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_001628 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (-4x² -7x +1) dx. | {
"A": "-489.6",
"B": "-408",
"C": "-39.8",
"D": "-326.4"
} | B | -408 | An antiderivative is (-4/3)x³+(-7/2)x²+(1)x. Evaluating between 0 and 6 gives (-4/3)(6)³+(-7/2)(6)²+(1)(6)=-408. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -408, not -489.6.",
"B": "Correct. The worked calculation gives -408.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -408, not -39.8.",
"D": "Incorrect. Substituting the stated values into th... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008164 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 11 A for 24081 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": "88.15326 g",
"B": "104.58391 g",
"C": "87.15326 g",
"D": "9.71533 g"
} | C | 87.15326 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×24081/(2×96500)=87.15326 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 87.15326 g, not 88.15326 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 87.15326 g, not 104.58391 g.",
"C": "Correct. The worked calculation gives 87.15326 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005498 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 13 μF capacitor is charged to a potential difference of 15 V. Calculate the energy stored, expressed in μJ. | {
"A": "2193.75 μJ",
"B": "-1462.5 μJ",
"C": "1462.5 μJ",
"D": "1170 μJ"
} | C | 1462.5 μJ | U=½CV². Since C=13 μF, U in μJ is ½×13×(15)²=1462.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1462.5 μJ, not 2193.75 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1462.5 μJ, not -1462.5 μJ.",
"C": "Correct. The worked calculation gives 1462.5 μJ.",
"D": "Incorrect. Substituting t... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000411 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 1 and common difference 15. Find the sum of its first 27 terms. | {
"A": "5292",
"B": "530.2",
"C": "6350.4",
"D": "3969"
} | A | 5292 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=1, d=15, n=27: Sₙ=27/2[2(1)+(27−1)(15)]=5292. | {
"A": "Correct. The worked calculation gives 5292.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5292, not 530.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5292, not 6350.4.",
"D": "Incorrect. Substituting the stated values into th... | [
"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_001892 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 11 elements can be selected from a set of 71 distinct elements? | {
"A": "1920410537682",
"B": "3072656860291.2002",
"C": "1280273691788",
"D": "2560547383576"
} | D | 2560547383576 | Order does not matter, so the count is C(71,11)=71!/[11!(60)!]=2560547383576. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2560547383576, not 1920410537682.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2560547383576, not 3072656860291.2002.",
"C": "Incorrect. Substituting the stated values into the governing rela... | [
"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_006952 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 44 mol H₂ and 25 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "44 mol",
"B": "33 mol",
"C": "43 mol",
"D": "52.8 mol"
} | A | 44 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 44 mol H₂O; O₂ can produce 50 mol H₂O. The limiting condition is H₂; product=44 mol. | {
"A": "Correct. The worked calculation gives 44 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 44 mol, not 33 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 44 mol, not 43 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001386 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (1x² +8x +2) dx. | {
"A": "171",
"B": "228",
"C": "230",
"D": "456"
} | B | 228 | An antiderivative is (1/3)x³+(8/2)x²+(2)x. Evaluating between 0 and 6 gives (1/3)(6)³+(8/2)(6)²+(2)(6)=228. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 228, not 171.",
"B": "Correct. The worked calculation gives 228.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 228, not 230.",
"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_002122 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 7 red, 11 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.32644",
"B": "0.16322",
"C": "-0.67356",
"D": "0.48966"
} | A | 0.32644 | Favourable pairs = C(7,2)+C(11,2)+C(12,2)=142. Total pairs=C(30,2)=435. Therefore P=142/435=0.32644. | {
"A": "Correct. The worked calculation gives 0.32644.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32644, not 0.16322.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32644, not -0.67356.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000048 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -11x +9=0, let its roots be α and β. What is α²+β²? | {
"A": "31.875",
"B": "15.9375",
"C": "19.25",
"D": "21.25"
} | D | 21.25 | By Vieta's relations, α+β = 11/2 and αβ = 9/2. Then α²+β²=(α+β)²−2αβ = (11/2)²−2(9/2) = 21.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21.25, not 31.875.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21.25, not 15.9375.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21.25, not 19.25.",
"... | [
"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_005148 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +1 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "5.55556 N",
"B": "1.55556 N",
"C": "4.55556 N",
"D": "4.16667 N"
} | A | 5.55556 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(1×10⁻⁶)/(9×10⁻²)²=5.55556 N. | {
"A": "Correct. The worked calculation gives 5.55556 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.55556 N, not 1.55556 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.55556 N, not 4.55556 N.",
"D": "Incorrect. Substituting the... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003935 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 10 m s⁻¹. A constant net force does 22 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "-592 J",
"B": "592 J",
"C": "296 J",
"D": "1184 J"
} | B | 592 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(10)²+(22)(11)=592 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 592 J, not -592 J.",
"B": "Correct. The worked calculation gives 592 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 592 J, not 296 J.",
"D": "Incorrect. Substituting the stated values into... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000952 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 4. What is the sum of its first 9 terms? | {
"A": "655357.5",
"B": "699048",
"C": "873810",
"D": "1048572"
} | C | 873810 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(4^9−1)/(4−1)=873810. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 873810, not 655357.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 873810, not 699048.",
"C": "Correct. The worked calculation gives 873810.",
"D": "Incorrect. Substituting the stated value... | [
"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_009406 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_12H_22N_3X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "1.3",
"C": "2.25",
"D": "6"
} | A | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×12+2+3−22−1)/2=3. | {
"A": "Correct. The worked calculation gives 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_006089 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 17 cm in front of a thin convex lens of focal length 5 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.20833",
"B": "-0.41667",
"C": "0.41667",
"D": "0.83333"
} | C | 0.41667 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(17)(5)/(17−5)=7.08333 cm. Thus |m|=v/u=7.08333/17=0.41667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.41667, not 0.20833.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.41667, not -0.41667.",
"C": "Correct. The worked calculation gives 0.41667.",
"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_009390 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_4H_2N_2X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "6",
"B": "2.25",
"C": "0",
"D": "3"
} | D | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×4+2+2−2−4)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 0.",
"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_009170 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.95 V, transfers 1 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.7136 V",
"B": "0.3568 V",
"C": "-0.7136 V",
"D": "-2.2864 V"
} | A | 0.7136 V | Apply the Nernst equation: E=0.95−(0.0591/1)(4)=0.7136 V. | {
"A": "Correct. The worked calculation gives 0.7136 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7136 V, not 0.3568 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7136 V, not -0.7136 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009335 | 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_17H_27N_1X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "5",
"B": "6",
"C": "8",
"D": "4"
} | D | 4 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×17+2+1−27−2)/2=4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 8.",
"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_009666 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_4H_5N_1X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "2",
"B": "3",
"C": "4",
"D": "5"
} | A | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×4+2+1−5−2)/2=2. | {
"A": "Correct. The worked calculation gives 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 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_002361 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -1], [7, 1]]. | {
"A": "6",
"B": "12",
"C": "2.2",
"D": "10"
} | B | 12 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(1)−(-1)(7)=12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12, not 6.",
"B": "Correct. The worked calculation gives 12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12, not 2.2.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002536 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, -4], [6, 8]]. | {
"A": "96",
"B": "60",
"C": "79",
"D": "80"
} | D | 80 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(8)−(-4)(6)=80. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 80, not 96.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 80, not 60.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 80, not 79.",
"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_004214 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 50 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.14. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "366 N",
"B": "-244 N",
"C": "242 N",
"D": "244 N"
} | D | 244 N | Net force=mg(sinθ−μcosθ)=50×10×(0.6−0.14×0.8)=244 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 244 N, not 366 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 244 N, not -244 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 244 N, not 242 N.",
"D"... | [
"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_003319 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-7-15i)/(2+7i). What is Re(z), the real part of z? | {
"A": "-3.24528",
"B": "-2.24528",
"C": "-4.49057",
"D": "-1.68396"
} | B | -2.24528 | Multiply numerator and denominator by the conjugate (2-7i). Then Re(z)=(ac+bd)/(c²+d²)=((-7)(2)+(-15)(7))/(2²+(7)²)=-2.24528. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2.24528, not -3.24528.",
"B": "Correct. The worked calculation gives -2.24528.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2.24528, not -4.49057.",
"D": "Incorrect. Substituting the stat... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002157 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 3 blue and 10 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.63241",
"B": "1.03676",
"C": "0.36759",
"D": "0.55138"
} | C | 0.36759 | Favourable pairs = C(10,2)+C(3,2)+C(10,2)=93. Total pairs=C(23,2)=253. Therefore P=93/253=0.36759. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.36759, not -0.63241.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36759, not 1.03676.",
"C": "Correct. The worked calculation gives 0.36759.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003708 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 3 m s⁻¹. A constant net force does 15 N of work over 14 m in the direction of motion. Find its final kinetic energy. | {
"A": "123 J",
"B": "25.6 J",
"C": "184.5 J",
"D": "246 J"
} | D | 246 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(3)²+(15)(14)=246 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 246 J, not 123 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 246 J, not 25.6 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 246 J, not 184.5 J.",
"... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003862 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 11 m s⁻¹. A constant net force does 17 N of work over 20 m in the direction of motion. Find its final kinetic energy. | {
"A": "762.5 J",
"B": "763.5 J",
"C": "761.5 J",
"D": "572.625 J"
} | B | 763.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(11)²+(17)(20)=763.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 763.5 J, not 762.5 J.",
"B": "Correct. The worked calculation gives 763.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 763.5 J, not 761.5 J.",
"D": "Incorrect. Substituting the stated va... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009574 | 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_7N_1X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "4",
"B": "2",
"C": "-2",
"D": "1"
} | B | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+1−7−4)/2=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 -2.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004668 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 11 kg and radius 1 m is acted on by a constant torque of 27 N m about its central axis. Find its angular acceleration. | {
"A": "1.49091 rad s⁻²",
"B": "5.90909 rad s⁻²",
"C": "3.90909 rad s⁻²",
"D": "4.90909 rad s⁻²"
} | D | 4.90909 rad s⁻² | For a solid disc, I=½MR²=½(11)(1)²=5.5 kg m². Using τ=Iα, α=27/5.5=4.90909 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.90909 rad s⁻², not 1.49091 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.90909 rad s⁻², not 5.90909 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing r... | [
"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_006072 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 33 cm in front of a thin convex lens of focal length 26 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "2.71429",
"B": "6.71429",
"C": "3.71429",
"D": "1.71429"
} | C | 3.71429 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(33)(26)/(33−26)=122.57143 cm. Thus |m|=v/u=122.57143/33=3.71429. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.71429, not 2.71429.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.71429, not 6.71429.",
"C": "Correct. The worked calculation gives 3.71429.",
"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_006160 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 31 cm in front of a thin convex lens of focal length 9 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.59091",
"B": "0.40909",
"C": "1.04091",
"D": "2.40909"
} | B | 0.40909 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(31)(9)/(31−9)=12.68182 cm. Thus |m|=v/u=12.68182/31=0.40909. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.40909, not -0.59091.",
"B": "Correct. The worked calculation gives 0.40909.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.40909, not 1.04091.",
"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_007559 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 48 mL of 0.10 M HCl is mixed with 91 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "14.49045",
"B": "15.49045",
"C": "12.49045",
"D": "9.49045"
} | C | 12.49045 | Excess OH⁻ moles=0.10×(91−48)/1000=0.004300 mol. Total volume=0.139 L, so [OH⁻]=0.030935 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.49045. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.49045, not 14.49045.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.49045, not 15.49045.",
"C": "Correct. The worked calculation gives 12.49045.",
"D": "Incorrect. Substituting the stat... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006513 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 12 kg is attached to an ideal spring of force constant 1175 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.15159 s",
"B": "-0.79788 s",
"C": "0.20212 s",
"D": "-1.79788 s"
} | C | 0.20212 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(12/1175)=0.20212 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.20212 s, not 0.15159 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.20212 s, not -0.79788 s.",
"C": "Correct. The worked calculation gives 0.20212 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006219 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 98 cm in front of a thin convex lens of focal length 30 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.44118",
"B": "1.04412",
"C": "0.44118",
"D": "2.44118"
} | C | 0.44118 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(98)(30)/(98−30)=43.23529 cm. Thus |m|=v/u=43.23529/98=0.44118. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.44118, not -0.44118.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.44118, not 1.04412.",
"C": "Correct. The worked calculation gives 0.44118.",
"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_004255 | 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 0.36. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "-49.92 N",
"B": "47.92 N",
"C": "74.88 N",
"D": "49.92 N"
} | D | 49.92 N | Net force=mg(sinθ−μcosθ)=16×10×(0.6−0.36×0.8)=49.92 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 49.92 N, not -49.92 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 49.92 N, not 47.92 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 49.92 N, not 74.8... | [
"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_003447 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 18 m s⁻¹ at 18° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "19.04424 m",
"B": "20.04424 m",
"C": "-19.04424 m",
"D": "2.90442 m"
} | A | 19.04424 m | Range R=u²sin(2θ)/g. Substituting u=18, θ=18° and g=10 gives R=(18)²sin(36°)/10=19.04424 m. | {
"A": "Correct. The worked calculation gives 19.04424 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19.04424 m, not 20.04424 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19.04424 m, not -19.04424 m.",
"D": "Incorrect. Substituti... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007846 | 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 90 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "2.10938 mmol L⁻¹",
"B": "2.8125 mmol L⁻¹",
"C": "3.8125 mmol L⁻¹",
"D": "5.625 mmol L⁻¹"
} | B | 2.8125 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=90/2^5=2.8125 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.8125 mmol L⁻¹, not 2.10938 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 2.8125 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.8125 mmol L⁻¹, not 3.8125 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_009204 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.27 V, transfers 3 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.2897 V",
"B": "0.2897 V",
"C": "0.64485 V",
"D": "3.2897 V"
} | A | 1.2897 V | Apply the Nernst equation: E=1.27−(0.0591/3)(-1)=1.2897 V. | {
"A": "Correct. The worked calculation gives 1.2897 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.2897 V, not 0.2897 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2897 V, not 0.64485 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004040 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.28. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "67.68 N",
"B": "55.4 N",
"C": "58.4 N",
"D": "56.4 N"
} | D | 56.4 N | Net force=mg(sinθ−μcosθ)=15×10×(0.6−0.28×0.8)=56.4 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 56.4 N, not 67.68 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 56.4 N, not 55.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 56.4 N, not 58.4 N.",... | [
"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_004206 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 23 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.45. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "66.24 N",
"B": "57.2 N",
"C": "54.2 N",
"D": "55.2 N"
} | D | 55.2 N | Net force=mg(sinθ−μcosθ)=23×10×(0.6−0.45×0.8)=55.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 55.2 N, not 66.24 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 55.2 N, not 57.2 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 55.2 N, not 54.2 N.",... | [
"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_006127 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 98 cm in front of a thin convex lens of focal length 24 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.32432",
"B": "-0.32432",
"C": "0.64865",
"D": "-0.67568"
} | A | 0.32432 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(98)(24)/(98−24)=31.78378 cm. Thus |m|=v/u=31.78378/98=0.32432. | {
"A": "Correct. The worked calculation gives 0.32432.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32432, not -0.32432.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32432, not 0.64865.",
"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_005403 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 53 μF capacitor is charged to a potential difference of 8 V. Calculate the energy stored, expressed in μJ. | {
"A": "1696 μJ",
"B": "1272 μJ",
"C": "3392 μJ",
"D": "-1696 μJ"
} | A | 1696 μJ | U=½CV². Since C=53 μF, U in μJ is ½×53×(8)²=1696 μJ. | {
"A": "Correct. The worked calculation gives 1696 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1696 μJ, not 1272 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1696 μJ, not 3392 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_002487 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, -3], [5, -7]]. | {
"A": "-13",
"B": "-14",
"C": "-16",
"D": "-26"
} | A | -13 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(-7)−(-3)(5)=-13. | {
"A": "Correct. The worked calculation gives -13.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -13, not -14.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -13, not -16.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002142 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 4 blue and 8 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "2.36232",
"B": "0.54348",
"C": "3.36232",
"D": "0.36232"
} | D | 0.36232 | Favourable pairs = C(12,2)+C(4,2)+C(8,2)=100. Total pairs=C(24,2)=276. Therefore P=100/276=0.36232. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.36232, not 2.36232.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36232, not 0.54348.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.36232, not 3.362... | [
"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_002136 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 4 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "2.37368",
"B": "-2.62632",
"C": "3.37368",
"D": "0.37368"
} | D | 0.37368 | Favourable pairs = C(5,2)+C(4,2)+C(11,2)=71. Total pairs=C(20,2)=190. Therefore P=71/190=0.37368. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.37368, not 2.37368.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.37368, not -2.62632.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.37368, not 3.37... | [
"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_009260 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.69 V, transfers 1 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.09855 V",
"B": "0.73912 V",
"C": "-2.0145 V",
"D": "0.9855 V"
} | D | 0.9855 V | Apply the Nernst equation: E=0.69−(0.0591/1)(-5)=0.9855 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9855 V, not 1.09855 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9855 V, not 0.73912 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9855 V, no... | [
"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_002898 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(8, 2, 1) and v=(3, -2, 3), calculate u·v. | {
"A": "23",
"B": "11.5",
"C": "22",
"D": "21"
} | A | 23 | The dot product is the sum of corresponding component products: (8)(3)+(2)(-2)+(1)(3)=23. | {
"A": "Correct. The worked calculation gives 23.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23, not 11.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23, not 22.",
"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_007058 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 9 mol of gas at 543 K and 2.62 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "122.44658 L",
"B": "153.05823 L",
"C": "183.66987 L",
"D": "76.52911 L"
} | B | 153.05823 L | PV=nRT, so V=nRT/P=(9)(0.082057)(543)/(2.62)=153.05823 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 153.05823 L, not 122.44658 L.",
"B": "Correct. The worked calculation gives 153.05823 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 153.05823 L, not 183.66987 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007361 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 87 mL of 0.10 M HCl is mixed with 43 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.20574",
"B": "1.47049",
"C": "3.47049",
"D": "-1.52951"
} | B | 1.47049 | Excess H⁺ moles=0.10×(87−43)/1000=0.004400 mol. Total volume=0.130 L, so [H⁺]=0.033846 M and pH=−log₁₀[H⁺]=1.47049. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.47049, not 2.20574.",
"B": "Correct. The worked calculation gives 1.47049.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.47049, not 3.47049.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008694 | 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 1.99 mol L⁻¹ and initially B is absent. At equilibrium, 11% of A has dissociated at constant volume. Find K_c. | {
"A": "3.10822",
"B": "0.08117",
"C": "0.10822",
"D": "1.10822"
} | C | 0.10822 | Let α=0.11. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.99)(0.11)²/(1−0.11)=0.10822. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.10822, not 3.10822.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.10822, not 0.08117.",
"C": "Correct. The worked calculation gives 0.10822.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008590 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.91 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.191 K",
"B": "1.91 K",
"C": "0.955 K",
"D": "3.82 K"
} | B | 1.91 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×1.0×1.91=1.91 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.91 K, not 1.191 K.",
"B": "Correct. The worked calculation gives 1.91 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.91 K, not 0.955 K.",
"D": "Incorrect. Substituting the stated value... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004979 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 11 Ω are connected in series; this combination is connected in parallel with a 8 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.13158 A",
"B": "1.06579 A",
"C": "2.13158 A",
"D": "1.13158 A"
} | C | 2.13158 A | Series branch resistance=8+11=19 Ω. Parallel equivalent R_eq=(19×8)/(19+8)=5.62963 Ω. Total current I=V/R_eq=12/5.62963=2.13158 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.13158 A, not 0.13158 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.13158 A, not 1.06579 A.",
"C": "Correct. The worked calculation gives 2.13158 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_003363 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 73 m s⁻¹ at 35° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1001.5244 m",
"B": "-500.7622 m",
"C": "500.7622 m",
"D": "751.1433 m"
} | C | 500.7622 m | Range R=u²sin(2θ)/g. Substituting u=73, θ=35° and g=10 gives R=(73)²sin(70°)/10=500.7622 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 500.7622 m, not 1001.5244 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 500.7622 m, not -500.7622 m.",
"C": "Correct. The worked calculation gives 500.7622 m.",
"D": "Incorrect. Substitut... | [
"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_009432 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_12H_24. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "1",
"C": "-1",
"D": "2"
} | B | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×12+2+0−24−0)/2=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 3.",
"B": "Correct. The worked calculation gives 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not -1.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009352 | 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_11H_18X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "1",
"B": "1.1",
"C": "-1",
"D": "1.5"
} | A | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+0−18−4)/2=1. | {
"A": "Correct. The worked calculation gives 1.",
"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.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"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_007985 | 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 49 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "1.53125 mmol L⁻¹",
"B": "-0.46875 mmol L⁻¹",
"C": "-1.53125 mmol L⁻¹",
"D": "3.0625 mmol L⁻¹"
} | A | 1.53125 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=49/2^5=1.53125 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 1.53125 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.53125 mmol L⁻¹, not -0.46875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.53125 mmol L⁻¹, not -1.53125 mmol L⁻¹."... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005549 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 69 μF capacitor is charged to a potential difference of 29 V. Calculate the energy stored, expressed in μJ. | {
"A": "21760.875 μJ",
"B": "29013.5 μJ",
"C": "58029 μJ",
"D": "29014.5 μJ"
} | D | 29014.5 μJ | U=½CV². Since C=69 μF, U in μJ is ½×69×(29)²=29014.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 29014.5 μJ, not 21760.875 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 29014.5 μJ, not 29013.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2901... | [
"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_004201 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 36 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": "112.32 N",
"B": "114.32 N",
"C": "84.24 N",
"D": "-112.32 N"
} | A | 112.32 N | Net force=mg(sinθ−μcosθ)=36×10×(0.6−0.36×0.8)=112.32 N. | {
"A": "Correct. The worked calculation gives 112.32 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 112.32 N, not 114.32 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 112.32 N, not 84.24 N.",
"D": "Incorrect. Substituting the state... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001523 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (-2x² +5x -2) dx. | {
"A": "-7.66667",
"B": "-16",
"C": "-10.66667",
"D": "-9.66667"
} | C | -10.66667 | An antiderivative is (-2/3)x³+(5/2)x²+(-2)x. Evaluating between 0 and 4 gives (-2/3)(4)³+(5/2)(4)²+(-2)(4)=-10.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -10.66667, not -7.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -10.66667, not -16.",
"C": "Correct. The worked calculation gives -10.66667.",
"D": "Incorrect. Substituting the stated... | [
"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_008827 | 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 1.2 mol L⁻¹ and initially B is absent. At equilibrium, 79% of A has dissociated at constant volume. Find K_c. | {
"A": "-14.26514",
"B": "10.69886",
"C": "14.26514",
"D": "17.26514"
} | C | 14.26514 | Let α=0.79. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.2)(0.79)²/(1−0.79)=14.26514. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14.26514, not -14.26514.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14.26514, not 10.69886.",
"C": "Correct. The worked calculation gives 14.26514.",
"D": "Incorrect. Substituting the sta... | [
"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_008793 | 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 1.07 mol L⁻¹ and initially B is absent. At equilibrium, 60% of A has dissociated at constant volume. Find K_c. | {
"A": "6.852",
"B": "7.704",
"C": "0.852",
"D": "3.852"
} | D | 3.852 | Let α=0.6. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.07)(0.6)²/(1−0.6)=3.852. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.852, not 6.852.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.852, not 7.704.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.852, not 0.852.",
"D":... | [
"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_006585 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 16 kg is attached to an ideal spring of force constant 795 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.71627 s",
"B": "0.28373 s",
"C": "-1.71627 s",
"D": "0.2128 s"
} | B | 0.28373 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(16/795)=0.28373 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.28373 s, not -0.71627 s.",
"B": "Correct. The worked calculation gives 0.28373 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.28373 s, not -1.71627 s.",
"D": "Incorrect. Substituting t... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005078 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +1 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "9.18367 N",
"B": "11.18367 N",
"C": "10.18367 N",
"D": "12.18367 N"
} | A | 9.18367 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(1×10⁻⁶)/(7×10⁻²)²=9.18367 N. | {
"A": "Correct. The worked calculation gives 9.18367 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.18367 N, not 11.18367 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.18367 N, not 10.18367 N.",
"D": "Incorrect. Substituting t... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006023 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 60 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": "-2.57143",
"B": "0.42857",
"C": "0.64286",
"D": "-1.57143"
} | B | 0.42857 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(60)(18)/(60−18)=25.71429 cm. Thus |m|=v/u=25.71429/60=0.42857. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.42857, not -2.57143.",
"B": "Correct. The worked calculation gives 0.42857.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.42857, not 0.64286.",
"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_002424 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 7], [4, -8]]. | {
"A": "-45",
"B": "-60",
"C": "-90",
"D": "-58"
} | B | -60 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(-8)−(7)(4)=-60. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -60, not -45.",
"B": "Correct. The worked calculation gives -60.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -60, not -90.",
"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_008376 | 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 0.99 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.98 K",
"B": "4.98 K",
"C": "2.97 K",
"D": "1.98 K"
} | D | 1.98 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×0.99=1.98 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.98 K, not 0.98 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.98 K, not 4.98 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.98 K, not 2.97 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_001789 | 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 90 distinct elements? | {
"A": "5720645481902",
"B": "5720645481903",
"C": "4576516385522.40039",
"D": "5720645481905"
} | B | 5720645481903 | Order does not matter, so the count is C(90,10)=90!/[10!(80)!]=5720645481903. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5720645481903, not 5720645481902.",
"B": "Correct. The worked calculation gives 5720645481903.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5720645481903, not 4576516385522.40039.",
"D": "I... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007615 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 91 mL of 0.10 M HCl is mixed with 67 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.81845",
"B": "1.81845",
"C": "-1.81845",
"D": "2.72767"
} | B | 1.81845 | Excess H⁺ moles=0.10×(91−67)/1000=0.002400 mol. Total volume=0.158 L, so [H⁺]=0.015190 M and pH=−log₁₀[H⁺]=1.81845. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.81845, not 2.81845.",
"B": "Correct. The worked calculation gives 1.81845.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.81845, not -1.81845.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003583 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 88 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1186.44963 m",
"B": "296.61241 m",
"C": "593.22482 m",
"D": "474.57985 m"
} | C | 593.22482 m | Range R=u²sin(2θ)/g. Substituting u=88, θ=25° and g=10 gives R=(88)²sin(50°)/10=593.22482 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 593.22482 m, not 1186.44963 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 593.22482 m, not 296.61241 m.",
"C": "Correct. The worked calculation gives 593.22482 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_009534 | 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_14N_3X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "-3",
"C": "1",
"D": "0"
} | D | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+3−14−3)/2=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"D": "Correct. The worked c... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006649 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 16 kg is attached to an ideal spring of force constant 410 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.19755 s",
"B": "0.39509 s",
"C": "-0.60491 s",
"D": "-1.60491 s"
} | B | 0.39509 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(16/410)=0.39509 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.39509 s, not 0.19755 s.",
"B": "Correct. The worked calculation gives 0.39509 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.39509 s, not -0.60491 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007936 | 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 69 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "41.4 mmol L⁻¹",
"B": "34.5 mmol L⁻¹",
"C": "51.75 mmol L⁻¹",
"D": "69 mmol L⁻¹"
} | B | 34.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=69/2^1=34.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 34.5 mmol L⁻¹, not 41.4 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 34.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 34.5 mmol L⁻¹, not 51.75 mmol L⁻¹.",
"D": "Incorr... | [
"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_009560 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_12H_7N_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "7.5",
"B": "2",
"C": "10",
"D": "7"
} | C | 10 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×12+2+1−7−0)/2=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 7.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 2.",
"C": "Correct. The worked calculation gives 10.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_008702 | 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 1.14 mol L⁻¹ and initially B is absent. At equilibrium, 44% of A has dissociated at constant volume. Find K_c. | {
"A": "4.57646",
"B": "1.57646",
"C": "1.15765",
"D": "0.78823"
} | B | 1.57646 | Let α=0.44. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.14)(0.44)²/(1−0.44)=1.57646. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.57646, not 4.57646.",
"B": "Correct. The worked calculation gives 1.57646.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.57646, not 1.15765.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002976 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-7, -2, 4) and v=(2, -4, 7), calculate u·v. | {
"A": "23",
"B": "22",
"C": "44",
"D": "33"
} | B | 22 | The dot product is the sum of corresponding component products: (-7)(2)+(-2)(-4)+(4)(7)=22. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22, not 23.",
"B": "Correct. The worked calculation gives 22.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22, not 44.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007526 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 76 mL of 0.10 M HCl is mixed with 76 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "5.25",
"B": "7",
"C": "9",
"D": "6"
} | B | 7 | Equal moles of strong acid and base are present. They neutralize completely, so at 25°C pH=7.00. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 5.25.",
"B": "Correct. The worked calculation gives 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 9.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007356 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 56 mL of 0.10 M HCl is mixed with 97 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.42809",
"B": "10.42809",
"C": "9.42809",
"D": "11.42809"
} | A | 12.42809 | Excess OH⁻ moles=0.10×(97−56)/1000=0.004100 mol. Total volume=0.153 L, so [OH⁻]=0.026797 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.42809. | {
"A": "Correct. The worked calculation gives 12.42809.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.42809, not 10.42809.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.42809, not 9.42809.",
"D": "Incorrect. Substituting the state... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004471 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 1 m is acted on by a constant torque of 31 N m about its central axis. Find its angular acceleration. | {
"A": "24.8 rad s⁻²",
"B": "31 rad s⁻²",
"C": "37.2 rad s⁻²",
"D": "4.1 rad s⁻²"
} | B | 31 rad s⁻² | For a solid disc, I=½MR²=½(2)(1)²=1 kg m². Using τ=Iα, α=31/1=31 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 31 rad s⁻², not 24.8 rad s⁻².",
"B": "Correct. The worked calculation gives 31 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 31 rad s⁻², not 37.2 rad s⁻².",
"D": "Incorrect. Substit... | [
"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_003012 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(10-9i)/(8+10i). What is Re(z), the real part of z? | {
"A": "0.9939",
"B": "-0.04573",
"C": "1.93902",
"D": "-0.06098"
} | D | -0.06098 | Multiply numerator and denominator by the conjugate (8-10i). Then Re(z)=(ac+bd)/(c²+d²)=((10)(8)+(-9)(10))/(8²+(10)²)=-0.06098. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.06098, not 0.9939.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.06098, not -0.04573.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.06098, not 1.... | [
"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_006778 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 36 mol H₂ and 20 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "38 mol",
"B": "27 mol",
"C": "34 mol",
"D": "36 mol"
} | D | 36 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 36 mol H₂O; O₂ can produce 40 mol H₂O. The limiting condition is H₂; product=36 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 36 mol, not 38 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 36 mol, not 27 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 36 mol, not 34 mol.",
... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006988 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 30 mol H₂ and 30 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "45 mol",
"B": "30 mol",
"C": "60 mol",
"D": "31 mol"
} | B | 30 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 30 mol H₂O; O₂ can produce 60 mol H₂O. The limiting condition is H₂; product=30 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 30 mol, not 45 mol.",
"B": "Correct. The worked calculation gives 30 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30 mol, not 60 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004919 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 12 Ω are connected in series; this combination is connected in parallel with a 6 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.75 A",
"B": "1.375 A",
"C": "1.03125 A",
"D": "0.375 A"
} | B | 1.375 A | Series branch resistance=4+12=16 Ω. Parallel equivalent R_eq=(16×6)/(16+6)=4.36364 Ω. Total current I=V/R_eq=6/4.36364=1.375 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.375 A, not 2.75 A.",
"B": "Correct. The worked calculation gives 1.375 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.375 A, not 1.03125 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_007414 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 18 mL of 0.10 M HCl is mixed with 68 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-12.76447",
"B": "14.76447",
"C": "9.57335",
"D": "12.76447"
} | D | 12.76447 | Excess OH⁻ moles=0.10×(68−18)/1000=0.005000 mol. Total volume=0.086 L, so [OH⁻]=0.058140 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.76447. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.76447, not -12.76447.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.76447, not 14.76447.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.76447, not... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003627 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 74 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "314.61445 m",
"B": "629.22891 m",
"C": "419.48594 m",
"D": "838.97187 m"
} | C | 419.48594 m | Range R=u²sin(2θ)/g. Substituting u=74, θ=25° and g=10 gives R=(74)²sin(50°)/10=419.48594 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 419.48594 m, not 314.61445 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 419.48594 m, not 629.22891 m.",
"C": "Correct. The worked calculation gives 419.48594 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005335 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +3 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "72 N",
"B": "180 N",
"C": "67.5 N",
"D": "90 N"
} | D | 90 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(3×10⁻⁶)/(3×10⁻²)²=90 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 90 N, not 72 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 90 N, not 180 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 90 N, not 67.5 N.",
"D": "C... | [
"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_006648 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 10 kg is attached to an ideal spring of force constant 56 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "2.84515 s",
"B": "-1.15485 s",
"C": "0.84515 s",
"D": "3.84515 s"
} | C | 0.84515 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(10/56)=0.84515 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.84515 s, not 2.84515 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.84515 s, not -1.15485 s.",
"C": "Correct. The worked calculation gives 0.84515 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005900 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.2 atm at 413 K. What is its pressure at 582 K? | {
"A": "6.10024 atm",
"B": "1.10024 atm",
"C": "0.10024 atm",
"D": "3.10024 atm"
} | D | 3.10024 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.2)(582)/(413)=3.10024 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.10024 atm, not 6.10024 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.10024 atm, not 1.10024 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.... | [
"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_008840 | 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 1.15 mol L⁻¹ and initially B is absent. At equilibrium, 55% of A has dissociated at constant volume. Find K_c. | {
"A": "2.09222",
"B": "-3.09222",
"C": "3.09222",
"D": "4.63833"
} | C | 3.09222 | Let α=0.55. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.15)(0.55)²/(1−0.55)=3.09222. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.09222, not 2.09222.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.09222, not -3.09222.",
"C": "Correct. The worked calculation gives 3.09222.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007700 | 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 63 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "2.49219 mmol L⁻¹",
"B": "0.49219 mmol L⁻¹",
"C": "0.24609 mmol L⁻¹",
"D": "1.49219 mmol L⁻¹"
} | B | 0.49219 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=63/2^7=0.49219 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.49219 mmol L⁻¹, not 2.49219 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.49219 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.49219 mmol L⁻¹, not 0.24609 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_003671 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 68 m s⁻¹ at 15° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "277.44 m",
"B": "173.4 m",
"C": "346.8 m",
"D": "231.2 m"
} | D | 231.2 m | Range R=u²sin(2θ)/g. Substituting u=68, θ=15° and g=10 gives R=(68)²sin(30°)/10=231.2 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 231.2 m, not 277.44 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 231.2 m, not 173.4 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 231.2 m, not 346.... | [
"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_008569 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.92 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "7.68 K",
"B": "5.76 K",
"C": "4.68 K",
"D": "15.36 K"
} | A | 7.68 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×1.0×1.92=7.68 K. | {
"A": "Correct. The worked calculation gives 7.68 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.68 K, not 5.76 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.68 K, not 4.68 K.",
"D": "Incorrect. Substituting the stated values ... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004618 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 4 kg and radius 2 m is acted on by a constant torque of 51 N m about its central axis. Find its angular acceleration. | {
"A": "6.375 rad s⁻²",
"B": "3.1875 rad s⁻²",
"C": "9.375 rad s⁻²",
"D": "12.75 rad s⁻²"
} | A | 6.375 rad s⁻² | For a solid disc, I=½MR²=½(4)(2)²=8 kg m². Using τ=Iα, α=51/8=6.375 rad s⁻². | {
"A": "Correct. The worked calculation gives 6.375 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.375 rad s⁻², not 3.1875 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.375 rad s⁻², not 9.375 rad s⁻².",
"D": "Incorr... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005137 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +4 μC are separated by 5 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "144 N",
"B": "54 N",
"C": "57.6 N",
"D": "72 N"
} | D | 72 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(4×10⁻⁶)/(5×10⁻²)²=72 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 72 N, not 144 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 72 N, not 54 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 72 N, not 57.6 N.",
"D": "C... | [
"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_008014 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 14 A for 28246 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": "195.16083 g",
"B": "65.05361 g",
"C": "14.01072 g",
"D": "130.10722 g"
} | D | 130.10722 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×28246/(2×96500)=130.10722 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 130.10722 g, not 195.16083 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 130.10722 g, not 65.05361 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 130... | [
"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_004599 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 15 kg and radius 3 m is acted on by a constant torque of 20 N m about its central axis. Find its angular acceleration. | {
"A": "0.14815 rad s⁻²",
"B": "0.2963 rad s⁻²",
"C": "-1.7037 rad s⁻²",
"D": "0.59259 rad s⁻²"
} | B | 0.2963 rad s⁻² | For a solid disc, I=½MR²=½(15)(3)²=67.5 kg m². Using τ=Iα, α=20/67.5=0.2963 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.2963 rad s⁻², not 0.14815 rad s⁻².",
"B": "Correct. The worked calculation gives 0.2963 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.2963 rad s⁻², not -1.7037 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_004864 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 5 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 19 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.77733 A",
"B": "0.77733 A",
"C": "2.77733 A",
"D": "1.77733 A"
} | B | 0.77733 A | Series branch resistance=5+8=13 Ω. Parallel equivalent R_eq=(13×19)/(13+19)=7.71875 Ω. Total current I=V/R_eq=6/7.71875=0.77733 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.77733 A, not 3.77733 A.",
"B": "Correct. The worked calculation gives 0.77733 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.77733 A, not 2.77733 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_005590 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 29 μF capacitor is charged to a potential difference of 33 V. Calculate the energy stored, expressed in μJ. | {
"A": "7895.25 μJ",
"B": "15790.5 μJ",
"C": "31581 μJ",
"D": "15788.5 μJ"
} | B | 15790.5 μJ | U=½CV². Since C=29 μF, U in μJ is ½×29×(33)²=15790.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15790.5 μJ, not 7895.25 μJ.",
"B": "Correct. The worked calculation gives 15790.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15790.5 μJ, not 31581 μJ.",
"D": "Incorrect. Substituting ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004774 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 3 Ω are connected in series; this combination is connected in parallel with a 15 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.1625 A",
"B": "2.325 A",
"C": "3.4875 A",
"D": "4.65 A"
} | B | 2.325 A | Series branch resistance=13+3=16 Ω. Parallel equivalent R_eq=(16×15)/(16+15)=7.74194 Ω. Total current I=V/R_eq=18/7.74194=2.325 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.325 A, not 1.1625 A.",
"B": "Correct. The worked calculation gives 2.325 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.325 A, not 3.4875 A.",
"D": "Incorrect. Substituting the stated ... | [
"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_005187 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +9 μC are separated by 5 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "32.4 N",
"B": "31.4 N",
"C": "-32.4 N",
"D": "33.4 N"
} | A | 32.4 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(9×10⁻⁶)/(5×10⁻²)²=32.4 N. | {
"A": "Correct. The worked calculation gives 32.4 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 32.4 N, not 31.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 32.4 N, not -32.4 N.",
"D": "Incorrect. Substituting the stated values... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009810 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(Cl)_4]^-1, each Cl ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "6",
"B": "4.5",
"C": "5",
"D": "3"
} | D | 3 | Let the formal oxidation state of Pt be x. Charge balance gives x+(4)(−1)=-1; hence x=-1+4=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 5.",
"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_000822 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 3 and common ratio 3. What is the sum of its first 11 terms? | {
"A": "212575.2",
"B": "265721",
"C": "265719",
"D": "265718"
} | C | 265719 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=3(3^11−1)/(3−1)=265719. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 265719, not 212575.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 265719, not 265721.",
"C": "Correct. The worked calculation gives 265719.",
"D": "Incorrect. Substituting the stated value... | [
"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_008533 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.23 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-2.51904 K",
"B": "2.51904 K",
"C": "4.51904 K",
"D": "1.88928 K"
} | B | 2.51904 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.512×1.23=2.51904 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.51904 K, not -2.51904 K.",
"B": "Correct. The worked calculation gives 2.51904 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.51904 K, not 4.51904 K.",
"D": "Incorrect. Substituting th... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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