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_008433 | 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 0.48 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "3.96 K",
"B": "0.48 K",
"C": "0.96 K",
"D": "2.96 K"
} | C | 0.96 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×0.48=0.96 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.96 K, not 3.96 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.96 K, not 0.48 K.",
"C": "Correct. The worked calculation gives 0.96 K.",
"D": "Incorrect. Substituting the stated values ... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007774 | 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 44 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "8.25 mmol L⁻¹",
"B": "8 mmol L⁻¹",
"C": "11 mmol L⁻¹",
"D": "-11 mmol L⁻¹"
} | C | 11 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=44/2^2=11 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11 mmol L⁻¹, not 8.25 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11 mmol L⁻¹, not 8 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 11 mmol L⁻¹.",
"D": "Incorrect. Subst... | [
"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_000212 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 +9x -2=0, let its roots be α and β. What is α²+β²? | {
"A": "-2.22449",
"B": "2.22449",
"C": "1.22245",
"D": "3.22449"
} | B | 2.22449 | By Vieta's relations, α+β = -9/7 and αβ = -2/7. Then α²+β²=(α+β)²−2αβ = (-9/7)²−2(-2/7) = 2.22449. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.22449, not -2.22449.",
"B": "Correct. The worked calculation gives 2.22449.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.22449, not 1.22245.",
"D": "Incorrect. Substituting the stated v... | [
"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_002992 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, 6, 0) and v=(-2, 6, 2), calculate u·v. | {
"A": "-34",
"B": "35",
"C": "34",
"D": "4.4"
} | C | 34 | The dot product is the sum of corresponding component products: (1)(-2)+(6)(6)+(0)(2)=34. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 34, not -34.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 34, not 35.",
"C": "Correct. The worked calculation gives 34.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007322 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 20 mol of gas at 361 K and 2.56 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "24.14264 L",
"B": "-231.42638 L",
"C": "115.71319 L",
"D": "231.42638 L"
} | D | 231.42638 L | PV=nRT, so V=nRT/P=(20)(0.082057)(361)/(2.56)=231.42638 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 231.42638 L, not 24.14264 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 231.42638 L, not -231.42638 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23... | [
"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_007200 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 20 mol of gas at 362 K and 1.09 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "545.03916 L",
"B": "654.04699 L",
"C": "1090.07831 L",
"D": "546.03916 L"
} | A | 545.03916 L | PV=nRT, so V=nRT/P=(20)(0.082057)(362)/(1.09)=545.03916 L. | {
"A": "Correct. The worked calculation gives 545.03916 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 545.03916 L, not 654.04699 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 545.03916 L, not 1090.07831 L.",
"D": "Incorrect. Subst... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007850 | 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 66 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "-33 mmol L⁻¹",
"B": "33 mmol L⁻¹",
"C": "24.75 mmol L⁻¹",
"D": "49.5 mmol L⁻¹"
} | B | 33 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=66/2^1=33 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33 mmol L⁻¹, not -33 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 33 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 33 mmol L⁻¹, not 24.75 mmol L⁻¹.",
"D": "Incorrect. Su... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003178 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(8-12i)/(8+8i). What is Re(z), the real part of z? | {
"A": "-1.25",
"B": "0.975",
"C": "-0.375",
"D": "-0.25"
} | D | -0.25 | Multiply numerator and denominator by the conjugate (8-8i). Then Re(z)=(ac+bd)/(c²+d²)=((8)(8)+(-12)(8))/(8²+(8)²)=-0.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.25, not -1.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.25, not 0.975.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.25, not -0.375.",
"D"... | [
"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_000441 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -13 and common difference 12. Find the sum of its first 19 terms. | {
"A": "1807",
"B": "1805",
"C": "2166",
"D": "2707.5"
} | B | 1805 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-13, d=12, n=19: Sₙ=19/2[2(-13)+(19−1)(12)]=1805. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1805, not 1807.",
"B": "Correct. The worked calculation gives 1805.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1805, not 2166.",
"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_001830 | 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 34 distinct elements? | {
"A": "286097759",
"B": "286097760",
"C": "343317312",
"D": "572195520"
} | B | 286097760 | Order does not matter, so the count is C(34,11)=34!/[11!(23)!]=286097760. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 286097760, not 286097759.",
"B": "Correct. The worked calculation gives 286097760.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 286097760, not 343317312.",
"D": "Incorrect. Substituting the... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003277 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-12-9i)/(10+8i). What is Re(z), the real part of z? | {
"A": "1.17073",
"B": "0.88293",
"C": "-4.17073",
"D": "-1.17073"
} | D | -1.17073 | Multiply numerator and denominator by the conjugate (10-8i). Then Re(z)=(ac+bd)/(c²+d²)=((-12)(10)+(-9)(8))/(10²+(8)²)=-1.17073. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.17073, not 1.17073.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.17073, not 0.88293.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.17073, not -4... | [
"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_009458 | 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_15H_27N_2X_3. 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 (2×15+2+2−27−3)/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_002414 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -7], [1, -6]]. | {
"A": "-25",
"B": "-34.5",
"C": "-21",
"D": "-23"
} | D | -23 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(-6)−(-7)(1)=-23. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -23, not -25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -23, not -34.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -23, not -21.",
"D": "Correct.... | [
"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_002358 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, 2], [9, -1]]. | {
"A": "-28.5",
"B": "-9.5",
"C": "-14.25",
"D": "-19"
} | D | -19 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(-1)−(2)(9)=-19. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -19, not -28.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -19, not -9.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -19, not -14.25.",
"D": "Corr... | [
"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_000678 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio -2. What is the sum of its first 8 terms? | {
"A": "-918",
"B": "-763",
"C": "765",
"D": "-765"
} | D | -765 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(-2^8−1)/(-2−1)=-765. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -765, not -918.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -765, not -763.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -765, not 765.",
"D": "Corre... | [
"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_001025 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=7x³ -10x² +6x+7. Evaluate f′(-1). | {
"A": "35.25",
"B": "-47",
"C": "48",
"D": "47"
} | D | 47 | Differentiate: f′(x)=3(7)x²+2(-10)x+(6). At x=-1, f′(-1)=3(7)(-1)²+2(-10)(-1)+(6)=47. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 47, not 35.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 47, not -47.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 47, not 48.",
"D": "Correct. The... | [
"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_004454 | 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 68 N m about its central axis. Find its angular acceleration. | {
"A": "1.04722 rad s⁻²",
"B": "0.47222 rad s⁻²",
"C": "2.47222 rad s⁻²",
"D": "-0.47222 rad s⁻²"
} | B | 0.47222 rad s⁻² | For a solid disc, I=½MR²=½(8)(6)²=144 kg m². Using τ=Iα, α=68/144=0.47222 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.47222 rad s⁻², not 1.04722 rad s⁻².",
"B": "Correct. The worked calculation gives 0.47222 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.47222 rad s⁻², not 2.47222 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_005314 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +8 μC and +3 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "239 N",
"B": "240 N",
"C": "192 N",
"D": "238 N"
} | B | 240 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(8×10⁻⁶)(3×10⁻⁶)/(3×10⁻²)²=240 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 240 N, not 239 N.",
"B": "Correct. The worked calculation gives 240 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 240 N, not 192 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001655 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (-2x² +6x +5) dx. | {
"A": "-108.33333",
"B": "-109.33333",
"C": "-164",
"D": "-110.33333"
} | B | -109.33333 | An antiderivative is (-2/3)x³+(6/2)x²+(5)x. Evaluating between 0 and 8 gives (-2/3)(8)³+(6/2)(8)²+(5)(8)=-109.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -109.33333, not -108.33333.",
"B": "Correct. The worked calculation gives -109.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -109.33333, not -164.",
"D": "Incorrect. Substituting the ... | [
"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_002822 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-1, -1, -5) and v=(3, -3, 9), calculate u·v. | {
"A": "-36",
"B": "-22.5",
"C": "-46",
"D": "-45"
} | D | -45 | The dot product is the sum of corresponding component products: (-1)(3)+(-1)(-3)+(-5)(9)=-45. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -45, not -36.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -45, not -22.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -45, not -46.",
"D": "Correct.... | [
"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_002803 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(5, 0, 2) and v=(1, -5, -6), calculate u·v. | {
"A": "-9",
"B": "-5",
"C": "-7",
"D": "0.3"
} | C | -7 | The dot product is the sum of corresponding component products: (5)(1)+(0)(-5)+(2)(-6)=-7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -7, not -9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -7, not -5.",
"C": "Correct. The worked calculation gives -7.",
"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_001030 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-3x³ -2x² -7x+7. Evaluate f′(5). | {
"A": "-251",
"B": "-252",
"C": "-24.2",
"D": "-302.4"
} | B | -252 | Differentiate: f′(x)=3(-3)x²+2(-2)x+(-7). At x=5, f′(5)=3(-3)(5)²+2(-2)(5)+(-7)=-252. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -252, not -251.",
"B": "Correct. The worked calculation gives -252.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -252, not -24.2.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_003989 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 0 m s⁻¹. A constant net force does 30 N of work over 4 m in the direction of motion. Find its final kinetic energy. | {
"A": "121 J",
"B": "118 J",
"C": "60 J",
"D": "120 J"
} | D | 120 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(0)²+(30)(4)=120 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 120 J, not 121 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 120 J, not 118 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 120 J, not 60 J.",
"D": ... | [
"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_007479 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 93 mL of 0.10 M HCl is mixed with 18 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.17026",
"B": "1.17026",
"C": "-1.17026",
"D": "3.17026"
} | B | 1.17026 | Excess H⁺ moles=0.10×(93−18)/1000=0.007500 mol. Total volume=0.111 L, so [H⁺]=0.067568 M and pH=−log₁₀[H⁺]=1.17026. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.17026, not 2.17026.",
"B": "Correct. The worked calculation gives 1.17026.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.17026, not -1.17026.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004605 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 15 kg and radius 5 m is acted on by a constant torque of 9 N m about its central axis. Find its angular acceleration. | {
"A": "0.024 rad s⁻²",
"B": "-0.048 rad s⁻²",
"C": "0.048 rad s⁻²",
"D": "-1.952 rad s⁻²"
} | C | 0.048 rad s⁻² | For a solid disc, I=½MR²=½(15)(5)²=187.5 kg m². Using τ=Iα, α=9/187.5=0.048 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.048 rad s⁻², not 0.024 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.048 rad s⁻², not -0.048 rad s⁻².",
"C": "Correct. The worked calculation gives 0.048 rad s⁻².",
"D": "Incorr... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002010 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 11 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": "0.25992",
"B": "0.34656",
"C": "-2.65344",
"D": "-1.65344"
} | B | 0.34656 | Favourable pairs = C(12,2)+C(11,2)+C(5,2)=131. Total pairs=C(28,2)=378. Therefore P=131/378=0.34656. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34656, not 0.25992.",
"B": "Correct. The worked calculation gives 0.34656.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34656, not -2.65344.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003269 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(12+9i)/(9+1i). What is Re(z), the real part of z? | {
"A": "-1.57317",
"B": "1.42683",
"C": "1.14268",
"D": "4.42683"
} | B | 1.42683 | Multiply numerator and denominator by the conjugate (9-1i). Then Re(z)=(ac+bd)/(c²+d²)=((12)(9)+(9)(1))/(9²+(1)²)=1.42683. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.42683, not -1.57317.",
"B": "Correct. The worked calculation gives 1.42683.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.42683, not 1.14268.",
"D": "Incorrect. Substituting the stated v... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005012 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +8 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "21.6 N",
"B": "17.28 N",
"C": "43.2 N",
"D": "3.16 N"
} | A | 21.6 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(8×10⁻⁶)/(10×10⁻²)²=21.6 N. | {
"A": "Correct. The worked calculation gives 21.6 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21.6 N, not 17.28 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21.6 N, not 43.2 N.",
"D": "Incorrect. Substituting the stated values... | [
"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_001192 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ +8x² +10x+7. Evaluate f′(-4). | {
"A": "276",
"B": "138",
"C": "139",
"D": "-138"
} | B | 138 | Differentiate: f′(x)=3(4)x²+2(8)x+(10). At x=-4, f′(-4)=3(4)(-4)²+2(8)(-4)+(10)=138. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 138, not 276.",
"B": "Correct. The worked calculation gives 138.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 138, not 139.",
"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_000780 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio 5. What is the sum of its first 5 terms? | {
"A": "7027",
"B": "7029",
"C": "7028",
"D": "10543.5"
} | B | 7029 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(5^5−1)/(5−1)=7029. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7029, not 7027.",
"B": "Correct. The worked calculation gives 7029.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7029, not 7028.",
"D": "Incorrect. Substituting the stated values into the g... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004213 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 33 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.33. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "166.32 N",
"B": "111.88 N",
"C": "110.88 N",
"D": "108.88 N"
} | C | 110.88 N | Net force=mg(sinθ−μcosθ)=33×10×(0.6−0.33×0.8)=110.88 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 110.88 N, not 166.32 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 110.88 N, not 111.88 N.",
"C": "Correct. The worked calculation gives 110.88 N.",
"D": "Incorrect. Substituting the stat... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004392 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 10 kg and radius 5 m is acted on by a constant torque of 100 N m about its central axis. Find its angular acceleration. | {
"A": "0.8 rad s⁻²",
"B": "0.6 rad s⁻²",
"C": "-0.8 rad s⁻²",
"D": "1.8 rad s⁻²"
} | A | 0.8 rad s⁻² | For a solid disc, I=½MR²=½(10)(5)²=125 kg m². Using τ=Iα, α=100/125=0.8 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.8 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8 rad s⁻², not 0.6 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8 rad s⁻², not -0.8 rad s⁻².",
"D": "Incorrect. Subst... | [
"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_008214 | 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 9650 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": "-3.175 g",
"B": "0.175 g",
"C": "3.175 g",
"D": "6.175 g"
} | C | 3.175 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×1×9650/(2×96500)=3.175 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.175 g, not -3.175 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.175 g, not 0.175 g.",
"C": "Correct. The worked calculation gives 3.175 g.",
"D": "Incorrect. Substituting the stated v... | [
"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_002602 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -4], [6, 3]]. | {
"A": "31.2",
"B": "19.5",
"C": "78",
"D": "39"
} | D | 39 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(3)−(-4)(6)=39. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 39, not 31.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39, not 19.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39, not 78.",
"D": "Correct. The... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006364 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 1 kg is attached to an ideal spring of force constant 316 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.08438 s",
"B": "-0.88749 s",
"C": "2.11251 s",
"D": "0.11251 s"
} | D | 0.11251 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(1/316)=0.11251 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.11251 s, not 0.08438 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.11251 s, not -0.88749 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.11251 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007465 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 37 mL of 0.10 M HCl is mixed with 64 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "15.42704",
"B": "14.42704",
"C": "12.42704",
"D": "10.42704"
} | C | 12.42704 | Excess OH⁻ moles=0.10×(64−37)/1000=0.002700 mol. Total volume=0.101 L, so [OH⁻]=0.026733 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.42704. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.42704, not 15.42704.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.42704, not 14.42704.",
"C": "Correct. The worked calculation gives 12.42704.",
"D": "Incorrect. Substituting the stat... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009558 | 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_15H_12. Treat X as the total number of monovalent halogen atoms. | {
"A": "10",
"B": "11",
"C": "8",
"D": "7.5"
} | A | 10 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×15+2+0−12−0)/2=10. | {
"A": "Correct. The worked calculation gives 10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 11.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 8.",
"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_001561 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (-1x² +6x -5) dx. | {
"A": "13.33333",
"B": "5.66667",
"C": "4.66667",
"D": "6.66667"
} | D | 6.66667 | An antiderivative is (-1/3)x³+(6/2)x²+(-5)x. Evaluating between 0 and 4 gives (-1/3)(4)³+(6/2)(4)²+(-5)(4)=6.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.66667, not 13.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.66667, not 5.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.66667, not 4.66... | [
"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_000729 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio -3. What is the sum of its first 12 terms? | {
"A": "-1328600",
"B": "-664300",
"C": "-797160",
"D": "-664298"
} | B | -664300 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(-3^12−1)/(-3−1)=-664300. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -664300, not -1328600.",
"B": "Correct. The worked calculation gives -664300.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -664300, not -797160.",
"D": "Incorrect. Substituting the stated v... | [
"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_007383 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 83 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": "1.54239",
"B": "-1.45761",
"C": "2.31358",
"D": "1.15424"
} | A | 1.54239 | Excess H⁺ moles=0.10×(83−46)/1000=0.003700 mol. Total volume=0.129 L, so [H⁺]=0.028682 M and pH=−log₁₀[H⁺]=1.54239. | {
"A": "Correct. The worked calculation gives 1.54239.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.54239, not -1.45761.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.54239, not 2.31358.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002114 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 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": "0.35333",
"B": "-2.64667",
"C": "0.17667",
"D": "-0.35333"
} | A | 0.35333 | Favourable pairs = C(10,2)+C(4,2)+C(11,2)=106. Total pairs=C(25,2)=300. Therefore P=106/300=0.35333. | {
"A": "Correct. The worked calculation gives 0.35333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35333, not -2.64667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35333, not 0.17667.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004457 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 6 kg and radius 5 m is acted on by a constant torque of 19 N m about its central axis. Find its angular acceleration. | {
"A": "0.50667 rad s⁻²",
"B": "0.25333 rad s⁻²",
"C": "0.38 rad s⁻²",
"D": "-2.74667 rad s⁻²"
} | B | 0.25333 rad s⁻² | For a solid disc, I=½MR²=½(6)(5)²=75 kg m². Using τ=Iα, α=19/75=0.25333 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25333 rad s⁻², not 0.50667 rad s⁻².",
"B": "Correct. The worked calculation gives 0.25333 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25333 rad s⁻², not 0.38 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_008773 | 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 1.32 mol L⁻¹ and initially B is absent. At equilibrium, 66% of A has dissociated at constant volume. Find K_c. | {
"A": "5.07346",
"B": "6.76461",
"C": "4.76461",
"D": "3.76461"
} | B | 6.76461 | Let α=0.66. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.32)(0.66)²/(1−0.66)=6.76461. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.76461, not 5.07346.",
"B": "Correct. The worked calculation gives 6.76461.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.76461, not 4.76461.",
"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_006337 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 75 cm in front of a thin convex lens of focal length 22 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.31132",
"B": "0.41509",
"C": "2.41509",
"D": "3.41509"
} | B | 0.41509 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(75)(22)/(75−22)=31.13208 cm. Thus |m|=v/u=31.13208/75=0.41509. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.41509, not 0.31132.",
"B": "Correct. The worked calculation gives 0.41509.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.41509, not 2.41509.",
"D": "Incorrect. Substituting the stated va... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005025 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +2 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "20.25 N",
"B": "33.75 N",
"C": "12.65625 N",
"D": "16.875 N"
} | D | 16.875 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(2×10⁻⁶)/(8×10⁻²)²=16.875 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16.875 N, not 20.25 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16.875 N, not 33.75 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16.875 N, not 12... | [
"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_000276 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 +18x +6=0, let its roots be α and β. What is α²+β²? | {
"A": "249.6",
"B": "234",
"C": "312",
"D": "311"
} | C | 312 | By Vieta's relations, α+β = -18/1 and αβ = 6/1. Then α²+β²=(α+β)²−2αβ = (-18/1)²−2(6/1) = 312. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 312, not 249.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 312, not 234.",
"C": "Correct. The worked calculation gives 312.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005045 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +6 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "136 N",
"B": "135 N",
"C": "162 N",
"D": "134 N"
} | B | 135 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(6×10⁻⁶)/(2×10⁻²)²=135 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 135 N, not 136 N.",
"B": "Correct. The worked calculation gives 135 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 135 N, not 162 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001331 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=7x³ -1x² -1x+7. Evaluate f′(4). | {
"A": "245.25",
"B": "327",
"C": "261.6",
"D": "326"
} | B | 327 | Differentiate: f′(x)=3(7)x²+2(-1)x+(-1). At x=4, f′(4)=3(7)(4)²+2(-1)(4)+(-1)=327. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 327, not 245.25.",
"B": "Correct. The worked calculation gives 327.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 327, not 261.6.",
"D": "Incorrect. Substituting the stated values into the g... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003246 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-10+14i)/(6+2i). What is Re(z), the real part of z? | {
"A": "-1.8",
"B": "-0.8",
"C": "-2.8",
"D": "-1.2"
} | B | -0.8 | Multiply numerator and denominator by the conjugate (6-2i). Then Re(z)=(ac+bd)/(c²+d²)=((-10)(6)+(14)(2))/(6²+(2)²)=-0.8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.8, not -1.8.",
"B": "Correct. The worked calculation gives -0.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.8, not -2.8.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_001439 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (0x² -1x +1) dx. | {
"A": "-1.125",
"B": "-2.25",
"C": "-1.5",
"D": "1.5"
} | C | -1.5 | An antiderivative is (0/3)x³+(-1/2)x²+(1)x. Evaluating between 0 and 3 gives (0/3)(3)³+(-1/2)(3)²+(1)(3)=-1.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.5, not -1.125.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.5, not -2.25.",
"C": "Correct. The worked calculation gives -1.5.",
"D": "Incorrect. Substituting the stated values into th... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009459 | 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_9H_3N_3X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "5",
"B": "8",
"C": "7",
"D": "6"
} | B | 8 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×9+2+3−3−4)/2=8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 5.",
"B": "Correct. The worked calculation gives 8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 7.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005214 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +2 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "4.44444 N",
"B": "2.22222 N",
"C": "1.66667 N",
"D": "1.22222 N"
} | B | 2.22222 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(2×10⁻⁶)/(9×10⁻²)²=2.22222 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.22222 N, not 4.44444 N.",
"B": "Correct. The worked calculation gives 2.22222 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.22222 N, not 1.66667 N.",
"D": "Incorrect. Substituting the... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006241 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 58 cm in front of a thin convex lens of focal length 15 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.34884",
"B": "0.34884",
"C": "-2.65116",
"D": "-0.65116"
} | B | 0.34884 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(58)(15)/(58−15)=20.23256 cm. Thus |m|=v/u=20.23256/58=0.34884. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34884, not 1.34884.",
"B": "Correct. The worked calculation gives 0.34884.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34884, not -2.65116.",
"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_000966 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio 5. What is the sum of its first 7 terms? | {
"A": "156249",
"B": "-156248",
"C": "156247",
"D": "156248"
} | D | 156248 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(5^7−1)/(5−1)=156248. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 156248, not 156249.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 156248, not -156248.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 156248, not 156247.",... | [
"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_006478 | 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 1120 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "3.29881 s",
"B": "-0.29881 s",
"C": "0.59761 s",
"D": "0.29881 s"
} | D | 0.29881 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(25/1120)=0.29881 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29881 s, not 3.29881 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29881 s, not -0.29881 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29881 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002714 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(8, 1, -1) and v=(-5, 1, -1), calculate u·v. | {
"A": "-45.6",
"B": "-38",
"C": "-19",
"D": "-2.8"
} | B | -38 | The dot product is the sum of corresponding component products: (8)(-5)+(1)(1)+(-1)(-1)=-38. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -38, not -45.6.",
"B": "Correct. The worked calculation gives -38.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -38, not -19.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002937 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-1, -2, 5) and v=(6, -7, 6), calculate u·v. | {
"A": "4.8",
"B": "45.6",
"C": "37",
"D": "38"
} | D | 38 | The dot product is the sum of corresponding component products: (-1)(6)+(-2)(-7)+(5)(6)=38. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 38, not 4.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 38, not 45.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 38, not 37.",
"D": "Correct. The ... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003464 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 26 m s⁻¹ at 65° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "51.7846 m",
"B": "41.42768 m",
"C": "50.7846 m",
"D": "62.14153 m"
} | A | 51.7846 m | Range R=u²sin(2θ)/g. Substituting u=26, θ=65° and g=10 gives R=(26)²sin(130°)/10=51.7846 m. | {
"A": "Correct. The worked calculation gives 51.7846 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 51.7846 m, not 41.42768 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 51.7846 m, not 50.7846 m.",
"D": "Incorrect. Substituting th... | [
"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_006833 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 25 mol H₂ and 31 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "30 mol",
"B": "18.75 mol",
"C": "25 mol",
"D": "37.5 mol"
} | C | 25 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 25 mol H₂O; O₂ can produce 62 mol H₂O. The limiting condition is H₂; product=25 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 25 mol, not 30 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 25 mol, not 18.75 mol.",
"C": "Correct. The worked calculation gives 25 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_007998 | 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 28 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "1.01094 mmol L⁻¹",
"B": "0.08203 mmol L⁻¹",
"C": "0.10938 mmol L⁻¹",
"D": "-1.89062 mmol L⁻¹"
} | C | 0.10938 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=28/2^8=0.10938 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.10938 mmol L⁻¹, not 1.01094 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.10938 mmol L⁻¹, not 0.08203 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.10938 mmol L⁻¹.",
... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006053 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 47 cm in front of a thin convex lens of focal length 12 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.25714",
"B": "0.68571",
"C": "0.17143",
"D": "0.34286"
} | D | 0.34286 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(47)(12)/(47−12)=16.11429 cm. Thus |m|=v/u=16.11429/47=0.34286. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34286, not 0.25714.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34286, not 0.68571.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34286, not 0.171... | [
"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_006196 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 36 cm in front of a thin convex lens of focal length 30 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.5",
"B": "7.5",
"C": "5",
"D": "10"
} | C | 5 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(36)(30)/(36−30)=180 cm. Thus |m|=v/u=180/36=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.5.",
"C": "Correct. The worked calculation gives 5.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_000287 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 +3x +7=0, let its roots be α and β. What is α²+β²? | {
"A": "2.08333",
"B": "-2.08333",
"C": "-1.08333",
"D": "-5.08333"
} | B | -2.08333 | By Vieta's relations, α+β = -3/6 and αβ = 7/6. Then α²+β²=(α+β)²−2αβ = (-3/6)²−2(7/6) = -2.08333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2.08333, not 2.08333.",
"B": "Correct. The worked calculation gives -2.08333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2.08333, not -1.08333.",
"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_004723 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 15 Ω are connected in series; this combination is connected in parallel with a 10 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "-3.25714 A",
"B": "6.51429 A",
"C": "3.25714 A",
"D": "4.88571 A"
} | C | 3.25714 A | Series branch resistance=13+15=28 Ω. Parallel equivalent R_eq=(28×10)/(28+10)=7.36842 Ω. Total current I=V/R_eq=24/7.36842=3.25714 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.25714 A, not -3.25714 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.25714 A, not 6.51429 A.",
"C": "Correct. The worked calculation gives 3.25714 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003479 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 106 m s⁻¹ at 70° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "361.11808 m",
"B": "722.23616 m",
"C": "724.23616 m",
"D": "720.23616 m"
} | B | 722.23616 m | Range R=u²sin(2θ)/g. Substituting u=106, θ=70° and g=10 gives R=(106)²sin(140°)/10=722.23616 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 722.23616 m, not 361.11808 m.",
"B": "Correct. The worked calculation gives 722.23616 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 722.23616 m, not 724.23616 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006536 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 15 kg is attached to an ideal spring of force constant 325 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.6445 s",
"B": "2.42967 s",
"C": "0.42967 s",
"D": "0.85934 s"
} | C | 0.42967 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(15/325)=0.42967 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.42967 s, not 0.6445 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.42967 s, not 2.42967 s.",
"C": "Correct. The worked calculation gives 0.42967 s.",
"D": "Incorrect. Substituting the ... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003838 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block initially moves at 3 m s⁻¹. A constant net force does 13 N of work over 17 m in the direction of motion. Find its final kinetic energy. | {
"A": "243.5 J",
"B": "245.5 J",
"C": "242.5 J",
"D": "121.75 J"
} | A | 243.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(5)(3)²+(13)(17)=243.5 J. | {
"A": "Correct. The worked calculation gives 243.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 243.5 J, not 245.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 243.5 J, not 242.5 J.",
"D": "Incorrect. Substituting the stated va... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003598 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 41 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "126.075 m",
"B": "168.1 m",
"C": "134.48 m",
"D": "-168.1 m"
} | B | 168.1 m | Range R=u²sin(2θ)/g. Substituting u=41, θ=45° and g=10 gives R=(41)²sin(90°)/10=168.1 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 168.1 m, not 126.075 m.",
"B": "Correct. The worked calculation gives 168.1 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 168.1 m, not 134.48 m.",
"D": "Incorrect. Substituting the stated... | [
"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_005491 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 60 μF capacitor is charged to a potential difference of 2 V. Calculate the energy stored, expressed in μJ. | {
"A": "240 μJ",
"B": "121 μJ",
"C": "120 μJ",
"D": "122 μJ"
} | C | 120 μJ | U=½CV². Since C=60 μF, U in μJ is ½×60×(2)²=120 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 120 μJ, not 240 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 120 μJ, not 121 μJ.",
"C": "Correct. The worked calculation gives 120 μJ.",
"D": "Incorrect. Substituting the stated values ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003264 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-4+0i)/(6+10i). What is Re(z), the real part of z? | {
"A": "-3.17647",
"B": "-0.17647",
"C": "-0.13235",
"D": "0.98235"
} | B | -0.17647 | Multiply numerator and denominator by the conjugate (6-10i). Then Re(z)=(ac+bd)/(c²+d²)=((-4)(6)+(0)(10))/(6²+(10)²)=-0.17647. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.17647, not -3.17647.",
"B": "Correct. The worked calculation gives -0.17647.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.17647, not -0.13235.",
"D": "Incorrect. Substituting the stat... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002406 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, 3], [8, -8]]. | {
"A": "32",
"B": "-34",
"C": "-64",
"D": "-32"
} | D | -32 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(-8)−(3)(8)=-32. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -32, not 32.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -32, not -34.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -32, not -64.",
"D": "Correct. Th... | [
"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_003646 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 110 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1210 m",
"B": "1452 m",
"C": "605 m",
"D": "1211 m"
} | A | 1210 m | Range R=u²sin(2θ)/g. Substituting u=110, θ=45° and g=10 gives R=(110)²sin(90°)/10=1210 m. | {
"A": "Correct. The worked calculation gives 1210 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1210 m, not 1452 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1210 m, not 605 m.",
"D": "Incorrect. Substituting the stated values i... | [
"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_004602 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 15 kg and radius 6 m is acted on by a constant torque of 43 N m about its central axis. Find its angular acceleration. | {
"A": "-1.84074 rad s⁻²",
"B": "0.07963 rad s⁻²",
"C": "0.15926 rad s⁻²",
"D": "2.15926 rad s⁻²"
} | C | 0.15926 rad s⁻² | For a solid disc, I=½MR²=½(15)(6)²=270 kg m². Using τ=Iα, α=43/270=0.15926 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.15926 rad s⁻², not -1.84074 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.15926 rad s⁻², not 0.07963 rad s⁻².",
"C": "Correct. The worked calculation gives 0.15926 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_008672 | 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 1.34 mol L⁻¹ and initially B is absent. At equilibrium, 61% of A has dissociated at constant volume. Find K_c. | {
"A": "2.11399",
"B": "6.11399",
"C": "5.11399",
"D": "7.67098"
} | C | 5.11399 | Let α=0.61. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.34)(0.61)²/(1−0.61)=5.11399. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.11399, not 2.11399.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.11399, not 6.11399.",
"C": "Correct. The worked calculation gives 5.11399.",
"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_002570 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, -1], [2, 2]]. | {
"A": "18",
"B": "21.6",
"C": "9",
"D": "19"
} | A | 18 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(2)−(-1)(2)=18. | {
"A": "Correct. The worked calculation gives 18.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18, not 21.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18, not 9.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001837 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 41 distinct elements? | {
"A": "1121099408",
"B": "1121099410",
"C": "1345319289.6",
"D": "896879526.4"
} | A | 1121099408 | Order does not matter, so the count is C(41,10)=41!/[10!(31)!]=1121099408. | {
"A": "Correct. The worked calculation gives 1121099408.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1121099408, not 1121099410.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1121099408, not 1345319289.6.",
"D": "Incorrect. Substitut... | [
"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_006678 | 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 14 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "10 mol",
"B": "7 mol",
"C": "4 mol",
"D": "6 mol"
} | B | 7 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 7 mol H₂O; O₂ can produce 28 mol H₂O. The limiting condition is H₂; product=7 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7 mol, not 10 mol.",
"B": "Correct. The worked calculation gives 7 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7 mol, not 4 mol.",
"D": "Incorrect. Substituting the stated values into... | [
"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_005923 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.1 atm at 271 K. What is its pressure at 416 K? | {
"A": "1.01535 atm",
"B": "0.15351 atm",
"C": "-2.84649 atm",
"D": "-1.84649 atm"
} | B | 0.15351 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.1)(416)/(271)=0.15351 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.15351 atm, not 1.01535 atm.",
"B": "Correct. The worked calculation gives 0.15351 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.15351 atm, not -2.84649 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_005929 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.7 atm at 198 K. What is its pressure at 672 K? | {
"A": "-9.16364 atm",
"B": "9.16364 atm",
"C": "4.58182 atm",
"D": "1.91636 atm"
} | B | 9.16364 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.7)(672)/(198)=9.16364 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.16364 atm, not -9.16364 atm.",
"B": "Correct. The worked calculation gives 9.16364 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.16364 atm, not 4.58182 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_006987 | 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 23 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "46 mol",
"B": "44 mol",
"C": "45 mol",
"D": "55.2 mol"
} | A | 46 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 50 mol H₂O; O₂ can produce 46 mol H₂O. The limiting condition is O₂; product=46 mol. | {
"A": "Correct. The worked calculation gives 46 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 46 mol, not 44 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 46 mol, not 45 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_006427 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 7 kg is attached to an ideal spring of force constant 264 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.32567 s",
"B": "0.65134 s",
"C": "2.32567 s",
"D": "3.32567 s"
} | A | 0.32567 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(7/264)=0.32567 s. | {
"A": "Correct. The worked calculation gives 0.32567 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32567 s, not 0.65134 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32567 s, not 2.32567 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006842 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 9 mol H₂ and 1 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "1.2 mol",
"B": "5 mol",
"C": "2 mol",
"D": "1.5 mol"
} | C | 2 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 9 mol H₂O; O₂ can produce 2 mol H₂O. The limiting condition is O₂; product=2 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 1.2 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 5 mol.",
"C": "Correct. The worked calculation gives 2 mol.",
"D": "Incorrect. Substituting the stated values int... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004005 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 5 m s⁻¹. A constant net force does 7 N of work over 14 m in the direction of motion. Find its final kinetic energy. | {
"A": "149 J",
"B": "148 J",
"C": "118.4 J",
"D": "177.6 J"
} | B | 148 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(5)²+(7)(14)=148 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 148 J, not 149 J.",
"B": "Correct. The worked calculation gives 148 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 148 J, not 118.4 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_004793 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 3 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 10 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.14545 A",
"B": "2.14545 A",
"C": "1.14545 A",
"D": "0.85909 A"
} | C | 1.14545 A | Series branch resistance=3+8=11 Ω. Parallel equivalent R_eq=(11×10)/(11+10)=5.2381 Ω. Total current I=V/R_eq=6/5.2381=1.14545 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.14545 A, not 0.14545 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.14545 A, not 2.14545 A.",
"C": "Correct. The worked calculation gives 1.14545 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006371 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 3 kg is attached to an ideal spring of force constant 620 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.86088 s",
"B": "1.13912 s",
"C": "0.20868 s",
"D": "0.13912 s"
} | D | 0.13912 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(3/620)=0.13912 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.13912 s, not -1.86088 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.13912 s, not 1.13912 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.13912 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006243 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 21 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": "-1.375",
"B": "0.625",
"C": "1.625",
"D": "1.1625"
} | C | 1.625 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(21)(13)/(21−13)=34.125 cm. Thus |m|=v/u=34.125/21=1.625. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.625, not -1.375.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.625, not 0.625.",
"C": "Correct. The worked calculation gives 1.625.",
"D": "Incorrect. Substituting the stated values into... | [
"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_009226 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.19 V, transfers 2 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.0127 V",
"B": "0.75953 V",
"C": "2.0254 V",
"D": "-1.9873 V"
} | A | 1.0127 V | Apply the Nernst equation: E=1.19−(0.0591/2)(6)=1.0127 V. | {
"A": "Correct. The worked calculation gives 1.0127 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0127 V, not 0.75953 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0127 V, not 2.0254 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_007834 | 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 81 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "4.53125 mmol L⁻¹",
"B": "2.53125 mmol L⁻¹",
"C": "3.53125 mmol L⁻¹",
"D": "5.0625 mmol L⁻¹"
} | B | 2.53125 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=81/2^5=2.53125 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.53125 mmol L⁻¹, not 4.53125 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 2.53125 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.53125 mmol L⁻¹, not 3.53125 mmol L⁻¹.",
... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007809 | 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 97 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "18.1875 mmol L⁻¹",
"B": "24.25 mmol L⁻¹",
"C": "22.25 mmol L⁻¹",
"D": "12.125 mmol L⁻¹"
} | B | 24.25 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=97/2^2=24.25 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24.25 mmol L⁻¹, not 18.1875 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 24.25 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24.25 mmol L⁻¹, not 22.25 mmol L⁻¹.",
"D": "... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004689 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 12 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.31818 A",
"B": "3.47727 A",
"C": "3.31818 A",
"D": "0.31818 A"
} | A | 2.31818 A | Series branch resistance=8+14=22 Ω. Parallel equivalent R_eq=(22×12)/(22+12)=7.76471 Ω. Total current I=V/R_eq=18/7.76471=2.31818 A. | {
"A": "Correct. The worked calculation gives 2.31818 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.31818 A, not 3.47727 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.31818 A, not 3.31818 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002622 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, 7], [1, 1]]. | {
"A": "4",
"B": "1",
"C": "3",
"D": "-2"
} | B | 1 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(1)−(7)(1)=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 4.",
"B": "Correct. The worked calculation gives 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 3.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000574 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -10 and common difference 13. Find the sum of its first 12 terms. | {
"A": "590.4",
"B": "738",
"C": "736",
"D": "740"
} | B | 738 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-10, d=13, n=12: Sₙ=12/2[2(-10)+(12−1)(13)]=738. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 738, not 590.4.",
"B": "Correct. The worked calculation gives 738.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 738, not 736.",
"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_003537 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 72 m s⁻¹ at 18° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "306.70787 m",
"B": "228.53091 m",
"C": "304.70787 m",
"D": "31.47079 m"
} | C | 304.70787 m | Range R=u²sin(2θ)/g. Substituting u=72, θ=18° and g=10 gives R=(72)²sin(36°)/10=304.70787 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 304.70787 m, not 306.70787 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 304.70787 m, not 228.53091 m.",
"C": "Correct. The worked calculation gives 304.70787 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000163 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 -10x +7=0, let its roots be α and β. What is α²+β²? | {
"A": "3.22222",
"B": "6.44444",
"C": "8.44444",
"D": "9.44444"
} | B | 6.44444 | By Vieta's relations, α+β = 10/3 and αβ = 7/3. Then α²+β²=(α+β)²−2αβ = (10/3)²−2(7/3) = 6.44444. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.44444, not 3.22222.",
"B": "Correct. The worked calculation gives 6.44444.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.44444, not 8.44444.",
"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_005687 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3 atm at 368 K. What is its pressure at 747 K? | {
"A": "3.04484 atm",
"B": "9.08967 atm",
"C": "6.08967 atm",
"D": "5.08967 atm"
} | C | 6.08967 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3)(747)/(368)=6.08967 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.08967 atm, not 3.04484 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.08967 atm, not 9.08967 atm.",
"C": "Correct. The worked calculation gives 6.08967 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004339 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 28 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.12. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "140.12 N",
"B": "112.896 N",
"C": "143.12 N",
"D": "141.12 N"
} | D | 141.12 N | Net force=mg(sinθ−μcosθ)=28×10×(0.6−0.12×0.8)=141.12 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 141.12 N, not 140.12 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 141.12 N, not 112.896 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 141.12 N, not... | [
"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_003047 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-11-7i)/(10+6i). What is Re(z), the real part of z? | {
"A": "-1.67647",
"B": "-4.11765",
"C": "-1.11765",
"D": "-0.11765"
} | C | -1.11765 | Multiply numerator and denominator by the conjugate (10-6i). Then Re(z)=(ac+bd)/(c²+d²)=((-11)(10)+(-7)(6))/(10²+(6)²)=-1.11765. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.11765, not -1.67647.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.11765, not -4.11765.",
"C": "Correct. The worked calculation gives -1.11765.",
"D": "Incorrect. Substituting the stat... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004006 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block initially moves at 5 m s⁻¹. A constant net force does 17 N of work over 8 m in the direction of motion. Find its final kinetic energy. | {
"A": "485.25 J",
"B": "323.5 J",
"C": "388.2 J",
"D": "258.8 J"
} | B | 323.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(15)(5)²+(17)(8)=323.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 323.5 J, not 485.25 J.",
"B": "Correct. The worked calculation gives 323.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 323.5 J, not 388.2 J.",
"D": "Incorrect. Substituting the stated v... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001924 | 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 39 distinct elements? | {
"A": "3352112088",
"B": "1257042033",
"C": "1676056044",
"D": "1676056045"
} | C | 1676056044 | Order does not matter, so the count is C(39,11)=39!/[11!(28)!]=1676056044. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1676056044, not 3352112088.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1676056044, not 1257042033.",
"C": "Correct. The worked calculation gives 1676056044.",
"D": "Incorrect. Substitutin... | [
"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_005278 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +5 μC are separated by 5 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "36 N",
"B": "54 N",
"C": "37 N",
"D": "35 N"
} | A | 36 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(5×10⁻⁶)/(5×10⁻²)²=36 N. | {
"A": "Correct. The worked calculation gives 36 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 36 N, not 54 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 36 N, not 37 N.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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 |
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