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_004505 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 13 kg and radius 2 m is acted on by a constant torque of 9 N m about its central axis. Find its angular acceleration. | {
"A": "0.34615 rad s⁻²",
"B": "3.34615 rad s⁻²",
"C": "0.25962 rad s⁻²",
"D": "-0.34615 rad s⁻²"
} | A | 0.34615 rad s⁻² | For a solid disc, I=½MR²=½(13)(2)²=26 kg m². Using τ=Iα, α=9/26=0.34615 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.34615 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34615 rad s⁻², not 3.34615 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34615 rad s⁻², not 0.25962 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_008306 | 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 5802 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": "4.8179 g",
"B": "5.72684 g",
"C": "3.8179 g",
"D": "2.86342 g"
} | C | 3.8179 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×2×5802/(2×96500)=3.8179 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.8179 g, not 4.8179 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.8179 g, not 5.72684 g.",
"C": "Correct. The worked calculation gives 3.8179 g.",
"D": "Incorrect. Substituting the sta... | [
"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_006805 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 26 mol H₂ and 5 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "13 mol",
"B": "7 mol",
"C": "-10 mol",
"D": "10 mol"
} | D | 10 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 26 mol H₂O; O₂ can produce 10 mol H₂O. The limiting condition is O₂; product=10 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 13 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 7 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not -10 mol.",
... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000384 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -13 and common difference 2. Find the sum of its first 13 terms. | {
"A": "-14",
"B": "-19.5",
"C": "-13",
"D": "-10"
} | C | -13 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-13, d=2, n=13: Sₙ=13/2[2(-13)+(13−1)(2)]=-13. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -13, not -14.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -13, not -19.5.",
"C": "Correct. The worked calculation gives -13.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_008645 | 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 0.66 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "2.70336 K",
"B": "2.35168 K",
"C": "0.67584 K",
"D": "1.35168 K"
} | D | 1.35168 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.512×0.66=1.35168 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.35168 K, not 2.70336 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.35168 K, not 2.35168 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.35168 K,... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003518 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 107 m s⁻¹ at 75° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "573.45 m",
"B": "572.45 m",
"C": "1144.9 m",
"D": "429.3375 m"
} | B | 572.45 m | Range R=u²sin(2θ)/g. Substituting u=107, θ=75° and g=10 gives R=(107)²sin(150°)/10=572.45 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 572.45 m, not 573.45 m.",
"B": "Correct. The worked calculation gives 572.45 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 572.45 m, not 1144.9 m.",
"D": "Incorrect. Substituting the stat... | [
"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_009828 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(OH)_4]^+3, each OH ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "14",
"B": "7",
"C": "6",
"D": "10"
} | B | 7 | Let the formal oxidation state of Fe be x. Charge balance gives x+(4)(−1)=+3; hence x=3+4=+7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 14.",
"B": "Correct. The worked calculation gives 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 6.",
"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_008976 | 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 1.78 mol L⁻¹ and initially B is absent. At equilibrium, 76% of A has dissociated at constant volume. Find K_c. | {
"A": "12.8516",
"B": "16.13547",
"C": "-17.13547",
"D": "17.13547"
} | D | 17.13547 | Let α=0.76. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.78)(0.76)²/(1−0.76)=17.13547. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 17.13547, not 12.8516.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17.13547, not 16.13547.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17.13547, not -... | [
"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_000059 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 +13x -1=0, let its roots be α and β. What is α²+β²? | {
"A": "205.2",
"B": "171",
"C": "342",
"D": "170"
} | B | 171 | By Vieta's relations, α+β = -13/1 and αβ = -1/1. Then α²+β²=(α+β)²−2αβ = (-13/1)²−2(-1/1) = 171. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 171, not 205.2.",
"B": "Correct. The worked calculation gives 171.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 171, not 342.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006152 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 42 cm in front of a thin convex lens of focal length 13 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.44828",
"B": "2.44828",
"C": "-0.55172",
"D": "0.44828"
} | D | 0.44828 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(42)(13)/(42−13)=18.82759 cm. Thus |m|=v/u=18.82759/42=0.44828. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.44828, not -0.44828.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.44828, not 2.44828.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.44828, not -0.5... | [
"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_002000 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 7 elements can be selected from a set of 50 distinct elements? | {
"A": "49942200",
"B": "99884400",
"C": "199768800",
"D": "99884398"
} | B | 99884400 | Order does not matter, so the count is C(50,7)=50!/[7!(43)!]=99884400. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 99884400, not 49942200.",
"B": "Correct. The worked calculation gives 99884400.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 99884400, not 199768800.",
"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_002836 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(3, -2, 0) and v=(5, 0, -1), calculate u·v. | {
"A": "2.5",
"B": "15",
"C": "18",
"D": "11.25"
} | B | 15 | The dot product is the sum of corresponding component products: (3)(5)+(-2)(0)+(0)(-1)=15. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15, not 2.5.",
"B": "Correct. The worked calculation gives 15.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15, not 18.",
"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_000423 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 9 and common difference 2. Find the sum of its first 10 terms. | {
"A": "180",
"B": "178",
"C": "179",
"D": "144"
} | A | 180 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=9, d=2, n=10: Sₙ=10/2[2(9)+(10−1)(2)]=180. | {
"A": "Correct. The worked calculation gives 180.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 180, not 178.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 180, not 179.",
"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_000433 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -2 and common difference 4. Find the sum of its first 21 terms. | {
"A": "399",
"B": "638.4",
"C": "1197",
"D": "798"
} | D | 798 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-2, d=4, n=21: Sₙ=21/2[2(-2)+(21−1)(4)]=798. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 798, not 399.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 798, not 638.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 798, not 1197.",
"D": "Correct... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007435 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 71 mL of 0.10 M HCl is mixed with 51 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.17853",
"B": "0.89266",
"C": "1.78533",
"D": "-1.78533"
} | C | 1.78533 | Excess H⁺ moles=0.10×(71−51)/1000=0.002000 mol. Total volume=0.122 L, so [H⁺]=0.016393 M and pH=−log₁₀[H⁺]=1.78533. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.78533, not 1.17853.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.78533, not 0.89266.",
"C": "Correct. The worked calculation gives 1.78533.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002306 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 8 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": "2.30736",
"B": "0.30736",
"C": "1.03074",
"D": "-0.30736"
} | B | 0.30736 | Favourable pairs = C(8,2)+C(8,2)+C(6,2)=71. Total pairs=C(22,2)=231. Therefore P=71/231=0.30736. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30736, not 2.30736.",
"B": "Correct. The worked calculation gives 0.30736.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30736, not 1.03074.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002397 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, 7], [7, 0]]. | {
"A": "-50",
"B": "-49",
"C": "-58.8",
"D": "-51"
} | B | -49 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(0)−(7)(7)=-49. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -49, not -50.",
"B": "Correct. The worked calculation gives -49.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -49, not -58.8.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006307 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 13 cm in front of a thin convex lens of focal length 6 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.42857",
"B": "0.85714",
"C": "1.85714",
"D": "-1.14286"
} | B | 0.85714 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(13)(6)/(13−6)=11.14286 cm. Thus |m|=v/u=11.14286/13=0.85714. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.85714, not 0.42857.",
"B": "Correct. The worked calculation gives 0.85714.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.85714, not 1.85714.",
"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_007441 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 41 mL of 0.10 M HCl is mixed with 99 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "13.6173",
"B": "12.6173",
"C": "18.92595",
"D": "11.6173"
} | B | 12.6173 | Excess OH⁻ moles=0.10×(99−41)/1000=0.005800 mol. Total volume=0.140 L, so [OH⁻]=0.041429 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.6173. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.6173, not 13.6173.",
"B": "Correct. The worked calculation gives 12.6173.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.6173, not 18.92595.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001916 | 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 70 distinct elements? | {
"A": "297528393162",
"B": "396704524217",
"C": "396704524218",
"D": "396704524216"
} | D | 396704524216 | Order does not matter, so the count is C(70,10)=70!/[10!(60)!]=396704524216. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 396704524216, not 297528393162.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 396704524216, not 396704524217.",
"C": "Incorrect. Substituting the stated values into the governing relation give... | [
"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_006662 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 13 kg is attached to an ideal spring of force constant 1177 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.21019 s",
"B": "2.21019 s",
"C": "3.21019 s",
"D": "0.21019 s"
} | D | 0.21019 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(13/1177)=0.21019 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.21019 s, not -0.21019 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.21019 s, not 2.21019 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.21019 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_004015 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 40 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.21. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "171.8 N",
"B": "174.8 N",
"C": "172.8 N",
"D": "86.4 N"
} | C | 172.8 N | Net force=mg(sinθ−μcosθ)=40×10×(0.6−0.21×0.8)=172.8 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 172.8 N, not 171.8 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 172.8 N, not 174.8 N.",
"C": "Correct. The worked calculation gives 172.8 N.",
"D": "Incorrect. Substituting the stated va... | [
"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_001038 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-1x³ +1x² -12x+7. Evaluate f′(-4). | {
"A": "-68",
"B": "-102",
"C": "68",
"D": "-67"
} | A | -68 | Differentiate: f′(x)=3(-1)x²+2(1)x+(-12). At x=-4, f′(-4)=3(-1)(-4)²+2(1)(-4)+(-12)=-68. | {
"A": "Correct. The worked calculation gives -68.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -68, not -102.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -68, not 68.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_002222 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 5 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "3.34167",
"B": "0.34167",
"C": "-0.34167",
"D": "2.34167"
} | B | 0.34167 | Favourable pairs = C(8,2)+C(5,2)+C(3,2)=41. Total pairs=C(16,2)=120. Therefore P=41/120=0.34167. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34167, not 3.34167.",
"B": "Correct. The worked calculation gives 0.34167.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34167, not -0.34167.",
"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_006394 | 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 809 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.3065 s",
"B": "-2.6935 s",
"C": "2.3065 s",
"D": "0.613 s"
} | A | 0.3065 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(19/809)=0.3065 s. | {
"A": "Correct. The worked calculation gives 0.3065 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3065 s, not -2.6935 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3065 s, not 2.3065 s.",
"D": "Incorrect. Substituting the sta... | [
"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_001573 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (-4x² -5x +7) dx. | {
"A": "-195.16667",
"B": "-97.08333",
"C": "-18.41667",
"D": "-194.16667"
} | D | -194.16667 | An antiderivative is (-4/3)x³+(-5/2)x²+(7)x. Evaluating between 0 and 5 gives (-4/3)(5)³+(-5/2)(5)²+(7)(5)=-194.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -194.16667, not -195.16667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -194.16667, not -97.08333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -194.16... | [
"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_001422 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (1x² +1x -3) dx. | {
"A": "-1.16667",
"B": "-1.625",
"C": "-2.16667",
"D": "-4.33333"
} | C | -2.16667 | An antiderivative is (1/3)x³+(1/2)x²+(-3)x. Evaluating between 0 and 1 gives (1/3)(1)³+(1/2)(1)²+(-3)(1)=-2.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2.16667, not -1.16667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2.16667, not -1.625.",
"C": "Correct. The worked calculation gives -2.16667.",
"D": "Incorrect. Substituting the stated... | [
"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_005615 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 14 μF capacitor is charged to a potential difference of 10 V. Calculate the energy stored, expressed in μJ. | {
"A": "701 μJ",
"B": "700 μJ",
"C": "702 μJ",
"D": "699 μJ"
} | B | 700 μJ | U=½CV². Since C=14 μF, U in μJ is ½×14×(10)²=700 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 700 μJ, not 701 μJ.",
"B": "Correct. The worked calculation gives 700 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 700 μJ, not 702 μJ.",
"D": "Incorrect. Substituting the stated values ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009789 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(Cl)_5]^-1, each Cl ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "1",
"B": "7",
"C": "4",
"D": "8"
} | C | 4 | Let the formal oxidation state of Ni be x. Charge balance gives x+(5)(−1)=-1; hence x=-1+5=+4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 7.",
"C": "Correct. The worked calculation gives 4.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000368 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 4 and common difference 9. Find the sum of its first 29 terms. | {
"A": "3770",
"B": "1885",
"C": "3768",
"D": "3016"
} | A | 3770 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=4, d=9, n=29: Sₙ=29/2[2(4)+(29−1)(9)]=3770. | {
"A": "Correct. The worked calculation gives 3770.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3770, not 1885.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3770, not 3768.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009783 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(CN)_2]^+1, each CN ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "2",
"B": "0",
"C": "1.5",
"D": "3"
} | D | 3 | Let the formal oxidation state of Pt be x. Charge balance gives x+(2)(−1)=+1; hence x=1+2=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 0.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.5.",
"D": "Correct. The worked ... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009423 | 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_3H_1X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "2.25",
"B": "-3",
"C": "3",
"D": "6"
} | C | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×3+2+0−1−1)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not -3.",
"C": "Correct. The worked calculation gives 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_001651 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (0x² -1x +3) dx. | {
"A": "-8",
"B": "-4",
"C": "0.2",
"D": "-16"
} | A | -8 | An antiderivative is (0/3)x³+(-1/2)x²+(3)x. Evaluating between 0 and 8 gives (0/3)(8)³+(-1/2)(8)²+(3)(8)=-8. | {
"A": "Correct. The worked calculation gives -8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -8, not -4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -8, not 0.2.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"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_009984 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(OH)_6]^-3, each OH ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "1.3",
"B": "6",
"C": "4",
"D": "3"
} | D | 3 | Let the formal oxidation state of Fe be x. Charge balance gives x+(6)(−1)=-3; hence x=-3+6=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.",
"D": "Correct. The worked ... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005972 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.2 atm at 397 K. What is its pressure at 719 K? | {
"A": "5.79547 atm",
"B": "11.59093 atm",
"C": "6.79547 atm",
"D": "3.79547 atm"
} | A | 5.79547 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.2)(719)/(397)=5.79547 atm. | {
"A": "Correct. The worked calculation gives 5.79547 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.79547 atm, not 11.59093 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.79547 atm, not 6.79547 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003772 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 3 m s⁻¹. A constant net force does 14 N of work over 4 m in the direction of motion. Find its final kinetic energy. | {
"A": "74 J",
"B": "148 J",
"C": "73 J",
"D": "75 J"
} | A | 74 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(3)²+(14)(4)=74 J. | {
"A": "Correct. The worked calculation gives 74 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 74 J, not 148 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 74 J, not 73 J.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_006811 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 19 mol H₂ and 31 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "22.8 mol",
"B": "19 mol",
"C": "9.5 mol",
"D": "14.25 mol"
} | B | 19 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 19 mol H₂O; O₂ can produce 62 mol H₂O. The limiting condition is H₂; product=19 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19 mol, not 22.8 mol.",
"B": "Correct. The worked calculation gives 19 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19 mol, not 9.5 mol.",
"D": "Incorrect. Substituting the stated valu... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009253 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.27 V, transfers 1 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.3291 V",
"B": "4.3291 V",
"C": "1.99365 V",
"D": "0.3291 V"
} | A | 1.3291 V | Apply the Nernst equation: E=1.27−(0.0591/1)(-1)=1.3291 V. | {
"A": "Correct. The worked calculation gives 1.3291 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.3291 V, not 4.3291 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.3291 V, not 1.99365 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000849 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio 2. What is the sum of its first 5 terms? | {
"A": "31",
"B": "4.1",
"C": "24.8",
"D": "33"
} | A | 31 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(2^5−1)/(2−1)=31. | {
"A": "Correct. The worked calculation gives 31.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 31, not 4.1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 31, not 24.8.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_007793 | 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 34 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "2.125 mmol L⁻¹",
"B": "3.1875 mmol L⁻¹",
"C": "1.59375 mmol L⁻¹",
"D": "-2.125 mmol L⁻¹"
} | A | 2.125 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=34/2^4=2.125 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 2.125 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.125 mmol L⁻¹, not 3.1875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.125 mmol L⁻¹, not 1.59375 mmol L⁻¹.",
"D": ... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004353 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 10 kg and radius 1 m is acted on by a constant torque of 51 N m about its central axis. Find its angular acceleration. | {
"A": "5.1 rad s⁻²",
"B": "2.02 rad s⁻²",
"C": "10.2 rad s⁻²",
"D": "15.3 rad s⁻²"
} | C | 10.2 rad s⁻² | For a solid disc, I=½MR²=½(10)(1)²=5 kg m². Using τ=Iα, α=51/5=10.2 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.2 rad s⁻², not 5.1 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.2 rad s⁻², not 2.02 rad s⁻².",
"C": "Correct. The worked calculation gives 10.2 rad s⁻².",
"D": "Incorrect. Su... | [
"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_003628 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 35 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "104.08811 m",
"B": "106.08811 m",
"C": "11.60881 m",
"D": "107.08811 m"
} | B | 106.08811 m | Range R=u²sin(2θ)/g. Substituting u=35, θ=60° and g=10 gives R=(35)²sin(120°)/10=106.08811 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 106.08811 m, not 104.08811 m.",
"B": "Correct. The worked calculation gives 106.08811 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 106.08811 m, not 11.60881 m.",
"D": "Incorrect. Substit... | [
"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_003938 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 4 m s⁻¹. A constant net force does 13 N of work over 7 m in the direction of motion. Find its final kinetic energy. | {
"A": "17.3 J",
"B": "-163 J",
"C": "163 J",
"D": "326 J"
} | C | 163 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(4)²+(13)(7)=163 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 163 J, not 17.3 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 163 J, not -163 J.",
"C": "Correct. The worked calculation gives 163 J.",
"D": "Incorrect. Substituting the stated values int... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004357 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 12 kg and radius 4 m is acted on by a constant torque of 30 N m about its central axis. Find its angular acceleration. | {
"A": "0.3125 rad s⁻²",
"B": "0.23438 rad s⁻²",
"C": "1.03125 rad s⁻²",
"D": "1.3125 rad s⁻²"
} | A | 0.3125 rad s⁻² | For a solid disc, I=½MR²=½(12)(4)²=96 kg m². Using τ=Iα, α=30/96=0.3125 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.3125 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3125 rad s⁻², not 0.23438 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3125 rad s⁻², not 1.03125 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_003525 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 70 m s⁻¹ at 50° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "241.2779 m",
"B": "483.5558 m",
"C": "49.25558 m",
"D": "482.5558 m"
} | D | 482.5558 m | Range R=u²sin(2θ)/g. Substituting u=70, θ=50° and g=10 gives R=(70)²sin(100°)/10=482.5558 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 482.5558 m, not 241.2779 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 482.5558 m, not 483.5558 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 482.55... | [
"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_000755 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio 5. What is the sum of its first 5 terms? | {
"A": "2928.75",
"B": "3903",
"C": "1952.5",
"D": "3905"
} | D | 3905 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(5^5−1)/(5−1)=3905. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3905, not 2928.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3905, not 3903.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3905, not 1952.5.",
"D": ... | [
"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_005748 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.7 atm at 345 K. What is its pressure at 698 K? | {
"A": "7.4858 atm",
"B": "4.4858 atm",
"C": "14.97159 atm",
"D": "10.4858 atm"
} | A | 7.4858 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.7)(698)/(345)=7.4858 atm. | {
"A": "Correct. The worked calculation gives 7.4858 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.4858 atm, not 4.4858 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.4858 atm, not 14.97159 atm.",
"D": "Incorrect. Substitut... | [
"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_004453 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 9 kg and radius 5 m is acted on by a constant torque of 68 N m about its central axis. Find its angular acceleration. | {
"A": "-0.39556 rad s⁻²",
"B": "0.45333 rad s⁻²",
"C": "1.60444 rad s⁻²",
"D": "0.60444 rad s⁻²"
} | D | 0.60444 rad s⁻² | For a solid disc, I=½MR²=½(9)(5)²=112.5 kg m². Using τ=Iα, α=68/112.5=0.60444 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.60444 rad s⁻², not -0.39556 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.60444 rad s⁻², not 0.45333 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing ... | [
"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_002893 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-2, 5, 9) and v=(9, -2, 2), calculate u·v. | {
"A": "-7.5",
"B": "-10",
"C": "-8",
"D": "-20"
} | B | -10 | The dot product is the sum of corresponding component products: (-2)(9)+(5)(-2)+(9)(2)=-10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -10, not -7.5.",
"B": "Correct. The worked calculation gives -10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -10, not -8.",
"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_008463 | 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 1.94 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "3.88 K",
"B": "5.88 K",
"C": "1.388 K",
"D": "6.88 K"
} | A | 3.88 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×1.94=3.88 K. | {
"A": "Correct. The worked calculation gives 3.88 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.88 K, not 5.88 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.88 K, not 1.388 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_005589 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 47 μF capacitor is charged to a potential difference of 22 V. Calculate the energy stored, expressed in μJ. | {
"A": "-11374 μJ",
"B": "11374 μJ",
"C": "8530.5 μJ",
"D": "1138.4 μJ"
} | B | 11374 μJ | U=½CV². Since C=47 μF, U in μJ is ½×47×(22)²=11374 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11374 μJ, not -11374 μJ.",
"B": "Correct. The worked calculation gives 11374 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11374 μJ, not 8530.5 μJ.",
"D": "Incorrect. Substituting the st... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001825 | 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 89 distinct elements? | {
"A": "41507640",
"B": "41507642",
"C": "33206113.6",
"D": "83015284"
} | B | 41507642 | Order does not matter, so the count is C(89,5)=89!/[5!(84)!]=41507642. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 41507642, not 41507640.",
"B": "Correct. The worked calculation gives 41507642.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 41507642, not 33206113.6.",
"D": "Incorrect. Substituting the st... | [
"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_009754 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(CN)_2]^-4, each CN ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "-2",
"B": "0",
"C": "-4",
"D": "-1"
} | A | -2 | Let the formal oxidation state of Pd be x. Charge balance gives x+(2)(−1)=-4; hence x=-4+2=-2. | {
"A": "Correct. The worked calculation gives -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2, not 0.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2, not -4.",
"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_002052 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 5 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": "0.64069",
"B": "-0.67965",
"C": "0.32035",
"D": "3.32035"
} | C | 0.32035 | Favourable pairs = C(9,2)+C(5,2)+C(8,2)=74. Total pairs=C(22,2)=231. Therefore P=74/231=0.32035. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32035, not 0.64069.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32035, not -0.67965.",
"C": "Correct. The worked calculation gives 0.32035.",
"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_000549 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 3 and common difference 6. Find the sum of its first 13 terms. | {
"A": "1014",
"B": "608.4",
"C": "507",
"D": "505"
} | C | 507 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=3, d=6, n=13: Sₙ=13/2[2(3)+(13−1)(6)]=507. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 507, not 1014.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 507, not 608.4.",
"C": "Correct. The worked calculation gives 507.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009161 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.26 V, transfers 2 electrons, and has reaction quotient Q=10^1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.23045 V",
"B": "-1.76955 V",
"C": "1.23045 V",
"D": "1.12305 V"
} | C | 1.23045 V | Apply the Nernst equation: E=1.26−(0.0591/2)(1)=1.23045 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.23045 V, not 0.23045 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.23045 V, not -1.76955 V.",
"C": "Correct. The worked calculation gives 1.23045 V.",
"D": "Incorrect. Substituting th... | [
"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_006315 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 62 cm in front of a thin convex lens of focal length 27 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.77143",
"B": "0.38571",
"C": "0.77143",
"D": "-2.22857"
} | C | 0.77143 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(62)(27)/(62−27)=47.82857 cm. Thus |m|=v/u=47.82857/62=0.77143. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.77143, not 1.77143.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.77143, not 0.38571.",
"C": "Correct. The worked calculation gives 0.77143.",
"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_008970 | 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 1.07 mol L⁻¹ and initially B is absent. At equilibrium, 18% of A has dissociated at constant volume. Find K_c. | {
"A": "1.01691",
"B": "-2.83089",
"C": "1.16911",
"D": "0.16911"
} | D | 0.16911 | Let α=0.18. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.07)(0.18)²/(1−0.18)=0.16911. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.16911, not 1.01691.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.16911, not -2.83089.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.16911, not 1.16... | [
"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_000948 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio 4. What is the sum of its first 10 terms? | {
"A": "2097150",
"B": "2097148",
"C": "1677720",
"D": "2097152"
} | A | 2097150 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(4^10−1)/(4−1)=2097150. | {
"A": "Correct. The worked calculation gives 2097150.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2097150, not 2097148.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2097150, not 1677720.",
"D": "Incorrect. Substituting the stated va... | [
"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_002162 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 11 red, 11 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": "3.32266",
"B": "1.03227",
"C": "0.32266",
"D": "0.242"
} | C | 0.32266 | Favourable pairs = C(11,2)+C(11,2)+C(7,2)=131. Total pairs=C(29,2)=406. Therefore P=131/406=0.32266. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32266, not 3.32266.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32266, not 1.03227.",
"C": "Correct. The worked calculation gives 0.32266.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004476 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 6 m is acted on by a constant torque of 20 N m about its central axis. Find its angular acceleration. | {
"A": "-2.44444 rad s⁻²",
"B": "0.55556 rad s⁻²",
"C": "-0.55556 rad s⁻²",
"D": "0.41667 rad s⁻²"
} | B | 0.55556 rad s⁻² | For a solid disc, I=½MR²=½(2)(6)²=36 kg m². Using τ=Iα, α=20/36=0.55556 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.55556 rad s⁻², not -2.44444 rad s⁻².",
"B": "Correct. The worked calculation gives 0.55556 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.55556 rad s⁻², not -0.55556 rad s⁻².",
"... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003900 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 3 m s⁻¹. A constant net force does 20 N of work over 4 m in the direction of motion. Find its final kinetic energy. | {
"A": "129.5 J",
"B": "128.5 J",
"C": "97.125 J",
"D": "130.5 J"
} | A | 129.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(3)²+(20)(4)=129.5 J. | {
"A": "Correct. The worked calculation gives 129.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 129.5 J, not 128.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 129.5 J, not 97.125 J.",
"D": "Incorrect. Substituting the stated v... | [
"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_000330 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 -9x -4=0, let its roots be α and β. What is α²+β²? | {
"A": "1.84",
"B": "4.84",
"C": "2.84",
"D": "3.63"
} | B | 4.84 | By Vieta's relations, α+β = 9/5 and αβ = -4/5. Then α²+β²=(α+β)²−2αβ = (9/5)²−2(-4/5) = 4.84. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.84, not 1.84.",
"B": "Correct. The worked calculation gives 4.84.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.84, not 2.84.",
"D": "Incorrect. Substituting the stated values into the g... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008988 | 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 0.35 mol L⁻¹ and initially B is absent. At equilibrium, 57% of A has dissociated at constant volume. Find K_c. | {
"A": "1.58672",
"B": "1.05781",
"C": "0.79336",
"D": "-1.05781"
} | B | 1.05781 | Let α=0.57. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.35)(0.57)²/(1−0.57)=1.05781. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.05781, not 1.58672.",
"B": "Correct. The worked calculation gives 1.05781.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.05781, not 0.79336.",
"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_006895 | 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 3 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "6 mol",
"B": "1.6 mol",
"C": "3 mol",
"D": "7 mol"
} | A | 6 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 15 mol H₂O; O₂ can produce 6 mol H₂O. The limiting condition is O₂; 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 1.6 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 3 mol.",
"D": "Incorrect. Substituting the stated values int... | [
"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_002693 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-2, -4, -5) and v=(4, -6, 4), calculate u·v. | {
"A": "-5",
"B": "-8",
"C": "-4",
"D": "-7"
} | C | -4 | The dot product is the sum of corresponding component products: (-2)(4)+(-4)(-6)+(-5)(4)=-4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4, not -5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -4, not -8.",
"C": "Correct. The worked calculation gives -4.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_009765 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(OH)_5]^+0, each OH ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "6",
"B": "3",
"C": "7.5",
"D": "5"
} | D | 5 | Let the formal oxidation state of Pd be x. Charge balance gives x+(5)(−1)=+0; hence x=0+5=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.5.",
"D": "Correct. The worked ... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006764 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 39 mol H₂ and 19 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "28.5 mol",
"B": "45.6 mol",
"C": "38 mol",
"D": "57 mol"
} | C | 38 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 39 mol H₂O; O₂ can produce 38 mol H₂O. The limiting condition is O₂; product=38 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 38 mol, not 28.5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 38 mol, not 45.6 mol.",
"C": "Correct. The worked calculation gives 38 mol.",
"D": "Incorrect. Substituting the stated val... | [
"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_004794 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 13 Ω are connected in series; this combination is connected in parallel with a 4 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "7.04348 A",
"B": "6.04348 A",
"C": "10.04348 A",
"D": "-7.04348 A"
} | A | 7.04348 A | Series branch resistance=10+13=23 Ω. Parallel equivalent R_eq=(23×4)/(23+4)=3.40741 Ω. Total current I=V/R_eq=24/3.40741=7.04348 A. | {
"A": "Correct. The worked calculation gives 7.04348 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.04348 A, not 6.04348 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.04348 A, not 10.04348 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000477 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 16 and common difference 14. Find the sum of its first 22 terms. | {
"A": "-3586",
"B": "1793",
"C": "4303.2",
"D": "3586"
} | D | 3586 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=16, d=14, n=22: Sₙ=22/2[2(16)+(22−1)(14)]=3586. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3586, not -3586.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3586, not 1793.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3586, not 4303.2.",
"D": "C... | [
"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_000619 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 29 and common difference 6. Find the sum of its first 25 terms. | {
"A": "2525",
"B": "3030",
"C": "2526",
"D": "-2525"
} | A | 2525 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=29, d=6, n=25: Sₙ=25/2[2(29)+(25−1)(6)]=2525. | {
"A": "Correct. The worked calculation gives 2525.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2525, not 3030.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2525, not 2526.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002025 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 10 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.15726",
"B": "1.31452",
"C": "0.31452",
"D": "-0.31452"
} | C | 0.31452 | Favourable pairs = C(10,2)+C(10,2)+C(12,2)=156. Total pairs=C(32,2)=496. Therefore P=156/496=0.31452. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31452, not 0.15726.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31452, not 1.31452.",
"C": "Correct. The worked calculation gives 0.31452.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008965 | 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 1.75 mol L⁻¹ and initially B is absent. At equilibrium, 56% of A has dissociated at constant volume. Find K_c. | {
"A": "1.98909",
"B": "4.98909",
"C": "-4.98909",
"D": "9.97818"
} | B | 4.98909 | Let α=0.56. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.75)(0.56)²/(1−0.56)=4.98909. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.98909, not 1.98909.",
"B": "Correct. The worked calculation gives 4.98909.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.98909, not -4.98909.",
"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_006038 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 24 cm in front of a thin convex lens of focal length 7 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-2.58824",
"B": "0.41176",
"C": "0.20588",
"D": "1.04118"
} | B | 0.41176 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(24)(7)/(24−7)=9.88235 cm. Thus |m|=v/u=9.88235/24=0.41176. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.41176, not -2.58824.",
"B": "Correct. The worked calculation gives 0.41176.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.41176, not 0.20588.",
"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_009237 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.15 V, transfers 3 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "3.1894 V",
"B": "1.1894 V",
"C": "1.7841 V",
"D": "2.3788 V"
} | B | 1.1894 V | Apply the Nernst equation: E=1.15−(0.0591/3)(-2)=1.1894 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.1894 V, not 3.1894 V.",
"B": "Correct. The worked calculation gives 1.1894 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1894 V, not 1.7841 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_005654 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 57 μF capacitor is charged to a potential difference of 20 V. Calculate the energy stored, expressed in μJ. | {
"A": "-11400 μJ",
"B": "11400 μJ",
"C": "9120 μJ",
"D": "11398 μJ"
} | B | 11400 μJ | U=½CV². Since C=57 μF, U in μJ is ½×57×(20)²=11400 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11400 μJ, not -11400 μJ.",
"B": "Correct. The worked calculation gives 11400 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11400 μJ, not 9120 μJ.",
"D": "Incorrect. Substituting the stat... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002993 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, 2, -7) and v=(9, -4, 0), calculate u·v. | {
"A": "56",
"B": "28",
"C": "-28",
"D": "27"
} | B | 28 | The dot product is the sum of corresponding component products: (4)(9)+(2)(-4)+(-7)(0)=28. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28, not 56.",
"B": "Correct. The worked calculation gives 28.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28, not -28.",
"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_003060 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-8+11i)/(10+4i). What is Re(z), the real part of z? | {
"A": "-0.23276",
"B": "-0.31034",
"C": "-0.15517",
"D": "2.68966"
} | B | -0.31034 | Multiply numerator and denominator by the conjugate (10-4i). Then Re(z)=(ac+bd)/(c²+d²)=((-8)(10)+(11)(4))/(10²+(4)²)=-0.31034. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.31034, not -0.23276.",
"B": "Correct. The worked calculation gives -0.31034.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.31034, not -0.15517.",
"D": "Incorrect. Substituting the stat... | [
"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_002276 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 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": "3.31905",
"B": "0.15952",
"C": "-0.68095",
"D": "0.31905"
} | D | 0.31905 | Favourable pairs = C(9,2)+C(5,2)+C(7,2)=67. Total pairs=C(21,2)=210. Therefore P=67/210=0.31905. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31905, not 3.31905.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31905, not 0.15952.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31905, not -0.68... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006664 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 2 kg is attached to an ideal spring of force constant 961 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.09124 s",
"B": "1.00912 s",
"C": "-1.90876 s",
"D": "0.09124 s"
} | D | 0.09124 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(2/961)=0.09124 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.09124 s, not 1.09124 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.09124 s, not 1.00912 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.09124 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_006507 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 13 kg is attached to an ideal spring of force constant 787 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.38557 s",
"B": "0.25705 s",
"C": "-1.74295 s",
"D": "3.25705 s"
} | B | 0.25705 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(13/787)=0.25705 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25705 s, not 0.38557 s.",
"B": "Correct. The worked calculation gives 0.25705 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25705 s, not -1.74295 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002099 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 6 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": "-1.69524",
"B": "3.30476",
"C": "0.30476",
"D": "0.15238"
} | C | 0.30476 | Favourable pairs = C(8,2)+C(6,2)+C(7,2)=64. Total pairs=C(21,2)=210. Therefore P=64/210=0.30476. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30476, not -1.69524.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30476, not 3.30476.",
"C": "Correct. The worked calculation gives 0.30476.",
"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_009545 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_18H_13N_1X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "11",
"B": "8.25",
"C": "2.1",
"D": "10"
} | A | 11 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+1−13−4)/2=11. | {
"A": "Correct. The worked calculation gives 11.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11, not 8.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11, not 2.1.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_007176 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 18 mol of gas at 195 K and 2.56 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "112.50784 L",
"B": "113.50784 L",
"C": "114.50784 L",
"D": "-112.50784 L"
} | A | 112.50784 L | PV=nRT, so V=nRT/P=(18)(0.082057)(195)/(2.56)=112.50784 L. | {
"A": "Correct. The worked calculation gives 112.50784 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 112.50784 L, not 113.50784 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 112.50784 L, not 114.50784 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005354 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 32 μF capacitor is charged to a potential difference of 18 V. Calculate the energy stored, expressed in μJ. | {
"A": "5184 μJ",
"B": "-5184 μJ",
"C": "10368 μJ",
"D": "5182 μJ"
} | A | 5184 μJ | U=½CV². Since C=32 μF, U in μJ is ½×32×(18)²=5184 μJ. | {
"A": "Correct. The worked calculation gives 5184 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5184 μJ, not -5184 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5184 μJ, not 10368 μJ.",
"D": "Incorrect. Substituting the stated ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005232 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +4 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "-22.22222 N",
"B": "22.22222 N",
"C": "33.33333 N",
"D": "23.22222 N"
} | B | 22.22222 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(4×10⁻⁶)/(9×10⁻²)²=22.22222 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22.22222 N, not -22.22222 N.",
"B": "Correct. The worked calculation gives 22.22222 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22.22222 N, not 33.33333 N.",
"D": "Incorrect. Substituti... | [
"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_002330 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 12 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "3.47059",
"B": "0.23529",
"C": "0.47059",
"D": "-0.47059"
} | C | 0.47059 | Favourable pairs = C(3,2)+C(12,2)+C(3,2)=72. Total pairs=C(18,2)=153. Therefore P=72/153=0.47059. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.47059, not 3.47059.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.47059, not 0.23529.",
"C": "Correct. The worked calculation gives 0.47059.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006777 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 7 mol H₂ and 13 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "9 mol",
"B": "1.7 mol",
"C": "-7 mol",
"D": "7 mol"
} | D | 7 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 7 mol H₂O; O₂ can produce 26 mol H₂O. The limiting condition is H₂; product=7 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7 mol, not 9 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7 mol, not 1.7 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7 mol, not -7 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_009747 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(Cl)_2]^+1, each Cl ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "5",
"B": "1.5",
"C": "3",
"D": "2.25"
} | C | 3 | Let the formal oxidation state of Ni be x. Charge balance gives x+(2)(−1)=+1; hence x=1+2=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.5.",
"C": "Correct. The worked calculation gives 3.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005695 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.4 atm at 359 K. What is its pressure at 463 K? | {
"A": "0.90279 atm",
"B": "3.80557 atm",
"C": "2.80557 atm",
"D": "1.80557 atm"
} | D | 1.80557 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.4)(463)/(359)=1.80557 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.80557 atm, not 0.90279 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.80557 atm, not 3.80557 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000086 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 +17x +2=0, let its roots be α and β. What is α²+β²? | {
"A": "286",
"B": "-285",
"C": "427.5",
"D": "285"
} | D | 285 | By Vieta's relations, α+β = -17/1 and αβ = 2/1. Then α²+β²=(α+β)²−2αβ = (-17/1)²−2(2/1) = 285. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 285, not 286.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 285, not -285.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 285, not 427.5.",
"D": "Correct... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007431 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 11 mL of 0.10 M HCl is mixed with 45 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "6.39165",
"B": "25.56658",
"C": "9.78329",
"D": "12.78329"
} | D | 12.78329 | Excess OH⁻ moles=0.10×(45−11)/1000=0.003400 mol. Total volume=0.056 L, so [OH⁻]=0.060714 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.78329. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.78329, not 6.39165.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.78329, not 25.56658.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.78329, not 9... | [
"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_003592 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 21 m s⁻¹ at 35° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "39.44044 m",
"B": "62.16067 m",
"C": "20.72022 m",
"D": "41.44044 m"
} | D | 41.44044 m | Range R=u²sin(2θ)/g. Substituting u=21, θ=35° and g=10 gives R=(21)²sin(70°)/10=41.44044 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 41.44044 m, not 39.44044 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 41.44044 m, not 62.16067 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 41.440... | [
"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_000552 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 28 and common difference 9. Find the sum of its first 21 terms. | {
"A": "1858.5",
"B": "2478",
"C": "-2478",
"D": "2477"
} | B | 2478 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=28, d=9, n=21: Sₙ=21/2[2(28)+(21−1)(9)]=2478. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2478, not 1858.5.",
"B": "Correct. The worked calculation gives 2478.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2478, not -2478.",
"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_007591 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 96 mL of 0.10 M HCl is mixed with 31 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.29089",
"B": "0.29089",
"C": "3.29089",
"D": "2.58178"
} | A | 1.29089 | Excess H⁺ moles=0.10×(96−31)/1000=0.006500 mol. Total volume=0.127 L, so [H⁺]=0.051181 M and pH=−log₁₀[H⁺]=1.29089. | {
"A": "Correct. The worked calculation gives 1.29089.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.29089, not 0.29089.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.29089, not 3.29089.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000908 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio -2. What is the sum of its first 12 terms? | {
"A": "-2728",
"B": "-3276",
"C": "-2730",
"D": "-2729"
} | C | -2730 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(-2^12−1)/(-2−1)=-2730. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2730, not -2728.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2730, not -3276.",
"C": "Correct. The worked calculation gives -2730.",
"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_002113 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 7 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.69231",
"B": "0.34615",
"C": "0.51923",
"D": "-1.65385"
} | B | 0.34615 | Favourable pairs = C(3,2)+C(7,2)+C(3,2)=27. Total pairs=C(13,2)=78. Therefore P=27/78=0.34615. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34615, not 0.69231.",
"B": "Correct. The worked calculation gives 0.34615.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34615, not 0.51923.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000119 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -1x +6=0, let its roots be α and β. What is α²+β²? | {
"A": "-4.75",
"B": "-5.75",
"C": "5.75",
"D": "-3.75"
} | B | -5.75 | By Vieta's relations, α+β = 1/2 and αβ = 6/2. Then α²+β²=(α+β)²−2αβ = (1/2)²−2(6/2) = -5.75. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -5.75, not -4.75.",
"B": "Correct. The worked calculation gives -5.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -5.75, not 5.75.",
"D": "Incorrect. Substituting the stated values into t... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005663 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 8 μF capacitor is charged to a potential difference of 15 V. Calculate the energy stored, expressed in μJ. | {
"A": "720 μJ",
"B": "902 μJ",
"C": "-900 μJ",
"D": "900 μJ"
} | D | 900 μJ | U=½CV². Since C=8 μF, U in μJ is ½×8×(15)²=900 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 900 μJ, not 720 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 900 μJ, not 902 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 900 μJ, not -900 μJ.",... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006233 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 22 cm in front of a thin convex lens of focal length 6 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.5625",
"B": "-1.625",
"C": "0.375",
"D": "0.28125"
} | C | 0.375 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(22)(6)/(22−6)=8.25 cm. Thus |m|=v/u=8.25/22=0.375. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.375, not 0.5625.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.375, not -1.625.",
"C": "Correct. The worked calculation gives 0.375.",
"D": "Incorrect. Substituting the stated values int... | [
"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 |
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