75 μF, U in μJ is ½×75×(33)²=40837.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 40837.5 μJ, not 40835.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 40837.5 μJ, not 20418.75 μJ.",
"C": "Correct. The worked calculation gives 40837.5 μJ.",
"D": "Incorrect. Substituti... | [
"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_006015 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 38 cm in front of a thin convex lens of focal length 25 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.19231",
"B": "1.92308",
"C": "3.84615",
"D": "4.92308"
} | B | 1.92308 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(38)(25)/(38−25)=73.07692 cm. Thus |m|=v/u=73.07692/38=1.92308. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.92308, not 1.19231.",
"B": "Correct. The worked calculation gives 1.92308.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.92308, not 3.84615.",
"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_006326 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 120 cm in front of a thin convex lens of focal length 24 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.75",
"B": "0.125",
"C": "1.025",
"D": "0.25"
} | D | 0.25 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(120)(24)/(120−24)=30 cm. Thus |m|=v/u=30/120=0.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25, not -0.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25, not 0.125.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25, not 1.025.",
"D": "C... | [
"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_003409 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 41 m s⁻¹ at 35° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "126.36986 m",
"B": "159.96233 m",
"C": "157.96233 m",
"D": "158.96233 m"
} | C | 157.96233 m | Range R=u²sin(2θ)/g. Substituting u=41, θ=35° and g=10 gives R=(41)²sin(70°)/10=157.96233 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 157.96233 m, not 126.36986 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 157.96233 m, not 159.96233 m.",
"C": "Correct. The worked calculation gives 157.96233 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009949 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(CN)_4]^+2, each CN ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "9",
"B": "1.6",
"C": "6",
"D": "5"
} | C | 6 | Let the formal oxidation state of Pd be x. Charge balance gives x+(4)(−1)=+2; hence x=2+4=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 1.6.",
"C": "Correct. The worked calculation gives 6.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006556 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 12 kg is attached to an ideal spring of force constant 678 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.73392 s",
"B": "-0.73392 s",
"C": "-1.73392 s",
"D": "0.26608 s"
} | D | 0.26608 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(12/678)=0.26608 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.26608 s, not -2.73392 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.26608 s, not -0.73392 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.26608 ... | [
"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_001396 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (6x² +1x -5) dx. | {
"A": "1016",
"B": "762",
"C": "102.6",
"D": "2032"
} | A | 1016 | An antiderivative is (6/3)x³+(1/2)x²+(-5)x. Evaluating between 0 and 8 gives (6/3)(8)³+(1/2)(8)²+(-5)(8)=1016. | {
"A": "Correct. The worked calculation gives 1016.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1016, not 762.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1016, not 102.6.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_006787 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 6 mol H₂ and 10 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "4 mol",
"B": "8 mol",
"C": "6 mol",
"D": "9 mol"
} | C | 6 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 6 mol H₂O; O₂ can produce 20 mol H₂O. The limiting condition is H₂; product=6 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 4 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 8 mol.",
"C": "Correct. The worked calculation gives 6 mol.",
"D": "Incorrect. Substituting the stated values into ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000486 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 2 and common difference 6. Find the sum of its first 21 terms. | {
"A": "1302",
"B": "-1302",
"C": "1041.6",
"D": "1301"
} | A | 1302 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=2, d=6, n=21: Sₙ=21/2[2(2)+(21−1)(6)]=1302. | {
"A": "Correct. The worked calculation gives 1302.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1302, not -1302.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1302, not 1041.6.",
"D": "Incorrect. Substituting the stated values into th... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004847 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 3 Ω are connected in series; this combination is connected in parallel with a 18 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.66667 A",
"B": "9.33333 A",
"C": "3.66667 A",
"D": "4.66667 A"
} | D | 4.66667 A | Series branch resistance=7+3=10 Ω. Parallel equivalent R_eq=(10×18)/(10+18)=6.42857 Ω. Total current I=V/R_eq=30/6.42857=4.66667 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.66667 A, not 2.66667 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.66667 A, not 9.33333 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.66667 A,... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000317 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -4x -6=0, let its roots be α and β. What is α²+β²? | {
"A": "10",
"B": "11",
"C": "-10",
"D": "20"
} | A | 10 | By Vieta's relations, α+β = 4/2 and αβ = -6/2. Then α²+β²=(α+β)²−2αβ = (4/2)²−2(-6/2) = 10. | {
"A": "Correct. The worked calculation gives 10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 11.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not -10.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"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_007598 | 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 46 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.59854",
"B": "1.15985",
"C": "1.59854",
"D": "3.19709"
} | C | 1.59854 | Excess H⁺ moles=0.10×(77−46)/1000=0.003100 mol. Total volume=0.123 L, so [H⁺]=0.025203 M and pH=−log₁₀[H⁺]=1.59854. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.59854, not 2.59854.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.59854, not 1.15985.",
"C": "Correct. The worked calculation gives 1.59854.",
"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_002189 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 3 blue and 5 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.29487",
"B": "-0.29487",
"C": "0.58974",
"D": "1.02949"
} | A | 0.29487 | Favourable pairs = C(5,2)+C(3,2)+C(5,2)=23. Total pairs=C(13,2)=78. Therefore P=23/78=0.29487. | {
"A": "Correct. The worked calculation gives 0.29487.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29487, not -0.29487.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29487, not 0.58974.",
"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_009330 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.01 V, transfers 3 electrons, and has reaction quotient Q=10^2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.9706 V",
"B": "3.9706 V",
"C": "1.9706 V",
"D": "1.9412 V"
} | A | 0.9706 V | Apply the Nernst equation: E=1.01−(0.0591/3)(2)=0.9706 V. | {
"A": "Correct. The worked calculation gives 0.9706 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9706 V, not 3.9706 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9706 V, not 1.9706 V.",
"D": "Incorrect. Substituting the stat... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007242 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 9 mol of gas at 300 K and 0.79 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "281.44797 L",
"B": "280.44797 L",
"C": "210.33598 L",
"D": "336.53757 L"
} | B | 280.44797 L | PV=nRT, so V=nRT/P=(9)(0.082057)(300)/(0.79)=280.44797 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 280.44797 L, not 281.44797 L.",
"B": "Correct. The worked calculation gives 280.44797 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 280.44797 L, not 210.33598 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_005039 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +9 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "202.5 N",
"B": "101.25 N",
"C": "151.875 N",
"D": "201.5 N"
} | A | 202.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(9×10⁻⁶)/(6×10⁻²)²=202.5 N. | {
"A": "Correct. The worked calculation gives 202.5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 202.5 N, not 101.25 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 202.5 N, not 151.875 N.",
"D": "Incorrect. Substituting the stated... | [
"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_008704 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.43 mol L⁻¹ and initially B is absent. At equilibrium, 79% of A has dissociated at constant volume. Find K_c. | {
"A": "3.11168",
"B": "3.83376",
"C": "5.11168",
"D": "2.11168"
} | C | 5.11168 | Let α=0.79. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.43)(0.79)²/(1−0.79)=5.11168. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.11168, not 3.11168.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.11168, not 3.83376.",
"C": "Correct. The worked calculation gives 5.11168.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007065 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 20 mol of gas at 485 K and 0.31 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "5135.18 L",
"B": "2567.59 L",
"C": "1283.795 L",
"D": "2568.59 L"
} | B | 2567.59 L | PV=nRT, so V=nRT/P=(20)(0.082057)(485)/(0.31)=2567.59 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2567.59 L, not 5135.18 L.",
"B": "Correct. The worked calculation gives 2567.59 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2567.59 L, not 1283.795 L.",
"D": "Incorrect. Substituting th... | [
"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_007159 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 13 mol of gas at 392 K and 0.82 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "382.46568 L",
"B": "51.99542 L",
"C": "507.95423 L",
"D": "509.95423 L"
} | D | 509.95423 L | PV=nRT, so V=nRT/P=(13)(0.082057)(392)/(0.82)=509.95423 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 509.95423 L, not 382.46568 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 509.95423 L, not 51.99542 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 509... | [
"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_008998 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.96 mol L⁻¹ and initially B is absent. At equilibrium, 45% of A has dissociated at constant volume. Find K_c. | {
"A": "3.41382",
"B": "2.82764",
"C": "-1.41382",
"D": "1.41382"
} | D | 1.41382 | Let α=0.45. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.96)(0.45)²/(1−0.45)=1.41382. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.41382, not 3.41382.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.41382, not 2.82764.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.41382, not -1.41... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009831 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(OH)_4]^-3, each OH ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "1.1",
"B": "2",
"C": "0",
"D": "1"
} | D | 1 | Let the formal oxidation state of Mn be x. Charge balance gives x+(4)(−1)=-3; hence x=-3+4=+1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.",
"D": "Correct. The worked ... | [
"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_001589 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (6x² -4x +2) dx. | {
"A": "3",
"B": "1.5",
"C": "2",
"D": "1.2"
} | C | 2 | An antiderivative is (6/3)x³+(-4/2)x²+(2)x. Evaluating between 0 and 1 gives (6/3)(1)³+(-4/2)(1)²+(2)(1)=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.5.",
"C": "Correct. The worked calculation gives 2.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_006266 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 60 cm in front of a thin convex lens of focal length 22 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "2.57895",
"B": "0.43421",
"C": "0.57895",
"D": "-1.42105"
} | C | 0.57895 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(60)(22)/(60−22)=34.73684 cm. Thus |m|=v/u=34.73684/60=0.57895. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.57895, not 2.57895.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.57895, not 0.43421.",
"C": "Correct. The worked calculation gives 0.57895.",
"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_003861 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 4 m s⁻¹. A constant net force does 24 N of work over 6 m in the direction of motion. Find its final kinetic energy. | {
"A": "207 J",
"B": "208 J",
"C": "249.6 J",
"D": "312 J"
} | B | 208 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(4)²+(24)(6)=208 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 208 J, not 207 J.",
"B": "Correct. The worked calculation gives 208 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 208 J, not 249.6 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_005468 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 48 μF capacitor is charged to a potential difference of 15 V. Calculate the energy stored, expressed in μJ. | {
"A": "5400 μJ",
"B": "541 μJ",
"C": "5402 μJ",
"D": "2700 μJ"
} | A | 5400 μJ | U=½CV². Since C=48 μF, U in μJ is ½×48×(15)²=5400 μJ. | {
"A": "Correct. The worked calculation gives 5400 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5400 μJ, not 541 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5400 μJ, not 5402 μJ.",
"D": "Incorrect. Substituting the stated val... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002545 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, 7], [7, -8]]. | {
"A": "-106",
"B": "-103",
"C": "-105",
"D": "-104"
} | C | -105 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(-8)−(7)(7)=-105. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -105, not -106.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -105, not -103.",
"C": "Correct. The worked calculation gives -105.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_008606 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.99 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "4.776 K",
"B": "1.4776 K",
"C": "1.776 K",
"D": "-4.776 K"
} | A | 4.776 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.6×1.99=4.776 K. | {
"A": "Correct. The worked calculation gives 4.776 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.776 K, not 1.4776 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.776 K, not 1.776 K.",
"D": "Incorrect. Substituting the stated v... | [
"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_003053 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(6-12i)/(2+11i). What is Re(z), the real part of z? | {
"A": "-0.96",
"B": "-3.96",
"C": "2.04",
"D": "-0.48"
} | A | -0.96 | Multiply numerator and denominator by the conjugate (2-11i). Then Re(z)=(ac+bd)/(c²+d²)=((6)(2)+(-12)(11))/(2²+(11)²)=-0.96. | {
"A": "Correct. The worked calculation gives -0.96.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.96, not -3.96.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.96, not 2.04.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_000113 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 -5x +2=0, let its roots be α and β. What is α²+β²? | {
"A": "-21",
"B": "25.2",
"C": "21",
"D": "3.1"
} | C | 21 | By Vieta's relations, α+β = 5/1 and αβ = 2/1. Then α²+β²=(α+β)²−2αβ = (5/1)²−2(2/1) = 21. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21, not -21.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21, not 25.2.",
"C": "Correct. The worked calculation gives 21.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_003106 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(3-6i)/(3+11i). What is Re(z), the real part of z? | {
"A": "-1.43846",
"B": "0.95615",
"C": "-0.43846",
"D": "0.56154"
} | C | -0.43846 | Multiply numerator and denominator by the conjugate (3-11i). Then Re(z)=(ac+bd)/(c²+d²)=((3)(3)+(-6)(11))/(3²+(11)²)=-0.43846. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.43846, not -1.43846.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.43846, not 0.95615.",
"C": "Correct. The worked calculation gives -0.43846.",
"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_008400 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.49 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.14432 K",
"B": "1.52576 K",
"C": "0.52576 K",
"D": "-1.52576 K"
} | B | 1.52576 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×1.49=1.52576 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.52576 K, not 1.14432 K.",
"B": "Correct. The worked calculation gives 1.52576 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.52576 K, not 0.52576 K.",
"D": "Incorrect. Substituting the... | [
"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_007943 | 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 33 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "1.54688 mmol L⁻¹",
"B": "-0.96875 mmol L⁻¹",
"C": "1.03125 mmol L⁻¹",
"D": "-1.03125 mmol L⁻¹"
} | C | 1.03125 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=33/2^5=1.03125 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.03125 mmol L⁻¹, not 1.54688 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.03125 mmol L⁻¹, not -0.96875 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 1.03125 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_002756 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(9, 2, 9) and v=(0, 3, -2), calculate u·v. | {
"A": "-11",
"B": "-12",
"C": "-14",
"D": "-18"
} | B | -12 | The dot product is the sum of corresponding component products: (9)(0)+(2)(3)+(9)(-2)=-12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -12, not -11.",
"B": "Correct. The worked calculation gives -12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -12, not -14.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004725 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 6 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 3 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "11.07692 A",
"B": "12.76923 A",
"C": "14.76923 A",
"D": "29.53846 A"
} | C | 14.76923 A | Series branch resistance=6+7=13 Ω. Parallel equivalent R_eq=(13×3)/(13+3)=2.4375 Ω. Total current I=V/R_eq=36/2.4375=14.76923 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14.76923 A, not 11.07692 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14.76923 A, not 12.76923 A.",
"C": "Correct. The worked calculation gives 14.76923 A.",
"D": "Incorrect. Substitutin... | [
"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_005660 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 2 μF capacitor is charged to a potential difference of 18 V. Calculate the energy stored, expressed in μJ. | {
"A": "648 μJ",
"B": "388.8 μJ",
"C": "324 μJ",
"D": "486 μJ"
} | C | 324 μJ | U=½CV². Since C=2 μF, U in μJ is ½×2×(18)²=324 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 324 μJ, not 648 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 324 μJ, not 388.8 μJ.",
"C": "Correct. The worked calculation gives 324 μJ.",
"D": "Incorrect. Substituting the stated value... | [
"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_001233 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=3x³ +7x² +11x+7. Evaluate f′(4). | {
"A": "316.5",
"B": "211",
"C": "253.2",
"D": "105.5"
} | B | 211 | Differentiate: f′(x)=3(3)x²+2(7)x+(11). At x=4, f′(4)=3(3)(4)²+2(7)(4)+(11)=211. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 211, not 316.5.",
"B": "Correct. The worked calculation gives 211.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 211, not 253.2.",
"D": "Incorrect. Substituting the stated values into the go... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006217 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 117 cm in front of a thin convex lens of focal length 27 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.3",
"B": "-1.7",
"C": "0.3",
"D": "-2.7"
} | C | 0.3 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(117)(27)/(117−27)=35.1 cm. Thus |m|=v/u=35.1/117=0.3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3, not -0.3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3, not -1.7.",
"C": "Correct. The worked calculation gives 0.3.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_002298 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 8 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": "2.31884",
"B": "-0.31884",
"C": "0.31884",
"D": "1.31884"
} | C | 0.31884 | Favourable pairs = C(6,2)+C(8,2)+C(10,2)=88. Total pairs=C(24,2)=276. Therefore P=88/276=0.31884. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31884, not 2.31884.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31884, not -0.31884.",
"C": "Correct. The worked calculation gives 0.31884.",
"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_009818 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(OH)_2]^-2, each OH ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "2",
"B": "-2",
"C": "-3",
"D": "0"
} | D | 0 | Let the formal oxidation state of Co be x. Charge balance gives x+(2)(−1)=-2; hence x=-2+2=+0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"D": "Correct. The worked ... | [
"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_002939 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(5, -3, 9) and v=(7, 2, 5), calculate u·v. | {
"A": "72",
"B": "88.8",
"C": "111",
"D": "74"
} | D | 74 | The dot product is the sum of corresponding component products: (5)(7)+(-3)(2)+(9)(5)=74. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 74, not 72.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 74, not 88.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 74, not 111.",
"D": "Correct. The ... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004368 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 4 kg and radius 4 m is acted on by a constant torque of 94 N m about its central axis. Find its angular acceleration. | {
"A": "3.9375 rad s⁻²",
"B": "0.9375 rad s⁻²",
"C": "-0.0625 rad s⁻²",
"D": "2.9375 rad s⁻²"
} | D | 2.9375 rad s⁻² | For a solid disc, I=½MR²=½(4)(4)²=32 kg m². Using τ=Iα, α=94/32=2.9375 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.9375 rad s⁻², not 3.9375 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.9375 rad s⁻², not 0.9375 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relat... | [
"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_004719 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 2 Ω are connected in series; this combination is connected in parallel with a 12 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "5.3 A",
"B": "3.3 A",
"C": "1.3 A",
"D": "4.3 A"
} | B | 3.3 A | Series branch resistance=8+2=10 Ω. Parallel equivalent R_eq=(10×12)/(10+12)=5.45455 Ω. Total current I=V/R_eq=18/5.45455=3.3 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.3 A, not 5.3 A.",
"B": "Correct. The worked calculation gives 3.3 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.3 A, not 1.3 A.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_004078 | 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 0.33. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "123.32 N",
"B": "125.32 N",
"C": "124.32 N",
"D": "122.32 N"
} | C | 124.32 N | Net force=mg(sinθ−μcosθ)=37×10×(0.6−0.33×0.8)=124.32 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 124.32 N, not 123.32 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 124.32 N, not 125.32 N.",
"C": "Correct. The worked calculation gives 124.32 N.",
"D": "Incorrect. Substituting the stat... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007456 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 99 mL of 0.10 M HCl is mixed with 34 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.31094",
"B": "2.31094",
"C": "0.65547",
"D": "0.31094"
} | A | 1.31094 | Excess H⁺ moles=0.10×(99−34)/1000=0.006500 mol. Total volume=0.133 L, so [H⁺]=0.048872 M and pH=−log₁₀[H⁺]=1.31094. | {
"A": "Correct. The worked calculation gives 1.31094.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.31094, not 2.31094.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.31094, not 0.65547.",
"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_005501 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 58 μF capacitor is charged to a potential difference of 17 V. Calculate the energy stored, expressed in μJ. | {
"A": "16762 μJ",
"B": "8381 μJ",
"C": "6285.75 μJ",
"D": "4190.5 μJ"
} | B | 8381 μJ | U=½CV². Since C=58 μF, U in μJ is ½×58×(17)²=8381 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8381 μJ, not 16762 μJ.",
"B": "Correct. The worked calculation gives 8381 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8381 μJ, not 6285.75 μJ.",
"D": "Incorrect. Substituting the state... | [
"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_002440 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, 6], [9, 2]]. | {
"A": "-52.8",
"B": "-44",
"C": "-42",
"D": "-43"
} | B | -44 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(2)−(6)(9)=-44. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -44, not -52.8.",
"B": "Correct. The worked calculation gives -44.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -44, not -42.",
"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_000286 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +0x -6=0, let its roots be α and β. What is α²+β²? | {
"A": "2.4",
"B": "4.4",
"C": "1.2",
"D": "1.4"
} | A | 2.4 | By Vieta's relations, α+β = 0/5 and αβ = -6/5. Then α²+β²=(α+β)²−2αβ = (0/5)²−2(-6/5) = 2.4. | {
"A": "Correct. The worked calculation gives 2.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.4, not 4.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.4, not 1.2.",
"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_006438 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 9 kg is attached to an ideal spring of force constant 889 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.20123 s",
"B": "-2.79877 s",
"C": "0.30185 s",
"D": "3.20123 s"
} | A | 0.20123 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(9/889)=0.20123 s. | {
"A": "Correct. The worked calculation gives 0.20123 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.20123 s, not -2.79877 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.20123 s, not 0.30185 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_005207 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +9 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "24.3 N",
"B": "16.2 N",
"C": "8.1 N",
"D": "17.2 N"
} | B | 16.2 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(9×10⁻⁶)/(10×10⁻²)²=16.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16.2 N, not 24.3 N.",
"B": "Correct. The worked calculation gives 16.2 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16.2 N, not 8.1 N.",
"D": "Incorrect. Substituting the stated values i... | [
"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_009842 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(Cl)_5]^+3, each Cl ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "6",
"B": "-8",
"C": "9",
"D": "8"
} | D | 8 | Let the formal oxidation state of Mn be x. Charge balance gives x+(5)(−1)=+3; hence x=3+5=+8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not -8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 9.",
"D": "Correct. The worked c... | [
"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_008354 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.36 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-3.264 K",
"B": "3.264 K",
"C": "2.448 K",
"D": "1.632 K"
} | B | 3.264 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.6×1.36=3.264 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.264 K, not -3.264 K.",
"B": "Correct. The worked calculation gives 3.264 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.264 K, not 2.448 K.",
"D": "Incorrect. Substituting the stated v... | [
"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_000243 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 -18x -12=0, let its roots be α and β. What is α²+β²? | {
"A": "278.4",
"B": "348",
"C": "522",
"D": "696"
} | B | 348 | By Vieta's relations, α+β = 18/1 and αβ = -12/1. Then α²+β²=(α+β)²−2αβ = (18/1)²−2(-12/1) = 348. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 348, not 278.4.",
"B": "Correct. The worked calculation gives 348.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 348, not 522.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_008580 | 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 0.35 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.7875 K",
"B": "3.05 K",
"C": "1.05 K",
"D": "0.05 K"
} | C | 1.05 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×1.0×0.35=1.05 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.05 K, not 0.7875 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.05 K, not 3.05 K.",
"C": "Correct. The worked calculation gives 1.05 K.",
"D": "Incorrect. Substituting the stated value... | [
"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_007409 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 72 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": "17.58187",
"B": "11.72125",
"C": "5.86062",
"D": "10.72125"
} | B | 11.72125 | Excess OH⁻ moles=0.10×(80−72)/1000=0.000800 mol. Total volume=0.152 L, so [OH⁻]=0.005263 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=11.72125. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.72125, not 17.58187.",
"B": "Correct. The worked calculation gives 11.72125.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.72125, not 5.86062.",
"D": "Incorrect. Substituting the state... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005398 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 53 μF capacitor is charged to a potential difference of 25 V. Calculate the energy stored, expressed in μJ. | {
"A": "12421.875 μJ",
"B": "16562.5 μJ",
"C": "8281.25 μJ",
"D": "16560.5 μJ"
} | B | 16562.5 μJ | U=½CV². Since C=53 μF, U in μJ is ½×53×(25)²=16562.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16562.5 μJ, not 12421.875 μJ.",
"B": "Correct. The worked calculation gives 16562.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16562.5 μJ, not 8281.25 μJ.",
"D": "Incorrect. Substitut... | [
"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_009531 | 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_11H_22N_1X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "0",
"B": "2",
"C": "1",
"D": "-2"
} | A | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+1−22−3)/2=0. | {
"A": "Correct. The worked calculation gives 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_004429 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 1 m is acted on by a constant torque of 11 N m about its central axis. Find its angular acceleration. | {
"A": "13 rad s⁻²",
"B": "10 rad s⁻²",
"C": "11 rad s⁻²",
"D": "14 rad s⁻²"
} | C | 11 rad s⁻² | For a solid disc, I=½MR²=½(2)(1)²=1 kg m². Using τ=Iα, α=11/1=11 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11 rad s⁻², not 13 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11 rad s⁻², not 10 rad s⁻².",
"C": "Correct. The worked calculation gives 11 rad s⁻².",
"D": "Incorrect. Substitutin... | [
"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_005750 | 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 0.3 atm at 251 K. What is its pressure at 381 K? | {
"A": "0.34153 atm",
"B": "-0.45538 atm",
"C": "1.45538 atm",
"D": "0.45538 atm"
} | D | 0.45538 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.3)(381)/(251)=0.45538 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.45538 atm, not 0.34153 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.45538 atm, not -0.45538 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_004894 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 6 Ω and 11 Ω are connected in series; this combination is connected in parallel with a 16 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.09191 A",
"B": "0.54596 A",
"C": "-1.09191 A",
"D": "4.09191 A"
} | A | 1.09191 A | Series branch resistance=6+11=17 Ω. Parallel equivalent R_eq=(17×16)/(17+16)=8.24242 Ω. Total current I=V/R_eq=9/8.24242=1.09191 A. | {
"A": "Correct. The worked calculation gives 1.09191 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.09191 A, not 0.54596 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.09191 A, not -1.09191 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008485 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.32 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "5.4912 K",
"B": "4.1184 K",
"C": "3.7456 K",
"D": "2.7456 K"
} | D | 2.7456 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.52×1.32=2.7456 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.7456 K, not 5.4912 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.7456 K, not 4.1184 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.7456 K, not ... | [
"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_003369 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 113 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "2211.65568 m",
"B": "1107.82784 m",
"C": "1105.82784 m",
"D": "1326.99341 m"
} | C | 1105.82784 m | Range R=u²sin(2θ)/g. Substituting u=113, θ=60° and g=10 gives R=(113)²sin(120°)/10=1105.82784 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1105.82784 m, not 2211.65568 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1105.82784 m, not 1107.82784 m.",
"C": "Correct. The worked calculation gives 1105.82784 m.",
"D": "Incorrect. S... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004412 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 1 m is acted on by a constant torque of 77 N m about its central axis. Find its angular acceleration. | {
"A": "77 rad s⁻²",
"B": "78 rad s⁻²",
"C": "38.5 rad s⁻²",
"D": "115.5 rad s⁻²"
} | A | 77 rad s⁻² | For a solid disc, I=½MR²=½(2)(1)²=1 kg m². Using τ=Iα, α=77/1=77 rad s⁻². | {
"A": "Correct. The worked calculation gives 77 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 77 rad s⁻², not 78 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 77 rad s⁻², not 38.5 rad s⁻².",
"D": "Incorrect. Substitut... | [
"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_006636 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 10 kg is attached to an ideal spring of force constant 51 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.88561 s",
"B": "-2.11439 s",
"C": "0.88561 s",
"D": "2.88561 s"
} | C | 0.88561 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(10/51)=0.88561 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.88561 s, not 1.88561 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.88561 s, not -2.11439 s.",
"C": "Correct. The worked calculation gives 0.88561 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_005716 | 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 300 K. What is its pressure at 465 K? | {
"A": "7.44 atm",
"B": "-7.44 atm",
"C": "11.16 atm",
"D": "6.44 atm"
} | A | 7.44 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.8)(465)/(300)=7.44 atm. | {
"A": "Correct. The worked calculation gives 7.44 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.44 atm, not -7.44 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.44 atm, not 11.16 atm.",
"D": "Incorrect. Substituting the st... | [
"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_003077 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-11-9i)/(11+8i). What is Re(z), the real part of z? | {
"A": "-4.04324",
"B": "1.95676",
"C": "-1.04324",
"D": "-2.04324"
} | C | -1.04324 | Multiply numerator and denominator by the conjugate (11-8i). Then Re(z)=(ac+bd)/(c²+d²)=((-11)(11)+(-9)(8))/(11²+(8)²)=-1.04324. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.04324, not -4.04324.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.04324, not 1.95676.",
"C": "Correct. The worked calculation gives -1.04324.",
"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_007817 | 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 40 minutes? | {
"A": "-20.25 mmol L⁻¹",
"B": "20.25 mmol L⁻¹",
"C": "19.25 mmol L⁻¹",
"D": "18.25 mmol L⁻¹"
} | B | 20.25 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=81/2^2=20.25 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20.25 mmol L⁻¹, not -20.25 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 20.25 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20.25 mmol L⁻¹, not 19.25 mmol L⁻¹.",
"D": "I... | [
"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_000208 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +10x +9=0, let its roots be α and β. What is α²+β²? | {
"A": "10.22222",
"B": "3.11111",
"C": "3.83333",
"D": "5.11111"
} | D | 5.11111 | By Vieta's relations, α+β = -10/3 and αβ = 9/3. Then α²+β²=(α+β)²−2αβ = (-10/3)²−2(9/3) = 5.11111. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.11111, not 10.22222.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.11111, not 3.11111.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.11111, not 3.83... | [
"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_007530 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 53 mL of 0.10 M HCl is mixed with 49 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-2.40654",
"B": "2.40654",
"C": "4.81308",
"D": "1.40654"
} | B | 2.40654 | Excess H⁺ moles=0.10×(53−49)/1000=0.000400 mol. Total volume=0.102 L, so [H⁺]=0.003922 M and pH=−log₁₀[H⁺]=2.40654. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.40654, not -2.40654.",
"B": "Correct. The worked calculation gives 2.40654.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.40654, not 4.81308.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003654 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 19 m s⁻¹ at 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "35.55156 m",
"B": "34.55156 m",
"C": "36.55156 m",
"D": "-35.55156 m"
} | A | 35.55156 m | Range R=u²sin(2θ)/g. Substituting u=19, θ=40° and g=10 gives R=(19)²sin(80°)/10=35.55156 m. | {
"A": "Correct. The worked calculation gives 35.55156 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 35.55156 m, not 34.55156 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 35.55156 m, not 36.55156 m.",
"D": "Incorrect. Substitutin... | [
"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_007619 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 17 mL of 0.10 M HCl is mixed with 46 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "18.99459",
"B": "12.66306",
"C": "-12.66306",
"D": "2.26631"
} | B | 12.66306 | Excess OH⁻ moles=0.10×(46−17)/1000=0.002900 mol. Total volume=0.063 L, so [OH⁻]=0.046032 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.66306. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.66306, not 18.99459.",
"B": "Correct. The worked calculation gives 12.66306.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.66306, not -12.66306.",
"D": "Incorrect. Substituting the sta... | [
"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_002165 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 10 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.62745",
"B": "0.27941",
"C": "0.7451",
"D": "0.37255"
} | D | 0.37255 | Favourable pairs = C(4,2)+C(10,2)+C(4,2)=57. Total pairs=C(18,2)=153. Therefore P=57/153=0.37255. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.37255, not -0.62745.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.37255, not 0.27941.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.37255, not 0.74... | [
"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_008754 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.25 mol L⁻¹ and initially B is absent. At equilibrium, 50% of A has dissociated at constant volume. Find K_c. | {
"A": "1.05",
"B": "0.5",
"C": "0.75",
"D": "1.5"
} | B | 0.5 | Let α=0.5. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.25)(0.5)²/(1−0.5)=0.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5, not 1.05.",
"B": "Correct. The worked calculation gives 0.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5, not 0.75.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001681 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 4 elements can be selected from a set of 87 distinct elements? | {
"A": "2671074",
"B": "2225895",
"C": "2225893",
"D": "-2225895"
} | B | 2225895 | Order does not matter, so the count is C(87,4)=87!/[4!(83)!]=2225895. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2225895, not 2671074.",
"B": "Correct. The worked calculation gives 2225895.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2225895, not 2225893.",
"D": "Incorrect. Substituting the stated va... | [
"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_006187 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 109 cm in front of a thin convex lens of focal length 30 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "2.37975",
"B": "0.37975",
"C": "-0.62025",
"D": "0.75949"
} | B | 0.37975 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(109)(30)/(109−30)=41.39241 cm. Thus |m|=v/u=41.39241/109=0.37975. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.37975, not 2.37975.",
"B": "Correct. The worked calculation gives 0.37975.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.37975, not -0.62025.",
"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_000014 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 +11x -12=0, let its roots be α and β. What is α²+β²? | {
"A": "6.78125",
"B": "12.5625",
"C": "13.5625",
"D": "10.17188"
} | C | 13.5625 | By Vieta's relations, α+β = -11/4 and αβ = -12/4. Then α²+β²=(α+β)²−2αβ = (-11/4)²−2(-12/4) = 13.5625. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13.5625, not 6.78125.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13.5625, not 12.5625.",
"C": "Correct. The worked calculation gives 13.5625.",
"D": "Incorrect. Substituting the stated va... | [
"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_008410 | 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 0.93 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.95232 K",
"B": "-1.04768 K",
"C": "-0.04768 K",
"D": "0.47616 K"
} | A | 0.95232 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×0.93=0.95232 K. | {
"A": "Correct. The worked calculation gives 0.95232 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.95232 K, not -1.04768 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.95232 K, not -0.04768 K.",
"D": "Incorrect. Substituting t... | [
"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_001170 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ -1x² +5x+7. Evaluate f′(5). | {
"A": "-295",
"B": "295",
"C": "236",
"D": "297"
} | B | 295 | Differentiate: f′(x)=3(4)x²+2(-1)x+(5). At x=5, f′(5)=3(4)(5)²+2(-1)(5)+(5)=295. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 295, not -295.",
"B": "Correct. The worked calculation gives 295.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 295, not 236.",
"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_000855 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio 5. What is the sum of its first 11 terms? | {
"A": "7324219.6",
"B": "58593748.8",
"C": "-73242186",
"D": "73242186"
} | D | 73242186 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(5^11−1)/(5−1)=73242186. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 73242186, not 7324219.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 73242186, not 58593748.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 73242186, n... | [
"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_007971 | 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 99 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "24.75 mmol L⁻¹",
"B": "37.125 mmol L⁻¹",
"C": "-24.75 mmol L⁻¹",
"D": "19.8 mmol L⁻¹"
} | A | 24.75 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=99/2^2=24.75 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 24.75 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24.75 mmol L⁻¹, not 37.125 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24.75 mmol L⁻¹, not -24.75 mmol L⁻¹.",
"D": "... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000788 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio -2. What is the sum of its first 11 terms? | {
"A": "4098",
"B": "3414",
"C": "3415",
"D": "342.5"
} | C | 3415 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(-2^11−1)/(-2−1)=3415. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3415, not 4098.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3415, not 3414.",
"C": "Correct. The worked calculation gives 3415.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_009801 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(Cl)_5]^-2, each Cl ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "2.25",
"B": "1.3",
"C": "3",
"D": "0"
} | C | 3 | Let the formal oxidation state of Cu be x. Charge balance gives x+(5)(−1)=-2; hence x=-2+5=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"C": "Correct. The worked calculation gives 3.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007915 | 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 65 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "8.125 mmol L⁻¹",
"B": "-4.0625 mmol L⁻¹",
"C": "3.04688 mmol L⁻¹",
"D": "4.0625 mmol L⁻¹"
} | D | 4.0625 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=65/2^4=4.0625 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.0625 mmol L⁻¹, not 8.125 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.0625 mmol L⁻¹, not -4.0625 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing r... | [
"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_005388 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 57 μF capacitor is charged to a potential difference of 23 V. Calculate the energy stored, expressed in μJ. | {
"A": "15077.5 μJ",
"B": "15075.5 μJ",
"C": "15076.5 μJ",
"D": "-15076.5 μJ"
} | C | 15076.5 μJ | U=½CV². Since C=57 μF, U in μJ is ½×57×(23)²=15076.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15076.5 μJ, not 15077.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15076.5 μJ, not 15075.5 μJ.",
"C": "Correct. The worked calculation gives 15076.5 μJ.",
"D": "Incorrect. Substitutin... | [
"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_002159 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 7 red, 3 blue and 5 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.32381",
"B": "0.32381",
"C": "2.32381",
"D": "1.03238"
} | B | 0.32381 | Favourable pairs = C(7,2)+C(3,2)+C(5,2)=34. Total pairs=C(15,2)=105. Therefore P=34/105=0.32381. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32381, not -0.32381.",
"B": "Correct. The worked calculation gives 0.32381.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32381, not 2.32381.",
"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_008195 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 13 A for 20364 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": "89.10094 g",
"B": "174.20189 g",
"C": "87.10094 g",
"D": "-87.10094 g"
} | C | 87.10094 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×20364/(2×96500)=87.10094 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 87.10094 g, not 89.10094 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 87.10094 g, not 174.20189 g.",
"C": "Correct. The worked calculation gives 87.10094 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002372 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 1], [6, -1]]. | {
"A": "-7",
"B": "-18",
"C": "-11",
"D": "-9"
} | D | -9 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(-1)−(1)(6)=-9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -9, not -7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -9, not -18.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -9, not -11.",
"D": "Correct. The w... | [
"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_008138 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 13 A for 21983 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": "92.02573 g",
"B": "94.02573 g",
"C": "95.02573 g",
"D": "75.22059 g"
} | B | 94.02573 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×21983/(2×96500)=94.02573 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 94.02573 g, not 92.02573 g.",
"B": "Correct. The worked calculation gives 94.02573 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 94.02573 g, not 95.02573 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_004131 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 49 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.31. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "86.24 N",
"B": "258.72 N",
"C": "137.984 N",
"D": "172.48 N"
} | D | 172.48 N | Net force=mg(sinθ−μcosθ)=49×10×(0.6−0.31×0.8)=172.48 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 172.48 N, not 86.24 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 172.48 N, not 258.72 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 172.48 N, not 1... | [
"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_001232 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ +7x² +3x+7. Evaluate f′(-3). | {
"A": "-123",
"B": "122",
"C": "123",
"D": "121"
} | C | 123 | Differentiate: f′(x)=3(6)x²+2(7)x+(3). At x=-3, f′(-3)=3(6)(-3)²+2(7)(-3)+(3)=123. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 123, not -123.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 123, not 122.",
"C": "Correct. The worked calculation gives 123.",
"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 |
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