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_008846 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.02 mol L⁻¹ and initially B is absent. At equilibrium, 63% of A has dissociated at constant volume. Find K_c. | {
"A": "3.37663",
"B": "-4.37663",
"C": "4.37663",
"D": "5.37663"
} | C | 4.37663 | Let α=0.63. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.02)(0.63)²/(1−0.63)=4.37663. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.37663, not 3.37663.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.37663, not -4.37663.",
"C": "Correct. The worked calculation gives 4.37663.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003475 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 74 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "55.76 m",
"B": "438.08 m",
"C": "547.6 m",
"D": "546.6 m"
} | C | 547.6 m | Range R=u²sin(2θ)/g. Substituting u=74, θ=45° and g=10 gives R=(74)²sin(90°)/10=547.6 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 547.6 m, not 55.76 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 547.6 m, not 438.08 m.",
"C": "Correct. The worked calculation gives 547.6 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_000374 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 26 and common difference 7. Find the sum of its first 18 terms. | {
"A": "154.9",
"B": "2308.5",
"C": "1539",
"D": "1154.25"
} | C | 1539 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=26, d=7, n=18: Sₙ=18/2[2(26)+(18−1)(7)]=1539. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1539, not 154.9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1539, not 2308.5.",
"C": "Correct. The worked calculation gives 1539.",
"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_008981 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.43 mol L⁻¹ and initially B is absent. At equilibrium, 27% of A has dissociated at constant volume. Find K_c. | {
"A": "0.08588",
"B": "0.17176",
"C": "-2.82824",
"D": "0.12882"
} | B | 0.17176 | Let α=0.27. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.43)(0.27)²/(1−0.27)=0.17176. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.17176, not 0.08588.",
"B": "Correct. The worked calculation gives 0.17176.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.17176, not -2.82824.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002823 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-4, -7, 8) and v=(4, -6, 0), calculate u·v. | {
"A": "3.6",
"B": "26",
"C": "27",
"D": "13"
} | B | 26 | The dot product is the sum of corresponding component products: (-4)(4)+(-7)(-6)+(8)(0)=26. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26, not 3.6.",
"B": "Correct. The worked calculation gives 26.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26, not 27.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008169 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 8 A for 22212 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": "57.46475 g",
"B": "58.46475 g",
"C": "116.92949 g",
"D": "56.46475 g"
} | B | 58.46475 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×8×22212/(2×96500)=58.46475 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 58.46475 g, not 57.46475 g.",
"B": "Correct. The worked calculation gives 58.46475 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 58.46475 g, not 116.92949 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006106 | 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 20 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.8",
"B": "1.4",
"C": "0.4",
"D": "-1.6"
} | C | 0.4 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(70)(20)/(70−20)=28 cm. Thus |m|=v/u=28/70=0.4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.4, not 0.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.4, not 1.4.",
"C": "Correct. The worked calculation gives 0.4.",
"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_001441 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (6x² +8x +0) dx. | {
"A": "1280",
"B": "129",
"C": "1279",
"D": "1536"
} | A | 1280 | An antiderivative is (6/3)x³+(8/2)x²+(0)x. Evaluating between 0 and 8 gives (6/3)(8)³+(8/2)(8)²+(0)(8)=1280. | {
"A": "Correct. The worked calculation gives 1280.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1280, not 129.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1280, not 1279.",
"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_006011 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 64 cm in front of a thin convex lens of focal length 19 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.42222",
"B": "1.42222",
"C": "0.21111",
"D": "3.42222"
} | A | 0.42222 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(64)(19)/(64−19)=27.02222 cm. Thus |m|=v/u=27.02222/64=0.42222. | {
"A": "Correct. The worked calculation gives 0.42222.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.42222, not 1.42222.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.42222, not 0.21111.",
"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_008390 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.7 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "4.26 K",
"B": "-0.74 K",
"C": "1.26 K",
"D": "2.52 K"
} | C | 1.26 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.6×0.7=1.26 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.26 K, not 4.26 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.26 K, not -0.74 K.",
"C": "Correct. The worked calculation gives 1.26 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001670 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (2x² +1x -2) dx. | {
"A": "120",
"B": "150",
"C": "16",
"D": "300"
} | B | 150 | An antiderivative is (2/3)x³+(1/2)x²+(-2)x. Evaluating between 0 and 6 gives (2/3)(6)³+(1/2)(6)²+(-2)(6)=150. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 150, not 120.",
"B": "Correct. The worked calculation gives 150.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 150, not 16.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_009474 | 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_11N_3X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "4.5",
"B": "3",
"C": "1.3",
"D": "2"
} | B | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×8+2+3−11−4)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.5.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_007890 | 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 89 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "-0.34766 mmol L⁻¹",
"B": "0.34766 mmol L⁻¹",
"C": "-2.65234 mmol L⁻¹",
"D": "0.52148 mmol L⁻¹"
} | B | 0.34766 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=89/2^8=0.34766 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34766 mmol L⁻¹, not -0.34766 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.34766 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34766 mmol L⁻¹, not -2.65234 mmol L⁻¹."... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002880 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-3, -3, 7) and v=(-3, 7, 0), calculate u·v. | {
"A": "-10",
"B": "-18",
"C": "-12",
"D": "-11"
} | C | -12 | The dot product is the sum of corresponding component products: (-3)(-3)+(-3)(7)+(7)(0)=-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 -18.",
"C": "Correct. The worked calculation gives -12.",
"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_006313 | 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 19 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "3.95",
"B": "0.95",
"C": "-2.05",
"D": "-0.95"
} | B | 0.95 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(39)(19)/(39−19)=37.05 cm. Thus |m|=v/u=37.05/39=0.95. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.95, not 3.95.",
"B": "Correct. The worked calculation gives 0.95.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.95, not -2.05.",
"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_008450 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.32 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-5.28 K",
"B": "5.28 K",
"C": "3.96 K",
"D": "3.28 K"
} | B | 5.28 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×1.0×1.32=5.28 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.28 K, not -5.28 K.",
"B": "Correct. The worked calculation gives 5.28 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.28 K, not 3.96 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001388 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (4x² -3x -4) dx. | {
"A": "210",
"B": "212",
"C": "157.5",
"D": "168"
} | A | 210 | An antiderivative is (4/3)x³+(-3/2)x²+(-4)x. Evaluating between 0 and 6 gives (4/3)(6)³+(-3/2)(6)²+(-4)(6)=210. | {
"A": "Correct. The worked calculation gives 210.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 210, not 212.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 210, not 157.5.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000354 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 17 and common difference 6. Find the sum of its first 12 terms. | {
"A": "720",
"B": "600",
"C": "598",
"D": "599"
} | B | 600 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=17, d=6, n=12: Sₙ=12/2[2(17)+(12−1)(6)]=600. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 600, not 720.",
"B": "Correct. The worked calculation gives 600.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 600, not 598.",
"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_007204 | 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 285 K and 1.18 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "319.10163 L",
"B": "253.6813 L",
"C": "317.10163 L",
"D": "318.10163 L"
} | C | 317.10163 L | PV=nRT, so V=nRT/P=(16)(0.082057)(285)/(1.18)=317.10163 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 317.10163 L, not 319.10163 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 317.10163 L, not 253.6813 L.",
"C": "Correct. The worked calculation gives 317.10163 L.",
"D": "Incorrect. Substit... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002480 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, -2], [9, -5]]. | {
"A": "0.8",
"B": "-2",
"C": "0",
"D": "-1"
} | B | -2 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(-5)−(-2)(9)=-2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2, not 0.8.",
"B": "Correct. The worked calculation gives -2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2, not 0.",
"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_000986 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio 5. What is the sum of its first 9 terms? | {
"A": "5371091",
"B": "5371089",
"C": "2685545.5",
"D": "5371090"
} | A | 5371091 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(5^9−1)/(5−1)=5371091. | {
"A": "Correct. The worked calculation gives 5371091.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5371091, not 5371089.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5371091, not 2685545.5.",
"D": "Incorrect. Substituting the stated ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004016 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.11. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "5.608 N",
"B": "44.08 N",
"C": "69.12 N",
"D": "46.08 N"
} | D | 46.08 N | Net force=mg(sinθ−μcosθ)=9×10×(0.6−0.11×0.8)=46.08 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 46.08 N, not 5.608 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 46.08 N, not 44.08 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 46.08 N, not 69.12... | [
"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_004398 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 6 kg and radius 6 m is acted on by a constant torque of 32 N m about its central axis. Find its angular acceleration. | {
"A": "1.2963 rad s⁻²",
"B": "0.2963 rad s⁻²",
"C": "-1.7037 rad s⁻²",
"D": "3.2963 rad s⁻²"
} | B | 0.2963 rad s⁻² | For a solid disc, I=½MR²=½(6)(6)²=108 kg m². Using τ=Iα, α=32/108=0.2963 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.2963 rad s⁻², not 1.2963 rad s⁻².",
"B": "Correct. The worked calculation gives 0.2963 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.2963 rad s⁻², not -1.7037 rad s⁻².",
"D": "I... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009262 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.21 V, transfers 3 electrons, and has reaction quotient Q=10^0. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.815 V",
"B": "1.21 V",
"C": "1.121 V",
"D": "2.21 V"
} | B | 1.21 V | Apply the Nernst equation: E=1.21−(0.0591/3)(0)=1.21 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.21 V, not 1.815 V.",
"B": "Correct. The worked calculation gives 1.21 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.21 V, not 1.121 V.",
"D": "Incorrect. Substituting the stated value... | [
"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_004899 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 2 Ω are connected in series; this combination is connected in parallel with a 9 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "4 A",
"B": "3 A",
"C": "7 A",
"D": "5 A"
} | D | 5 A | Series branch resistance=4+2=6 Ω. Parallel equivalent R_eq=(6×9)/(6+9)=3.6 Ω. Total current I=V/R_eq=18/3.6=5 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5 A, not 4 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5 A, not 3 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5 A, not 7 A.",
"D": "Correct. T... | [
"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_008419 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.16 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.1664 K",
"B": "1.1664 K",
"C": "2.1664 K",
"D": "0.2496 K"
} | A | 0.1664 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×0.16=0.1664 K. | {
"A": "Correct. The worked calculation gives 0.1664 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.1664 K, not 1.1664 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.1664 K, not 2.1664 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_000500 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -14 and common difference 10. Find the sum of its first 29 terms. | {
"A": "366.4",
"B": "3655",
"C": "-3654",
"D": "3654"
} | D | 3654 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-14, d=10, n=29: Sₙ=29/2[2(-14)+(29−1)(10)]=3654. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3654, not 366.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3654, not 3655.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3654, not -3654.",
"D": "Co... | [
"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_006983 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 15 mol H₂ and 10 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "7.5 mol",
"B": "15 mol",
"C": "18 mol",
"D": "13 mol"
} | B | 15 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 15 mol H₂O; O₂ can produce 20 mol H₂O. The limiting condition is H₂; product=15 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15 mol, not 7.5 mol.",
"B": "Correct. The worked calculation gives 15 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15 mol, not 18 mol.",
"D": "Incorrect. Substituting the stated values... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006020 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 106 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": "-1.7381",
"B": "0.2619",
"C": "0.13095",
"D": "-2.7381"
} | B | 0.2619 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(106)(22)/(106−22)=27.7619 cm. Thus |m|=v/u=27.7619/106=0.2619. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.2619, not -1.7381.",
"B": "Correct. The worked calculation gives 0.2619.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.2619, not 0.13095.",
"D": "Incorrect. Substituting the stated value... | [
"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_001675 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 81 distinct elements? | {
"A": "19216197",
"B": "25621595",
"C": "20497276.8",
"D": "25621596"
} | D | 25621596 | Order does not matter, so the count is C(81,5)=81!/[5!(76)!]=25621596. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 25621596, not 19216197.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 25621596, not 25621595.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 25621596, not ... | [
"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_007750 | 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 120 minutes? | {
"A": "3.375 mmol L⁻¹",
"B": "2.75 mmol L⁻¹",
"C": "4.375 mmol L⁻¹",
"D": "1.375 mmol L⁻¹"
} | D | 1.375 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=88/2^6=1.375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.375 mmol L⁻¹, not 3.375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.375 mmol L⁻¹, not 2.75 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relati... | [
"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_009996 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(Cl)_2]^-4, each Cl ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "-3",
"B": "-2",
"C": "0",
"D": "2"
} | B | -2 | Let the formal oxidation state of Ni be x. Charge balance gives x+(2)(−1)=-4; hence x=-4+2=-2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2, not -3.",
"B": "Correct. The worked calculation gives -2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2, not 0.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_009699 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(CN)_3]^-2, each CN ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "2",
"B": "-1",
"C": "1",
"D": "1.5"
} | C | 1 | Let the formal oxidation state of Fe be x. Charge balance gives x+(3)(−1)=-2; hence x=-2+3=+1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not -1.",
"C": "Correct. The worked calculation gives 1.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001859 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 6 elements can be selected from a set of 69 distinct elements? | {
"A": "119877473",
"B": "119877472",
"C": "119877471",
"D": "95901977.6"
} | B | 119877472 | Order does not matter, so the count is C(69,6)=69!/[6!(63)!]=119877472. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 119877472, not 119877473.",
"B": "Correct. The worked calculation gives 119877472.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 119877472, not 119877471.",
"D": "Incorrect. Substituting the... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007338 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 33 mL of 0.10 M HCl is mixed with 76 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.59604",
"B": "18.89406",
"C": "-12.59604",
"D": "9.59604"
} | A | 12.59604 | Excess OH⁻ moles=0.10×(76−33)/1000=0.004300 mol. Total volume=0.109 L, so [OH⁻]=0.039450 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.59604. | {
"A": "Correct. The worked calculation gives 12.59604.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.59604, not 18.89406.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.59604, not -12.59604.",
"D": "Incorrect. Substituting the sta... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008612 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.51 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "3.612 K",
"B": "-1.388 K",
"C": "0.612 K",
"D": "1.0612 K"
} | C | 0.612 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.6×0.51=0.612 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.612 K, not 3.612 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.612 K, not -1.388 K.",
"C": "Correct. The worked calculation gives 0.612 K.",
"D": "Incorrect. Substituting the stated v... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001287 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-1x³ -7x² +11x+7. Evaluate f′(4). | {
"A": "-69.75",
"B": "-93",
"C": "-95",
"D": "-74.4"
} | B | -93 | Differentiate: f′(x)=3(-1)x²+2(-7)x+(11). At x=4, f′(4)=3(-1)(4)²+2(-7)(4)+(11)=-93. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -93, not -69.75.",
"B": "Correct. The worked calculation gives -93.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -93, not -95.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000710 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio 5. What is the sum of its first 7 terms? | {
"A": "78122",
"B": "117186",
"C": "78124",
"D": "78126"
} | C | 78124 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(5^7−1)/(5−1)=78124. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 78124, not 78122.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 78124, not 117186.",
"C": "Correct. The worked calculation gives 78124.",
"D": "Incorrect. Substituting the stated values into... | [
"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_006695 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 21 mol H₂ and 31 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "21 mol",
"B": "22 mol",
"C": "3.1 mol",
"D": "-21 mol"
} | A | 21 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 21 mol H₂O; O₂ can produce 62 mol H₂O. The limiting condition is H₂; product=21 mol. | {
"A": "Correct. The worked calculation gives 21 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21 mol, not 22 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21 mol, not 3.1 mol.",
"D": "Incorrect. Substituting the stated values... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000548 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -20 and common difference 7. Find the sum of its first 27 terms. | {
"A": "1916",
"B": "1918",
"C": "1533.6",
"D": "1917"
} | D | 1917 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-20, d=7, n=27: Sₙ=27/2[2(-20)+(27−1)(7)]=1917. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1917, not 1916.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1917, not 1918.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1917, not 1533.6.",
"D": "Co... | [
"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_000641 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 24 and common difference 3. Find the sum of its first 29 terms. | {
"A": "2871",
"B": "1914",
"C": "-1914",
"D": "3828"
} | B | 1914 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=24, d=3, n=29: Sₙ=29/2[2(24)+(29−1)(3)]=1914. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1914, not 2871.",
"B": "Correct. The worked calculation gives 1914.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1914, not -1914.",
"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_002596 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, -1], [6, 4]]. | {
"A": "9",
"B": "13.5",
"C": "21.6",
"D": "18"
} | D | 18 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(4)−(-1)(6)=18. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18, not 9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18, not 13.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18, not 21.6.",
"D": "Correct. The ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006702 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 6 mol H₂ and 14 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "6 mol",
"B": "-6 mol",
"C": "4.5 mol",
"D": "9 mol"
} | A | 6 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 6 mol H₂O; O₂ can produce 28 mol H₂O. The limiting condition is H₂; product=6 mol. | {
"A": "Correct. The worked calculation gives 6 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not -6 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 4.5 mol.",
"D": "Incorrect. Substituting the stated values in... | [
"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_008159 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 3 A for 25029 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": "24.70479 g",
"B": "26.70479 g",
"C": "3.47048 g",
"D": "12.3524 g"
} | A | 24.70479 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×3×25029/(2×96500)=24.70479 g. | {
"A": "Correct. The worked calculation gives 24.70479 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24.70479 g, not 26.70479 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24.70479 g, not 3.47048 g.",
"D": "Incorrect. Substituting... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003404 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 92 m s⁻¹ at 35° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "795.35583 m",
"B": "80.53558 m",
"C": "1193.03375 m",
"D": "596.51688 m"
} | A | 795.35583 m | Range R=u²sin(2θ)/g. Substituting u=92, θ=35° and g=10 gives R=(92)²sin(70°)/10=795.35583 m. | {
"A": "Correct. The worked calculation gives 795.35583 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 795.35583 m, not 80.53558 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 795.35583 m, not 1193.03375 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001632 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (5x² +2x +2) dx. | {
"A": "1.66667",
"B": "1.46667",
"C": "4.66667",
"D": "9.33333"
} | C | 4.66667 | An antiderivative is (5/3)x³+(2/2)x²+(2)x. Evaluating between 0 and 1 gives (5/3)(1)³+(2/2)(1)²+(2)(1)=4.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.66667, not 1.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.66667, not 1.46667.",
"C": "Correct. The worked calculation gives 4.66667.",
"D": "Incorrect. Substituting the stated va... | [
"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_007689 | 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 90 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "22.5 mmol L⁻¹",
"B": "45 mmol L⁻¹",
"C": "67.5 mmol L⁻¹",
"D": "36 mmol L⁻¹"
} | B | 45 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=90/2^1=45 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45 mmol L⁻¹, not 22.5 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 45 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 45 mmol L⁻¹, not 67.5 mmol L⁻¹.",
"D": "Incorrect. Su... | [
"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_006244 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 34 cm in front of a thin convex lens of focal length 10 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.58333",
"B": "1.04167",
"C": "0.20833",
"D": "0.41667"
} | D | 0.41667 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(34)(10)/(34−10)=14.16667 cm. Thus |m|=v/u=14.16667/34=0.41667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.41667, not -0.58333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.41667, not 1.04167.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.41667, not 0.20... | [
"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_002777 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(0, 7, 4) and v=(-7, -3, 0), calculate u·v. | {
"A": "-1.1",
"B": "-21",
"C": "21",
"D": "-23"
} | B | -21 | The dot product is the sum of corresponding component products: (0)(-7)+(7)(-3)+(4)(0)=-21. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -21, not -1.1.",
"B": "Correct. The worked calculation gives -21.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -21, not 21.",
"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_006823 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 41 mol H₂ and 27 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "-41 mol",
"B": "32.8 mol",
"C": "5.1 mol",
"D": "41 mol"
} | D | 41 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 41 mol H₂O; O₂ can produce 54 mol H₂O. The limiting condition is H₂; product=41 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 41 mol, not -41 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 41 mol, not 32.8 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 41 mol, not 5.1 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_001177 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=0x³ +8x² -7x+7. Evaluate f′(4). | {
"A": "68.4",
"B": "85.5",
"C": "57",
"D": "58"
} | C | 57 | Differentiate: f′(x)=3(0)x²+2(8)x+(-7). At x=4, f′(4)=3(0)(4)²+2(8)(4)+(-7)=57. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 57, not 68.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 57, not 85.5.",
"C": "Correct. The worked calculation gives 57.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003809 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block initially moves at 11 m s⁻¹. A constant net force does 20 N of work over 4 m in the direction of motion. Find its final kinetic energy. | {
"A": "93.7 J",
"B": "927 J",
"C": "463.5 J",
"D": "741.6 J"
} | B | 927 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(14)(11)²+(20)(4)=927 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 927 J, not 93.7 J.",
"B": "Correct. The worked calculation gives 927 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 927 J, not 463.5 J.",
"D": "Incorrect. Substituting the stated values in... | [
"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_006574 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 7 kg is attached to an ideal spring of force constant 417 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.38869 s",
"B": "2.25913 s",
"C": "1.02591 s",
"D": "0.25913 s"
} | D | 0.25913 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(7/417)=0.25913 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25913 s, not 0.38869 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25913 s, not 2.25913 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25913 s,... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001842 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 33 distinct elements? | {
"A": "1388416.6",
"B": "13884156",
"C": "27768312",
"D": "16660987.2"
} | B | 13884156 | Order does not matter, so the count is C(33,8)=33!/[8!(25)!]=13884156. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13884156, not 1388416.6.",
"B": "Correct. The worked calculation gives 13884156.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13884156, not 27768312.",
"D": "Incorrect. Substituting the sta... | [
"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_008200 | 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 2 A for 7332 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": "1.48247 g",
"B": "3.61851 g",
"C": "-4.82468 g",
"D": "4.82468 g"
} | D | 4.82468 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×2×7332/(2×96500)=4.82468 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.82468 g, not 1.48247 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.82468 g, not 3.61851 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.82468 g,... | [
"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_001988 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 2 elements can be selected from a set of 84 distinct elements? | {
"A": "3485",
"B": "1743",
"C": "2614.5",
"D": "3486"
} | D | 3486 | Order does not matter, so the count is C(84,2)=84!/[2!(82)!]=3486. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3486, not 3485.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3486, not 1743.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3486, not 2614.5.",
"D": "Co... | [
"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_006560 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 14 kg is attached to an ideal spring of force constant 49 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.93096 s",
"B": "0.80178 s",
"C": "3.06904 s",
"D": "1.06904 s"
} | D | 1.06904 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(14/49)=1.06904 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.06904 s, not -1.93096 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.06904 s, not 0.80178 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.06904 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002076 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 6 blue and 8 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.30994",
"B": "-2.69006",
"C": "-0.69006",
"D": "1.03099"
} | A | 0.30994 | Favourable pairs = C(5,2)+C(6,2)+C(8,2)=53. Total pairs=C(19,2)=171. Therefore P=53/171=0.30994. | {
"A": "Correct. The worked calculation gives 0.30994.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30994, not -2.69006.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30994, not -0.69006.",
"D": "Incorrect. Substituting the stated ... | [
"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_000992 | 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 5 terms? | {
"A": "1364",
"B": "681",
"C": "682",
"D": "545.6"
} | C | 682 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(4^5−1)/(4−1)=682. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 682, not 1364.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 682, not 681.",
"C": "Correct. The worked calculation gives 682.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004386 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 1 m is acted on by a constant torque of 20 N m about its central axis. Find its angular acceleration. | {
"A": "21 rad s⁻²",
"B": "16 rad s⁻²",
"C": "19 rad s⁻²",
"D": "20 rad s⁻²"
} | D | 20 rad s⁻² | For a solid disc, I=½MR²=½(2)(1)²=1 kg m². Using τ=Iα, α=20/1=20 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20 rad s⁻², not 21 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20 rad s⁻², not 16 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20 rad... | [
"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_008225 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 12 A for 29076 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": "86.0981 g",
"B": "57.39874 g",
"C": "113.79747 g",
"D": "114.79747 g"
} | D | 114.79747 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×12×29076/(2×96500)=114.79747 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 114.79747 g, not 86.0981 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 114.79747 g, not 57.39874 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 114.7... | [
"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_006075 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 18 cm in front of a thin convex lens of focal length 10 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.875",
"B": "0.9375",
"C": "4.25",
"D": "1.25"
} | D | 1.25 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(18)(10)/(18−10)=22.5 cm. Thus |m|=v/u=22.5/18=1.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.25, not 1.875.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.25, not 0.9375.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.25, not 4.25.",
"D": "C... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009886 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(OH)_3]^-4, each OH ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "-1",
"B": "0.9",
"C": "2",
"D": "-3"
} | A | -1 | Let the formal oxidation state of Cr be x. Charge balance gives x+(3)(−1)=-4; hence x=-4+3=-1. | {
"A": "Correct. The worked calculation gives -1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1, not 0.9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1, not 2.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009040 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.49 V, transfers 1 electrons, and has reaction quotient Q=10^-4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.7264 V",
"B": "2.5896 V",
"C": "4.7264 V",
"D": "-1.2736 V"
} | A | 1.7264 V | Apply the Nernst equation: E=1.49−(0.0591/1)(-4)=1.7264 V. | {
"A": "Correct. The worked calculation gives 1.7264 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.7264 V, not 2.5896 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.7264 V, not 4.7264 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_002207 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 9 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": "-0.64706",
"B": "0.70588",
"C": "0.17647",
"D": "0.35294"
} | D | 0.35294 | Favourable pairs = C(3,2)+C(9,2)+C(6,2)=54. Total pairs=C(18,2)=153. Therefore P=54/153=0.35294. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35294, not -0.64706.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35294, not 0.70588.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35294, not 0.17... | [
"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_007354 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 62 mL of 0.10 M HCl is mixed with 96 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.33282",
"B": "6.16641",
"C": "15.33282",
"D": "14.33282"
} | A | 12.33282 | Excess OH⁻ moles=0.10×(96−62)/1000=0.003400 mol. Total volume=0.158 L, so [OH⁻]=0.021519 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.33282. | {
"A": "Correct. The worked calculation gives 12.33282.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.33282, not 6.16641.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.33282, not 15.33282.",
"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_004988 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 11 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 5 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.16 A",
"B": "1.216 A",
"C": "1.62 A",
"D": "2.16 A"
} | D | 2.16 A | Series branch resistance=11+14=25 Ω. Parallel equivalent R_eq=(25×5)/(25+5)=4.16667 Ω. Total current I=V/R_eq=9/4.16667=2.16 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.16 A, not 4.16 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.16 A, not 1.216 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.16 A, not 1.62 A.",... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006224 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 49 cm in front of a thin convex lens of focal length 26 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.13043",
"B": "1.69565",
"C": "0.13043",
"D": "2.13043"
} | A | 1.13043 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(49)(26)/(49−26)=55.3913 cm. Thus |m|=v/u=55.3913/49=1.13043. | {
"A": "Correct. The worked calculation gives 1.13043.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.13043, not 1.69565.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.13043, not 0.13043.",
"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_003161 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(6+10i)/(10+12i). What is Re(z), the real part of z? | {
"A": "2.7377",
"B": "-0.2623",
"C": "0.7377",
"D": "-2.2623"
} | C | 0.7377 | Multiply numerator and denominator by the conjugate (10-12i). Then Re(z)=(ac+bd)/(c²+d²)=((6)(10)+(10)(12))/(10²+(12)²)=0.7377. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7377, not 2.7377.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7377, not -0.2623.",
"C": "Correct. The worked calculation gives 0.7377.",
"D": "Incorrect. Substituting the stated values... | [
"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_004624 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 4 m is acted on by a constant torque of 12 N m about its central axis. Find its angular acceleration. | {
"A": "1.075 rad s⁻²",
"B": "-0.25 rad s⁻²",
"C": "0.75 rad s⁻²",
"D": "-2.25 rad s⁻²"
} | C | 0.75 rad s⁻² | For a solid disc, I=½MR²=½(2)(4)²=16 kg m². Using τ=Iα, α=12/16=0.75 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.75 rad s⁻², not 1.075 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.75 rad s⁻², not -0.25 rad s⁻².",
"C": "Correct. The worked calculation gives 0.75 rad s⁻².",
"D": "Incorrect.... | [
"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_003560 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 26 m s⁻¹ at 50° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "79.8876 m",
"B": "7.6573 m",
"C": "66.573 m",
"D": "33.2865 m"
} | C | 66.573 m | Range R=u²sin(2θ)/g. Substituting u=26, θ=50° and g=10 gives R=(26)²sin(100°)/10=66.573 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 66.573 m, not 79.8876 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 66.573 m, not 7.6573 m.",
"C": "Correct. The worked calculation gives 66.573 m.",
"D": "Incorrect. Substituting the sta... | [
"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_000563 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 15 and common difference 14. Find the sum of its first 13 terms. | {
"A": "1287",
"B": "1930.5",
"C": "-1287",
"D": "1285"
} | A | 1287 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=15, d=14, n=13: Sₙ=13/2[2(15)+(13−1)(14)]=1287. | {
"A": "Correct. The worked calculation gives 1287.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1287, not 1930.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1287, not -1287.",
"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_008192 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 9 A for 16982 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": "49.28608 g",
"B": "51.28608 g",
"C": "50.28608 g",
"D": "48.28608 g"
} | C | 50.28608 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×9×16982/(2×96500)=50.28608 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 50.28608 g, not 49.28608 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 50.28608 g, not 51.28608 g.",
"C": "Correct. The worked calculation gives 50.28608 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_006400 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 19 kg is attached to an ideal spring of force constant 878 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "3.29421 s",
"B": "1.02942 s",
"C": "0.29421 s",
"D": "0.14711 s"
} | C | 0.29421 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(19/878)=0.29421 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29421 s, not 3.29421 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29421 s, not 1.02942 s.",
"C": "Correct. The worked calculation gives 0.29421 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_009210 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.73 V, transfers 3 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.63615 V",
"B": "1.2723 V",
"C": "1.08482 V",
"D": "0.8482 V"
} | D | 0.8482 V | Apply the Nernst equation: E=0.73−(0.0591/3)(-6)=0.8482 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8482 V, not 0.63615 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8482 V, not 1.2723 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8482 V, not... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000564 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -13 and common difference 15. Find the sum of its first 18 terms. | {
"A": "1545.75",
"B": "2062",
"C": "2061",
"D": "207.1"
} | C | 2061 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-13, d=15, n=18: Sₙ=18/2[2(-13)+(18−1)(15)]=2061. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2061, not 1545.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2061, not 2062.",
"C": "Correct. The worked calculation gives 2061.",
"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_005796 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.1 atm at 369 K. What is its pressure at 743 K? | {
"A": "2.11423 atm",
"B": "4.22846 atm",
"C": "1.22846 atm",
"D": "2.22846 atm"
} | B | 4.22846 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.1)(743)/(369)=4.22846 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.22846 atm, not 2.11423 atm.",
"B": "Correct. The worked calculation gives 4.22846 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.22846 atm, not 1.22846 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_008856 | 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 2 mol L⁻¹ and initially B is absent. At equilibrium, 45% of A has dissociated at constant volume. Find K_c. | {
"A": "1.94545",
"B": "2.94545",
"C": "1.47273",
"D": "5.89091"
} | B | 2.94545 | Let α=0.45. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(2)(0.45)²/(1−0.45)=2.94545. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.94545, not 1.94545.",
"B": "Correct. The worked calculation gives 2.94545.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.94545, not 1.47273.",
"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_002690 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-4, 9, 7) and v=(9, -1, -6), calculate u·v. | {
"A": "-85",
"B": "-69.6",
"C": "-87",
"D": "-43.5"
} | C | -87 | The dot product is the sum of corresponding component products: (-4)(9)+(9)(-1)+(7)(-6)=-87. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -87, not -85.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -87, not -69.6.",
"C": "Correct. The worked calculation gives -87.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_004189 | 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 0.13. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "96.72 N",
"B": "290.16 N",
"C": "386.88 N",
"D": "193.44 N"
} | D | 193.44 N | Net force=mg(sinθ−μcosθ)=39×10×(0.6−0.13×0.8)=193.44 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 193.44 N, not 96.72 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 193.44 N, not 290.16 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 193.44 N, not 3... | [
"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_002686 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, -5, 3) and v=(7, -2, 2), calculate u·v. | {
"A": "27.6",
"B": "18.4",
"C": "23",
"D": "11.5"
} | C | 23 | The dot product is the sum of corresponding component products: (1)(7)+(-5)(-2)+(3)(2)=23. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 23, not 27.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23, not 18.4.",
"C": "Correct. The worked calculation gives 23.",
"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_002365 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, 4], [6, 8]]. | {
"A": "46",
"B": "72",
"C": "38.4",
"D": "48"
} | D | 48 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(8)−(4)(6)=48. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 48, not 46.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 48, not 72.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 48, not 38.4.",
"D": "Correct. The w... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002606 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, -2], [1, 2]]. | {
"A": "19",
"B": "14.4",
"C": "17",
"D": "18"
} | D | 18 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(2)−(-2)(1)=18. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18, not 19.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18, not 14.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18, not 17.",
"D": "Correct. The w... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006203 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 29 cm in front of a thin convex lens of focal length 17 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.70833",
"B": "1.41667",
"C": "-1.41667",
"D": "4.41667"
} | B | 1.41667 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(29)(17)/(29−17)=41.08333 cm. Thus |m|=v/u=41.08333/29=1.41667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.41667, not 0.70833.",
"B": "Correct. The worked calculation gives 1.41667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.41667, not -1.41667.",
"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_005226 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +9 μC are separated by 12 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "22.5 N",
"B": "27 N",
"C": "33.75 N",
"D": "-22.5 N"
} | A | 22.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(9×10⁻⁶)/(12×10⁻²)²=22.5 N. | {
"A": "Correct. The worked calculation gives 22.5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22.5 N, not 27 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22.5 N, not 33.75 N.",
"D": "Incorrect. Substituting the stated values i... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002385 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, 2], [6, 1]]. | {
"A": "-8",
"B": "-10",
"C": "-15",
"D": "-13"
} | B | -10 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(1)−(2)(6)=-10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -10, not -8.",
"B": "Correct. The worked calculation gives -10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -10, not -15.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_001704 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 39 distinct elements? | {
"A": "317872698",
"B": "635745396",
"C": "953618094",
"D": "635745398"
} | B | 635745396 | Order does not matter, so the count is C(39,10)=39!/[10!(29)!]=635745396. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 635745396, not 317872698.",
"B": "Correct. The worked calculation gives 635745396.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 635745396, not 953618094.",
"D": "Incorrect. Substituting the... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005955 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.4 atm at 190 K. What is its pressure at 273 K? | {
"A": "1.34484 atm",
"B": "2.44842 atm",
"C": "5.44842 atm",
"D": "3.44842 atm"
} | D | 3.44842 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.4)(273)/(190)=3.44842 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.44842 atm, not 1.34484 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.44842 atm, not 2.44842 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006206 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 18 cm in front of a thin convex lens of focal length 5 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-2.61538",
"B": "0.38462",
"C": "-0.61538",
"D": "0.28846"
} | B | 0.38462 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(18)(5)/(18−5)=6.92308 cm. Thus |m|=v/u=6.92308/18=0.38462. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.38462, not -2.61538.",
"B": "Correct. The worked calculation gives 0.38462.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.38462, not -0.61538.",
"D": "Incorrect. Substituting the stated ... | [
"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_008621 | 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 1.03 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "3.05472 K",
"B": "1.58208 K",
"C": "1.05472 K",
"D": "2.10944 K"
} | C | 1.05472 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×1.03=1.05472 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.05472 K, not 3.05472 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.05472 K, not 1.58208 K.",
"C": "Correct. The worked calculation gives 1.05472 K.",
"D": "Incorrect. Substituting the... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003121 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-11+8i)/(5+8i). What is Re(z), the real part of z? | {
"A": "1.10112",
"B": "0.10112",
"C": "-2.89888",
"D": "-0.89888"
} | B | 0.10112 | Multiply numerator and denominator by the conjugate (5-8i). Then Re(z)=(ac+bd)/(c²+d²)=((-11)(5)+(8)(8))/(5²+(8)²)=0.10112. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.10112, not 1.10112.",
"B": "Correct. The worked calculation gives 0.10112.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.10112, not -2.89888.",
"D": "Incorrect. Substituting the stated v... | [
"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_004925 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 15 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 9 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.34848 A",
"B": "4.69697 A",
"C": "6.69697 A",
"D": "1.69697 A"
} | B | 4.69697 A | Series branch resistance=15+7=22 Ω. Parallel equivalent R_eq=(22×9)/(22+9)=6.3871 Ω. Total current I=V/R_eq=30/6.3871=4.69697 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.69697 A, not 2.34848 A.",
"B": "Correct. The worked calculation gives 4.69697 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.69697 A, not 6.69697 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_003228 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-8+6i)/(10+9i). What is Re(z), the real part of z? | {
"A": "0.14365",
"B": "-3.14365",
"C": "-0.10773",
"D": "-0.14365"
} | D | -0.14365 | Multiply numerator and denominator by the conjugate (10-9i). Then Re(z)=(ac+bd)/(c²+d²)=((-8)(10)+(6)(9))/(10²+(9)²)=-0.14365. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.14365, not 0.14365.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.14365, not -3.14365.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.14365, not -... | [
"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_009691 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(CN)_3]^-1, each CN ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "-2",
"B": "1.2",
"C": "2",
"D": "4"
} | C | 2 | Let the formal oxidation state of Pd be x. Charge balance gives x+(3)(−1)=-1; hence x=-1+3=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.2.",
"C": "Correct. The worked calculation gives 2.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"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_004347 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 13 kg and radius 6 m is acted on by a constant torque of 8 N m about its central axis. Find its angular acceleration. | {
"A": "0.01709 rad s⁻²",
"B": "0.03419 rad s⁻²",
"C": "1.00342 rad s⁻²",
"D": "0.05128 rad s⁻²"
} | B | 0.03419 rad s⁻² | For a solid disc, I=½MR²=½(13)(6)²=234 kg m². Using τ=Iα, α=8/234=0.03419 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.03419 rad s⁻², not 0.01709 rad s⁻².",
"B": "Correct. The worked calculation gives 0.03419 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.03419 rad s⁻², not 1.00342 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_002342 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 4], [8, 6]]. | {
"A": "-17",
"B": "-13",
"C": "-21",
"D": "-14"
} | D | -14 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(6)−(4)(8)=-14. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -14, not -17.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -14, not -13.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -14, not -21.",
"D": "Correct. T... | [
"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_002840 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(2, 3, 0) and v=(5, -6, 7), calculate u·v. | {
"A": "-12",
"B": "-16",
"C": "-8",
"D": "-4"
} | C | -8 | The dot product is the sum of corresponding component products: (2)(5)+(3)(-6)+(0)(7)=-8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -8, not -12.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -8, not -16.",
"C": "Correct. The worked calculation gives -8.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002258 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 5 blue and 7 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.32381",
"B": "-0.32381",
"C": "1.03238",
"D": "0.48571"
} | A | 0.32381 | Favourable pairs = C(3,2)+C(5,2)+C(7,2)=34. Total pairs=C(15,2)=105. Therefore P=34/105=0.32381. | {
"A": "Correct. The worked calculation gives 0.32381.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32381, not -0.32381.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32381, not 1.03238.",
"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_002525 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 7], [3, 0]]. | {
"A": "-21",
"B": "-19",
"C": "-42",
"D": "-31.5"
} | A | -21 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(0)−(7)(3)=-21. | {
"A": "Correct. The worked calculation gives -21.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -21, not -19.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -21, not -42.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000616 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 28 and common difference 4. Find the sum of its first 32 terms. | {
"A": "2880",
"B": "2878",
"C": "5760",
"D": "2304"
} | A | 2880 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=28, d=4, n=32: Sₙ=32/2[2(28)+(32−1)(4)]=2880. | {
"A": "Correct. The worked calculation gives 2880.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2880, not 2878.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2880, not 5760.",
"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 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.