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_002793 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(0, 3, 2) and v=(6, -4, -5), calculate u·v. | {
"A": "22",
"B": "-1.2",
"C": "-33",
"D": "-22"
} | D | -22 | The dot product is the sum of corresponding component products: (0)(6)+(3)(-4)+(2)(-5)=-22. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -22, not 22.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -22, not -1.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -22, not -33.",
"D": "Correct. T... | [
"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_000623 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 4 and common difference 9. Find the sum of its first 15 terms. | {
"A": "1206",
"B": "1005",
"C": "502.5",
"D": "1003"
} | B | 1005 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=4, d=9, n=15: Sₙ=15/2[2(4)+(15−1)(9)]=1005. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1005, not 1206.",
"B": "Correct. The worked calculation gives 1005.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1005, not 502.5.",
"D": "Incorrect. Substituting the stated values into the ... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005246 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +7 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "-5.20661 N",
"B": "7.20661 N",
"C": "4.20661 N",
"D": "5.20661 N"
} | D | 5.20661 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(7×10⁻⁶)/(11×10⁻²)²=5.20661 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.20661 N, not -5.20661 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.20661 N, not 7.20661 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.20661 N... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006036 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 37 cm in front of a thin convex lens of focal length 8 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.02759",
"B": "0.27586",
"C": "-0.27586",
"D": "-1.72414"
} | B | 0.27586 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(37)(8)/(37−8)=10.2069 cm. Thus |m|=v/u=10.2069/37=0.27586. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.27586, not 1.02759.",
"B": "Correct. The worked calculation gives 0.27586.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.27586, not -0.27586.",
"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_009312 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.62 V, transfers 2 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.37635 V",
"B": "0.5018 V",
"C": "-0.5018 V",
"D": "-0.4982 V"
} | B | 0.5018 V | Apply the Nernst equation: E=0.62−(0.0591/2)(4)=0.5018 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5018 V, not 0.37635 V.",
"B": "Correct. The worked calculation gives 0.5018 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5018 V, not -0.5018 V.",
"D": "Incorrect. Substituting the st... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000606 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 0 and common difference 4. Find the sum of its first 15 terms. | {
"A": "420",
"B": "418",
"C": "419",
"D": "840"
} | A | 420 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=0, d=4, n=15: Sₙ=15/2[2(0)+(15−1)(4)]=420. | {
"A": "Correct. The worked calculation gives 420.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 420, not 418.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 420, not 419.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001402 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (-3x² -8x -5) dx. | {
"A": "-40.8",
"B": "-25.5",
"C": "-35",
"D": "-34"
} | D | -34 | An antiderivative is (-3/3)x³+(-8/2)x²+(-5)x. Evaluating between 0 and 2 gives (-3/3)(2)³+(-8/2)(2)²+(-5)(2)=-34. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -34, not -40.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -34, not -25.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -34, not -35.",
"D": "Correc... | [
"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_003436 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 33 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "54.45 m",
"B": "108.9 m",
"C": "217.8 m",
"D": "130.68 m"
} | B | 108.9 m | Range R=u²sin(2θ)/g. Substituting u=33, θ=45° and g=10 gives R=(33)²sin(90°)/10=108.9 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 108.9 m, not 54.45 m.",
"B": "Correct. The worked calculation gives 108.9 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 108.9 m, not 217.8 m.",
"D": "Incorrect. Substituting the stated va... | [
"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_007284 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 16 mol of gas at 391 K and 0.2 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "1925.05722 L",
"B": "3850.11444 L",
"C": "2567.74296 L",
"D": "2566.74296 L"
} | D | 2566.74296 L | PV=nRT, so V=nRT/P=(16)(0.082057)(391)/(0.2)=2566.74296 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2566.74296 L, not 1925.05722 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2566.74296 L, not 3850.11444 L.",
"C": "Incorrect. Substituting the stated values into the governing relation give... | [
"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_009116 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.85 V, transfers 1 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.5545 V",
"B": "1.109 V",
"C": "0.5545 V",
"D": "3.5545 V"
} | C | 0.5545 V | Apply the Nernst equation: E=0.85−(0.0591/1)(5)=0.5545 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5545 V, not -0.5545 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.5545 V, not 1.109 V.",
"C": "Correct. The worked calculation gives 0.5545 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_008343 | 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 1.53 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": "-4.59 K",
"B": "5.59 K",
"C": "3.59 K",
"D": "4.59 K"
} | D | 4.59 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×1.0×1.53=4.59 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.59 K, not -4.59 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.59 K, not 5.59 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.59 K, not 3.59 K.",... | [
"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_002620 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, -4], [7, -8]]. | {
"A": "-88",
"B": "-35.2",
"C": "-42",
"D": "-44"
} | D | -44 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(-8)−(-4)(7)=-44. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -44, not -88.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -44, not -35.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -44, not -42.",
"D": "Correct.... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005860 | 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 3.4 atm at 379 K. What is its pressure at 536 K? | {
"A": "4.80844 atm",
"B": "7.21266 atm",
"C": "-4.80844 atm",
"D": "1.80844 atm"
} | A | 4.80844 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.4)(536)/(379)=4.80844 atm. | {
"A": "Correct. The worked calculation gives 4.80844 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.80844 atm, not 7.21266 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.80844 atm, not -4.80844 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004273 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 39 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.39. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "110.32 N",
"B": "56.16 N",
"C": "112.32 N",
"D": "89.856 N"
} | C | 112.32 N | Net force=mg(sinθ−μcosθ)=39×10×(0.6−0.39×0.8)=112.32 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 112.32 N, not 110.32 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 112.32 N, not 56.16 N.",
"C": "Correct. The worked calculation gives 112.32 N.",
"D": "Incorrect. Substituting the state... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009851 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(CN)_5]^+1, each CN ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "4.5",
"B": "3",
"C": "6",
"D": "8"
} | C | 6 | Let the formal oxidation state of Cr be x. Charge balance gives x+(5)(−1)=+1; hence x=1+5=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"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_009191 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.48 V, transfers 3 electrons, and has reaction quotient Q=10^3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.4209 V",
"B": "0.4209 V",
"C": "1.4209 V",
"D": "3.4209 V"
} | C | 1.4209 V | Apply the Nernst equation: E=1.48−(0.0591/3)(3)=1.4209 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.4209 V, not 2.4209 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4209 V, not 0.4209 V.",
"C": "Correct. The worked calculation gives 1.4209 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_009225 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.54 V, transfers 3 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.89865 V",
"B": "-1.4009 V",
"C": "1.5991 V",
"D": "0.5991 V"
} | D | 0.5991 V | Apply the Nernst equation: E=0.54−(0.0591/3)(-3)=0.5991 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5991 V, not 0.89865 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.5991 V, not -1.4009 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5991 V, no... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003489 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 33 m s⁻¹ at 15° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "54.45 m",
"B": "65.34 m",
"C": "27.225 m",
"D": "108.9 m"
} | A | 54.45 m | Range R=u²sin(2θ)/g. Substituting u=33, θ=15° and g=10 gives R=(33)²sin(30°)/10=54.45 m. | {
"A": "Correct. The worked calculation gives 54.45 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 54.45 m, not 65.34 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 54.45 m, not 27.225 m.",
"D": "Incorrect. Substituting the stated v... | [
"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_005096 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +7 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "315 N",
"B": "630 N",
"C": "504 N",
"D": "1260 N"
} | B | 630 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(7×10⁻⁶)/(3×10⁻²)²=630 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 630 N, not 315 N.",
"B": "Correct. The worked calculation gives 630 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 630 N, not 504 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_000359 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 14 and common difference 11. Find the sum of its first 29 terms. | {
"A": "-4872",
"B": "4874",
"C": "4872",
"D": "4873"
} | C | 4872 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=14, d=11, n=29: Sₙ=29/2[2(14)+(29−1)(11)]=4872. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4872, not -4872.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4872, not 4874.",
"C": "Correct. The worked calculation gives 4872.",
"D": "Incorrect. Substituting the stated values into the ... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006618 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 20 kg is attached to an ideal spring of force constant 672 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.25877 s",
"B": "0.34503 s",
"C": "-1.65497 s",
"D": "2.34503 s"
} | B | 0.34503 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(20/672)=0.34503 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34503 s, not 0.25877 s.",
"B": "Correct. The worked calculation gives 0.34503 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34503 s, not -1.65497 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_006279 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 54 cm in front of a thin convex lens of focal length 20 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.58824",
"B": "2.58824",
"C": "-0.58824",
"D": "-0.41176"
} | A | 0.58824 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(54)(20)/(54−20)=31.76471 cm. Thus |m|=v/u=31.76471/54=0.58824. | {
"A": "Correct. The worked calculation gives 0.58824.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.58824, not 2.58824.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.58824, not -0.58824.",
"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_006958 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 49 mol H₂ and 18 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "4.6 mol",
"B": "43.2 mol",
"C": "36 mol",
"D": "-36 mol"
} | C | 36 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 49 mol H₂O; O₂ can produce 36 mol H₂O. The limiting condition is O₂; product=36 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 36 mol, not 4.6 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 36 mol, not 43.2 mol.",
"C": "Correct. The worked calculation gives 36 mol.",
"D": "Incorrect. Substituting the stated valu... | [
"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_006436 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 23 kg is attached to an ideal spring of force constant 447 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.54633 s",
"B": "0.90734 s",
"C": "0.45367 s",
"D": "0.68051 s"
} | C | 0.45367 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(23/447)=0.45367 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.45367 s, not -0.54633 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.45367 s, not 0.90734 s.",
"C": "Correct. The worked calculation gives 0.45367 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_009570 | 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_20N_2X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "-2",
"B": "2",
"C": "-1",
"D": "3"
} | B | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+2−20−2)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not -1.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_009514 | 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_15H_2N_1X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "-14",
"B": "14",
"C": "13",
"D": "15"
} | B | 14 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×15+2+1−2−3)/2=14. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14, not -14.",
"B": "Correct. The worked calculation gives 14.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14, not 13.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009760 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(OH)_6]^-2, each OH ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "3",
"B": "4",
"C": "1.4",
"D": "2"
} | B | 4 | Let the formal oxidation state of Pd be x. Charge balance gives x+(6)(−1)=-2; hence x=-2+6=+4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 3.",
"B": "Correct. The worked calculation gives 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.4.",
"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_000528 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 4 and common difference 7. Find the sum of its first 14 terms. | {
"A": "695",
"B": "694",
"C": "-693",
"D": "693"
} | D | 693 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=4, d=7, n=14: Sₙ=14/2[2(4)+(14−1)(7)]=693. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 693, not 695.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 693, not 694.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 693, not -693.",
"D": "Correct. ... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006231 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 42 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": "4.1",
"B": "0.1",
"C": "1.1",
"D": "1.11"
} | C | 1.1 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(42)(22)/(42−22)=46.2 cm. Thus |m|=v/u=46.2/42=1.1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.1, not 4.1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1, not 0.1.",
"C": "Correct. The worked calculation gives 1.1.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_003391 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 70 m s⁻¹ at 15° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "196 m",
"B": "243 m",
"C": "245 m",
"D": "244 m"
} | C | 245 m | Range R=u²sin(2θ)/g. Substituting u=70, θ=15° and g=10 gives R=(70)²sin(30°)/10=245 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 245 m, not 196 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 245 m, not 243 m.",
"C": "Correct. The worked calculation gives 245 m.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_002887 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-1, -6, 2) and v=(-7, 5, 6), calculate u·v. | {
"A": "-13",
"B": "-11",
"C": "-22",
"D": "-10"
} | B | -11 | The dot product is the sum of corresponding component products: (-1)(-7)+(-6)(5)+(2)(6)=-11. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -11, not -13.",
"B": "Correct. The worked calculation gives -11.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -11, not -22.",
"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_009550 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_6H_7N_3X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "2.25",
"B": "6",
"C": "5",
"D": "3"
} | D | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+3−7−4)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 5.",
"D": "Correct. The worked... | [
"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_002567 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -7], [6, 0]]. | {
"A": "42",
"B": "21",
"C": "43",
"D": "5.2"
} | A | 42 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(0)−(-7)(6)=42. | {
"A": "Correct. The worked calculation gives 42.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 42, not 21.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 42, not 43.",
"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_004643 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 4 m is acted on by a constant torque of 89 N m about its central axis. Find its angular acceleration. | {
"A": "2.225 rad s⁻²",
"B": "5.225 rad s⁻²",
"C": "3.3375 rad s⁻²",
"D": "1.225 rad s⁻²"
} | A | 2.225 rad s⁻² | For a solid disc, I=½MR²=½(5)(4)²=40 kg m². Using τ=Iα, α=89/40=2.225 rad s⁻². | {
"A": "Correct. The worked calculation gives 2.225 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.225 rad s⁻², not 5.225 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.225 rad s⁻², not 3.3375 rad s⁻².",
"D": "Incorr... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000661 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 29 and common difference 10. Find the sum of its first 28 terms. | {
"A": "4593",
"B": "4592",
"C": "6888",
"D": "3444"
} | B | 4592 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=29, d=10, n=28: Sₙ=28/2[2(29)+(28−1)(10)]=4592. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4592, not 4593.",
"B": "Correct. The worked calculation gives 4592.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4592, not 6888.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_007686 | 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 80 minutes? | {
"A": "8.0625 mmol L⁻¹",
"B": "5.0625 mmol L⁻¹",
"C": "2.53125 mmol L⁻¹",
"D": "4.0625 mmol L⁻¹"
} | B | 5.0625 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=81/2^4=5.0625 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.0625 mmol L⁻¹, not 8.0625 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 5.0625 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.0625 mmol L⁻¹, not 2.53125 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_003774 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 12 m s⁻¹. A constant net force does 30 N of work over 3 m in the direction of motion. Find its final kinetic energy. | {
"A": "-882 J",
"B": "441 J",
"C": "883 J",
"D": "882 J"
} | D | 882 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(12)²+(30)(3)=882 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 882 J, not -882 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 882 J, not 441 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 882 J, not 883 J.",
"D"... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008905 | 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 0.68 mol L⁻¹ and initially B is absent. At equilibrium, 30% of A has dissociated at constant volume. Find K_c. | {
"A": "1.03497",
"B": "0.34971",
"C": "3.34971",
"D": "-0.65029"
} | B | 0.34971 | Let α=0.3. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.68)(0.3)²/(1−0.3)=0.34971. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34971, not 1.03497.",
"B": "Correct. The worked calculation gives 0.34971.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34971, not 3.34971.",
"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_009024 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.95 V, transfers 2 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.0773 V",
"B": "1.55798 V",
"C": "1.03865 V",
"D": "2.03865 V"
} | C | 1.03865 V | Apply the Nernst equation: E=0.95−(0.0591/2)(-3)=1.03865 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.03865 V, not 2.0773 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.03865 V, not 1.55798 V.",
"C": "Correct. The worked calculation gives 1.03865 V.",
"D": "Incorrect. Substituting the ... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008584 | 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 1.27 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.6604 K",
"B": "0.6604 K",
"C": "0.3302 K",
"D": "0.9906 K"
} | B | 0.6604 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.52×1.27=0.6604 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6604 K, not 1.6604 K.",
"B": "Correct. The worked calculation gives 0.6604 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.6604 K, not 0.3302 K.",
"D": "Incorrect. Substituting the stat... | [
"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_006373 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 15 kg is attached to an ideal spring of force constant 60 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "3 s",
"B": "2 s",
"C": "1 s",
"D": "0.5 s"
} | C | 1 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(15/60)=1 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1 s, not 3 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1 s, not 2 s.",
"C": "Correct. The worked calculation gives 1 s.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_006482 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 18 kg is attached to an ideal spring of force constant 122 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.76822 s",
"B": "-2.23178 s",
"C": "1.15233 s",
"D": "-1.23178 s"
} | A | 0.76822 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(18/122)=0.76822 s. | {
"A": "Correct. The worked calculation gives 0.76822 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.76822 s, not -2.23178 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.76822 s, not 1.15233 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_009187 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.94 V, transfers 2 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.96955 V",
"B": "1.09695 V",
"C": "1.9391 V",
"D": "0.96955 V"
} | D | 0.96955 V | Apply the Nernst equation: E=0.94−(0.0591/2)(-1)=0.96955 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.96955 V, not 2.96955 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.96955 V, not 1.09695 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.96955 V,... | [
"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_006242 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 39 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": "-3.33333",
"B": "3.33333",
"C": "5.33333",
"D": "2.5"
} | B | 3.33333 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(39)(30)/(39−30)=130 cm. Thus |m|=v/u=130/39=3.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.33333, not -3.33333.",
"B": "Correct. The worked calculation gives 3.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.33333, not 5.33333.",
"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_002343 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, 0], [9, -7]]. | {
"A": "-47.25",
"B": "-31.5",
"C": "-50.4",
"D": "-63"
} | D | -63 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(-7)−(0)(9)=-63. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -63, not -47.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -63, not -31.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -63, not -50.4.",
"D": "Cor... | [
"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_006652 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 3 kg is attached to an ideal spring of force constant 815 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.87866 s",
"B": "0.12134 s",
"C": "-1.87866 s",
"D": "0.06067 s"
} | B | 0.12134 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(3/815)=0.12134 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.12134 s, not -0.87866 s.",
"B": "Correct. The worked calculation gives 0.12134 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.12134 s, not -1.87866 s.",
"D": "Incorrect. Substituting t... | [
"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_004941 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 12 Ω and 5 Ω are connected in series; this combination is connected in parallel with a 16 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "-0.27206 A",
"B": "-1.27206 A",
"C": "2.72794 A",
"D": "0.72794 A"
} | D | 0.72794 A | Series branch resistance=12+5=17 Ω. Parallel equivalent R_eq=(17×16)/(17+16)=8.24242 Ω. Total current I=V/R_eq=6/8.24242=0.72794 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.72794 A, not -0.27206 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.72794 A, not -1.27206 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.72794 ... | [
"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_007385 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 44 mL of 0.10 M HCl is mixed with 56 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.07918",
"B": "10.07918",
"C": "6.03959",
"D": "15.07918"
} | A | 12.07918 | Excess OH⁻ moles=0.10×(56−44)/1000=0.001200 mol. Total volume=0.100 L, so [OH⁻]=0.012000 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.07918. | {
"A": "Correct. The worked calculation gives 12.07918.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.07918, not 10.07918.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.07918, not 6.03959.",
"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_001378 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (6x² -5x -5) dx. | {
"A": "-5.5",
"B": "-7.5",
"C": "-11",
"D": "-2.5"
} | A | -5.5 | An antiderivative is (6/3)x³+(-5/2)x²+(-5)x. Evaluating between 0 and 1 gives (6/3)(1)³+(-5/2)(1)²+(-5)(1)=-5.5. | {
"A": "Correct. The worked calculation gives -5.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -5.5, not -7.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -5.5, not -11.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_000715 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio 4. What is the sum of its first 8 terms? | {
"A": "4370",
"B": "43690",
"C": "43692",
"D": "87380"
} | B | 43690 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(4^8−1)/(4−1)=43690. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 43690, not 4370.",
"B": "Correct. The worked calculation gives 43690.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 43690, not 43692.",
"D": "Incorrect. Substituting the stated values into t... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003112 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-6+8i)/(11+7i). What is Re(z), the real part of z? | {
"A": "0.05882",
"B": "-0.02941",
"C": "-0.05882",
"D": "-1.05882"
} | C | -0.05882 | Multiply numerator and denominator by the conjugate (11-7i). Then Re(z)=(ac+bd)/(c²+d²)=((-6)(11)+(8)(7))/(11²+(7)²)=-0.05882. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.05882, not 0.05882.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.05882, not -0.02941.",
"C": "Correct. The worked calculation gives -0.05882.",
"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_004519 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 13 kg and radius 1 m is acted on by a constant torque of 53 N m about its central axis. Find its angular acceleration. | {
"A": "8.15385 rad s⁻²",
"B": "16.30769 rad s⁻²",
"C": "10.15385 rad s⁻²",
"D": "6.11538 rad s⁻²"
} | A | 8.15385 rad s⁻² | For a solid disc, I=½MR²=½(13)(1)²=6.5 kg m². Using τ=Iα, α=53/6.5=8.15385 rad s⁻². | {
"A": "Correct. The worked calculation gives 8.15385 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.15385 rad s⁻², not 16.30769 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.15385 rad s⁻², not 10.15385 rad s⁻².",
"... | [
"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_004612 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 4 kg and radius 1 m is acted on by a constant torque of 37 N m about its central axis. Find its angular acceleration. | {
"A": "18.5 rad s⁻²",
"B": "22.2 rad s⁻²",
"C": "9.25 rad s⁻²",
"D": "13.875 rad s⁻²"
} | A | 18.5 rad s⁻² | For a solid disc, I=½MR²=½(4)(1)²=2 kg m². Using τ=Iα, α=37/2=18.5 rad s⁻². | {
"A": "Correct. The worked calculation gives 18.5 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18.5 rad s⁻², not 22.2 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18.5 rad s⁻², not 9.25 rad s⁻².",
"D": "Incorrect. S... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001562 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (2x² -1x +6) dx. | {
"A": "17.2",
"B": "162",
"C": "160",
"D": "324"
} | B | 162 | An antiderivative is (2/3)x³+(-1/2)x²+(6)x. Evaluating between 0 and 6 gives (2/3)(6)³+(-1/2)(6)²+(6)(6)=162. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 162, not 17.2.",
"B": "Correct. The worked calculation gives 162.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 162, not 160.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_009384 | 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_15H_7N_3X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "12",
"B": "-12",
"C": "10",
"D": "24"
} | A | 12 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×15+2+3−7−4)/2=12. | {
"A": "Correct. The worked calculation gives 12.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12, not -12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12, not 10.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004701 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 14 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 18 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.64286 A",
"B": "1.64286 A",
"C": "0.64286 A",
"D": "1.23214 A"
} | B | 1.64286 A | Series branch resistance=14+14=28 Ω. Parallel equivalent R_eq=(28×18)/(28+18)=10.95652 Ω. Total current I=V/R_eq=18/10.95652=1.64286 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.64286 A, not 2.64286 A.",
"B": "Correct. The worked calculation gives 1.64286 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.64286 A, not 0.64286 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002269 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 6 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-2.69231",
"B": "0.61538",
"C": "0.30769",
"D": "-1.69231"
} | C | 0.30769 | Favourable pairs = C(4,2)+C(6,2)+C(3,2)=24. Total pairs=C(13,2)=78. Therefore P=24/78=0.30769. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not -2.69231.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not 0.61538.",
"C": "Correct. The worked calculation gives 0.30769.",
"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_004445 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 6 kg and radius 3 m is acted on by a constant torque of 77 N m about its central axis. Find its angular acceleration. | {
"A": "2.85185 rad s⁻²",
"B": "-2.85185 rad s⁻²",
"C": "5.7037 rad s⁻²",
"D": "4.85185 rad s⁻²"
} | A | 2.85185 rad s⁻² | For a solid disc, I=½MR²=½(6)(3)²=27 kg m². Using τ=Iα, α=77/27=2.85185 rad s⁻². | {
"A": "Correct. The worked calculation gives 2.85185 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.85185 rad s⁻², not -2.85185 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.85185 rad s⁻², not 5.7037 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_007319 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 5 mol of gas at 457 K and 0.75 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "500.00065 L",
"B": "-250.00033 L",
"C": "125.00016 L",
"D": "250.00033 L"
} | D | 250.00033 L | PV=nRT, so V=nRT/P=(5)(0.082057)(457)/(0.75)=250.00033 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 250.00033 L, not 500.00065 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 250.00033 L, not -250.00033 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2... | [
"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_003885 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block initially moves at 4 m s⁻¹. A constant net force does 15 N of work over 17 m in the direction of motion. Find its final kinetic energy. | {
"A": "442.5 J",
"B": "221.25 J",
"C": "297 J",
"D": "295 J"
} | D | 295 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(5)(4)²+(15)(17)=295 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 295 J, not 442.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 295 J, not 221.25 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 295 J, not 297 J.",
... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003544 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 58 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "168.2 m",
"B": "336.4 m",
"C": "403.68 m",
"D": "337.4 m"
} | B | 336.4 m | Range R=u²sin(2θ)/g. Substituting u=58, θ=45° and g=10 gives R=(58)²sin(90°)/10=336.4 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 336.4 m, not 168.2 m.",
"B": "Correct. The worked calculation gives 336.4 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 336.4 m, not 403.68 m.",
"D": "Incorrect. Substituting the stated v... | [
"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_004664 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 14 kg and radius 2 m is acted on by a constant torque of 42 N m about its central axis. Find its angular acceleration. | {
"A": "2.25 rad s⁻²",
"B": "1.5 rad s⁻²",
"C": "3.5 rad s⁻²",
"D": "-0.5 rad s⁻²"
} | B | 1.5 rad s⁻² | For a solid disc, I=½MR²=½(14)(2)²=28 kg m². Using τ=Iα, α=42/28=1.5 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.5 rad s⁻², not 2.25 rad s⁻².",
"B": "Correct. The worked calculation gives 1.5 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.5 rad s⁻², not 3.5 rad s⁻².",
"D": "Incorrect. Subst... | [
"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_009592 | 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_13H_17N_1X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "5",
"B": "7.5",
"C": "6",
"D": "1.5"
} | A | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×13+2+1−17−2)/2=5. | {
"A": "Correct. The worked calculation gives 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 6.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_004097 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 46 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.17. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "211.44 N",
"B": "22.344 N",
"C": "213.44 N",
"D": "214.44 N"
} | C | 213.44 N | Net force=mg(sinθ−μcosθ)=46×10×(0.6−0.17×0.8)=213.44 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 213.44 N, not 211.44 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 213.44 N, not 22.344 N.",
"C": "Correct. The worked calculation gives 213.44 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_006293 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 70 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": "0.55556",
"B": "-1.44444",
"C": "1.05556",
"D": "-0.44444"
} | A | 0.55556 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(70)(25)/(70−25)=38.88889 cm. Thus |m|=v/u=38.88889/70=0.55556. | {
"A": "Correct. The worked calculation gives 0.55556.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.55556, not -1.44444.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.55556, not 1.05556.",
"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_000850 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio 3. What is the sum of its first 7 terms? | {
"A": "-5465",
"B": "4098.75",
"C": "5465",
"D": "4372"
} | C | 5465 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(3^7−1)/(3−1)=5465. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5465, not -5465.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5465, not 4098.75.",
"C": "Correct. The worked calculation gives 5465.",
"D": "Incorrect. Substituting the stated values into t... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002283 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 11 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "2.37229",
"B": "0.27922",
"C": "0.37229",
"D": "1.37229"
} | C | 0.37229 | Favourable pairs = C(8,2)+C(11,2)+C(3,2)=86. Total pairs=C(22,2)=231. Therefore P=86/231=0.37229. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.37229, not 2.37229.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.37229, not 0.27922.",
"C": "Correct. The worked calculation gives 0.37229.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009741 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(Cl)_5]^-2, each Cl ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "4",
"B": "3",
"C": "1",
"D": "2.25"
} | B | 3 | Let the formal oxidation state of Ni 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 4.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000128 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 +13x -1=0, let its roots be α and β. What is α²+β²? | {
"A": "43.25",
"B": "32.4375",
"C": "42.25",
"D": "-43.25"
} | A | 43.25 | By Vieta's relations, α+β = -13/2 and αβ = -1/2. Then α²+β²=(α+β)²−2αβ = (-13/2)²−2(-1/2) = 43.25. | {
"A": "Correct. The worked calculation gives 43.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 43.25, not 32.4375.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 43.25, not 42.25.",
"D": "Incorrect. Substituting the stated values int... | [
"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_005699 | 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 0.5 atm at 387 K. What is its pressure at 657 K? | {
"A": "2.84884 atm",
"B": "0.84884 atm",
"C": "1.84884 atm",
"D": "1.08488 atm"
} | B | 0.84884 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.5)(657)/(387)=0.84884 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.84884 atm, not 2.84884 atm.",
"B": "Correct. The worked calculation gives 0.84884 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.84884 atm, not 1.84884 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008338 | 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 1.95 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "2.34 K",
"B": "0.17 K",
"C": "2.17 K",
"D": "1.17 K"
} | D | 1.17 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.6×1.95=1.17 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.17 K, not 2.34 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.17 K, not 0.17 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.17 K, not 2.17 K.",
... | [
"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_007882 | 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 88 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "-5.5 mmol L⁻¹",
"B": "4.125 mmol L⁻¹",
"C": "6.5 mmol L⁻¹",
"D": "5.5 mmol L⁻¹"
} | D | 5.5 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=88/2^4=5.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.5 mmol L⁻¹, not -5.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.5 mmol L⁻¹, not 4.125 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation g... | [
"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_009363 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_8H_0N_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "20",
"B": "7",
"C": "12",
"D": "10"
} | D | 10 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×8+2+2−0−0)/2=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 20.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 12.",
"D": "Correct. The work... | [
"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_006897 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 10 mol H₂ and 34 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "12 mol",
"B": "7 mol",
"C": "7.5 mol",
"D": "10 mol"
} | D | 10 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 10 mol H₂O; O₂ can produce 68 mol H₂O. The limiting condition is H₂; product=10 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 12 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 7 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 7.5 mol.",
... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001970 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 9 elements can be selected from a set of 20 distinct elements? | {
"A": "83980",
"B": "167960",
"C": "201552",
"D": "16797"
} | B | 167960 | Order does not matter, so the count is C(20,9)=20!/[9!(11)!]=167960. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 167960, not 83980.",
"B": "Correct. The worked calculation gives 167960.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 167960, not 201552.",
"D": "Incorrect. Substituting the stated values i... | [
"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_001551 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (4x² -3x -4) dx. | {
"A": "-2.33333",
"B": "-3.33333",
"C": "0.66667",
"D": "-5.33333"
} | B | -3.33333 | An antiderivative is (4/3)x³+(-3/2)x²+(-4)x. Evaluating between 0 and 2 gives (4/3)(2)³+(-3/2)(2)²+(-4)(2)=-3.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -3.33333, not -2.33333.",
"B": "Correct. The worked calculation gives -3.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -3.33333, not 0.66667.",
"D": "Incorrect. Substituting the state... | [
"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_006118 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 32 cm in front of a thin convex lens of focal length 7 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.028",
"B": "0.14",
"C": "0.28",
"D": "0.42"
} | C | 0.28 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(32)(7)/(32−7)=8.96 cm. Thus |m|=v/u=8.96/32=0.28. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.28, not 1.028.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.28, not 0.14.",
"C": "Correct. The worked calculation gives 0.28.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_003303 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-7-1i)/(10+9i). What is Re(z), the real part of z? | {
"A": "0.56354",
"B": "0.43646",
"C": "-0.43646",
"D": "1.56354"
} | C | -0.43646 | Multiply numerator and denominator by the conjugate (10-9i). Then Re(z)=(ac+bd)/(c²+d²)=((-7)(10)+(-1)(9))/(10²+(9)²)=-0.43646. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.43646, not 0.56354.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.43646, not 0.43646.",
"C": "Correct. The worked calculation gives -0.43646.",
"D": "Incorrect. Substituting the stated... | [
"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_009117 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.56 V, transfers 3 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.49388 V",
"B": "-2.3415 V",
"C": "-0.3415 V",
"D": "0.6585 V"
} | D | 0.6585 V | Apply the Nernst equation: E=0.56−(0.0591/3)(-5)=0.6585 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6585 V, not 0.49388 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6585 V, not -2.3415 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.6585 V, no... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007851 | 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 19 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "5.375 mmol L⁻¹",
"B": "2.375 mmol L⁻¹",
"C": "1.375 mmol L⁻¹",
"D": "1.1875 mmol L⁻¹"
} | B | 2.375 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=19/2^3=2.375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.375 mmol L⁻¹, not 5.375 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 2.375 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.375 mmol L⁻¹, not 1.375 mmol L⁻¹.",
"D": "In... | [
"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_002749 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(6, 2, 6) and v=(-1, -6, 1), calculate u·v. | {
"A": "-10",
"B": "-6",
"C": "-12",
"D": "-0.2"
} | C | -12 | The dot product is the sum of corresponding component products: (6)(-1)+(2)(-6)+(6)(1)=-12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -12, not -10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -12, not -6.",
"C": "Correct. The worked calculation gives -12.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_003318 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(5-13i)/(2+4i). What is Re(z), the real part of z? | {
"A": "-2.1",
"B": "-0.1",
"C": "0.9",
"D": "-1.1"
} | A | -2.1 | Multiply numerator and denominator by the conjugate (2-4i). Then Re(z)=(ac+bd)/(c²+d²)=((5)(2)+(-13)(4))/(2²+(4)²)=-2.1. | {
"A": "Correct. The worked calculation gives -2.1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2.1, not -0.1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2.1, not 0.9.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_009761 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(Cl)_3]^+3, each Cl ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "6",
"B": "4.5",
"C": "8",
"D": "7"
} | A | 6 | Let the formal oxidation state of Pd be x. Charge balance gives x+(3)(−1)=+3; hence x=3+3=+6. | {
"A": "Correct. The worked calculation gives 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 8.",
"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_007398 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 85 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": "2.51851",
"B": "1.25926",
"C": "5.03703",
"D": "3.77777"
} | A | 2.51851 | Excess H⁺ moles=0.10×(85−80)/1000=0.000500 mol. Total volume=0.165 L, so [H⁺]=0.003030 M and pH=−log₁₀[H⁺]=2.51851. | {
"A": "Correct. The worked calculation gives 2.51851.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.51851, not 1.25926.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.51851, not 5.03703.",
"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_006195 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 79 cm in front of a thin convex lens of focal length 23 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.41071",
"B": "0.30804",
"C": "1.04107",
"D": "-2.58929"
} | A | 0.41071 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(79)(23)/(79−23)=32.44643 cm. Thus |m|=v/u=32.44643/79=0.41071. | {
"A": "Correct. The worked calculation gives 0.41071.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.41071, not 0.30804.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.41071, not 1.04107.",
"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_003471 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 37 m s⁻¹ at 75° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "102.675 m",
"B": "66.45 m",
"C": "7.845 m",
"D": "68.45 m"
} | D | 68.45 m | Range R=u²sin(2θ)/g. Substituting u=37, θ=75° and g=10 gives R=(37)²sin(150°)/10=68.45 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 68.45 m, not 102.675 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 68.45 m, not 66.45 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 68.45 m, not 7.8... | [
"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_003150 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(6+4i)/(8+12i). What is Re(z), the real part of z? | {
"A": "0.69231",
"B": "3.46154",
"C": "0.46154",
"D": "1.46154"
} | C | 0.46154 | Multiply numerator and denominator by the conjugate (8-12i). Then Re(z)=(ac+bd)/(c²+d²)=((6)(8)+(4)(12))/(8²+(12)²)=0.46154. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.46154, not 0.69231.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.46154, not 3.46154.",
"C": "Correct. The worked calculation gives 0.46154.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002018 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 5 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.29412",
"B": "0.29412",
"C": "0.58824",
"D": "-1.70588"
} | B | 0.29412 | Favourable pairs = C(6,2)+C(5,2)+C(6,2)=40. Total pairs=C(17,2)=136. Therefore P=40/136=0.29412. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29412, not -0.29412.",
"B": "Correct. The worked calculation gives 0.29412.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29412, not 0.58824.",
"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_001513 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (5x² -8x +6) dx. | {
"A": "-66.66667",
"B": "133.33333",
"C": "64.66667",
"D": "66.66667"
} | D | 66.66667 | An antiderivative is (5/3)x³+(-8/2)x²+(6)x. Evaluating between 0 and 4 gives (5/3)(4)³+(-8/2)(4)²+(6)(4)=66.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 66.66667, not -66.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 66.66667, not 133.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 66.66667, no... | [
"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_002848 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, 7, -7) and v=(-6, -6, 4), calculate u·v. | {
"A": "-6.6",
"B": "-60.8",
"C": "-77",
"D": "-76"
} | D | -76 | The dot product is the sum of corresponding component products: (1)(-6)+(7)(-6)+(-7)(4)=-76. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -76, not -6.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -76, not -60.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -76, not -77.",
"D": "Correct... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008287 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 10 A for 15525 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": "25.53983 g",
"B": "52.07966 g",
"C": "51.07966 g",
"D": "61.2956 g"
} | C | 51.07966 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×10×15525/(2×96500)=51.07966 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 51.07966 g, not 25.53983 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 51.07966 g, not 52.07966 g.",
"C": "Correct. The worked calculation gives 51.07966 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_000091 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 +8x -5=0, let its roots be α and β. What is α²+β²? | {
"A": "2.05102",
"B": "2.73469",
"C": "5.46939",
"D": "-0.26531"
} | B | 2.73469 | By Vieta's relations, α+β = -8/7 and αβ = -5/7. Then α²+β²=(α+β)²−2αβ = (-8/7)²−2(-5/7) = 2.73469. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.73469, not 2.05102.",
"B": "Correct. The worked calculation gives 2.73469.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.73469, not 5.46939.",
"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_000357 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 4 and common difference 6. Find the sum of its first 26 terms. | {
"A": "1540.5",
"B": "2054",
"C": "-2054",
"D": "2464.8"
} | B | 2054 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=4, d=6, n=26: Sₙ=26/2[2(4)+(26−1)(6)]=2054. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2054, not 1540.5.",
"B": "Correct. The worked calculation gives 2054.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2054, not -2054.",
"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_003041 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(5+2i)/(1+6i). What is Re(z), the real part of z? | {
"A": "0.34459",
"B": "3.45946",
"C": "0.45946",
"D": "0.68919"
} | C | 0.45946 | Multiply numerator and denominator by the conjugate (1-6i). Then Re(z)=(ac+bd)/(c²+d²)=((5)(1)+(2)(6))/(1²+(6)²)=0.45946. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.45946, not 0.34459.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.45946, not 3.45946.",
"C": "Correct. The worked calculation gives 0.45946.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001917 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 12 elements can be selected from a set of 81 distinct elements? | {
"A": "70724320184700",
"B": "56579456147760",
"C": "106086480277050",
"D": "53043240138525"
} | A | 70724320184700 | Order does not matter, so the count is C(81,12)=81!/[12!(69)!]=70724320184700. | {
"A": "Correct. The worked calculation gives 70724320184700.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 70724320184700, not 56579456147760.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 70724320184700, not 106086480277050.",
"D": "I... | [
"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_006611 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 3 kg is attached to an ideal spring of force constant 350 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "3.18516 s",
"B": "0.27775 s",
"C": "0.18516 s",
"D": "0.37033 s"
} | C | 0.18516 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(3/350)=0.18516 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.18516 s, not 3.18516 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.18516 s, not 0.27775 s.",
"C": "Correct. The worked calculation gives 0.18516 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006986 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 16 mol H₂ and 28 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "12.8 mol",
"B": "12 mol",
"C": "32 mol",
"D": "16 mol"
} | D | 16 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 16 mol H₂O; O₂ can produce 56 mol H₂O. The limiting condition is H₂; product=16 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 12.8 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 12 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 32 mol."... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003271 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(6+2i)/(12+11i). What is Re(z), the real part of z? | {
"A": "3.35472",
"B": "1.35472",
"C": "0.35472",
"D": "0.17736"
} | C | 0.35472 | Multiply numerator and denominator by the conjugate (12-11i). Then Re(z)=(ac+bd)/(c²+d²)=((6)(12)+(2)(11))/(12²+(11)²)=0.35472. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35472, not 3.35472.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35472, not 1.35472.",
"C": "Correct. The worked calculation gives 0.35472.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005519 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 53 μF capacitor is charged to a potential difference of 7 V. Calculate the energy stored, expressed in μJ. | {
"A": "1296.5 μJ",
"B": "2597 μJ",
"C": "1298.5 μJ",
"D": "1558.2 μJ"
} | C | 1298.5 μJ | U=½CV². Since C=53 μF, U in μJ is ½×53×(7)²=1298.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1298.5 μJ, not 1296.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1298.5 μJ, not 2597 μJ.",
"C": "Correct. The worked calculation gives 1298.5 μJ.",
"D": "Incorrect. Substituting the s... | [
"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_003766 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 13 kg block initially moves at 4 m s⁻¹. A constant net force does 16 N of work over 9 m in the direction of motion. Find its final kinetic energy. | {
"A": "198.4 J",
"B": "248 J",
"C": "496 J",
"D": "297.6 J"
} | B | 248 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(13)(4)²+(16)(9)=248 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 248 J, not 198.4 J.",
"B": "Correct. The worked calculation gives 248 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 248 J, not 496 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 |
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