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_007505 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 65 mL of 0.10 M HCl is mixed with 82 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "24.12626",
"B": "11.06313",
"C": "12.06313",
"D": "9.04735"
} | C | 12.06313 | Excess OH⁻ moles=0.10×(82−65)/1000=0.001700 mol. Total volume=0.147 L, so [OH⁻]=0.011565 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.06313. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.06313, not 24.12626.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.06313, not 11.06313.",
"C": "Correct. The worked calculation gives 12.06313.",
"D": "Incorrect. Substituting the stat... | [
"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_000147 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 -13x -6=0, let its roots be α and β. What is α²+β²? | {
"A": "180",
"B": "271.5",
"C": "181",
"D": "144.8"
} | C | 181 | By Vieta's relations, α+β = 13/1 and αβ = -6/1. Then α²+β²=(α+β)²−2αβ = (13/1)²−2(-6/1) = 181. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 181, not 180.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 181, not 271.5.",
"C": "Correct. The worked calculation gives 181.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001119 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ +2x² +11x+7. Evaluate f′(-3). | {
"A": "-163.5",
"B": "-108",
"C": "-107",
"D": "-109"
} | D | -109 | Differentiate: f′(x)=3(-4)x²+2(2)x+(11). At x=-3, f′(-3)=3(-4)(-3)²+2(2)(-3)+(11)=-109. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -109, not -163.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -109, not -108.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -109, not -107.",
"D": "Co... | [
"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_002224 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 5 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": "-1.71212",
"B": "0.28788",
"C": "0.43182",
"D": "0.57576"
} | B | 0.28788 | Favourable pairs = C(3,2)+C(5,2)+C(4,2)=19. Total pairs=C(12,2)=66. Therefore P=19/66=0.28788. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.28788, not -1.71212.",
"B": "Correct. The worked calculation gives 0.28788.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.28788, not 0.43182.",
"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_006970 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 15 mol H₂ and 26 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "13 mol",
"B": "2.5 mol",
"C": "18 mol",
"D": "15 mol"
} | D | 15 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 15 mol H₂O; O₂ can produce 52 mol H₂O. The limiting condition is H₂; product=15 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15 mol, not 13 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15 mol, not 2.5 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15 mol, not 18 mol.",... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009604 | 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_10H_13N_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "7.5",
"B": "5",
"C": "4",
"D": "3.75"
} | B | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×10+2+1−13−0)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.5.",
"B": "Correct. The worked calculation gives 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 4.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006128 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 93 cm in front of a thin convex lens of focal length 21 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.29167",
"B": "-0.70833",
"C": "0.21875",
"D": "-2.70833"
} | A | 0.29167 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(93)(21)/(93−21)=27.125 cm. Thus |m|=v/u=27.125/93=0.29167. | {
"A": "Correct. The worked calculation gives 0.29167.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29167, not -0.70833.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29167, not 0.21875.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001502 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (3x² +1x +4) dx. | {
"A": "258",
"B": "129",
"C": "26.8",
"D": "257"
} | A | 258 | An antiderivative is (3/3)x³+(1/2)x²+(4)x. Evaluating between 0 and 6 gives (3/3)(6)³+(1/2)(6)²+(4)(6)=258. | {
"A": "Correct. The worked calculation gives 258.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 258, not 129.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 258, not 26.8.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005761 | 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 1.8 atm at 268 K. What is its pressure at 629 K? | {
"A": "4.22463 atm",
"B": "2.11231 atm",
"C": "1.42246 atm",
"D": "-4.22463 atm"
} | A | 4.22463 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.8)(629)/(268)=4.22463 atm. | {
"A": "Correct. The worked calculation gives 4.22463 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.22463 atm, not 2.11231 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.22463 atm, not 1.42246 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_004190 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.28. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "15.04 N",
"B": "22.56 N",
"C": "30.08 N",
"D": "-15.04 N"
} | A | 15.04 N | Net force=mg(sinθ−μcosθ)=4×10×(0.6−0.28×0.8)=15.04 N. | {
"A": "Correct. The worked calculation gives 15.04 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15.04 N, not 22.56 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15.04 N, not 30.08 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_003357 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 65 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "476.42416 m",
"B": "297.7651 m",
"C": "317.61611 m",
"D": "397.02013 m"
} | D | 397.02013 m | Range R=u²sin(2θ)/g. Substituting u=65, θ=55° and g=10 gives R=(65)²sin(110°)/10=397.02013 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 397.02013 m, not 476.42416 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 397.02013 m, not 297.7651 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 397... | [
"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_006192 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 137 cm in front of a thin convex lens of focal length 30 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-2.71963",
"B": "0.28037",
"C": "-0.71963",
"D": "-0.28037"
} | B | 0.28037 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(137)(30)/(137−30)=38.41121 cm. Thus |m|=v/u=38.41121/137=0.28037. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.28037, not -2.71963.",
"B": "Correct. The worked calculation gives 0.28037.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.28037, not -0.71963.",
"D": "Incorrect. Substituting the stated ... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007668 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 41 mL of 0.10 M HCl is mixed with 36 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-0.81248",
"B": "2.18752",
"C": "5.18752",
"D": "1.09376"
} | B | 2.18752 | Excess H⁺ moles=0.10×(41−36)/1000=0.000500 mol. Total volume=0.077 L, so [H⁺]=0.006494 M and pH=−log₁₀[H⁺]=2.18752. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.18752, not -0.81248.",
"B": "Correct. The worked calculation gives 2.18752.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.18752, not 5.18752.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005950 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.8 atm at 385 K. What is its pressure at 553 K? | {
"A": "2.45818 atm",
"B": "10.91636 atm",
"C": "1.54582 atm",
"D": "5.45818 atm"
} | D | 5.45818 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.8)(553)/(385)=5.45818 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.45818 atm, not 2.45818 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.45818 atm, not 10.91636 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5... | [
"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_001014 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-3x³ +1x² -6x+7. Evaluate f′(2). | {
"A": "-38",
"B": "-19",
"C": "-76",
"D": "-37"
} | A | -38 | Differentiate: f′(x)=3(-3)x²+2(1)x+(-6). At x=2, f′(2)=3(-3)(2)²+2(1)(2)+(-6)=-38. | {
"A": "Correct. The worked calculation gives -38.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -38, not -19.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -38, not -76.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002817 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-7, 0, -7) and v=(5, -4, -1), calculate u·v. | {
"A": "-14",
"B": "-33.6",
"C": "-28",
"D": "-27"
} | C | -28 | The dot product is the sum of corresponding component products: (-7)(5)+(0)(-4)+(-7)(-1)=-28. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -28, not -14.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -28, not -33.6.",
"C": "Correct. The worked calculation gives -28.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008667 | 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 0.61 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.61 K",
"B": "1.061 K",
"C": "1.22 K",
"D": "0.305 K"
} | A | 0.61 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×1.0×0.61=0.61 K. | {
"A": "Correct. The worked calculation gives 0.61 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.61 K, not 1.061 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.61 K, not 1.22 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002968 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, 0, -1) and v=(-3, -3, -7), calculate u·v. | {
"A": "-7",
"B": "0.5",
"C": "-6",
"D": "-5"
} | D | -5 | The dot product is the sum of corresponding component products: (4)(-3)+(0)(-3)+(-1)(-7)=-5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -5, not -7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -5, not 0.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -5, not -6.",
"D": "Correct. The wo... | [
"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_001550 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (4x² +3x +0) dx. | {
"A": "204.16667",
"B": "306.25",
"C": "408.33333",
"D": "202.16667"
} | A | 204.16667 | An antiderivative is (4/3)x³+(3/2)x²+(0)x. Evaluating between 0 and 5 gives (4/3)(5)³+(3/2)(5)²+(0)(5)=204.16667. | {
"A": "Correct. The worked calculation gives 204.16667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 204.16667, not 306.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 204.16667, not 408.33333.",
"D": "Incorrect. Substituting the st... | [
"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_006131 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 72 cm in front of a thin convex lens of focal length 27 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "3.6",
"B": "0.9",
"C": "0.6",
"D": "1.06"
} | C | 0.6 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(72)(27)/(72−27)=43.2 cm. Thus |m|=v/u=43.2/72=0.6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6, not 3.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6, not 0.9.",
"C": "Correct. The worked calculation gives 0.6.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005802 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.9 atm at 327 K. What is its pressure at 410 K? | {
"A": "9.14373 atm",
"B": "4.14373 atm",
"C": "-6.14373 atm",
"D": "6.14373 atm"
} | D | 6.14373 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.9)(410)/(327)=6.14373 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.14373 atm, not 9.14373 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.14373 atm, not 4.14373 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.... | [
"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_002997 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(9, 1, 0) and v=(0, 6, 0), calculate u·v. | {
"A": "5",
"B": "9",
"C": "-6",
"D": "6"
} | D | 6 | The dot product is the sum of corresponding component products: (9)(0)+(1)(6)+(0)(0)=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not -6.",
"D": "Correct. The worked c... | [
"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_002454 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, 4], [7, 4]]. | {
"A": "8",
"B": "4",
"C": "2",
"D": "6"
} | B | 4 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(4)−(4)(7)=4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 8.",
"B": "Correct. The worked calculation gives 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_005633 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 65 μF capacitor is charged to a potential difference of 10 V. Calculate the energy stored, expressed in μJ. | {
"A": "4875 μJ",
"B": "3250 μJ",
"C": "3249 μJ",
"D": "3900 μJ"
} | B | 3250 μJ | U=½CV². Since C=65 μF, U in μJ is ½×65×(10)²=3250 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3250 μJ, not 4875 μJ.",
"B": "Correct. The worked calculation gives 3250 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3250 μJ, not 3249 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_009016 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.06 V, transfers 1 electrons, and has reaction quotient Q=10^3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.8827 V",
"B": "1.8827 V",
"C": "-0.8827 V",
"D": "-2.1173 V"
} | A | 0.8827 V | Apply the Nernst equation: E=1.06−(0.0591/1)(3)=0.8827 V. | {
"A": "Correct. The worked calculation gives 0.8827 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8827 V, not 1.8827 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8827 V, not -0.8827 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000993 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 12 and common ratio 5. What is the sum of its first 11 terms? | {
"A": "146484374",
"B": "-146484372",
"C": "146484370",
"D": "146484372"
} | D | 146484372 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=12(5^11−1)/(5−1)=146484372. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 146484372, not 146484374.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 146484372, not -146484372.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 146484372... | [
"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_002214 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 7 red, 5 blue and 7 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.22807",
"B": "0.30409",
"C": "1.30409",
"D": "-0.30409"
} | B | 0.30409 | Favourable pairs = C(7,2)+C(5,2)+C(7,2)=52. Total pairs=C(19,2)=171. Therefore P=52/171=0.30409. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30409, not 0.22807.",
"B": "Correct. The worked calculation gives 0.30409.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30409, not 1.30409.",
"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_005824 | 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 360 K. What is its pressure at 413 K? | {
"A": "-0.62333 atm",
"B": "1.37667 atm",
"C": "-1.62333 atm",
"D": "2.37667 atm"
} | B | 1.37667 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.2)(413)/(360)=1.37667 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.37667 atm, not -0.62333 atm.",
"B": "Correct. The worked calculation gives 1.37667 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.37667 atm, not -1.62333 atm.",
"D": "Incorrect. Subs... | [
"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_001433 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (-3x² +2x +3) dx. | {
"A": "-2",
"B": "-1",
"C": "2",
"D": "4"
} | C | 2 | An antiderivative is (-3/3)x³+(2/2)x²+(3)x. Evaluating between 0 and 2 gives (-3/3)(2)³+(2/2)(2)²+(3)(2)=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not -1.",
"C": "Correct. The worked calculation gives 2.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006940 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 47 mol H₂ and 22 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "22 mol",
"B": "33 mol",
"C": "42 mol",
"D": "44 mol"
} | D | 44 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 47 mol H₂O; O₂ can produce 44 mol H₂O. The limiting condition is O₂; product=44 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 44 mol, not 22 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 44 mol, not 33 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 44 mol, not 42 mol.",
... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001417 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (0x² -2x +3) dx. | {
"A": "0",
"B": "2",
"C": "-2",
"D": "-3"
} | A | 0 | An antiderivative is (0/3)x³+(-2/2)x²+(3)x. Evaluating between 0 and 3 gives (0/3)(3)³+(-2/2)(3)²+(3)(3)=0. | {
"A": "Correct. The worked calculation gives 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_007520 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 43 mL of 0.10 M HCl is mixed with 27 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "4.64098",
"B": "1.64098",
"C": "-0.35902",
"D": "2.46147"
} | B | 1.64098 | Excess H⁺ moles=0.10×(43−27)/1000=0.001600 mol. Total volume=0.070 L, so [H⁺]=0.022857 M and pH=−log₁₀[H⁺]=1.64098. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.64098, not 4.64098.",
"B": "Correct. The worked calculation gives 1.64098.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.64098, not -0.35902.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002709 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-3, -3, 3) and v=(-4, 6, 0), calculate u·v. | {
"A": "-4.5",
"B": "-12",
"C": "-9",
"D": "-6"
} | D | -6 | The dot product is the sum of corresponding component products: (-3)(-4)+(-3)(6)+(3)(0)=-6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -6, not -4.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -6, not -12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -6, not -9.",
"D": "Correct. The ... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008941 | 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 0.41 mol L⁻¹ and initially B is absent. At equilibrium, 69% of A has dissociated at constant volume. Find K_c. | {
"A": "5.03745",
"B": "1.25187",
"C": "5.51872",
"D": "2.51872"
} | D | 2.51872 | Let α=0.69. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.41)(0.69)²/(1−0.69)=2.51872. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.51872, not 5.03745.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.51872, not 1.25187.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.51872, not 5.518... | [
"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_000100 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -18x -5=0, let its roots be α and β. What is α²+β²? | {
"A": "103.2",
"B": "-86",
"C": "86",
"D": "88"
} | C | 86 | By Vieta's relations, α+β = 18/2 and αβ = -5/2. Then α²+β²=(α+β)²−2αβ = (18/2)²−2(-5/2) = 86. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 86, not 103.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 86, not -86.",
"C": "Correct. The worked calculation gives 86.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_005767 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.8 atm at 360 K. What is its pressure at 771 K? | {
"A": "8.99667 atm",
"B": "5.99667 atm",
"C": "2.99833 atm",
"D": "8.995 atm"
} | B | 5.99667 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.8)(771)/(360)=5.99667 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.99667 atm, not 8.99667 atm.",
"B": "Correct. The worked calculation gives 5.99667 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.99667 atm, not 2.99833 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_002979 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(6, 8, -5) and v=(-2, -3, 9), calculate u·v. | {
"A": "-83",
"B": "-97.2",
"C": "-121.5",
"D": "-81"
} | D | -81 | The dot product is the sum of corresponding component products: (6)(-2)+(8)(-3)+(-5)(9)=-81. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -81, not -83.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -81, not -97.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -81, not -121.5.",
"D": "Corre... | [
"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_003243 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-3-8i)/(12+2i). What is Re(z), the real part of z? | {
"A": "-0.35135",
"B": "-0.17568",
"C": "-0.7027",
"D": "-0.26351"
} | A | -0.35135 | Multiply numerator and denominator by the conjugate (12-2i). Then Re(z)=(ac+bd)/(c²+d²)=((-3)(12)+(-8)(2))/(12²+(2)²)=-0.35135. | {
"A": "Correct. The worked calculation gives -0.35135.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.35135, not -0.17568.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.35135, not -0.7027.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006658 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 24 kg is attached to an ideal spring of force constant 392 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.49487 s",
"B": "-2.50513 s",
"C": "3.49487 s",
"D": "0.49487 s"
} | D | 0.49487 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(24/392)=0.49487 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.49487 s, not -0.49487 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.49487 s, not -2.50513 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.49487 ... | [
"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_001420 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (5x² -4x -1) dx. | {
"A": "717.33333",
"B": "1076",
"C": "715.33333",
"D": "716.33333"
} | A | 717.33333 | An antiderivative is (5/3)x³+(-4/2)x²+(-1)x. Evaluating between 0 and 8 gives (5/3)(8)³+(-4/2)(8)²+(-1)(8)=717.33333. | {
"A": "Correct. The worked calculation gives 717.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 717.33333, not 1076.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 717.33333, not 715.33333.",
"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_002373 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, 1], [7, 6]]. | {
"A": "-29",
"B": "34.8",
"C": "30",
"D": "29"
} | D | 29 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(6)−(1)(7)=29. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 29, not -29.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 29, not 34.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29, not 30.",
"D": "Correct. The ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007057 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 18 mol of gas at 363 K and 0.95 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "564.37941 L",
"B": "423.28456 L",
"C": "282.1897 L",
"D": "563.37941 L"
} | A | 564.37941 L | PV=nRT, so V=nRT/P=(18)(0.082057)(363)/(0.95)=564.37941 L. | {
"A": "Correct. The worked calculation gives 564.37941 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 564.37941 L, not 423.28456 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 564.37941 L, not 282.1897 L.",
"D": "Incorrect. Substit... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001357 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (1x² -4x +3) dx. | {
"A": "3.33333",
"B": "2",
"C": "2.66667",
"D": "1.33333"
} | D | 1.33333 | An antiderivative is (1/3)x³+(-4/2)x²+(3)x. Evaluating between 0 and 4 gives (1/3)(4)³+(-4/2)(4)²+(3)(4)=1.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.33333, not 3.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.33333, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.33333, not 2.66667.",
... | [
"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_008644 | 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 0.06 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": "2.12 K",
"B": "1.12 K",
"C": "0.12 K",
"D": "1.012 K"
} | C | 0.12 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×0.06=0.12 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.12 K, not 2.12 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.12 K, not 1.12 K.",
"C": "Correct. The worked calculation gives 0.12 K.",
"D": "Incorrect. Substituting the stated values ... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002762 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-6, -7, -4) and v=(-3, 6, -2), calculate u·v. | {
"A": "-8",
"B": "-12",
"C": "-16",
"D": "-14"
} | C | -16 | The dot product is the sum of corresponding component products: (-6)(-3)+(-7)(6)+(-4)(-2)=-16. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -16, not -8.",
"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 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_008524 | 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 2 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.351 K",
"B": "-0.468 K",
"C": "0.234 K",
"D": "0.468 K"
} | D | 0.468 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×0.45=0.468 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.468 K, not 0.351 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.468 K, not -0.468 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.468 K, not 0.23... | [
"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_005588 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 15 μF capacitor is charged to a potential difference of 15 V. Calculate the energy stored, expressed in μJ. | {
"A": "2025 μJ",
"B": "1685.5 μJ",
"C": "1687.5 μJ",
"D": "1265.625 μJ"
} | C | 1687.5 μJ | U=½CV². Since C=15 μF, U in μJ is ½×15×(15)²=1687.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1687.5 μJ, not 2025 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1687.5 μJ, not 1685.5 μJ.",
"C": "Correct. The worked calculation gives 1687.5 μJ.",
"D": "Incorrect. Substituting the s... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000221 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -9x +2=0, let its roots be α and β. What is α²+β²? | {
"A": "2.825",
"B": "-18.25",
"C": "13.6875",
"D": "18.25"
} | D | 18.25 | By Vieta's relations, α+β = 9/2 and αβ = 2/2. Then α²+β²=(α+β)²−2αβ = (9/2)²−2(2/2) = 18.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18.25, not 2.825.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18.25, not -18.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18.25, not 13.6875.",
"... | [
"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_002149 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 8 blue and 10 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.24605",
"B": "3.32806",
"C": "0.32806",
"D": "1.32806"
} | C | 0.32806 | Favourable pairs = C(5,2)+C(8,2)+C(10,2)=83. Total pairs=C(23,2)=253. Therefore P=83/253=0.32806. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32806, not 0.24605.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32806, not 3.32806.",
"C": "Correct. The worked calculation gives 0.32806.",
"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_007799 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 34 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "3.26562 mmol L⁻¹",
"B": "1.26562 mmol L⁻¹",
"C": "1.02656 mmol L⁻¹",
"D": "0.26562 mmol L⁻¹"
} | D | 0.26562 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=34/2^7=0.26562 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.26562 mmol L⁻¹, not 3.26562 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.26562 mmol L⁻¹, not 1.26562 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governi... | [
"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_006150 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 65 cm in front of a thin convex lens of focal length 26 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.66667",
"B": "0.5",
"C": "-0.33333",
"D": "1.33333"
} | A | 0.66667 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(65)(26)/(65−26)=43.33333 cm. Thus |m|=v/u=43.33333/65=0.66667. | {
"A": "Correct. The worked calculation gives 0.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.66667, not 0.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.66667, not -0.33333.",
"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_006641 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 4 kg is attached to an ideal spring of force constant 40 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.36754 s",
"B": "0.31623 s",
"C": "-0.63246 s",
"D": "0.63246 s"
} | D | 0.63246 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(4/40)=0.63246 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.63246 s, not -1.36754 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.63246 s, not 0.31623 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.63246 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_003501 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 120 m s⁻¹ at 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "2127.18475 m",
"B": "709.06158 m",
"C": "1417.12316 m",
"D": "1418.12316 m"
} | D | 1418.12316 m | Range R=u²sin(2θ)/g. Substituting u=120, θ=40° and g=10 gives R=(120)²sin(80°)/10=1418.12316 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1418.12316 m, not 2127.18475 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1418.12316 m, not 709.06158 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives... | [
"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_006584 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 9 kg is attached to an ideal spring of force constant 111 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.43051 s",
"B": "3.56949 s",
"C": "1.05695 s",
"D": "0.56949 s"
} | D | 0.56949 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(9/111)=0.56949 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.56949 s, not -1.43051 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.56949 s, not 3.56949 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.56949 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_004090 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.41. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "38.08 N",
"B": "4.808 N",
"C": "30.464 N",
"D": "76.16 N"
} | A | 38.08 N | Net force=mg(sinθ−μcosθ)=14×10×(0.6−0.41×0.8)=38.08 N. | {
"A": "Correct. The worked calculation gives 38.08 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 38.08 N, not 4.808 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 38.08 N, not 30.464 N.",
"D": "Incorrect. Substituting the stated v... | [
"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_006454 | 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 330 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.8899 s",
"B": "1.01101 s",
"C": "0.05505 s",
"D": "0.1101 s"
} | D | 0.1101 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(1/330)=0.1101 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.1101 s, not -1.8899 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.1101 s, not 1.01101 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.1101 s, no... | [
"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_000467 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 26 and common difference 15. Find the sum of its first 27 terms. | {
"A": "2983.5",
"B": "4475.25",
"C": "-5967",
"D": "5967"
} | D | 5967 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=26, d=15, n=27: Sₙ=27/2[2(26)+(27−1)(15)]=5967. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5967, not 2983.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5967, not 4475.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5967, not -5967.",
"D":... | [
"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_005572 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 52 μF capacitor is charged to a potential difference of 11 V. Calculate the energy stored, expressed in μJ. | {
"A": "6292 μJ",
"B": "3144 μJ",
"C": "3148 μJ",
"D": "3146 μJ"
} | D | 3146 μJ | U=½CV². Since C=52 μF, U in μJ is ½×52×(11)²=3146 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3146 μJ, not 6292 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3146 μJ, not 3144 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3146 μJ, not 3148 ... | [
"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_007320 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 13 mol of gas at 268 K and 2.44 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "118.16663 L",
"B": "175.74995 L",
"C": "115.16663 L",
"D": "117.16663 L"
} | D | 117.16663 L | PV=nRT, so V=nRT/P=(13)(0.082057)(268)/(2.44)=117.16663 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 117.16663 L, not 118.16663 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 117.16663 L, not 175.74995 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11... | [
"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_005840 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.3 atm at 251 K. What is its pressure at 283 K? | {
"A": "0.72072 atm",
"B": "3.72072 atm",
"C": "5.58108 atm",
"D": "1.37207 atm"
} | B | 3.72072 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.3)(283)/(251)=3.72072 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.72072 atm, not 0.72072 atm.",
"B": "Correct. The worked calculation gives 3.72072 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.72072 atm, not 5.58108 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_005604 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 80 μF capacitor is charged to a potential difference of 16 V. Calculate the energy stored, expressed in μJ. | {
"A": "10239 μJ",
"B": "12288 μJ",
"C": "-10240 μJ",
"D": "10240 μJ"
} | D | 10240 μJ | U=½CV². Since C=80 μF, U in μJ is ½×80×(16)²=10240 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10240 μJ, not 10239 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10240 μJ, not 12288 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10240 μJ, not ... | [
"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_007212 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 11 mol of gas at 399 K and 0.48 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "900.37043 L",
"B": "751.30869 L",
"C": "750.30869 L",
"D": "76.03087 L"
} | C | 750.30869 L | PV=nRT, so V=nRT/P=(11)(0.082057)(399)/(0.48)=750.30869 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 750.30869 L, not 900.37043 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 750.30869 L, not 751.30869 L.",
"C": "Correct. The worked calculation gives 750.30869 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_009974 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(CN)_3]^+3, each CN ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "12",
"B": "-6",
"C": "3",
"D": "6"
} | D | 6 | Let the formal oxidation state of Co be x. Charge balance gives x+(3)(−1)=+3; hence x=3+3=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 12.",
"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 3.",
"D": "Correct. The worked ... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009498 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_3H_6N_2X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "-2",
"B": "2",
"C": "0",
"D": "-1"
} | C | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×3+2+2−6−4)/2=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 2.",
"C": "Correct. The worked calculation gives 0.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_005372 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 59 μF capacitor is charged to a potential difference of 15 V. Calculate the energy stored, expressed in μJ. | {
"A": "664.75 μJ",
"B": "6636.5 μJ",
"C": "6637.5 μJ",
"D": "5310 μJ"
} | C | 6637.5 μJ | U=½CV². Since C=59 μF, U in μJ is ½×59×(15)²=6637.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6637.5 μJ, not 664.75 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6637.5 μJ, not 6636.5 μJ.",
"C": "Correct. The worked calculation gives 6637.5 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_008576 | 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 1.45 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "6.8 K",
"B": "5.8 K",
"C": "11.6 K",
"D": "1.58 K"
} | B | 5.8 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×1.0×1.45=5.8 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.8 K, not 6.8 K.",
"B": "Correct. The worked calculation gives 5.8 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.8 K, not 11.6 K.",
"D": "Incorrect. Substituting the stated values into... | [
"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_008738 | 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 1.58 mol L⁻¹ and initially B is absent. At equilibrium, 25% of A has dissociated at constant volume. Find K_c. | {
"A": "-2.47333",
"B": "0.52667",
"C": "-1.47333",
"D": "-0.47333"
} | B | 0.52667 | Let α=0.25. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.58)(0.25)²/(1−0.25)=0.52667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.52667, not -2.47333.",
"B": "Correct. The worked calculation gives 0.52667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.52667, not -1.47333.",
"D": "Incorrect. Substituting the stated ... | [
"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_003526 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 85 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "678.92792 m",
"B": "814.7135 m",
"C": "543.14233 m",
"D": "339.46396 m"
} | A | 678.92792 m | Range R=u²sin(2θ)/g. Substituting u=85, θ=55° and g=10 gives R=(85)²sin(110°)/10=678.92792 m. | {
"A": "Correct. The worked calculation gives 678.92792 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 678.92792 m, not 814.7135 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 678.92792 m, not 543.14233 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_009408 | 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_25N_1X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "1",
"B": "2",
"C": "-1",
"D": "1.1"
} | A | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×13+2+1−25−2)/2=1. | {
"A": "Correct. The worked calculation gives 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not -1.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_006404 | 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 648 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.26058 s",
"B": "3.26058 s",
"C": "2.26058 s",
"D": "-1.73942 s"
} | A | 0.26058 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(11/648)=0.26058 s. | {
"A": "Correct. The worked calculation gives 0.26058 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.26058 s, not 3.26058 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.26058 s, not 2.26058 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003340 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-3+0i)/(6+7i). What is Re(z), the real part of z? | {
"A": "-0.10588",
"B": "-0.31765",
"C": "-0.21176",
"D": "-2.21176"
} | C | -0.21176 | Multiply numerator and denominator by the conjugate (6-7i). Then Re(z)=(ac+bd)/(c²+d²)=((-3)(6)+(0)(7))/(6²+(7)²)=-0.21176. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.21176, not -0.10588.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.21176, not -0.31765.",
"C": "Correct. The worked calculation gives -0.21176.",
"D": "Incorrect. Substituting the stat... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009552 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_6H_11X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "-2",
"B": "1",
"C": "-3",
"D": "0"
} | D | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+0−11−3)/2=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"D": "Correct. The worked ... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007722 | 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 23 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "-1.64062 mmol L⁻¹",
"B": "0.71875 mmol L⁻¹",
"C": "0.35938 mmol L⁻¹",
"D": "-2.64062 mmol L⁻¹"
} | C | 0.35938 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=23/2^6=0.35938 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35938 mmol L⁻¹, not -1.64062 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35938 mmol L⁻¹, not 0.71875 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.35938 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_004120 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 50 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.31. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "174 N",
"B": "176 N",
"C": "264 N",
"D": "140.8 N"
} | B | 176 N | Net force=mg(sinθ−μcosθ)=50×10×(0.6−0.31×0.8)=176 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 176 N, not 174 N.",
"B": "Correct. The worked calculation gives 176 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 176 N, not 264 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_009144 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.00 V, transfers 3 electrons, and has reaction quotient Q=10^1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.9803 V",
"B": "-1.0197 V",
"C": "0.9803 V",
"D": "3.9803 V"
} | C | 0.9803 V | Apply the Nernst equation: E=1.00−(0.0591/3)(1)=0.9803 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9803 V, not 1.9803 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9803 V, not -1.0197 V.",
"C": "Correct. The worked calculation gives 0.9803 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001229 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=2x³ +1x² +7x+7. Evaluate f′(-2). | {
"A": "29",
"B": "-27",
"C": "3.7",
"D": "27"
} | D | 27 | Differentiate: f′(x)=3(2)x²+2(1)x+(7). At x=-2, f′(-2)=3(2)(-2)²+2(1)(-2)+(7)=27. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 27, not 29.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 27, not -27.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 27, not 3.7.",
"D": "Correct. The w... | [
"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_007445 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 73 mL of 0.10 M HCl is mixed with 53 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "3.59868",
"B": "3.79934",
"C": "1.34951",
"D": "1.79934"
} | D | 1.79934 | Excess H⁺ moles=0.10×(73−53)/1000=0.002000 mol. Total volume=0.126 L, so [H⁺]=0.015873 M and pH=−log₁₀[H⁺]=1.79934. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.79934, not 3.59868.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.79934, not 3.79934.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.79934, not 1.349... | [
"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_005422 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 33 μF capacitor is charged to a potential difference of 39 V. Calculate the energy stored, expressed in μJ. | {
"A": "37644.75 μJ",
"B": "25096.5 μJ",
"C": "50193 μJ",
"D": "25098.5 μJ"
} | B | 25096.5 μJ | U=½CV². Since C=33 μF, U in μJ is ½×33×(39)²=25096.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 25096.5 μJ, not 37644.75 μJ.",
"B": "Correct. The worked calculation gives 25096.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 25096.5 μJ, not 50193 μJ.",
"D": "Incorrect. Substituting... | [
"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_005083 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +7 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "-49.21875 N",
"B": "98.4375 N",
"C": "48.21875 N",
"D": "49.21875 N"
} | D | 49.21875 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(7×10⁻⁶)/(8×10⁻²)²=49.21875 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 49.21875 N, not -49.21875 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 49.21875 N, not 98.4375 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 49.218... | [
"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_007535 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 38 mL of 0.10 M HCl is mixed with 35 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.1931",
"B": "-0.6138",
"C": "3.3862",
"D": "2.3862"
} | D | 2.3862 | Excess H⁺ moles=0.10×(38−35)/1000=0.000300 mol. Total volume=0.073 L, so [H⁺]=0.004110 M and pH=−log₁₀[H⁺]=2.3862. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.3862, not 1.1931.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.3862, not -0.6138.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.3862, not 3.3862.",... | [
"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_004237 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 28 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.38. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "-82.88 N",
"B": "84.88 N",
"C": "165.76 N",
"D": "82.88 N"
} | D | 82.88 N | Net force=mg(sinθ−μcosθ)=28×10×(0.6−0.38×0.8)=82.88 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 82.88 N, not -82.88 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 82.88 N, not 84.88 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 82.88 N, not 165.... | [
"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_008820 | 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 1.82 mol L⁻¹ and initially B is absent. At equilibrium, 28% of A has dissociated at constant volume. Find K_c. | {
"A": "1.79271",
"B": "0.59453",
"C": "0.79271",
"D": "-1.20729"
} | C | 0.79271 | Let α=0.28. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.82)(0.28)²/(1−0.28)=0.79271. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.79271, not 1.79271.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.79271, not 0.59453.",
"C": "Correct. The worked calculation gives 0.79271.",
"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_005098 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +9 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "33.75 N",
"B": "-45 N",
"C": "45 N",
"D": "36 N"
} | C | 45 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(9×10⁻⁶)/(6×10⁻²)²=45 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45 N, not 33.75 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 45 N, not -45 N.",
"C": "Correct. The worked calculation gives 45 N.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_000706 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio -2. What is the sum of its first 12 terms? | {
"A": "-9555",
"B": "-11466",
"C": "9555",
"D": "-9556"
} | A | -9555 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(-2^12−1)/(-2−1)=-9555. | {
"A": "Correct. The worked calculation gives -9555.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -9555, not -11466.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -9555, not 9555.",
"D": "Incorrect. Substituting the stated values into ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005649 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 66 μF capacitor is charged to a potential difference of 31 V. Calculate the energy stored, expressed in μJ. | {
"A": "25370.4 μJ",
"B": "31712 μJ",
"C": "31713 μJ",
"D": "31715 μJ"
} | C | 31713 μJ | U=½CV². Since C=66 μF, U in μJ is ½×66×(31)²=31713 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 31713 μJ, not 25370.4 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 31713 μJ, not 31712 μJ.",
"C": "Correct. The worked calculation gives 31713 μJ.",
"D": "Incorrect. Substituting the st... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003021 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-1-7i)/(12+9i). What is Re(z), the real part of z? | {
"A": "0.33333",
"B": "-0.33333",
"C": "-0.16667",
"D": "-1.33333"
} | B | -0.33333 | Multiply numerator and denominator by the conjugate (12-9i). Then Re(z)=(ac+bd)/(c²+d²)=((-1)(12)+(-7)(9))/(12²+(9)²)=-0.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.33333, not 0.33333.",
"B": "Correct. The worked calculation gives -0.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.33333, not -0.16667.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003710 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 13 kg block initially moves at 1 m s⁻¹. A constant net force does 20 N of work over 7 m in the direction of motion. Find its final kinetic energy. | {
"A": "109.875 J",
"B": "117.2 J",
"C": "293 J",
"D": "146.5 J"
} | D | 146.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(13)(1)²+(20)(7)=146.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 146.5 J, not 109.875 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 146.5 J, not 117.2 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 146.5 J, not 293... | [
"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_007909 | 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 20 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "-2.6875 mmol L⁻¹",
"B": "0.15625 mmol L⁻¹",
"C": "0.3125 mmol L⁻¹",
"D": "1.3125 mmol L⁻¹"
} | C | 0.3125 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=20/2^6=0.3125 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3125 mmol L⁻¹, not -2.6875 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3125 mmol L⁻¹, not 0.15625 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.3125 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_009461 | 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_12N_2X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "0",
"B": "1",
"C": "2",
"D": "0.75"
} | B | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+2−12−4)/2=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.",
"B": "Correct. The worked calculation gives 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001552 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (6x² +7x +4) dx. | {
"A": "6.5",
"B": "1.95",
"C": "9.5",
"D": "4.75"
} | C | 9.5 | An antiderivative is (6/3)x³+(7/2)x²+(4)x. Evaluating between 0 and 1 gives (6/3)(1)³+(7/2)(1)²+(4)(1)=9.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.5, not 6.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.5, not 1.95.",
"C": "Correct. The worked calculation gives 9.5.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008162 | 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 24785 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": "-65.2372 g",
"B": "52.18976 g",
"C": "65.2372 g",
"D": "32.6186 g"
} | C | 65.2372 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×8×24785/(2×96500)=65.2372 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 65.2372 g, not -65.2372 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 65.2372 g, not 52.18976 g.",
"C": "Correct. The worked calculation gives 65.2372 g.",
"D": "Incorrect. Substituting t... | [
"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_000350 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -11 and common difference 2. Find the sum of its first 11 terms. | {
"A": "-12",
"B": "-11",
"C": "-8.25",
"D": "-9"
} | B | -11 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-11, d=2, n=11: Sₙ=11/2[2(-11)+(11−1)(2)]=-11. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -11, not -12.",
"B": "Correct. The worked calculation gives -11.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -11, not -8.25.",
"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_005393 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 42 μF capacitor is charged to a potential difference of 8 V. Calculate the energy stored, expressed in μJ. | {
"A": "2016 μJ",
"B": "1344 μJ",
"C": "2688 μJ",
"D": "1075.2 μJ"
} | B | 1344 μJ | U=½CV². Since C=42 μF, U in μJ is ½×42×(8)²=1344 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1344 μJ, not 2016 μJ.",
"B": "Correct. The worked calculation gives 1344 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1344 μJ, not 2688 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_009626 | 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_5H_10X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "0",
"B": "1",
"C": "-2",
"D": "3"
} | A | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×5+2+0−10−2)/2=0. | {
"A": "Correct. The worked calculation gives 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_001469 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (5x² -1x -4) dx. | {
"A": "789.33333",
"B": "1184",
"C": "947.2",
"D": "592"
} | A | 789.33333 | An antiderivative is (5/3)x³+(-1/2)x²+(-4)x. Evaluating between 0 and 8 gives (5/3)(8)³+(-1/2)(8)²+(-4)(8)=789.33333. | {
"A": "Correct. The worked calculation gives 789.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 789.33333, not 1184.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 789.33333, not 947.2.",
"D": "Incorrect. Substituting the stated v... | [
"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_004527 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 3 kg and radius 4 m is acted on by a constant torque of 63 N m about its central axis. Find its angular acceleration. | {
"A": "3.625 rad s⁻²",
"B": "1.3125 rad s⁻²",
"C": "2.625 rad s⁻²",
"D": "1.2625 rad s⁻²"
} | C | 2.625 rad s⁻² | For a solid disc, I=½MR²=½(3)(4)²=24 kg m². Using τ=Iα, α=63/24=2.625 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.625 rad s⁻², not 3.625 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.625 rad s⁻², not 1.3125 rad s⁻².",
"C": "Correct. The worked calculation gives 2.625 rad s⁻².",
"D": "Incorr... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003309 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-10-8i)/(5+7i). What is Re(z), the real part of z? | {
"A": "-2.43243",
"B": "-3.43243",
"C": "-1.43243",
"D": "1.56757"
} | C | -1.43243 | Multiply numerator and denominator by the conjugate (5-7i). Then Re(z)=(ac+bd)/(c²+d²)=((-10)(5)+(-8)(7))/(5²+(7)²)=-1.43243. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.43243, not -2.43243.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.43243, not -3.43243.",
"C": "Correct. The worked calculation gives -1.43243.",
"D": "Incorrect. Substituting the stat... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009501 | 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_12H_23X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "2",
"B": "0",
"C": "1",
"D": "3"
} | B | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×12+2+0−23−3)/2=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 2.",
"B": "Correct. The worked calculation gives 0.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001265 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ +1x² +12x+7. Evaluate f′(3). | {
"A": "-119",
"B": "-140.4",
"C": "117",
"D": "-117"
} | D | -117 | Differentiate: f′(x)=3(-5)x²+2(1)x+(12). At x=3, f′(3)=3(-5)(3)²+2(1)(3)+(12)=-117. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -117, not -119.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -117, not -140.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -117, not 117.",
"D": "Cor... | [
"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_008540 | 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 0.4 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-2.76 K",
"B": "-0.76 K",
"C": "0.24 K",
"D": "0.18 K"
} | C | 0.24 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.6×0.4=0.24 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.24 K, not -2.76 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.24 K, not -0.76 K.",
"C": "Correct. The worked calculation gives 0.24 K.",
"D": "Incorrect. Substituting the stated value... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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