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_004228 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.37. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "66.88 N",
"B": "25.08 N",
"C": "33.44 N",
"D": "34.44 N"
} | C | 33.44 N | Net force=mg(sinθ−μcosθ)=11×10×(0.6−0.37×0.8)=33.44 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33.44 N, not 66.88 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33.44 N, not 25.08 N.",
"C": "Correct. The worked calculation gives 33.44 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_006159 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 111 cm in front of a thin convex lens of focal length 25 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.02907",
"B": "-0.7093",
"C": "0.2907",
"D": "2.2907"
} | C | 0.2907 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(111)(25)/(111−25)=32.26744 cm. Thus |m|=v/u=32.26744/111=0.2907. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.2907, not 1.02907.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.2907, not -0.7093.",
"C": "Correct. The worked calculation gives 0.2907.",
"D": "Incorrect. Substituting the stated value... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005111 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +1 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "-8.1 N",
"B": "8.1 N",
"C": "5.1 N",
"D": "6.1 N"
} | B | 8.1 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(1×10⁻⁶)/(10×10⁻²)²=8.1 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.1 N, not -8.1 N.",
"B": "Correct. The worked calculation gives 8.1 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.1 N, not 5.1 N.",
"D": "Incorrect. Substituting the stated values into... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002482 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, -5], [7, -2]]. | {
"A": "17",
"B": "13.6",
"C": "15",
"D": "20.4"
} | A | 17 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(-2)−(-5)(7)=17. | {
"A": "Correct. The worked calculation gives 17.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17, not 13.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17, not 15.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003308 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(3+2i)/(4+1i). What is Re(z), the real part of z? | {
"A": "1.08235",
"B": "0.82353",
"C": "1.82353",
"D": "1.23529"
} | B | 0.82353 | Multiply numerator and denominator by the conjugate (4-1i). Then Re(z)=(ac+bd)/(c²+d²)=((3)(4)+(2)(1))/(4²+(1)²)=0.82353. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.82353, not 1.08235.",
"B": "Correct. The worked calculation gives 0.82353.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.82353, not 1.82353.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000473 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -18 and common difference 4. Find the sum of its first 8 terms. | {
"A": "-32",
"B": "-64",
"C": "-2.2",
"D": "-31"
} | A | -32 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-18, d=4, n=8: Sₙ=8/2[2(-18)+(8−1)(4)]=-32. | {
"A": "Correct. The worked calculation gives -32.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -32, not -64.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -32, not -2.2.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008543 | 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 1.05 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": "2.1504 K",
"B": "4.1504 K",
"C": "5.1504 K",
"D": "4.3008 K"
} | A | 2.1504 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.512×1.05=2.1504 K. | {
"A": "Correct. The worked calculation gives 2.1504 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.1504 K, not 4.1504 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.1504 K, not 5.1504 K.",
"D": "Incorrect. Substituting the stat... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008175 | 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 6 A for 23898 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": "48.17688 g",
"B": "47.17688 g",
"C": "5.71769 g",
"D": "23.58844 g"
} | B | 47.17688 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×6×23898/(2×96500)=47.17688 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 47.17688 g, not 48.17688 g.",
"B": "Correct. The worked calculation gives 47.17688 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 47.17688 g, not 5.71769 g.",
"D": "Incorrect. Substituting... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004853 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 3 Ω are connected in series; this combination is connected in parallel with a 12 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.65625 A",
"B": "-1.125 A",
"C": "2.875 A",
"D": "0.875 A"
} | D | 0.875 A | Series branch resistance=13+3=16 Ω. Parallel equivalent R_eq=(16×12)/(16+12)=6.85714 Ω. Total current I=V/R_eq=6/6.85714=0.875 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.875 A, not 0.65625 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.875 A, not -1.125 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.875 A, not 2.... | [
"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_002087 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 9 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": "-0.68775",
"B": "1.31225",
"C": "0.31225",
"D": "3.31225"
} | C | 0.31225 | Favourable pairs = C(6,2)+C(9,2)+C(8,2)=79. Total pairs=C(23,2)=253. Therefore P=79/253=0.31225. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31225, not -0.68775.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31225, not 1.31225.",
"C": "Correct. The worked calculation gives 0.31225.",
"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_003496 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 55 m s⁻¹ at 15° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "226.875 m",
"B": "113.4375 m",
"C": "151.25 m",
"D": "153.25 m"
} | C | 151.25 m | Range R=u²sin(2θ)/g. Substituting u=55, θ=15° and g=10 gives R=(55)²sin(30°)/10=151.25 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 151.25 m, not 226.875 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 151.25 m, not 113.4375 m.",
"C": "Correct. The worked calculation gives 151.25 m.",
"D": "Incorrect. Substituting the s... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002014 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 4 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.7",
"B": "-2.7",
"C": "1.3",
"D": "0.3"
} | D | 0.3 | Favourable pairs = C(6,2)+C(4,2)+C(6,2)=36. Total pairs=C(16,2)=120. Therefore P=36/120=0.3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3, not -0.7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3, not -2.7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3, not 1.3.",
"D": "Correct.... | [
"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_002949 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(8, 7, 2) and v=(0, 7, 2), calculate u·v. | {
"A": "106",
"B": "53",
"C": "26.5",
"D": "79.5"
} | B | 53 | The dot product is the sum of corresponding component products: (8)(0)+(7)(7)+(2)(2)=53. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 53, not 106.",
"B": "Correct. The worked calculation gives 53.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 53, not 26.5.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_000042 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +11x +6=0, let its roots be α and β. What is α²+β²? | {
"A": "1.83",
"B": "3.44",
"C": "2.44",
"D": "3.66"
} | C | 2.44 | By Vieta's relations, α+β = -11/5 and αβ = 6/5. Then α²+β²=(α+β)²−2αβ = (-11/5)²−2(6/5) = 2.44. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.44, not 1.83.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.44, not 3.44.",
"C": "Correct. The worked calculation gives 2.44.",
"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_000471 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 4 and common difference 14. Find the sum of its first 33 terms. | {
"A": "7525",
"B": "9028.8",
"C": "7524",
"D": "3762"
} | C | 7524 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=4, d=14, n=33: Sₙ=33/2[2(4)+(33−1)(14)]=7524. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7524, not 7525.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7524, not 9028.8.",
"C": "Correct. The worked calculation gives 7524.",
"D": "Incorrect. Substituting the stated values into the... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000772 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio -3. What is the sum of its first 6 terms? | {
"A": "-908",
"B": "-910",
"C": "-912",
"D": "-90"
} | B | -910 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(-3^6−1)/(-3−1)=-910. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -910, not -908.",
"B": "Correct. The worked calculation gives -910.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -910, not -912.",
"D": "Incorrect. Substituting the stated values into the g... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007671 | 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 36 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "4.5 mmol L⁻¹",
"B": "6.75 mmol L⁻¹",
"C": "9 mmol L⁻¹",
"D": "10 mmol L⁻¹"
} | C | 9 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=36/2^2=9 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9 mmol L⁻¹, not 4.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9 mmol L⁻¹, not 6.75 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 9 mmol L⁻¹.",
"D": "Incorrect. Substi... | [
"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_008958 | 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 1.93 mol L⁻¹ and initially B is absent. At equilibrium, 66% of A has dissociated at constant volume. Find K_c. | {
"A": "9.89068",
"B": "8.89068",
"C": "4.94534",
"D": "19.78136"
} | A | 9.89068 | Let α=0.66. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.93)(0.66)²/(1−0.66)=9.89068. | {
"A": "Correct. The worked calculation gives 9.89068.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.89068, not 8.89068.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.89068, not 4.94534.",
"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_007415 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 87 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": "2.37536",
"B": "0.58358",
"C": "-0.41642",
"D": "1.58358"
} | D | 1.58358 | Excess H⁺ moles=0.10×(87−51)/1000=0.003600 mol. Total volume=0.138 L, so [H⁺]=0.026087 M and pH=−log₁₀[H⁺]=1.58358. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.58358, not 2.37536.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.58358, not 0.58358.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.58358, not -0.41... | [
"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_001705 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 11 elements can be selected from a set of 80 distinct elements? | {
"A": "10477677064400",
"B": "20955354128800",
"C": "1047767706441",
"D": "8382141651520"
} | A | 10477677064400 | Order does not matter, so the count is C(80,11)=80!/[11!(69)!]=10477677064400. | {
"A": "Correct. The worked calculation gives 10477677064400.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10477677064400, not 20955354128800.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10477677064400, not 1047767706441.",
"D": "Inc... | [
"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_001566 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (5x² +1x -2) dx. | {
"A": "368",
"B": "365",
"C": "367",
"D": "366"
} | D | 366 | An antiderivative is (5/3)x³+(1/2)x²+(-2)x. Evaluating between 0 and 6 gives (5/3)(6)³+(1/2)(6)²+(-2)(6)=366. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 366, not 368.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 366, not 365.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 366, not 367.",
"D": "Correct. T... | [
"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_007068 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 4 mol of gas at 603 K and 1.22 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "160.23072 L",
"B": "-162.23072 L",
"C": "162.23072 L",
"D": "121.67304 L"
} | C | 162.23072 L | PV=nRT, so V=nRT/P=(4)(0.082057)(603)/(1.22)=162.23072 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 162.23072 L, not 160.23072 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 162.23072 L, not -162.23072 L.",
"C": "Correct. The worked calculation gives 162.23072 L.",
"D": "Incorrect. Subst... | [
"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_006917 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 50 mol H₂ and 34 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "60 mol",
"B": "52 mol",
"C": "50 mol",
"D": "100 mol"
} | C | 50 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 50 mol H₂O; O₂ can produce 68 mol H₂O. The limiting condition is H₂; product=50 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 50 mol, not 60 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 50 mol, not 52 mol.",
"C": "Correct. The worked calculation gives 50 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009525 | 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_4H_8N_1X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "-2",
"B": "0.75",
"C": "2",
"D": "1"
} | D | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×4+2+1−8−1)/2=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"D": "Correct. The worke... | [
"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_008594 | 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 0.96 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.9984 K",
"B": "1.4976 K",
"C": "0.9984 K",
"D": "1.9984 K"
} | C | 0.9984 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×0.96=0.9984 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9984 K, not -0.9984 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9984 K, not 1.4976 K.",
"C": "Correct. The worked calculation gives 0.9984 K.",
"D": "Incorrect. Substituting the sta... | [
"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_000588 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 6 and common difference 9. Find the sum of its first 11 terms. | {
"A": "562",
"B": "561",
"C": "841.5",
"D": "420.75"
} | B | 561 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=6, d=9, n=11: Sₙ=11/2[2(6)+(11−1)(9)]=561. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 561, not 562.",
"B": "Correct. The worked calculation gives 561.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 561, not 841.5.",
"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_009577 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_13H_2N_3X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "11",
"B": "13",
"C": "2.3",
"D": "-13"
} | B | 13 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×13+2+3−2−3)/2=13. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13, not 11.",
"B": "Correct. The worked calculation gives 13.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13, not 2.3.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001622 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (6x² -6x -5) dx. | {
"A": "75",
"B": "148",
"C": "300",
"D": "150"
} | D | 150 | An antiderivative is (6/3)x³+(-6/2)x²+(-5)x. Evaluating between 0 and 5 gives (6/3)(5)³+(-6/2)(5)²+(-5)(5)=150. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 150, not 75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 150, not 148.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 150, not 300.",
"D": "Correct. Th... | [
"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_005576 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 37 μF capacitor is charged to a potential difference of 19 V. Calculate the energy stored, expressed in μJ. | {
"A": "6679.5 μJ",
"B": "5008.875 μJ",
"C": "6678.5 μJ",
"D": "668.85 μJ"
} | C | 6678.5 μJ | U=½CV². Since C=37 μF, U in μJ is ½×37×(19)²=6678.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6678.5 μJ, not 6679.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6678.5 μJ, not 5008.875 μJ.",
"C": "Correct. The worked calculation gives 6678.5 μJ.",
"D": "Incorrect. Substituting t... | [
"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_000860 | 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 11 terms? | {
"A": "-4094",
"B": "4095",
"C": "4094",
"D": "3070.5"
} | C | 4094 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(2^11−1)/(2−1)=4094. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4094, not -4094.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4094, not 4095.",
"C": "Correct. The worked calculation gives 4094.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_007988 | 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 39 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "1.60938 mmol L⁻¹",
"B": "1.06094 mmol L⁻¹",
"C": "0.60938 mmol L⁻¹",
"D": "-0.60938 mmol L⁻¹"
} | C | 0.60938 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=39/2^6=0.60938 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.60938 mmol L⁻¹, not 1.60938 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.60938 mmol L⁻¹, not 1.06094 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.60938 mmol L⁻¹.",
... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008231 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 13 A for 16852 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": "-72.07941 g",
"B": "57.66353 g",
"C": "72.07941 g",
"D": "108.11911 g"
} | C | 72.07941 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×16852/(2×96500)=72.07941 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 72.07941 g, not -72.07941 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 72.07941 g, not 57.66353 g.",
"C": "Correct. The worked calculation gives 72.07941 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001820 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 2 elements can be selected from a set of 64 distinct elements? | {
"A": "2016",
"B": "202.6",
"C": "3024",
"D": "2419.2"
} | A | 2016 | Order does not matter, so the count is C(64,2)=64!/[2!(62)!]=2016. | {
"A": "Correct. The worked calculation gives 2016.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2016, not 202.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2016, not 3024.",
"D": "Incorrect. Substituting the stated values into the ... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007761 | 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 51 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "0.39844 mmol L⁻¹",
"B": "1.79688 mmol L⁻¹",
"C": "0.79688 mmol L⁻¹",
"D": "2.79688 mmol L⁻¹"
} | C | 0.79688 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=51/2^6=0.79688 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.79688 mmol L⁻¹, not 0.39844 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.79688 mmol L⁻¹, not 1.79688 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.79688 mmol L⁻¹.",
... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008382 | 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 0.45 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.06912 K",
"B": "0.6912 K",
"C": "3.6912 K",
"D": "1.0368 K"
} | B | 0.6912 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.512×0.45=0.6912 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6912 K, not 1.06912 K.",
"B": "Correct. The worked calculation gives 0.6912 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.6912 K, not 3.6912 K.",
"D": "Incorrect. Substituting the sta... | [
"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_000773 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio 4. What is the sum of its first 6 terms? | {
"A": "6823",
"B": "10237.5",
"C": "6825",
"D": "683.5"
} | C | 6825 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(4^6−1)/(4−1)=6825. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6825, not 6823.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6825, not 10237.5.",
"C": "Correct. The worked calculation gives 6825.",
"D": "Incorrect. Substituting the stated values into th... | [
"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_000897 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio 5. What is the sum of its first 12 terms? | {
"A": "671386717",
"B": "1342773432",
"C": "671386716",
"D": "671386718"
} | C | 671386716 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(5^12−1)/(5−1)=671386716. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 671386716, not 671386717.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 671386716, not 1342773432.",
"C": "Correct. The worked calculation gives 671386716.",
"D": "Incorrect. Substituting th... | [
"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_008937 | 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 0.77 mol L⁻¹ and initially B is absent. At equilibrium, 35% of A has dissociated at constant volume. Find K_c. | {
"A": "3.58046",
"B": "0.58046",
"C": "-0.58046",
"D": "0.43535"
} | B | 0.58046 | Let α=0.35. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.77)(0.35)²/(1−0.35)=0.58046. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.58046, not 3.58046.",
"B": "Correct. The worked calculation gives 0.58046.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.58046, not -0.58046.",
"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_002995 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-1, 9, 5) and v=(-6, -4, 8), calculate u·v. | {
"A": "9",
"B": "12",
"C": "13",
"D": "10"
} | D | 10 | The dot product is the sum of corresponding component products: (-1)(-6)+(9)(-4)+(5)(8)=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 13.",
"D": "Correct. The work... | [
"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_003860 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 5 m s⁻¹. A constant net force does 22 N of work over 12 m in the direction of motion. Find its final kinetic energy. | {
"A": "376.5 J",
"B": "375.5 J",
"C": "301.2 J",
"D": "188.25 J"
} | A | 376.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(5)²+(22)(12)=376.5 J. | {
"A": "Correct. The worked calculation gives 376.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 376.5 J, not 375.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 376.5 J, not 301.2 J.",
"D": "Incorrect. Substituting the stated va... | [
"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_004168 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 31 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.17. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "71.92 N",
"B": "143.84 N",
"C": "-143.84 N",
"D": "172.608 N"
} | B | 143.84 N | Net force=mg(sinθ−μcosθ)=31×10×(0.6−0.17×0.8)=143.84 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 143.84 N, not 71.92 N.",
"B": "Correct. The worked calculation gives 143.84 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 143.84 N, not -143.84 N.",
"D": "Incorrect. Substituting the stat... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005377 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 33 μF capacitor is charged to a potential difference of 17 V. Calculate the energy stored, expressed in μJ. | {
"A": "4770.5 μJ",
"B": "4768.5 μJ",
"C": "3814.8 μJ",
"D": "3576.375 μJ"
} | B | 4768.5 μJ | U=½CV². Since C=33 μF, U in μJ is ½×33×(17)²=4768.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4768.5 μJ, not 4770.5 μJ.",
"B": "Correct. The worked calculation gives 4768.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4768.5 μJ, not 3814.8 μJ.",
"D": "Incorrect. Substituting the... | [
"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_003538 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 89 m s⁻¹ at 20° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "51.91521 m",
"B": "610.98248 m",
"C": "509.15207 m",
"D": "1018.30413 m"
} | C | 509.15207 m | Range R=u²sin(2θ)/g. Substituting u=89, θ=20° and g=10 gives R=(89)²sin(40°)/10=509.15207 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 509.15207 m, not 51.91521 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 509.15207 m, not 610.98248 m.",
"C": "Correct. The worked calculation gives 509.15207 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_006342 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 1 kg is attached to an ideal spring of force constant 471 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.09216 s",
"B": "-0.09216 s",
"C": "-2.90784 s",
"D": "0.13823 s"
} | A | 0.09216 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(1/471)=0.09216 s. | {
"A": "Correct. The worked calculation gives 0.09216 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.09216 s, not -0.09216 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.09216 s, not -2.90784 s.",
"D": "Incorrect. Substituting t... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008061 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 8 A for 26798 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": "141.07134 g",
"B": "70.53567 g",
"C": "52.90175 g",
"D": "71.53567 g"
} | B | 70.53567 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×8×26798/(2×96500)=70.53567 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 70.53567 g, not 141.07134 g.",
"B": "Correct. The worked calculation gives 70.53567 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 70.53567 g, not 52.90175 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008487 | 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 0.59 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.2272 K",
"B": "1.2272 K",
"C": "3.2272 K",
"D": "-1.7728 K"
} | B | 1.2272 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.52×0.59=1.2272 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.2272 K, not 0.2272 K.",
"B": "Correct. The worked calculation gives 1.2272 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2272 K, not 3.2272 K.",
"D": "Incorrect. Substituting the stat... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003580 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 82 m s⁻¹ at 35° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "631.84932 m",
"B": "473.88699 m",
"C": "505.47945 m",
"D": "64.18493 m"
} | A | 631.84932 m | Range R=u²sin(2θ)/g. Substituting u=82, θ=35° and g=10 gives R=(82)²sin(70°)/10=631.84932 m. | {
"A": "Correct. The worked calculation gives 631.84932 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 631.84932 m, not 473.88699 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 631.84932 m, not 505.47945 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000930 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio -2. What is the sum of its first 8 terms? | {
"A": "-340",
"B": "-510",
"C": "-339",
"D": "-342"
} | A | -340 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(-2^8−1)/(-2−1)=-340. | {
"A": "Correct. The worked calculation gives -340.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -340, not -510.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -340, not -339.",
"D": "Incorrect. Substituting the stated values into the g... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009381 | 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_7H_0N_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "8",
"B": "4.5",
"C": "13.5",
"D": "9"
} | D | 9 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+2−0−0)/2=9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9, not 8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9, not 4.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9, not 13.5.",
"D": "Correct. The work... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000869 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 3 and common ratio 3. What is the sum of its first 5 terms? | {
"A": "364",
"B": "363",
"C": "-363",
"D": "181.5"
} | B | 363 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=3(3^5−1)/(3−1)=363. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 363, not 364.",
"B": "Correct. The worked calculation gives 363.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 363, not -363.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003120 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(14-2i)/(6+6i). What is Re(z), the real part of z? | {
"A": "2",
"B": "-1",
"C": "3",
"D": "1"
} | D | 1 | Multiply numerator and denominator by the conjugate (6-6i). Then Re(z)=(ac+bd)/(c²+d²)=((14)(6)+(-2)(6))/(6²+(6)²)=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not -1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 3.",
"D": "Correct. The worked c... | [
"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_003752 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 13 kg block initially moves at 0 m s⁻¹. A constant net force does 15 N of work over 7 m in the direction of motion. Find its final kinetic energy. | {
"A": "105 J",
"B": "107 J",
"C": "126 J",
"D": "106 J"
} | A | 105 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(13)(0)²+(15)(7)=105 J. | {
"A": "Correct. The worked calculation gives 105 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 105 J, not 107 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 105 J, not 126 J.",
"D": "Incorrect. Substituting the stated values into ... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002438 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 1], [6, -1]]. | {
"A": "-20",
"B": "-11",
"C": "-10",
"D": "-8"
} | C | -10 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(-1)−(1)(6)=-10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -10, not -20.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -10, not -11.",
"C": "Correct. The worked calculation gives -10.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005138 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +4 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "128 N",
"B": "160 N",
"C": "240 N",
"D": "159 N"
} | B | 160 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(4×10⁻⁶)/(3×10⁻²)²=160 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 160 N, not 128 N.",
"B": "Correct. The worked calculation gives 160 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 160 N, not 240 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000649 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 19 and common difference 10. Find the sum of its first 27 terms. | {
"A": "4827.6",
"B": "4024",
"C": "-4023",
"D": "4023"
} | D | 4023 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=19, d=10, n=27: Sₙ=27/2[2(19)+(27−1)(10)]=4023. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4023, not 4827.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4023, not 4024.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4023, not -4023.",
"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_003735 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 3 kg block initially moves at 10 m s⁻¹. A constant net force does 18 N of work over 6 m in the direction of motion. Find its final kinetic energy. | {
"A": "258 J",
"B": "309.6 J",
"C": "26.8 J",
"D": "387 J"
} | A | 258 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(3)(10)²+(18)(6)=258 J. | {
"A": "Correct. The worked calculation gives 258 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 258 J, not 309.6 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 258 J, not 26.8 J.",
"D": "Incorrect. Substituting the stated values in... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000160 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +14x +11=0, let its roots be α and β. What is α²+β²? | {
"A": "3.44",
"B": "5.16",
"C": "2.58",
"D": "1.72"
} | A | 3.44 | By Vieta's relations, α+β = -14/5 and αβ = 11/5. Then α²+β²=(α+β)²−2αβ = (-14/5)²−2(11/5) = 3.44. | {
"A": "Correct. The worked calculation gives 3.44.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.44, not 5.16.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.44, not 2.58.",
"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_008363 | 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 1.13 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "4.034 K",
"B": "3.034 K",
"C": "2.034 K",
"D": "1.017 K"
} | C | 2.034 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.6×1.13=2.034 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.034 K, not 4.034 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.034 K, not 3.034 K.",
"C": "Correct. The worked calculation gives 2.034 K.",
"D": "Incorrect. Substituting the stated va... | [
"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_005104 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +9 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "38.5 N",
"B": "-40.5 N",
"C": "5.05 N",
"D": "40.5 N"
} | D | 40.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(9×10⁻⁶)/(10×10⁻²)²=40.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 40.5 N, not 38.5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 40.5 N, not -40.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 40.5 N, not 5.05 N.",... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000859 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio -3. What is the sum of its first 10 terms? | {
"A": "-194858.4",
"B": "-121786.5",
"C": "-162384",
"D": "-162382"
} | D | -162382 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(-3^10−1)/(-3−1)=-162382. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -162382, not -194858.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -162382, not -121786.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -162382, not -... | [
"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_002062 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 6 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "2.30769",
"B": "0.15385",
"C": "0.30769",
"D": "-1.69231"
} | C | 0.30769 | Favourable pairs = C(3,2)+C(6,2)+C(4,2)=24. Total pairs=C(13,2)=78. Therefore P=24/78=0.30769. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not 2.30769.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not 0.15385.",
"C": "Correct. The worked calculation gives 0.30769.",
"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_000717 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio 3. What is the sum of its first 11 terms? | {
"A": "531436",
"B": "531439",
"C": "637725.6",
"D": "531438"
} | D | 531438 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(3^11−1)/(3−1)=531438. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 531438, not 531436.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 531438, not 531439.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 531438, not 637725.6."... | [
"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_005932 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.3 atm at 400 K. What is its pressure at 593 K? | {
"A": "-0.55525 atm",
"B": "2.44475 atm",
"C": "3.44475 atm",
"D": "0.44475 atm"
} | D | 0.44475 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.3)(593)/(400)=0.44475 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.44475 atm, not -0.55525 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.44475 atm, not 2.44475 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008365 | 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 1.21 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": "1.42 K",
"B": "-0.58 K",
"C": "4.84 K",
"D": "2.42 K"
} | D | 2.42 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×1.21=2.42 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.42 K, not 1.42 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.42 K, not -0.58 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.42 K, not 4.84 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_005053 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +3 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "4.46281 N",
"B": "1.44628 N",
"C": "8.92562 N",
"D": "2.46281 N"
} | A | 4.46281 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(3×10⁻⁶)/(11×10⁻²)²=4.46281 N. | {
"A": "Correct. The worked calculation gives 4.46281 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.46281 N, not 1.44628 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.46281 N, not 8.92562 N.",
"D": "Incorrect. Substituting the... | [
"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_004667 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 5 m is acted on by a constant torque of 80 N m about its central axis. Find its angular acceleration. | {
"A": "-2.08571 rad s⁻²",
"B": "-1.08571 rad s⁻²",
"C": "0.91429 rad s⁻²",
"D": "1.82857 rad s⁻²"
} | C | 0.91429 rad s⁻² | For a solid disc, I=½MR²=½(7)(5)²=87.5 kg m². Using τ=Iα, α=80/87.5=0.91429 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.91429 rad s⁻², not -2.08571 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.91429 rad s⁻², not -1.08571 rad s⁻².",
"C": "Correct. The worked calculation gives 0.91429 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_003743 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 12 m s⁻¹. A constant net force does 14 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "1527 J",
"B": "1020 J",
"C": "1018 J",
"D": "1221.6 J"
} | C | 1018 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(12)²+(14)(11)=1018 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1018 J, not 1527 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1018 J, not 1020 J.",
"C": "Correct. The worked calculation gives 1018 J.",
"D": "Incorrect. Substituting the stated values ... | [
"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_008797 | 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 0.34 mol L⁻¹ and initially B is absent. At equilibrium, 54% of A has dissociated at constant volume. Find K_c. | {
"A": "0.86212",
"B": "3.86212",
"C": "0.43106",
"D": "1.08621"
} | A | 0.86212 | Let α=0.54. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.34)(0.54)²/(1−0.54)=0.86212. | {
"A": "Correct. The worked calculation gives 0.86212.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.86212, not 3.86212.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.86212, not 0.43106.",
"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_005554 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 68 μF capacitor is charged to a potential difference of 8 V. Calculate the energy stored, expressed in μJ. | {
"A": "2176 μJ",
"B": "4352 μJ",
"C": "3264 μJ",
"D": "2177 μJ"
} | A | 2176 μJ | U=½CV². Since C=68 μF, U in μJ is ½×68×(8)²=2176 μJ. | {
"A": "Correct. The worked calculation gives 2176 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2176 μJ, not 4352 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2176 μJ, not 3264 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008538 | 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 0.57 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.1108 K",
"B": "0.8892 K",
"C": "0.6669 K",
"D": "3.8892 K"
} | B | 0.8892 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.52×0.57=0.8892 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8892 K, not -0.1108 K.",
"B": "Correct. The worked calculation gives 0.8892 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8892 K, not 0.6669 K.",
"D": "Incorrect. Substituting the sta... | [
"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_008819 | 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 1.86 mol L⁻¹ and initially B is absent. At equilibrium, 13% of A has dissociated at constant volume. Find K_c. | {
"A": "0.14452",
"B": "0.28905",
"C": "2.14452",
"D": "0.21679"
} | A | 0.14452 | Let α=0.13. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.86)(0.13)²/(1−0.13)=0.14452. | {
"A": "Correct. The worked calculation gives 0.14452.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.14452, not 0.28905.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.14452, not 2.14452.",
"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_007399 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 27 mL of 0.10 M HCl is mixed with 29 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "11.55284",
"B": "5.77642",
"C": "17.32926",
"D": "-11.55284"
} | A | 11.55284 | Excess OH⁻ moles=0.10×(29−27)/1000=0.000200 mol. Total volume=0.056 L, so [OH⁻]=0.003571 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=11.55284. | {
"A": "Correct. The worked calculation gives 11.55284.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.55284, not 5.77642.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.55284, not 17.32926.",
"D": "Incorrect. Substituting the state... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002515 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -2], [7, -6]]. | {
"A": "-15",
"B": "-12",
"C": "-16",
"D": "-24"
} | C | -16 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(-6)−(-2)(7)=-16. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -16, not -15.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -16, not -12.",
"C": "Correct. The worked calculation gives -16.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003729 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 6 m s⁻¹. A constant net force does 27 N of work over 7 m in the direction of motion. Find its final kinetic energy. | {
"A": "208.8 J",
"B": "195.75 J",
"C": "261 J",
"D": "27.1 J"
} | C | 261 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(6)²+(27)(7)=261 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 261 J, not 208.8 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 261 J, not 195.75 J.",
"C": "Correct. The worked calculation gives 261 J.",
"D": "Incorrect. Substituting the stated values ... | [
"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_001427 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (4x² +1x +3) dx. | {
"A": "291.25",
"B": "194.16667",
"C": "20.41667",
"D": "145.625"
} | B | 194.16667 | An antiderivative is (4/3)x³+(1/2)x²+(3)x. Evaluating between 0 and 5 gives (4/3)(5)³+(1/2)(5)²+(3)(5)=194.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 194.16667, not 291.25.",
"B": "Correct. The worked calculation gives 194.16667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 194.16667, not 20.41667.",
"D": "Incorrect. Substituting the sta... | [
"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_009587 | 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_16H_19X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "-6",
"C": "9",
"D": "6"
} | D | 6 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×16+2+0−19−3)/2=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not -6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"D": "Correct. The worked c... | [
"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_005407 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 40 μF capacitor is charged to a potential difference of 23 V. Calculate the energy stored, expressed in μJ. | {
"A": "10579 μJ",
"B": "10580 μJ",
"C": "15870 μJ",
"D": "10582 μJ"
} | B | 10580 μJ | U=½CV². Since C=40 μF, U in μJ is ½×40×(23)²=10580 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10580 μJ, not 10579 μJ.",
"B": "Correct. The worked calculation gives 10580 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10580 μJ, not 15870 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_005340 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 67 μF capacitor is charged to a potential difference of 25 V. Calculate the energy stored, expressed in μJ. | {
"A": "-20937.5 μJ",
"B": "20936.5 μJ",
"C": "20935.5 μJ",
"D": "20937.5 μJ"
} | D | 20937.5 μJ | U=½CV². Since C=67 μF, U in μJ is ½×67×(25)²=20937.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20937.5 μJ, not -20937.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20937.5 μJ, not 20936.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20937... | [
"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_001636 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (2x² +8x -4) dx. | {
"A": "565.33333",
"B": "848",
"C": "-565.33333",
"D": "567.33333"
} | A | 565.33333 | An antiderivative is (2/3)x³+(8/2)x²+(-4)x. Evaluating between 0 and 8 gives (2/3)(8)³+(8/2)(8)²+(-4)(8)=565.33333. | {
"A": "Correct. The worked calculation gives 565.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 565.33333, not 848.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 565.33333, not -565.33333.",
"D": "Incorrect. Substituting the stat... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003619 | 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 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "-122.5 m",
"B": "13.25 m",
"C": "183.75 m",
"D": "122.5 m"
} | D | 122.5 m | Range R=u²sin(2θ)/g. Substituting u=35, θ=45° and g=10 gives R=(35)²sin(90°)/10=122.5 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 122.5 m, not -122.5 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 122.5 m, not 13.25 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 122.5 m, not 183.... | [
"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_006323 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 131 cm in front of a thin convex lens of focal length 30 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-1.70297",
"B": "-0.29703",
"C": "0.44554",
"D": "0.29703"
} | D | 0.29703 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(131)(30)/(131−30)=38.91089 cm. Thus |m|=v/u=38.91089/131=0.29703. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29703, not -1.70297.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29703, not -0.29703.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29703, not 0.4... | [
"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_004722 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 5 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 19 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "9.32794 A",
"B": "4.66397 A",
"C": "1.4664 A",
"D": "1.66397 A"
} | B | 4.66397 A | Series branch resistance=5+8=13 Ω. Parallel equivalent R_eq=(13×19)/(13+19)=7.71875 Ω. Total current I=V/R_eq=36/7.71875=4.66397 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.66397 A, not 9.32794 A.",
"B": "Correct. The worked calculation gives 4.66397 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.66397 A, not 1.4664 A.",
"D": "Incorrect. Substituting the ... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009933 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(Cl)_5]^+1, each Cl ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "12",
"B": "6",
"C": "4",
"D": "8"
} | B | 6 | Let the formal oxidation state of Co be x. Charge balance gives x+(5)(−1)=+1; hence x=1+5=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 12.",
"B": "Correct. The worked calculation gives 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.",
"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_005587 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 20 μF capacitor is charged to a potential difference of 40 V. Calculate the energy stored, expressed in μJ. | {
"A": "19200 μJ",
"B": "16000 μJ",
"C": "16001 μJ",
"D": "15998 μJ"
} | B | 16000 μJ | U=½CV². Since C=20 μF, U in μJ is ½×20×(40)²=16000 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16000 μJ, not 19200 μJ.",
"B": "Correct. The worked calculation gives 16000 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16000 μJ, not 16001 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_000732 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio -3. What is the sum of its first 9 terms? | {
"A": "3690.75",
"B": "493.1",
"C": "-4921",
"D": "4921"
} | D | 4921 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(-3^9−1)/(-3−1)=4921. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4921, not 3690.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4921, not 493.1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4921, not -4921.",
"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_005562 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 2 μF capacitor is charged to a potential difference of 16 V. Calculate the energy stored, expressed in μJ. | {
"A": "204.8 μJ",
"B": "128 μJ",
"C": "254 μJ",
"D": "256 μJ"
} | D | 256 μJ | U=½CV². Since C=2 μF, U in μJ is ½×2×(16)²=256 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 256 μJ, not 204.8 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 256 μJ, not 128 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 256 μJ, not 254 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_002804 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(8, -3, -4) and v=(-4, -2, 6), calculate u·v. | {
"A": "50",
"B": "-50",
"C": "-52",
"D": "-4"
} | B | -50 | The dot product is the sum of corresponding component products: (8)(-4)+(-3)(-2)+(-4)(6)=-50. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -50, not 50.",
"B": "Correct. The worked calculation gives -50.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -50, not -52.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002555 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, -1], [7, 3]]. | {
"A": "46.5",
"B": "37.2",
"C": "31",
"D": "15.5"
} | C | 31 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(3)−(-1)(7)=31. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 31, not 46.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 31, not 37.2.",
"C": "Correct. The worked calculation gives 31.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001171 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ -4x² +4x+7. Evaluate f′(-4). | {
"A": "-202",
"B": "-408",
"C": "-204",
"D": "-203"
} | C | -204 | Differentiate: f′(x)=3(-5)x²+2(-4)x+(4). At x=-4, f′(-4)=3(-5)(-4)²+2(-4)(-4)+(4)=-204. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -204, not -202.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -204, not -408.",
"C": "Correct. The worked calculation gives -204.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_007113 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 17 mol of gas at 277 K and 1.32 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "290.73213 L",
"B": "146.36607 L",
"C": "292.73213 L",
"D": "-292.73213 L"
} | C | 292.73213 L | PV=nRT, so V=nRT/P=(17)(0.082057)(277)/(1.32)=292.73213 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 292.73213 L, not 290.73213 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 292.73213 L, not 146.36607 L.",
"C": "Correct. The worked calculation gives 292.73213 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_006593 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 11 kg is attached to an ideal spring of force constant 1069 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "2.20288 s",
"B": "0.10144 s",
"C": "-0.79712 s",
"D": "0.20288 s"
} | D | 0.20288 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(11/1069)=0.20288 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.20288 s, not 2.20288 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.20288 s, not 0.10144 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.20288 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_002479 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, 2], [9, 2]]. | {
"A": "-0.6",
"B": "-16",
"C": "-12",
"D": "16"
} | B | -16 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(2)−(2)(9)=-16. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -16, not -0.6.",
"B": "Correct. The worked calculation gives -16.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -16, not -12.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_002472 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 0], [3, -1]]. | {
"A": "-5",
"B": "-4",
"C": "-7",
"D": "-6"
} | B | -4 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(-1)−(0)(3)=-4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4, not -5.",
"B": "Correct. The worked calculation gives -4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -4, not -7.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005727 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.2 atm at 379 K. What is its pressure at 606 K? | {
"A": "1.91873 atm",
"B": "2.91873 atm",
"C": "3.91873 atm",
"D": "-1.08127 atm"
} | A | 1.91873 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.2)(606)/(379)=1.91873 atm. | {
"A": "Correct. The worked calculation gives 1.91873 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.91873 atm, not 2.91873 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.91873 atm, not 3.91873 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003617 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 67 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "35.38774 m",
"B": "515.81603 m",
"C": "343.87735 m",
"D": "687.7547 m"
} | C | 343.87735 m | Range R=u²sin(2θ)/g. Substituting u=67, θ=25° and g=10 gives R=(67)²sin(50°)/10=343.87735 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 343.87735 m, not 35.38774 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 343.87735 m, not 515.81603 m.",
"C": "Correct. The worked calculation gives 343.87735 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_002038 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 12 blue and 5 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.34462",
"B": "0.51692",
"C": "1.03446",
"D": "3.34462"
} | A | 0.34462 | Favourable pairs = C(9,2)+C(12,2)+C(5,2)=112. Total pairs=C(26,2)=325. Therefore P=112/325=0.34462. | {
"A": "Correct. The worked calculation gives 0.34462.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34462, not 0.51692.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34462, not 1.03446.",
"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_000818 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio 3. What is the sum of its first 12 terms? | {
"A": "212576",
"B": "265719",
"C": "265720",
"D": "265718"
} | C | 265720 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(3^12−1)/(3−1)=265720. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 265720, not 212576.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 265720, not 265719.",
"C": "Correct. The worked calculation gives 265720.",
"D": "Incorrect. Substituting the stated values ... | [
"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_007982 | 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 32 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "-0.5 mmol L⁻¹",
"B": "0.5 mmol L⁻¹",
"C": "3.5 mmol L⁻¹",
"D": "1.5 mmol L⁻¹"
} | B | 0.5 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=32/2^6=0.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5 mmol L⁻¹, not -0.5 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5 mmol L⁻¹, not 3.5 mmol L⁻¹.",
"D": "Incorrect. ... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000308 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 -9x -12=0, let its roots be α and β. What is α²+β²? | {
"A": "6.25",
"B": "9.375",
"C": "12.5",
"D": "4.25"
} | A | 6.25 | By Vieta's relations, α+β = 9/6 and αβ = -12/6. Then α²+β²=(α+β)²−2αβ = (9/6)²−2(-12/6) = 6.25. | {
"A": "Correct. The worked calculation gives 6.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.25, not 9.375.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.25, not 12.5.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_000425 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 13 and common difference 15. Find the sum of its first 16 terms. | {
"A": "1506",
"B": "4016",
"C": "2008",
"D": "3012"
} | C | 2008 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=13, d=15, n=16: Sₙ=16/2[2(13)+(16−1)(15)]=2008. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2008, not 1506.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2008, not 4016.",
"C": "Correct. The worked calculation gives 2008.",
"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 |
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