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_006916 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 49 mol H₂ and 19 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "30.4 mol",
"B": "76 mol",
"C": "19 mol",
"D": "38 mol"
} | D | 38 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 49 mol H₂O; O₂ can produce 38 mol H₂O. The limiting condition is O₂; product=38 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 38 mol, not 30.4 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 38 mol, not 76 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 38 mol, not 19 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_008465 | 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 1.14 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.4072 K",
"B": "0.5928 K",
"C": "0.4446 K",
"D": "2.5928 K"
} | B | 0.5928 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.52×1.14=0.5928 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5928 K, not -0.4072 K.",
"B": "Correct. The worked calculation gives 0.5928 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5928 K, not 0.4446 K.",
"D": "Incorrect. Substituting the sta... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000451 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -17 and common difference 10. Find the sum of its first 17 terms. | {
"A": "1072",
"B": "1071",
"C": "1073",
"D": "803.25"
} | B | 1071 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-17, d=10, n=17: Sₙ=17/2[2(-17)+(17−1)(10)]=1071. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1071, not 1072.",
"B": "Correct. The worked calculation gives 1071.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1071, not 1073.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000112 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 +5x -2=0, let its roots be α and β. What is α²+β²? | {
"A": "1.36111",
"B": "3.36111",
"C": "2.36111",
"D": "1.13611"
} | A | 1.36111 | By Vieta's relations, α+β = -5/6 and αβ = -2/6. Then α²+β²=(α+β)²−2αβ = (-5/6)²−2(-2/6) = 1.36111. | {
"A": "Correct. The worked calculation gives 1.36111.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.36111, not 3.36111.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.36111, not 2.36111.",
"D": "Incorrect. Substituting the stated va... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004209 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 32 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.29. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "116.76 N",
"B": "117.76 N",
"C": "88.32 N",
"D": "119.76 N"
} | B | 117.76 N | Net force=mg(sinθ−μcosθ)=32×10×(0.6−0.29×0.8)=117.76 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 117.76 N, not 116.76 N.",
"B": "Correct. The worked calculation gives 117.76 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 117.76 N, not 88.32 N.",
"D": "Incorrect. Substituting the state... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000571 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -18 and common difference 6. Find the sum of its first 17 terms. | {
"A": "510",
"B": "382.5",
"C": "765",
"D": "509"
} | A | 510 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-18, d=6, n=17: Sₙ=17/2[2(-18)+(17−1)(6)]=510. | {
"A": "Correct. The worked calculation gives 510.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 510, not 382.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 510, not 765.",
"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_003095 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(2-4i)/(11+4i). What is Re(z), the real part of z? | {
"A": "-0.9562",
"B": "2.0438",
"C": "1.00438",
"D": "0.0438"
} | D | 0.0438 | Multiply numerator and denominator by the conjugate (11-4i). Then Re(z)=(ac+bd)/(c²+d²)=((2)(11)+(-4)(4))/(11²+(4)²)=0.0438. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.0438, not -0.9562.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.0438, not 2.0438.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.0438, not 1.00438."... | [
"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_006707 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 50 mol H₂ and 14 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "22.4 mol",
"B": "30 mol",
"C": "29 mol",
"D": "28 mol"
} | D | 28 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 50 mol H₂O; O₂ can produce 28 mol H₂O. The limiting condition is O₂; product=28 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28 mol, not 22.4 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28 mol, not 30 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28 mol, not 29 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_002071 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 4 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.65263",
"B": "1.03474",
"C": "1.34737",
"D": "0.34737"
} | D | 0.34737 | Favourable pairs = C(10,2)+C(4,2)+C(6,2)=66. Total pairs=C(20,2)=190. Therefore P=66/190=0.34737. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34737, not -0.65263.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34737, not 1.03474.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34737, not 1.34... | [
"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_000004 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -10x -10=0, let its roots be α and β. What is α²+β²? | {
"A": "4.5",
"B": "26.25",
"C": "28",
"D": "35"
} | D | 35 | By Vieta's relations, α+β = 10/2 and αβ = -10/2. Then α²+β²=(α+β)²−2αβ = (10/2)²−2(-10/2) = 35. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 35, not 4.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 35, not 26.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 35, not 28.",
"D": "Correct. The... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001279 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=2x³ +10x² +12x+7. Evaluate f′(3). | {
"A": "126",
"B": "151.2",
"C": "13.6",
"D": "100.8"
} | A | 126 | Differentiate: f′(x)=3(2)x²+2(10)x+(12). At x=3, f′(3)=3(2)(3)²+2(10)(3)+(12)=126. | {
"A": "Correct. The worked calculation gives 126.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 126, not 151.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 126, not 13.6.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001205 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ -5x² +3x+7. Evaluate f′(-4). | {
"A": "330",
"B": "331",
"C": "332",
"D": "397.2"
} | B | 331 | Differentiate: f′(x)=3(6)x²+2(-5)x+(3). At x=-4, f′(-4)=3(6)(-4)²+2(-5)(-4)+(3)=331. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 331, not 330.",
"B": "Correct. The worked calculation gives 331.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 331, not 332.",
"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_004577 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 2 m is acted on by a constant torque of 69 N m about its central axis. Find its angular acceleration. | {
"A": "5.175 rad s⁻²",
"B": "6.9 rad s⁻²",
"C": "-6.9 rad s⁻²",
"D": "10.35 rad s⁻²"
} | B | 6.9 rad s⁻² | For a solid disc, I=½MR²=½(5)(2)²=10 kg m². Using τ=Iα, α=69/10=6.9 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.9 rad s⁻², not 5.175 rad s⁻².",
"B": "Correct. The worked calculation gives 6.9 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.9 rad s⁻², not -6.9 rad s⁻².",
"D": "Incorrect. Sub... | [
"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_002863 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-4, -5, -6) and v=(2, -5, 2), calculate u·v. | {
"A": "2.5",
"B": "5",
"C": "3.75",
"D": "7.5"
} | B | 5 | The dot product is the sum of corresponding component products: (-4)(2)+(-5)(-5)+(-6)(2)=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.5.",
"B": "Correct. The worked calculation gives 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.75.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005804 | 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 323 K. What is its pressure at 499 K? | {
"A": "7.56997 atm",
"B": "11.35495 atm",
"C": "10.56997 atm",
"D": "8.56997 atm"
} | A | 7.56997 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.9)(499)/(323)=7.56997 atm. | {
"A": "Correct. The worked calculation gives 7.56997 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.56997 atm, not 11.35495 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.56997 atm, not 10.56997 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_005435 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 29 μF capacitor is charged to a potential difference of 25 V. Calculate the energy stored, expressed in μJ. | {
"A": "7250 μJ",
"B": "9063.5 μJ",
"C": "9061.5 μJ",
"D": "9062.5 μJ"
} | D | 9062.5 μJ | U=½CV². Since C=29 μF, U in μJ is ½×29×(25)²=9062.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9062.5 μJ, not 7250 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9062.5 μJ, not 9063.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9062.5 μJ, n... | [
"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_002563 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, 5], [6, 5]]. | {
"A": "-19",
"B": "-18",
"C": "-40",
"D": "-20"
} | D | -20 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(5)−(5)(6)=-20. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -20, not -19.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -20, not -18.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -20, not -40.",
"D": "Correct. T... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000266 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 -10x +10=0, let its roots be α and β. What is α²+β²? | {
"A": "0",
"B": "-1",
"C": "2",
"D": "-2"
} | A | 0 | By Vieta's relations, α+β = 10/5 and αβ = 10/5. Then α²+β²=(α+β)²−2αβ = (10/5)²−2(10/5) = 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... | [
"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_000049 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 +8x +7=0, let its roots be α and β. What is α²+β²? | {
"A": "-0.83333",
"B": "0.44444",
"C": "-0.55556",
"D": "0.55556"
} | C | -0.55556 | By Vieta's relations, α+β = -8/6 and αβ = 7/6. Then α²+β²=(α+β)²−2αβ = (-8/6)²−2(7/6) = -0.55556. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.55556, not -0.83333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.55556, not 0.44444.",
"C": "Correct. The worked calculation gives -0.55556.",
"D": "Incorrect. Substituting the state... | [
"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_006030 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 27 cm in front of a thin convex lens of focal length 9 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.5",
"B": "-2.5",
"C": "0.75",
"D": "0.5"
} | D | 0.5 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(27)(9)/(27−9)=13.5 cm. Thus |m|=v/u=13.5/27=0.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5, not -0.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.5, not -2.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5, not 0.75.",
"D": "Correct... | [
"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_001618 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (6x² -4x +2) dx. | {
"A": "12",
"B": "2.2",
"C": "9",
"D": "6"
} | A | 12 | An antiderivative is (6/3)x³+(-4/2)x²+(2)x. Evaluating between 0 and 2 gives (6/3)(2)³+(-4/2)(2)²+(2)(2)=12. | {
"A": "Correct. The worked calculation gives 12.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12, not 2.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12, not 9.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_002329 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 4 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.03619",
"B": "0.3619",
"C": "0.72381",
"D": "1.3619"
} | B | 0.3619 | Favourable pairs = C(6,2)+C(4,2)+C(11,2)=76. Total pairs=C(21,2)=210. Therefore P=76/210=0.3619. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3619, not 1.03619.",
"B": "Correct. The worked calculation gives 0.3619.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3619, not 0.72381.",
"D": "Incorrect. Substituting the stated value... | [
"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_001718 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 2 elements can be selected from a set of 58 distinct elements? | {
"A": "1654",
"B": "1653",
"C": "166.3",
"D": "2479.5"
} | B | 1653 | Order does not matter, so the count is C(58,2)=58!/[2!(56)!]=1653. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1653, not 1654.",
"B": "Correct. The worked calculation gives 1653.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1653, not 166.3.",
"D": "Incorrect. Substituting the stated values into the ... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007974 | 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 22 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "0.25781 mmol L⁻¹",
"B": "0.12891 mmol L⁻¹",
"C": "-0.82812 mmol L⁻¹",
"D": "0.17188 mmol L⁻¹"
} | D | 0.17188 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=22/2^7=0.17188 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.17188 mmol L⁻¹, not 0.25781 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.17188 mmol L⁻¹, not 0.12891 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_003934 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block initially moves at 4 m s⁻¹. A constant net force does 9 N of work over 17 m in the direction of motion. Find its final kinetic energy. | {
"A": "198.75 J",
"B": "27.5 J",
"C": "263 J",
"D": "265 J"
} | D | 265 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(14)(4)²+(9)(17)=265 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 265 J, not 198.75 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 265 J, not 27.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 265 J, not 263 J.",
... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000418 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -2 and common difference 2. Find the sum of its first 30 terms. | {
"A": "82",
"B": "-810",
"C": "810",
"D": "811"
} | C | 810 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-2, d=2, n=30: Sₙ=30/2[2(-2)+(30−1)(2)]=810. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 810, not 82.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 810, not -810.",
"C": "Correct. The worked calculation gives 810.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007297 | 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 627 K and 2.43 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "550.49103 L",
"B": "220.19641 L",
"C": "275.24552 L",
"D": "273.24552 L"
} | C | 275.24552 L | PV=nRT, so V=nRT/P=(13)(0.082057)(627)/(2.43)=275.24552 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 275.24552 L, not 550.49103 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 275.24552 L, not 220.19641 L.",
"C": "Correct. The worked calculation gives 275.24552 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_006870 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 23 mol H₂ and 5 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "10 mol",
"B": "-10 mol",
"C": "2 mol",
"D": "8 mol"
} | A | 10 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 23 mol H₂O; O₂ can produce 10 mol H₂O. The limiting condition is O₂; product=10 mol. | {
"A": "Correct. The worked calculation gives 10 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not -10 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 2 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008246 | 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 7 A for 8259 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": "9.51069 g",
"B": "22.82565 g",
"C": "19.02138 g",
"D": "15.2171 g"
} | C | 19.02138 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×7×8259/(2×96500)=19.02138 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19.02138 g, not 9.51069 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19.02138 g, not 22.82565 g.",
"C": "Correct. The worked calculation gives 19.02138 g.",
"D": "Incorrect. Substituting... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008866 | 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 0.04 mol L⁻¹ and initially B is absent. At equilibrium, 24% of A has dissociated at constant volume. Find K_c. | {
"A": "0.01213",
"B": "0.00909",
"C": "0.02425",
"D": "3.01213"
} | A | 0.01213 | Let α=0.24. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.04)(0.24)²/(1−0.24)=0.01213. | {
"A": "Correct. The worked calculation gives 0.01213.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.01213, not 0.00909.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.01213, not 0.02425.",
"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_003855 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block initially moves at 9 m s⁻¹. A constant net force does 18 N of work over 8 m in the direction of motion. Find its final kinetic energy. | {
"A": "223 J",
"B": "112.5 J",
"C": "225 J",
"D": "180 J"
} | C | 225 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(2)(9)²+(18)(8)=225 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 225 J, not 223 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 225 J, not 112.5 J.",
"C": "Correct. The worked calculation gives 225 J.",
"D": "Incorrect. Substituting the stated values int... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003515 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 28 m s⁻¹ at 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "77.20893 m",
"B": "115.81339 m",
"C": "79.20893 m",
"D": "-77.20893 m"
} | A | 77.20893 m | Range R=u²sin(2θ)/g. Substituting u=28, θ=40° and g=10 gives R=(28)²sin(80°)/10=77.20893 m. | {
"A": "Correct. The worked calculation gives 77.20893 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 77.20893 m, not 115.81339 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 77.20893 m, not 79.20893 m.",
"D": "Incorrect. Substituti... | [
"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_004971 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 14 Ω and 2 Ω are connected in series; this combination is connected in parallel with a 5 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.725 A",
"B": "6.725 A",
"C": "5.725 A",
"D": "-4.725 A"
} | A | 4.725 A | Series branch resistance=14+2=16 Ω. Parallel equivalent R_eq=(16×5)/(16+5)=3.80952 Ω. Total current I=V/R_eq=18/3.80952=4.725 A. | {
"A": "Correct. The worked calculation gives 4.725 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.725 A, not 6.725 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.725 A, not 5.725 A.",
"D": "Incorrect. Substituting the stated va... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001140 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=0x³ +2x² +12x+7. Evaluate f′(-3). | {
"A": "-1",
"B": "1",
"C": "-2",
"D": "0"
} | D | 0 | Differentiate: f′(x)=3(0)x²+2(2)x+(12). At x=-3, f′(-3)=3(0)(-3)²+2(2)(-3)+(12)=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not -1.",
"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": "Correct. The worked ... | [
"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_000362 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 1 and common difference 5. Find the sum of its first 20 terms. | {
"A": "1940",
"B": "970",
"C": "969",
"D": "972"
} | B | 970 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=1, d=5, n=20: Sₙ=20/2[2(1)+(20−1)(5)]=970. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 970, not 1940.",
"B": "Correct. The worked calculation gives 970.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 970, not 969.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009920 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(OH)_2]^-3, each OH ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "-2",
"B": "-1.5",
"C": "-1",
"D": "1"
} | C | -1 | Let the formal oxidation state of Mn be x. Charge balance gives x+(2)(−1)=-3; hence x=-3+2=-1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1, not -1.5.",
"C": "Correct. The worked calculation gives -1.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"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_009457 | 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_14H_26N_2X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "0",
"C": "1",
"D": "2"
} | D | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×14+2+2−26−2)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 0.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"D": "Correct. The worked ca... | [
"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_003017 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(2-12i)/(3+6i). What is Re(z), the real part of z? | {
"A": "-1.1",
"B": "-1.46667",
"C": "-2.2",
"D": "-4.46667"
} | B | -1.46667 | Multiply numerator and denominator by the conjugate (3-6i). Then Re(z)=(ac+bd)/(c²+d²)=((2)(3)+(-12)(6))/(3²+(6)²)=-1.46667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.46667, not -1.1.",
"B": "Correct. The worked calculation gives -1.46667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.46667, not -2.2.",
"D": "Incorrect. Substituting the stated value... | [
"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_006060 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 52 cm in front of a thin convex lens of focal length 13 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.03333",
"B": "-0.33333",
"C": "0.16667",
"D": "0.33333"
} | D | 0.33333 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(52)(13)/(52−13)=17.33333 cm. Thus |m|=v/u=17.33333/52=0.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not 1.03333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not -0.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not 0.16... | [
"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_008303 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 10 A for 21661 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": "71.26806 g",
"B": "70.26806 g",
"C": "57.01445 g",
"D": "72.26806 g"
} | A | 71.26806 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×10×21661/(2×96500)=71.26806 g. | {
"A": "Correct. The worked calculation gives 71.26806 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 71.26806 g, not 70.26806 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 71.26806 g, not 57.01445 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000910 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio 4. What is the sum of its first 9 terms? | {
"A": "218452.5",
"B": "436905",
"C": "43691.5",
"D": "524286"
} | B | 436905 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(4^9−1)/(4−1)=436905. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 436905, not 218452.5.",
"B": "Correct. The worked calculation gives 436905.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 436905, not 43691.5.",
"D": "Incorrect. Substituting the stated valu... | [
"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_006736 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 29 mol H₂ and 16 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "29 mol",
"B": "3.9 mol",
"C": "43.5 mol",
"D": "23.2 mol"
} | A | 29 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 29 mol H₂O; O₂ can produce 32 mol H₂O. The limiting condition is H₂; product=29 mol. | {
"A": "Correct. The worked calculation gives 29 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 29 mol, not 3.9 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29 mol, not 43.5 mol.",
"D": "Incorrect. Substituting the stated valu... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001738 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 11 elements can be selected from a set of 74 distinct elements? | {
"A": "-4179822305984",
"B": "3343857844787.2002",
"C": "4179822305984",
"D": "5015786767180.7998"
} | C | 4179822305984 | Order does not matter, so the count is C(74,11)=74!/[11!(63)!]=4179822305984. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4179822305984, not -4179822305984.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4179822305984, not 3343857844787.2002.",
"C": "Correct. The worked calculation gives 4179822305984.",
"D": "I... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002897 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-7, -4, 2) and v=(0, 4, -7), calculate u·v. | {
"A": "-30",
"B": "-29",
"C": "-32",
"D": "-24"
} | A | -30 | The dot product is the sum of corresponding component products: (-7)(0)+(-4)(4)+(2)(-7)=-30. | {
"A": "Correct. The worked calculation gives -30.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -30, not -29.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -30, not -32.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008235 | 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 1 A for 18082 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": "-5.94926 g",
"B": "4.46194 g",
"C": "8.94926 g",
"D": "5.94926 g"
} | D | 5.94926 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×1×18082/(2×96500)=5.94926 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.94926 g, not -5.94926 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.94926 g, not 4.46194 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.94926 g... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008131 | 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 11 A for 20303 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": "146.96006 g",
"B": "73.48003 g",
"C": "58.78402 g",
"D": "71.48003 g"
} | B | 73.48003 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×20303/(2×96500)=73.48003 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 73.48003 g, not 146.96006 g.",
"B": "Correct. The worked calculation gives 73.48003 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 73.48003 g, not 58.78402 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008167 | 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 5 A for 27768 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": "68.52078 g",
"B": "45.68052 g",
"C": "36.54441 g",
"D": "22.84026 g"
} | B | 45.68052 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×5×27768/(2×96500)=45.68052 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45.68052 g, not 68.52078 g.",
"B": "Correct. The worked calculation gives 45.68052 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 45.68052 g, not 36.54441 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007537 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 33 mL of 0.10 M HCl is mixed with 30 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.32222",
"B": "4.64444",
"C": "5.32222",
"D": "1.74166"
} | A | 2.32222 | Excess H⁺ moles=0.10×(33−30)/1000=0.000300 mol. Total volume=0.063 L, so [H⁺]=0.004762 M and pH=−log₁₀[H⁺]=2.32222. | {
"A": "Correct. The worked calculation gives 2.32222.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.32222, not 4.64444.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.32222, not 5.32222.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002557 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, 1], [3, 1]]. | {
"A": "2",
"B": "3",
"C": "1.2",
"D": "1.5"
} | A | 2 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(1)−(1)(3)=2. | {
"A": "Correct. The worked calculation gives 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.2.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_003579 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 14 m s⁻¹ at 20° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "25.19727 m",
"B": "12.59864 m",
"C": "13.59864 m",
"D": "15.59864 m"
} | B | 12.59864 m | Range R=u²sin(2θ)/g. Substituting u=14, θ=20° and g=10 gives R=(14)²sin(40°)/10=12.59864 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.59864 m, not 25.19727 m.",
"B": "Correct. The worked calculation gives 12.59864 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.59864 m, not 13.59864 m.",
"D": "Incorrect. Substitutin... | [
"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_002097 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 11 blue and 8 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-2.67333",
"B": "-0.32667",
"C": "0.16333",
"D": "0.32667"
} | D | 0.32667 | Favourable pairs = C(6,2)+C(11,2)+C(8,2)=98. Total pairs=C(25,2)=300. Therefore P=98/300=0.32667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32667, not -2.67333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32667, not -0.32667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32667, not 0.1... | [
"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_007433 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 28 mL of 0.10 M HCl is mixed with 46 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "13.38604",
"B": "14.38604",
"C": "9.38604",
"D": "12.38604"
} | D | 12.38604 | Excess OH⁻ moles=0.10×(46−28)/1000=0.001800 mol. Total volume=0.074 L, so [OH⁻]=0.024324 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.38604. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.38604, not 13.38604.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.38604, not 14.38604.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.38604, not ... | [
"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_002218 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 7 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.03117",
"B": "3.31169",
"C": "-1.68831",
"D": "0.31169"
} | D | 0.31169 | Favourable pairs = C(9,2)+C(7,2)+C(6,2)=72. Total pairs=C(22,2)=231. Therefore P=72/231=0.31169. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31169, not 1.03117.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31169, not 3.31169.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31169, not -1.68... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001529 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (-3x² +5x +0) dx. | {
"A": "-354",
"B": "-281.6",
"C": "-350",
"D": "-352"
} | D | -352 | An antiderivative is (-3/3)x³+(5/2)x²+(0)x. Evaluating between 0 and 8 gives (-3/3)(8)³+(5/2)(8)²+(0)(8)=-352. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -352, not -354.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -352, not -281.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -352, not -350.",
"D": "Co... | [
"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_007789 | 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 100 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "0.58594 mmol L⁻¹",
"B": "0.19531 mmol L⁻¹",
"C": "1.03906 mmol L⁻¹",
"D": "0.39062 mmol L⁻¹"
} | D | 0.39062 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=100/2^8=0.39062 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.39062 mmol L⁻¹, not 0.58594 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.39062 mmol L⁻¹, not 0.19531 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_008379 | 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 1.55 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "5.79 K",
"B": "2.79 K",
"C": "0.79 K",
"D": "1.279 K"
} | B | 2.79 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.6×1.55=2.79 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.79 K, not 5.79 K.",
"B": "Correct. The worked calculation gives 2.79 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.79 K, not 0.79 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_009092 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.12 V, transfers 3 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.5618 V",
"B": "1.0412 V",
"C": "0.7809 V",
"D": "-1.9588 V"
} | B | 1.0412 V | Apply the Nernst equation: E=1.12−(0.0591/3)(4)=1.0412 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0412 V, not 1.5618 V.",
"B": "Correct. The worked calculation gives 1.0412 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0412 V, not 0.7809 V.",
"D": "Incorrect. Substituting the stat... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001237 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-3x³ +2x² +1x+7. Evaluate f′(-1). | {
"A": "-10",
"B": "-9",
"C": "-12",
"D": "-18"
} | C | -12 | Differentiate: f′(x)=3(-3)x²+2(2)x+(1). At x=-1, f′(-1)=3(-3)(-1)²+2(2)(-1)+(1)=-12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -12, not -10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -12, not -9.",
"C": "Correct. The worked calculation gives -12.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000027 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 +16x +3=0, let its roots be α and β. What is α²+β²? | {
"A": "10.875",
"B": "14.5",
"C": "12.5",
"D": "11.5"
} | B | 14.5 | By Vieta's relations, α+β = -16/4 and αβ = 3/4. Then α²+β²=(α+β)²−2αβ = (-16/4)²−2(3/4) = 14.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14.5, not 10.875.",
"B": "Correct. The worked calculation gives 14.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14.5, not 12.5.",
"D": "Incorrect. Substituting the stated values into the... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006881 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 7 mol H₂ and 17 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "1.7 mol",
"B": "5.25 mol",
"C": "10.5 mol",
"D": "7 mol"
} | D | 7 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 7 mol H₂O; O₂ can produce 34 mol H₂O. The limiting condition is H₂; product=7 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7 mol, not 1.7 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7 mol, not 5.25 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7 mol, not 10.5 mol."... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004073 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.13. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "28.76 N",
"B": "27.76 N",
"C": "29.76 N",
"D": "35.712 N"
} | C | 29.76 N | Net force=mg(sinθ−μcosθ)=6×10×(0.6−0.13×0.8)=29.76 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 29.76 N, not 28.76 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 29.76 N, not 27.76 N.",
"C": "Correct. The worked calculation gives 29.76 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_001241 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ +1x² +11x+7. Evaluate f′(4). | {
"A": "211",
"B": "316.5",
"C": "213",
"D": "105.5"
} | A | 211 | Differentiate: f′(x)=3(4)x²+2(1)x+(11). At x=4, f′(4)=3(4)(4)²+2(1)(4)+(11)=211. | {
"A": "Correct. The worked calculation gives 211.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 211, not 316.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 211, not 213.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_002321 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 8 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": "0.48246",
"B": "1.32164",
"C": "0.32164",
"D": "0.24123"
} | C | 0.32164 | Favourable pairs = C(4,2)+C(8,2)+C(7,2)=55. Total pairs=C(19,2)=171. Therefore P=55/171=0.32164. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32164, not 0.48246.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32164, not 1.32164.",
"C": "Correct. The worked calculation gives 0.32164.",
"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_003896 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 1 m s⁻¹. A constant net force does 22 N of work over 13 m in the direction of motion. Find its final kinetic energy. | {
"A": "292 J",
"B": "294 J",
"C": "584 J",
"D": "291 J"
} | A | 292 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(1)²+(22)(13)=292 J. | {
"A": "Correct. The worked calculation gives 292 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 292 J, not 294 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 292 J, not 584 J.",
"D": "Incorrect. Substituting the stated values into ... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006059 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 102 cm in front of a thin convex lens of focal length 23 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.29114",
"B": "0.58228",
"C": "-0.29114",
"D": "3.29114"
} | A | 0.29114 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(102)(23)/(102−23)=29.6962 cm. Thus |m|=v/u=29.6962/102=0.29114. | {
"A": "Correct. The worked calculation gives 0.29114.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29114, not 0.58228.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29114, not -0.29114.",
"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_001363 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (-1x² +5x -1) dx. | {
"A": "2.33333",
"B": "4.33333",
"C": "3.33333",
"D": "5.33333"
} | D | 5.33333 | An antiderivative is (-1/3)x³+(5/2)x²+(-1)x. Evaluating between 0 and 2 gives (-1/3)(2)³+(5/2)(2)²+(-1)(2)=5.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.33333, not 2.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.33333, not 4.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.33333, not 3.333... | [
"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_005933 | 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 4.3 atm at 382 K. What is its pressure at 584 K? | {
"A": "4.57382 atm",
"B": "9.57382 atm",
"C": "1.65738 atm",
"D": "6.57382 atm"
} | D | 6.57382 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.3)(584)/(382)=6.57382 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.57382 atm, not 4.57382 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.57382 atm, not 9.57382 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_004940 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 3 Ω and 3 Ω are connected in series; this combination is connected in parallel with a 6 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.5 A",
"B": "0 A",
"C": "1.5 A",
"D": "3 A"
} | D | 3 A | Series branch resistance=3+3=6 Ω. Parallel equivalent R_eq=(6×6)/(6+6)=3 Ω. Total current I=V/R_eq=9/3=3 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3 A, not 4.5 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3 A, not 0 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3 A, not 1.5 A.",
"D": "Correc... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000067 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 +7x +12=0, let its roots be α and β. What is α²+β²? | {
"A": "-5.63889",
"B": "0.36111",
"C": "-0.63889",
"D": "-2.63889"
} | D | -2.63889 | By Vieta's relations, α+β = -7/6 and αβ = 12/6. Then α²+β²=(α+β)²−2αβ = (-7/6)²−2(12/6) = -2.63889. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2.63889, not -5.63889.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2.63889, not 0.36111.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2.63889, not -... | [
"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_004679 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 5 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.66667 A",
"B": "8.66667 A",
"C": "6.66667 A",
"D": "7.66667 A"
} | D | 7.66667 A | Series branch resistance=10+8=18 Ω. Parallel equivalent R_eq=(18×5)/(18+5)=3.91304 Ω. Total current I=V/R_eq=30/3.91304=7.66667 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.66667 A, not 4.66667 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.66667 A, not 8.66667 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.66667 A,... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001663 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (3x² +3x +5) dx. | {
"A": "301",
"B": "300",
"C": "240",
"D": "450"
} | B | 300 | An antiderivative is (3/3)x³+(3/2)x²+(5)x. Evaluating between 0 and 6 gives (3/3)(6)³+(3/2)(6)²+(5)(6)=300. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 300, not 301.",
"B": "Correct. The worked calculation gives 300.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 300, not 240.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_008701 | 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 0.23 mol L⁻¹ and initially B is absent. At equilibrium, 40% of A has dissociated at constant volume. Find K_c. | {
"A": "1.24533",
"B": "0.368",
"C": "0.184",
"D": "0.24533"
} | D | 0.24533 | Let α=0.4. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.23)(0.4)²/(1−0.4)=0.24533. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.24533, not 1.24533.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.24533, not 0.368.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.24533, not 0.184."... | [
"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_002635 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 5], [5, -5]]. | {
"A": "-47",
"B": "-45",
"C": "45",
"D": "-67.5"
} | B | -45 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(-5)−(5)(5)=-45. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -45, not -47.",
"B": "Correct. The worked calculation gives -45.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -45, not 45.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003387 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 51 m s⁻¹ at 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "255.1485 m",
"B": "256.1485 m",
"C": "258.1485 m",
"D": "26.61485 m"
} | B | 256.1485 m | Range R=u²sin(2θ)/g. Substituting u=51, θ=40° and g=10 gives R=(51)²sin(80°)/10=256.1485 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 256.1485 m, not 255.1485 m.",
"B": "Correct. The worked calculation gives 256.1485 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 256.1485 m, not 258.1485 m.",
"D": "Incorrect. Substitutin... | [
"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_001182 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-2x³ +0x² +6x+7. Evaluate f′(1). | {
"A": "-3",
"B": "2",
"C": "-2",
"D": "0"
} | D | 0 | Differentiate: f′(x)=3(-2)x²+2(0)x+(6). At x=1, f′(1)=3(-2)(1)²+2(0)(1)+(6)=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"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": "Correct. The worked ... | [
"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_003907 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block initially moves at 2 m s⁻¹. A constant net force does 19 N of work over 10 m in the direction of motion. Find its final kinetic energy. | {
"A": "101 J",
"B": "202 J",
"C": "303 J",
"D": "-202 J"
} | B | 202 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(6)(2)²+(19)(10)=202 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 202 J, not 101 J.",
"B": "Correct. The worked calculation gives 202 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 202 J, not 303 J.",
"D": "Incorrect. Substituting the stated values into ... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008464 | 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 1.23 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.9188 K",
"B": "2.5584 K",
"C": "0.5584 K",
"D": "5.5584 K"
} | B | 2.5584 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.52×1.23=2.5584 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.5584 K, not 1.9188 K.",
"B": "Correct. The worked calculation gives 2.5584 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.5584 K, not 0.5584 K.",
"D": "Incorrect. Substituting the stat... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006421 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 25 kg is attached to an ideal spring of force constant 679 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.19188 s",
"B": "0.38376 s",
"C": "-0.61624 s",
"D": "0.28782 s"
} | B | 0.38376 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(25/679)=0.38376 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.38376 s, not 0.19188 s.",
"B": "Correct. The worked calculation gives 0.38376 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.38376 s, not -0.61624 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008262 | 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 4 A for 6447 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": "10.48465 g",
"B": "8.48465 g",
"C": "5.48465 g",
"D": "-8.48465 g"
} | B | 8.48465 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×6447/(2×96500)=8.48465 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.48465 g, not 10.48465 g.",
"B": "Correct. The worked calculation gives 8.48465 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.48465 g, not 5.48465 g.",
"D": "Incorrect. Substituting th... | [
"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_008830 | 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 1.23 mol L⁻¹ and initially B is absent. At equilibrium, 61% of A has dissociated at constant volume. Find K_c. | {
"A": "4.69418",
"B": "-4.69418",
"C": "1.46942",
"D": "7.04128"
} | A | 4.69418 | Let α=0.61. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.23)(0.61)²/(1−0.61)=4.69418. | {
"A": "Correct. The worked calculation gives 4.69418.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.69418, not -4.69418.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.69418, not 1.46942.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000064 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +1x +9=0, let its roots be α and β. What is α²+β²? | {
"A": "-5.56",
"B": "-6.56",
"C": "-3.56",
"D": "-2.67"
} | C | -3.56 | By Vieta's relations, α+β = -1/5 and αβ = 9/5. Then α²+β²=(α+β)²−2αβ = (-1/5)²−2(9/5) = -3.56. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -3.56, not -5.56.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -3.56, not -6.56.",
"C": "Correct. The worked calculation gives -3.56.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_006946 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 45 mol H₂ and 13 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "27 mol",
"B": "39 mol",
"C": "13 mol",
"D": "26 mol"
} | D | 26 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 45 mol H₂O; O₂ can produce 26 mol H₂O. The limiting condition is O₂; product=26 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 27 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 39 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 13 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_005181 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +8 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "6.66667 N",
"B": "10.88889 N",
"C": "7.88889 N",
"D": "8.88889 N"
} | D | 8.88889 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(8×10⁻⁶)/(9×10⁻²)²=8.88889 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.88889 N, not 6.66667 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.88889 N, not 10.88889 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.88889 N... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003830 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 9 m s⁻¹. A constant net force does 27 N of work over 5 m in the direction of motion. Find its final kinetic energy. | {
"A": "458 J",
"B": "229.5 J",
"C": "-459 J",
"D": "459 J"
} | D | 459 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(9)²+(27)(5)=459 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 459 J, not 458 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 459 J, not 229.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 459 J, not -459 J.",
"... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008223 | 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 11 A for 5812 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": "21.03462 g",
"B": "23.03462 g",
"C": "19.03462 g",
"D": "42.06924 g"
} | A | 21.03462 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×5812/(2×96500)=21.03462 g. | {
"A": "Correct. The worked calculation gives 21.03462 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21.03462 g, not 23.03462 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21.03462 g, not 19.03462 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002643 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 7], [8, 6]]. | {
"A": "-30.4",
"B": "-39",
"C": "-38",
"D": "-76"
} | C | -38 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(6)−(7)(8)=-38. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -38, not -30.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -38, not -39.",
"C": "Correct. The worked calculation gives -38.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003948 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 1 m s⁻¹. A constant net force does 15 N of work over 10 m in the direction of motion. Find its final kinetic energy. | {
"A": "154 J",
"B": "231 J",
"C": "156 J",
"D": "-154 J"
} | A | 154 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(1)²+(15)(10)=154 J. | {
"A": "Correct. The worked calculation gives 154 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 154 J, not 231 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 154 J, not 156 J.",
"D": "Incorrect. Substituting the stated values into ... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008393 | 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 0.49 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.6615 K",
"B": "0.882 K",
"C": "3.882 K",
"D": "1.882 K"
} | B | 0.882 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.6×0.49=0.882 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.882 K, not 0.6615 K.",
"B": "Correct. The worked calculation gives 0.882 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.882 K, not 3.882 K.",
"D": "Incorrect. Substituting the stated v... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004515 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 6 m is acted on by a constant torque of 59 N m about its central axis. Find its angular acceleration. | {
"A": "-0.59028 rad s⁻²",
"B": "0.40972 rad s⁻²",
"C": "3.40972 rad s⁻²",
"D": "0.81944 rad s⁻²"
} | B | 0.40972 rad s⁻² | For a solid disc, I=½MR²=½(8)(6)²=144 kg m². Using τ=Iα, α=59/144=0.40972 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.40972 rad s⁻², not -0.59028 rad s⁻².",
"B": "Correct. The worked calculation gives 0.40972 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.40972 rad s⁻², not 3.40972 rad s⁻².",
"D... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000296 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 -7x +2=0, let its roots be α and β. What is α²+β²? | {
"A": "2.0625",
"B": "5.0625",
"C": "1.0625",
"D": "3.09375"
} | A | 2.0625 | By Vieta's relations, α+β = 7/4 and αβ = 2/4. Then α²+β²=(α+β)²−2αβ = (7/4)²−2(2/4) = 2.0625. | {
"A": "Correct. The worked calculation gives 2.0625.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.0625, not 5.0625.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.0625, not 1.0625.",
"D": "Incorrect. Substituting the stated values ... | [
"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_001525 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (-3x² +3x +4) dx. | {
"A": "-5.75",
"B": "-67.5",
"C": "67.5",
"D": "-50.625"
} | B | -67.5 | An antiderivative is (-3/3)x³+(3/2)x²+(4)x. Evaluating between 0 and 5 gives (-3/3)(5)³+(3/2)(5)²+(4)(5)=-67.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -67.5, not -5.75.",
"B": "Correct. The worked calculation gives -67.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -67.5, not 67.5.",
"D": "Incorrect. Substituting the stated values into t... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000455 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -19 and common difference 10. Find the sum of its first 10 terms. | {
"A": "-260",
"B": "390",
"C": "262",
"D": "260"
} | D | 260 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-19, d=10, n=10: Sₙ=10/2[2(-19)+(10−1)(10)]=260. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 260, not -260.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 260, not 390.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 260, not 262.",
"D": "Correct. ... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002065 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 5 blue and 5 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.34211",
"B": "-2.65789",
"C": "1.34211",
"D": "0.34211"
} | D | 0.34211 | Favourable pairs = C(10,2)+C(5,2)+C(5,2)=65. Total pairs=C(20,2)=190. Therefore P=65/190=0.34211. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34211, not -0.34211.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34211, not -2.65789.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34211, not 1.3... | [
"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_008924 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.34 mol L⁻¹ and initially B is absent. At equilibrium, 74% of A has dissociated at constant volume. Find K_c. | {
"A": "0.86437",
"B": "3.86437",
"C": "-2.86437",
"D": "2.86437"
} | D | 2.86437 | Let α=0.74. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.34)(0.74)²/(1−0.74)=2.86437. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.86437, not 0.86437.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.86437, not 3.86437.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.86437, not -2.86... | [
"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_009162 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.89 V, transfers 1 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.5354 V",
"B": "-1.4646 V",
"C": "0.2677 V",
"D": "1.05354 V"
} | A | 0.5354 V | Apply the Nernst equation: E=0.89−(0.0591/1)(6)=0.5354 V. | {
"A": "Correct. The worked calculation gives 0.5354 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.5354 V, not -1.4646 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5354 V, not 0.2677 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_007021 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 17 mol of gas at 363 K and 2.3 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "23.01625 L",
"B": "221.1625 L",
"C": "264.195 L",
"D": "220.1625 L"
} | D | 220.1625 L | PV=nRT, so V=nRT/P=(17)(0.082057)(363)/(2.3)=220.1625 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 220.1625 L, not 23.01625 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 220.1625 L, not 221.1625 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 220.16... | [
"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_005696 | 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 363 K. What is its pressure at 487 K? | {
"A": "13.14766 atm",
"B": "6.57383 atm",
"C": "4.57383 atm",
"D": "9.86074 atm"
} | B | 6.57383 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.9)(487)/(363)=6.57383 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.57383 atm, not 13.14766 atm.",
"B": "Correct. The worked calculation gives 6.57383 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.57383 atm, not 4.57383 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009405 | 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_5X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "20",
"B": "2",
"C": "10",
"D": "13"
} | C | 10 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×12+2+0−5−1)/2=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 20.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 2.",
"C": "Correct. The worked calculation gives 10.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008274 | 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 14 A for 18200 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": "82.83316 g",
"B": "85.83316 g",
"C": "125.74974 g",
"D": "83.83316 g"
} | D | 83.83316 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×18200/(2×96500)=83.83316 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 83.83316 g, not 82.83316 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 83.83316 g, not 85.83316 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 83.833... | [
"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_008904 | 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 1.54 mol L⁻¹ and initially B is absent. At equilibrium, 80% of A has dissociated at constant volume. Find K_c. | {
"A": "19.712",
"B": "29.568",
"C": "15.7696",
"D": "9.856"
} | A | 19.712 | Let α=0.8. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.54)(0.8)²/(1−0.8)=19.712. | {
"A": "Correct. The worked calculation gives 19.712.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19.712, not 29.568.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19.712, not 15.7696.",
"D": "Incorrect. Substituting the stated values... | [
"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 |
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