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_004456 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 3 kg and radius 1 m is acted on by a constant torque of 40 N m about its central axis. Find its angular acceleration. | {
"A": "21.33333 rad s⁻²",
"B": "-26.66667 rad s⁻²",
"C": "26.66667 rad s⁻²",
"D": "32 rad s⁻²"
} | C | 26.66667 rad s⁻² | For a solid disc, I=½MR²=½(3)(1)²=1.5 kg m². Using τ=Iα, α=40/1.5=26.66667 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26.66667 rad s⁻², not 21.33333 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26.66667 rad s⁻², not -26.66667 rad s⁻².",
"C": "Correct. The worked calculation gives 26.66667 rad s⁻².",... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001750 | 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 74 distinct elements? | {
"A": "718406958841",
"B": "718406958843",
"C": "718406958840",
"D": "718406958839"
} | A | 718406958841 | Order does not matter, so the count is C(74,10)=74!/[10!(64)!]=718406958841. | {
"A": "Correct. The worked calculation gives 718406958841.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 718406958841, not 718406958843.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 718406958841, not 718406958840.",
"D": "Incorrect. S... | [
"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_008685 | 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 1.16 mol L⁻¹ and initially B is absent. At equilibrium, 36% of A has dissociated at constant volume. Find K_c. | {
"A": "0.9396",
"B": "3.9396",
"C": "0.4698",
"D": "0.7047"
} | A | 0.9396 | Let α=0.36. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.16)(0.36)²/(1−0.36)=0.9396. | {
"A": "Correct. The worked calculation gives 0.9396.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9396, not 3.9396.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9396, not 0.4698.",
"D": "Incorrect. Substituting the stated values ... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001638 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (-4x² -5x +3) dx. | {
"A": "-432",
"B": "-270",
"C": "-360",
"D": "-362"
} | C | -360 | An antiderivative is (-4/3)x³+(-5/2)x²+(3)x. Evaluating between 0 and 6 gives (-4/3)(6)³+(-5/2)(6)²+(3)(6)=-360. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -360, not -432.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -360, not -270.",
"C": "Correct. The worked calculation gives -360.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_004832 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 3 Ω and 2 Ω are connected in series; this combination is connected in parallel with a 7 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.08571 A",
"B": "1.54286 A",
"C": "3.08571 A",
"D": "5.08571 A"
} | C | 3.08571 A | Series branch resistance=3+2=5 Ω. Parallel equivalent R_eq=(5×7)/(5+7)=2.91667 Ω. Total current I=V/R_eq=9/2.91667=3.08571 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.08571 A, not 0.08571 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.08571 A, not 1.54286 A.",
"C": "Correct. The worked calculation gives 3.08571 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_002376 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, 5], [9, -4]]. | {
"A": "-60.75",
"B": "-81",
"C": "-82",
"D": "-80"
} | B | -81 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(-4)−(5)(9)=-81. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -81, not -60.75.",
"B": "Correct. The worked calculation gives -81.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -81, not -82.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_002890 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, 9, -1) and v=(6, 7, -5), calculate u·v. | {
"A": "74",
"B": "59.2",
"C": "88.8",
"D": "8.4"
} | A | 74 | The dot product is the sum of corresponding component products: (1)(6)+(9)(7)+(-1)(-5)=74. | {
"A": "Correct. The worked calculation gives 74.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 74, not 59.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 74, not 88.8.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001852 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 75 distinct elements? | {
"A": "33742107450",
"B": "16871053725",
"C": "16871053726",
"D": "12653290293.75"
} | B | 16871053725 | Order does not matter, so the count is C(75,8)=75!/[8!(67)!]=16871053725. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16871053725, not 33742107450.",
"B": "Correct. The worked calculation gives 16871053725.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16871053725, not 16871053726.",
"D": "Incorrect. Substi... | [
"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_000007 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 +18x +9=0, let its roots be α and β. What is α²+β²? | {
"A": "5",
"B": "6",
"C": "3",
"D": "4"
} | B | 6 | By Vieta's relations, α+β = -18/6 and αβ = 9/6. Then α²+β²=(α+β)²−2αβ = (-18/6)²−2(9/6) = 6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 5.",
"B": "Correct. The worked calculation gives 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_002404 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, 7], [1, 6]]. | {
"A": "35",
"B": "26.25",
"C": "34",
"D": "37"
} | A | 35 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(6)−(7)(1)=35. | {
"A": "Correct. The worked calculation gives 35.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 35, not 26.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 35, not 34.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_004537 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 10 kg and radius 2 m is acted on by a constant torque of 18 N m about its central axis. Find its angular acceleration. | {
"A": "0.9 rad s⁻²",
"B": "2.9 rad s⁻²",
"C": "1.9 rad s⁻²",
"D": "-1.1 rad s⁻²"
} | A | 0.9 rad s⁻² | For a solid disc, I=½MR²=½(10)(2)²=20 kg m². Using τ=Iα, α=18/20=0.9 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.9 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9 rad s⁻², not 2.9 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9 rad s⁻², not 1.9 rad s⁻².",
"D": "Incorrect. Substi... | [
"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_000009 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 -13x +8=0, let its roots be α and β. What is α²+β²? | {
"A": "3.5625",
"B": "6.5625",
"C": "3.28125",
"D": "8.5625"
} | B | 6.5625 | By Vieta's relations, α+β = 13/4 and αβ = 8/4. Then α²+β²=(α+β)²−2αβ = (13/4)²−2(8/4) = 6.5625. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.5625, not 3.5625.",
"B": "Correct. The worked calculation gives 6.5625.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.5625, not 3.28125.",
"D": "Incorrect. Substituting the stated values... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007677 | 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 68 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "7.5 mmol L⁻¹",
"B": "11.5 mmol L⁻¹",
"C": "8.5 mmol L⁻¹",
"D": "1.85 mmol L⁻¹"
} | C | 8.5 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=68/2^3=8.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.5 mmol L⁻¹, not 7.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.5 mmol L⁻¹, not 11.5 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 8.5 mmol L⁻¹.",
"D": "Incorrect. ... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008978 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.24 mol L⁻¹ and initially B is absent. At equilibrium, 71% of A has dissociated at constant volume. Find K_c. | {
"A": "1.16687",
"B": "-1.66874",
"C": "2.50312",
"D": "1.66874"
} | D | 1.66874 | Let α=0.71. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.24)(0.71)²/(1−0.71)=1.66874. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.66874, not 1.16687.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.66874, not -1.66874.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.66874, not 2.50... | [
"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_007813 | 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 70 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "21 mmol L⁻¹",
"B": "16.5 mmol L⁻¹",
"C": "17.5 mmol L⁻¹",
"D": "26.25 mmol L⁻¹"
} | C | 17.5 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=70/2^2=17.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 17.5 mmol L⁻¹, not 21 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17.5 mmol L⁻¹, not 16.5 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 17.5 mmol L⁻¹.",
"D": "Incorrect... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002473 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, -7], [5, 7]]. | {
"A": "64",
"B": "7.3",
"C": "50.4",
"D": "63"
} | D | 63 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(7)−(-7)(5)=63. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 63, not 64.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 63, not 7.3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 63, not 50.4.",
"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_001037 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ +9x² -10x+7. Evaluate f′(2). | {
"A": "-22",
"B": "-1.2",
"C": "-11",
"D": "-24"
} | A | -22 | Differentiate: f′(x)=3(-4)x²+2(9)x+(-10). At x=2, f′(2)=3(-4)(2)²+2(9)(2)+(-10)=-22. | {
"A": "Correct. The worked calculation gives -22.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -22, not -1.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -22, not -11.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_005023 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +9 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "270 N",
"B": "539 N",
"C": "-540 N",
"D": "540 N"
} | D | 540 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(9×10⁻⁶)/(3×10⁻²)²=540 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 540 N, not 270 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 540 N, not 539 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 540 N, not -540 N.",
"D"... | [
"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_009532 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_10H_20N_3X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "0",
"B": "3",
"C": "0.5",
"D": "1"
} | D | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×10+2+3−20−3)/2=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.5.",
"D": "Correct. The worked ... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004732 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 2 Ω are connected in series; this combination is connected in parallel with a 7 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.52381 A",
"B": "2.28571 A",
"C": "3.04762 A",
"D": "-1.52381 A"
} | A | 1.52381 A | Series branch resistance=7+2=9 Ω. Parallel equivalent R_eq=(9×7)/(9+7)=3.9375 Ω. Total current I=V/R_eq=6/3.9375=1.52381 A. | {
"A": "Correct. The worked calculation gives 1.52381 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.52381 A, not 2.28571 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.52381 A, not 3.04762 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_001322 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=0x³ +0x² +5x+7. Evaluate f′(2). | {
"A": "5",
"B": "2",
"C": "4",
"D": "1.5"
} | A | 5 | Differentiate: f′(x)=3(0)x²+2(0)x+(5). At x=2, f′(2)=3(0)(2)²+2(0)(2)+(5)=5. | {
"A": "Correct. The worked calculation gives 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 4.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_003442 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 28 m s⁻¹ at 18° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "5.60824 m",
"B": "46.08236 m",
"C": "69.12355 m",
"D": "34.56177 m"
} | B | 46.08236 m | Range R=u²sin(2θ)/g. Substituting u=28, θ=18° and g=10 gives R=(28)²sin(36°)/10=46.08236 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 46.08236 m, not 5.60824 m.",
"B": "Correct. The worked calculation gives 46.08236 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 46.08236 m, not 69.12355 m.",
"D": "Incorrect. Substituting... | [
"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_001642 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (-2x² +7x +3) dx. | {
"A": "45",
"B": "22.5",
"C": "-22.5",
"D": "33.75"
} | B | 22.5 | An antiderivative is (-2/3)x³+(7/2)x²+(3)x. Evaluating between 0 and 3 gives (-2/3)(3)³+(7/2)(3)²+(3)(3)=22.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22.5, not 45.",
"B": "Correct. The worked calculation gives 22.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22.5, not -22.5.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_005450 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 3 μF capacitor is charged to a potential difference of 3 V. Calculate the energy stored, expressed in μJ. | {
"A": "16.5 μJ",
"B": "6.75 μJ",
"C": "13.5 μJ",
"D": "10.125 μJ"
} | C | 13.5 μJ | U=½CV². Since C=3 μF, U in μJ is ½×3×(3)²=13.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13.5 μJ, not 16.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13.5 μJ, not 6.75 μJ.",
"C": "Correct. The worked calculation gives 13.5 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009977 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(CN)_6]^-4, each CN ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "-2",
"B": "1.2",
"C": "2",
"D": "5"
} | C | 2 | Let the formal oxidation state of Fe be x. Charge balance gives x+(6)(−1)=-4; hence x=-4+6=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.2.",
"C": "Correct. The worked calculation gives 2.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005065 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +8 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "288 N",
"B": "360 N",
"C": "240 N",
"D": "180 N"
} | C | 240 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(8×10⁻⁶)/(3×10⁻²)²=240 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 240 N, not 288 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 240 N, not 360 N.",
"C": "Correct. The worked calculation gives 240 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006048 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 76 cm in front of a thin convex lens of focal length 18 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.68966",
"B": "0.31034",
"C": "3.31034",
"D": "1.31034"
} | B | 0.31034 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(76)(18)/(76−18)=23.58621 cm. Thus |m|=v/u=23.58621/76=0.31034. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31034, not -0.68966.",
"B": "Correct. The worked calculation gives 0.31034.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31034, not 3.31034.",
"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_005304 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +8 μC and +3 μC are separated by 6 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "60 N",
"B": "7 N",
"C": "30 N",
"D": "90 N"
} | A | 60 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(8×10⁻⁶)(3×10⁻⁶)/(6×10⁻²)²=60 N. | {
"A": "Correct. The worked calculation gives 60 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 60 N, not 7 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 60 N, not 30 N.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_004435 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 4 kg and radius 5 m is acted on by a constant torque of 73 N m about its central axis. Find its angular acceleration. | {
"A": "-1.54 rad s⁻²",
"B": "0.73 rad s⁻²",
"C": "1.46 rad s⁻²",
"D": "2.46 rad s⁻²"
} | C | 1.46 rad s⁻² | For a solid disc, I=½MR²=½(4)(5)²=50 kg m². Using τ=Iα, α=73/50=1.46 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.46 rad s⁻², not -1.54 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.46 rad s⁻², not 0.73 rad s⁻².",
"C": "Correct. The worked calculation gives 1.46 rad s⁻².",
"D": "Incorrect. ... | [
"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_006655 | 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 579 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.0144 s",
"B": "-0.14396 s",
"C": "3.14396 s",
"D": "0.14396 s"
} | D | 0.14396 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(3/579)=0.14396 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.14396 s, not 1.0144 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.14396 s, not -0.14396 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.14396 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_005859 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.3 atm at 245 K. What is its pressure at 727 K? | {
"A": "4.85755 atm",
"B": "1.85755 atm",
"C": "3.85755 atm",
"D": "1.92878 atm"
} | C | 3.85755 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.3)(727)/(245)=3.85755 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.85755 atm, not 4.85755 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.85755 atm, not 1.85755 atm.",
"C": "Correct. The worked calculation gives 3.85755 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_008027 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 5 A for 12212 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": "19.08969 g",
"B": "22.08969 g",
"C": "20.08969 g",
"D": "16.07175 g"
} | C | 20.08969 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×5×12212/(2×96500)=20.08969 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20.08969 g, not 19.08969 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20.08969 g, not 22.08969 g.",
"C": "Correct. The worked calculation gives 20.08969 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009690 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(OH)_5]^-4, each OH ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "0.75",
"B": "1.1",
"C": "1.5",
"D": "1"
} | D | 1 | Let the formal oxidation state of Co be x. Charge balance gives x+(5)(−1)=-4; hence x=-4+5=+1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.5.",
"D": "Correct. The wo... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009608 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_7H_11N_1X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "2",
"C": "4",
"D": "5"
} | B | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+1−11−2)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 4.",
"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_009677 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(OH)_6]^+3, each OH ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "9",
"B": "-9",
"C": "7",
"D": "18"
} | A | 9 | Let the formal oxidation state of Mn be x. Charge balance gives x+(6)(−1)=+3; hence x=3+6=+9. | {
"A": "Correct. The worked calculation gives 9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9, not -9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9, not 7.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006550 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 2 kg is attached to an ideal spring of force constant 383 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "3.14453 s",
"B": "0.14453 s",
"C": "2.14453 s",
"D": "-0.14453 s"
} | B | 0.14453 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(2/383)=0.14453 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.14453 s, not 3.14453 s.",
"B": "Correct. The worked calculation gives 0.14453 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.14453 s, not 2.14453 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_005682 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.2 atm at 339 K. What is its pressure at 481 K? | {
"A": "5.95929 atm",
"B": "6.95929 atm",
"C": "4.46947 atm",
"D": "1.59593 atm"
} | A | 5.95929 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.2)(481)/(339)=5.95929 atm. | {
"A": "Correct. The worked calculation gives 5.95929 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.95929 atm, not 6.95929 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.95929 atm, not 4.46947 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_001087 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=2x³ -6x² +12x+7. Evaluate f′(2). | {
"A": "14",
"B": "10",
"C": "9",
"D": "12"
} | D | 12 | Differentiate: f′(x)=3(2)x²+2(-6)x+(12). At x=2, f′(2)=3(2)(2)²+2(-6)(2)+(12)=12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12, not 14.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12, not 10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12, not 9.",
"D": "Correct. The work... | [
"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_004459 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 4 m is acted on by a constant torque of 25 N m about its central axis. Find its angular acceleration. | {
"A": "-2.55357 rad s⁻²",
"B": "0.89286 rad s⁻²",
"C": "-0.55357 rad s⁻²",
"D": "0.44643 rad s⁻²"
} | D | 0.44643 rad s⁻² | For a solid disc, I=½MR²=½(7)(4)²=56 kg m². Using τ=Iα, α=25/56=0.44643 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.44643 rad s⁻², not -2.55357 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.44643 rad s⁻², not 0.89286 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing ... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004128 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 16 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.39. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "5.608 N",
"B": "46.08 N",
"C": "44.08 N",
"D": "55.296 N"
} | B | 46.08 N | Net force=mg(sinθ−μcosθ)=16×10×(0.6−0.39×0.8)=46.08 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 46.08 N, not 5.608 N.",
"B": "Correct. The worked calculation gives 46.08 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 46.08 N, not 44.08 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008312 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 6 A for 16564 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": "24.52416 g",
"B": "32.69888 g",
"C": "26.1591 g",
"D": "-32.69888 g"
} | B | 32.69888 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×6×16564/(2×96500)=32.69888 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 32.69888 g, not 24.52416 g.",
"B": "Correct. The worked calculation gives 32.69888 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 32.69888 g, not 26.1591 g.",
"D": "Incorrect. Substituting... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005899 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.8 atm at 245 K. What is its pressure at 549 K? | {
"A": "21.51184 atm",
"B": "13.75592 atm",
"C": "5.37796 atm",
"D": "10.75592 atm"
} | D | 10.75592 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.8)(549)/(245)=10.75592 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.75592 atm, not 21.51184 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.75592 atm, not 13.75592 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation give... | [
"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_008902 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.3 mol L⁻¹ and initially B is absent. At equilibrium, 36% of A has dissociated at constant volume. Find K_c. | {
"A": "0.243",
"B": "-1.757",
"C": "0.486",
"D": "1.243"
} | A | 0.243 | Let α=0.36. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.3)(0.36)²/(1−0.36)=0.243. | {
"A": "Correct. The worked calculation gives 0.243.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.243, not -1.757.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.243, not 0.486.",
"D": "Incorrect. Substituting the stated values into... | [
"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_002630 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, 0], [8, -6]]. | {
"A": "-72",
"B": "-96",
"C": "-48",
"D": "-3.8"
} | C | -48 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(-6)−(0)(8)=-48. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -48, not -72.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -48, not -96.",
"C": "Correct. The worked calculation gives -48.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007747 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 100 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "3.125 mmol L⁻¹",
"B": "1.5625 mmol L⁻¹",
"C": "4.6875 mmol L⁻¹",
"D": "0.125 mmol L⁻¹"
} | A | 3.125 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=100/2^5=3.125 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 3.125 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.125 mmol L⁻¹, not 1.5625 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.125 mmol L⁻¹, not 4.6875 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_003550 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 42 m s⁻¹ at 70° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "136.06528 m",
"B": "12.33877 m",
"C": "111.38773 m",
"D": "113.38773 m"
} | D | 113.38773 m | Range R=u²sin(2θ)/g. Substituting u=42, θ=70° and g=10 gives R=(42)²sin(140°)/10=113.38773 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 113.38773 m, not 136.06528 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 113.38773 m, not 12.33877 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 113... | [
"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_003964 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block initially moves at 5 m s⁻¹. A constant net force does 16 N of work over 17 m in the direction of motion. Find its final kinetic energy. | {
"A": "447 J",
"B": "335.25 J",
"C": "45.7 J",
"D": "223.5 J"
} | A | 447 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(14)(5)²+(16)(17)=447 J. | {
"A": "Correct. The worked calculation gives 447 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 447 J, not 335.25 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 447 J, not 45.7 J.",
"D": "Incorrect. Substituting the stated values i... | [
"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_006462 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 4 kg is attached to an ideal spring of force constant 453 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "3.18794 s",
"B": "0.14095 s",
"C": "-0.18794 s",
"D": "0.18794 s"
} | D | 0.18794 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(4/453)=0.18794 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.18794 s, not 3.18794 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.18794 s, not 0.14095 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.18794 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_002948 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(0, 8, 3) and v=(8, 6, -1), calculate u·v. | {
"A": "47",
"B": "67.5",
"C": "45",
"D": "33.75"
} | C | 45 | The dot product is the sum of corresponding component products: (0)(8)+(8)(6)+(3)(-1)=45. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 45, not 47.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 45, not 67.5.",
"C": "Correct. The worked calculation gives 45.",
"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_002621 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 3], [8, 0]]. | {
"A": "-19.2",
"B": "-25",
"C": "-23",
"D": "-24"
} | D | -24 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(0)−(3)(8)=-24. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -24, not -19.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -24, not -25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -24, not -23.",
"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_005294 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +8 μC are separated by 12 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "3 N",
"B": "7.5 N",
"C": "5 N",
"D": "1.5 N"
} | C | 5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(8×10⁻⁶)/(12×10⁻²)²=5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5 N, not 3 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5 N, not 7.5 N.",
"C": "Correct. The worked calculation gives 5 N.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_007103 | 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 461 K and 2.31 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "33.75175 L",
"B": "245.63816 L",
"C": "491.27632 L",
"D": "327.51755 L"
} | D | 327.51755 L | PV=nRT, so V=nRT/P=(20)(0.082057)(461)/(2.31)=327.51755 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 327.51755 L, not 33.75175 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 327.51755 L, not 245.63816 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 327... | [
"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_009364 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_13H_26N_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "5",
"B": "3",
"C": "0",
"D": "2"
} | D | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×13+2+2−26−0)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 0.",
"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_005073 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +7 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "38.57143 N",
"B": "51.42857 N",
"C": "25.71429 N",
"D": "30.85714 N"
} | C | 25.71429 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(7×10⁻⁶)/(7×10⁻²)²=25.71429 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 25.71429 N, not 38.57143 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 25.71429 N, not 51.42857 N.",
"C": "Correct. The worked calculation gives 25.71429 N.",
"D": "Incorrect. Substitutin... | [
"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_002280 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 3 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.03684",
"B": "0.55263",
"C": "0.36842",
"D": "0.27632"
} | C | 0.36842 | Favourable pairs = C(10,2)+C(3,2)+C(6,2)=63. Total pairs=C(19,2)=171. Therefore P=63/171=0.36842. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.36842, not 1.03684.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36842, not 0.55263.",
"C": "Correct. The worked calculation gives 0.36842.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000945 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio 5. What is the sum of its first 5 terms? | {
"A": "781",
"B": "624.8",
"C": "779",
"D": "1171.5"
} | A | 781 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(5^5−1)/(5−1)=781. | {
"A": "Correct. The worked calculation gives 781.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 781, not 624.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 781, not 779.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_001268 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ -8x² +2x+7. Evaluate f′(-3). | {
"A": "-83",
"B": "-85",
"C": "-7.5",
"D": "-68"
} | B | -85 | Differentiate: f′(x)=3(-5)x²+2(-8)x+(2). At x=-3, f′(-3)=3(-5)(-3)²+2(-8)(-3)+(2)=-85. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -85, not -83.",
"B": "Correct. The worked calculation gives -85.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -85, not -7.5.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_000533 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 9 and common difference 15. Find the sum of its first 19 terms. | {
"A": "274.6",
"B": "2738",
"C": "2736",
"D": "-2736"
} | C | 2736 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=9, d=15, n=19: Sₙ=19/2[2(9)+(19−1)(15)]=2736. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2736, not 274.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2736, not 2738.",
"C": "Correct. The worked calculation gives 2736.",
"D": "Incorrect. Substituting the stated values into the ... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004304 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 40 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.36. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "62.4 N",
"B": "124.8 N",
"C": "149.76 N",
"D": "187.2 N"
} | B | 124.8 N | Net force=mg(sinθ−μcosθ)=40×10×(0.6−0.36×0.8)=124.8 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 124.8 N, not 62.4 N.",
"B": "Correct. The worked calculation gives 124.8 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 124.8 N, not 149.76 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009454 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_6H_4N_1X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "-4",
"B": "3",
"C": "4",
"D": "6"
} | C | 4 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+1−4−3)/2=4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not -4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 3.",
"C": "Correct. The worked calculation gives 4.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003702 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 8 m s⁻¹. A constant net force does 12 N of work over 19 m in the direction of motion. Find its final kinetic energy. | {
"A": "870 J",
"B": "1160 J",
"C": "290 J",
"D": "580 J"
} | D | 580 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(8)²+(12)(19)=580 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 580 J, not 870 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 580 J, not 1160 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 580 J, not 290 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_009200 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.66 V, transfers 2 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.4382 V",
"B": "-2.2809 V",
"C": "1.07191 V",
"D": "0.7191 V"
} | D | 0.7191 V | Apply the Nernst equation: E=0.66−(0.0591/2)(-2)=0.7191 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7191 V, not 1.4382 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7191 V, not -2.2809 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7191 V, not... | [
"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_002885 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, 0, 5) and v=(-7, 5, -6), calculate u·v. | {
"A": "-4.8",
"B": "-58",
"C": "-56",
"D": "-87"
} | B | -58 | The dot product is the sum of corresponding component products: (4)(-7)+(0)(5)+(5)(-6)=-58. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -58, not -4.8.",
"B": "Correct. The worked calculation gives -58.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -58, not -56.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_005472 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 69 μF capacitor is charged to a potential difference of 17 V. Calculate the energy stored, expressed in μJ. | {
"A": "-9970.5 μJ",
"B": "9969.5 μJ",
"C": "9970.5 μJ",
"D": "11964.6 μJ"
} | C | 9970.5 μJ | U=½CV². Since C=69 μF, U in μJ is ½×69×(17)²=9970.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9970.5 μJ, not -9970.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9970.5 μJ, not 9969.5 μJ.",
"C": "Correct. The worked calculation gives 9970.5 μJ.",
"D": "Incorrect. Substituting th... | [
"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_002390 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, 2], [4, 3]]. | {
"A": "-4",
"B": "-2",
"C": "-1.5",
"D": "-1"
} | B | -2 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(3)−(2)(4)=-2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2, not -4.",
"B": "Correct. The worked calculation gives -2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2, not -1.5.",
"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_003859 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 0 m s⁻¹. A constant net force does 26 N of work over 13 m in the direction of motion. Find its final kinetic energy. | {
"A": "270.4 J",
"B": "338 J",
"C": "339 J",
"D": "337 J"
} | B | 338 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(0)²+(26)(13)=338 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 338 J, not 270.4 J.",
"B": "Correct. The worked calculation gives 338 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 338 J, not 339 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_003618 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 58 m s⁻¹ at 20° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "108.11688 m",
"B": "-216.23375 m",
"C": "216.23375 m",
"D": "217.23375 m"
} | C | 216.23375 m | Range R=u²sin(2θ)/g. Substituting u=58, θ=20° and g=10 gives R=(58)²sin(40°)/10=216.23375 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 216.23375 m, not 108.11688 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 216.23375 m, not -216.23375 m.",
"C": "Correct. The worked calculation gives 216.23375 m.",
"D": "Incorrect. Subst... | [
"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_002653 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, -4], [2, 1]]. | {
"A": "17",
"B": "16",
"C": "19.2",
"D": "12.8"
} | B | 16 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(1)−(-4)(2)=16. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16, not 17.",
"B": "Correct. The worked calculation gives 16.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16, not 19.2.",
"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_004833 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 14 Ω and 6 Ω are connected in series; this combination is connected in parallel with a 16 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.675 A",
"B": "1.675 A",
"C": "0.3375 A",
"D": "-0.325 A"
} | A | 0.675 A | Series branch resistance=14+6=20 Ω. Parallel equivalent R_eq=(20×16)/(20+16)=8.88889 Ω. Total current I=V/R_eq=6/8.88889=0.675 A. | {
"A": "Correct. The worked calculation gives 0.675 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.675 A, not 1.675 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.675 A, not 0.3375 A.",
"D": "Incorrect. Substituting the stated v... | [
"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_008190 | 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 4354 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": "2.43253 g",
"B": "2.86507 g",
"C": "1.43253 g",
"D": "-1.43253 g"
} | C | 1.43253 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×1×4354/(2×96500)=1.43253 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.43253 g, not 2.43253 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.43253 g, not 2.86507 g.",
"C": "Correct. The worked calculation gives 1.43253 g.",
"D": "Incorrect. Substituting the... | [
"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_007860 | 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 12 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "0.1875 mmol L⁻¹",
"B": "-1.8125 mmol L⁻¹",
"C": "-2.8125 mmol L⁻¹",
"D": "1.01875 mmol L⁻¹"
} | A | 0.1875 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=12/2^6=0.1875 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 0.1875 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.1875 mmol L⁻¹, not -1.8125 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.1875 mmol L⁻¹, not -2.8125 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_007812 | 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 87 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "1.35938 mmol L⁻¹",
"B": "2.03906 mmol L⁻¹",
"C": "2.35938 mmol L⁻¹",
"D": "-1.64062 mmol L⁻¹"
} | A | 1.35938 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=87/2^6=1.35938 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 1.35938 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.35938 mmol L⁻¹, not 2.03906 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.35938 mmol L⁻¹, not 2.35938 mmol L⁻¹.",
... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003023 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(15-6i)/(4+4i). What is Re(z), the real part of z? | {
"A": "0.84375",
"B": "3.125",
"C": "1.125",
"D": "-1.875"
} | C | 1.125 | Multiply numerator and denominator by the conjugate (4-4i). Then Re(z)=(ac+bd)/(c²+d²)=((15)(4)+(-6)(4))/(4²+(4)²)=1.125. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.125, not 0.84375.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.125, not 3.125.",
"C": "Correct. The worked calculation gives 1.125.",
"D": "Incorrect. Substituting the stated values int... | [
"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_002820 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, 9, -7) and v=(8, 2, -2), calculate u·v. | {
"A": "51.2",
"B": "-64",
"C": "65",
"D": "64"
} | D | 64 | The dot product is the sum of corresponding component products: (4)(8)+(9)(2)+(-7)(-2)=64. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 64, not 51.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 64, not -64.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 64, not 65.",
"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_001801 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 90 distinct elements? | {
"A": "77515521435",
"B": "-77515521435",
"C": "77515521434",
"D": "77515521433"
} | A | 77515521435 | Order does not matter, so the count is C(90,8)=90!/[8!(82)!]=77515521435. | {
"A": "Correct. The worked calculation gives 77515521435.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 77515521435, not -77515521435.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 77515521435, not 77515521434.",
"D": "Incorrect. Subst... | [
"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_001885 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 9 elements can be selected from a set of 37 distinct elements? | {
"A": "248807240",
"B": "124403620",
"C": "124403618",
"D": "124403621"
} | B | 124403620 | Order does not matter, so the count is C(37,9)=37!/[9!(28)!]=124403620. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 124403620, not 248807240.",
"B": "Correct. The worked calculation gives 124403620.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 124403620, not 124403618.",
"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_008122 | 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 3 A for 7486 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "5.54177 g",
"B": "4.38903 g",
"C": "7.38903 g",
"D": "1.7389 g"
} | C | 7.38903 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×3×7486/(2×96500)=7.38903 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.38903 g, not 5.54177 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.38903 g, not 4.38903 g.",
"C": "Correct. The worked calculation gives 7.38903 g.",
"D": "Incorrect. Substituting the... | [
"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_008747 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.35 mol L⁻¹ and initially B is absent. At equilibrium, 79% of A has dissociated at constant volume. Find K_c. | {
"A": "4.16067",
"B": "1.16067",
"C": "3.1205",
"D": "6.241"
} | A | 4.16067 | Let α=0.79. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.35)(0.79)²/(1−0.79)=4.16067. | {
"A": "Correct. The worked calculation gives 4.16067.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.16067, not 1.16067.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.16067, not 3.1205.",
"D": "Incorrect. Substituting the stated val... | [
"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_004246 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 37 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.22. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "156.88 N",
"B": "157.88 N",
"C": "158.88 N",
"D": "125.504 N"
} | A | 156.88 N | Net force=mg(sinθ−μcosθ)=37×10×(0.6−0.22×0.8)=156.88 N. | {
"A": "Correct. The worked calculation gives 156.88 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 156.88 N, not 157.88 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 156.88 N, not 158.88 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_002609 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, 5], [2, 2]]. | {
"A": "-11",
"B": "-5",
"C": "-10",
"D": "-8"
} | D | -8 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(2)−(5)(2)=-8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -8, not -11.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -8, not -5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -8, not -10.",
"D": "Correct. The w... | [
"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_005847 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.9 atm at 312 K. What is its pressure at 702 K? | {
"A": "10.025 atm",
"B": "11.025 atm",
"C": "8.26875 atm",
"D": "-11.025 atm"
} | B | 11.025 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.9)(702)/(312)=11.025 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.025 atm, not 10.025 atm.",
"B": "Correct. The worked calculation gives 11.025 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.025 atm, not 8.26875 atm.",
"D": "Incorrect. Substituti... | [
"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_002466 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, -7], [2, -1]]. | {
"A": "26",
"B": "16",
"C": "12",
"D": "13"
} | D | 13 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(-1)−(-7)(2)=13. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13, not 26.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13, not 16.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13, not 12.",
"D": "Correct. The wor... | [
"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_009915 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(CN)_5]^+1, each CN ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "5",
"B": "4.5",
"C": "3",
"D": "6"
} | D | 6 | Let the formal oxidation state of Pt be x. Charge balance gives x+(5)(−1)=+1; hence x=1+5=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"D": "Correct. The worked ... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006435 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 5 kg is attached to an ideal spring of force constant 886 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.15024 s",
"B": "0.11268 s",
"C": "1.01502 s",
"D": "0.07512 s"
} | A | 0.15024 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(5/886)=0.15024 s. | {
"A": "Correct. The worked calculation gives 0.15024 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.15024 s, not 0.11268 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.15024 s, not 1.01502 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_005582 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 18 μF capacitor is charged to a potential difference of 13 V. Calculate the energy stored, expressed in μJ. | {
"A": "1520 μJ",
"B": "1521 μJ",
"C": "2281.5 μJ",
"D": "1519 μJ"
} | B | 1521 μJ | U=½CV². Since C=18 μF, U in μJ is ½×18×(13)²=1521 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1521 μJ, not 1520 μJ.",
"B": "Correct. The worked calculation gives 1521 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1521 μJ, not 2281.5 μJ.",
"D": "Incorrect. Substituting the stated ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002819 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(5, 8, 4) and v=(7, -6, 2), calculate u·v. | {
"A": "-2.5",
"B": "-3",
"C": "0.5",
"D": "-5"
} | D | -5 | The dot product is the sum of corresponding component products: (5)(7)+(8)(-6)+(4)(2)=-5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -5, not -2.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -5, not -3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -5, not 0.5.",
"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_004545 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 2 m is acted on by a constant torque of 77 N m about its central axis. Find its angular acceleration. | {
"A": "4.125 rad s⁻²",
"B": "8.25 rad s⁻²",
"C": "5.5 rad s⁻²",
"D": "8.5 rad s⁻²"
} | C | 5.5 rad s⁻² | For a solid disc, I=½MR²=½(7)(2)²=14 kg m². Using τ=Iα, α=77/14=5.5 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.5 rad s⁻², not 4.125 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.5 rad s⁻², not 8.25 rad s⁻².",
"C": "Correct. The worked calculation gives 5.5 rad s⁻².",
"D": "Incorrect. Sub... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004662 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 10 kg and radius 1 m is acted on by a constant torque of 98 N m about its central axis. Find its angular acceleration. | {
"A": "19.6 rad s⁻²",
"B": "39.2 rad s⁻²",
"C": "18.6 rad s⁻²",
"D": "21.6 rad s⁻²"
} | A | 19.6 rad s⁻² | For a solid disc, I=½MR²=½(10)(1)²=5 kg m². Using τ=Iα, α=98/5=19.6 rad s⁻². | {
"A": "Correct. The worked calculation gives 19.6 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19.6 rad s⁻², not 39.2 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19.6 rad s⁻², not 18.6 rad s⁻².",
"D": "Incorrect. S... | [
"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_004614 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 12 kg and radius 6 m is acted on by a constant torque of 26 N m about its central axis. Find its angular acceleration. | {
"A": "1.12037 rad s⁻²",
"B": "0.09028 rad s⁻²",
"C": "0.12037 rad s⁻²",
"D": "-0.87963 rad s⁻²"
} | C | 0.12037 rad s⁻² | For a solid disc, I=½MR²=½(12)(6)²=216 kg m². Using τ=Iα, α=26/216=0.12037 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.12037 rad s⁻², not 1.12037 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.12037 rad s⁻², not 0.09028 rad s⁻².",
"C": "Correct. The worked calculation gives 0.12037 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_002228 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 3 blue and 8 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.3619",
"B": "0.54286",
"C": "0.27143",
"D": "1.03619"
} | A | 0.3619 | Favourable pairs = C(10,2)+C(3,2)+C(8,2)=76. Total pairs=C(21,2)=210. Therefore P=76/210=0.3619. | {
"A": "Correct. The worked calculation gives 0.3619.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3619, not 0.54286.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3619, not 0.27143.",
"D": "Incorrect. Substituting the stated value... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001053 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=1x³ +1x² +11x+7. Evaluate f′(-2). | {
"A": "18",
"B": "19",
"C": "14.25",
"D": "21"
} | B | 19 | Differentiate: f′(x)=3(1)x²+2(1)x+(11). At x=-2, f′(-2)=3(1)(-2)²+2(1)(-2)+(11)=19. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19, not 18.",
"B": "Correct. The worked calculation gives 19.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19, not 14.25.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_009521 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_16H_7N_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "12",
"B": "15",
"C": "2.5",
"D": "-15"
} | B | 15 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×16+2+3−7−0)/2=15. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15, not 12.",
"B": "Correct. The worked calculation gives 15.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15, not 2.5.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003043 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(6+6i)/(1+4i). What is Re(z), the real part of z? | {
"A": "2.76471",
"B": "3.52941",
"C": "1.76471",
"D": "-1.76471"
} | C | 1.76471 | Multiply numerator and denominator by the conjugate (1-4i). Then Re(z)=(ac+bd)/(c²+d²)=((6)(1)+(6)(4))/(1²+(4)²)=1.76471. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.76471, not 2.76471.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.76471, not 3.52941.",
"C": "Correct. The worked calculation gives 1.76471.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006890 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 11 mol H₂ and 32 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "12 mol",
"B": "11 mol",
"C": "16.5 mol",
"D": "9 mol"
} | B | 11 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 11 mol H₂O; O₂ can produce 64 mol H₂O. The limiting condition is H₂; product=11 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11 mol, not 12 mol.",
"B": "Correct. The worked calculation gives 11 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11 mol, not 16.5 mol.",
"D": "Incorrect. Substituting the stated value... | [
"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_008415 | 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 0.32 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.49152 K",
"B": "2.49152 K",
"C": "0.98304 K",
"D": "0.49152 K"
} | D | 0.49152 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.512×0.32=0.49152 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.49152 K, not 1.49152 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.49152 K, not 2.49152 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.49152 K,... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001342 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (-3x² -2x -5) dx. | {
"A": "-102",
"B": "-51",
"C": "51",
"D": "-38.25"
} | B | -51 | An antiderivative is (-3/3)x³+(-2/2)x²+(-5)x. Evaluating between 0 and 3 gives (-3/3)(3)³+(-2/2)(3)²+(-5)(3)=-51. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -51, not -102.",
"B": "Correct. The worked calculation gives -51.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -51, not 51.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002883 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, -6, 4) and v=(-1, -5, 8), calculate u·v. | {
"A": "57",
"B": "43.5",
"C": "58",
"D": "59"
} | C | 58 | The dot product is the sum of corresponding component products: (4)(-1)+(-6)(-5)+(4)(8)=58. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 58, not 57.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 58, not 43.5.",
"C": "Correct. The worked calculation gives 58.",
"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_007254 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 2 mol of gas at 340 K and 0.71 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "78.5898 L",
"B": "76.5898 L",
"C": "62.87184 L",
"D": "157.17961 L"
} | A | 78.5898 L | PV=nRT, so V=nRT/P=(2)(0.082057)(340)/(0.71)=78.5898 L. | {
"A": "Correct. The worked calculation gives 78.5898 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 78.5898 L, not 76.5898 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 78.5898 L, not 62.87184 L.",
"D": "Incorrect. Substituting th... | [
"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_006009 | 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 14 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.31818",
"B": "0.63636",
"C": "0.23864",
"D": "0.15909"
} | A | 0.31818 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(58)(14)/(58−14)=18.45455 cm. Thus |m|=v/u=18.45455/58=0.31818. | {
"A": "Correct. The worked calculation gives 0.31818.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31818, not 0.63636.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31818, not 0.23864.",
"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_007712 | 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 92 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "3.875 mmol L⁻¹",
"B": "0.875 mmol L⁻¹",
"C": "2.875 mmol L⁻¹",
"D": "5.75 mmol L⁻¹"
} | C | 2.875 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=92/2^5=2.875 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.875 mmol L⁻¹, not 3.875 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.875 mmol L⁻¹, not 0.875 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 2.875 mmol L⁻¹.",
"D": "In... | [
"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 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.