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_000978 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 6 and common ratio 5. What is the sum of its first 10 terms? | {
"A": "1464844.6",
"B": "14648435",
"C": "21972654",
"D": "14648436"
} | D | 14648436 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=6(5^10−1)/(5−1)=14648436. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14648436, not 1464844.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14648436, not 14648435.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14648436, not... | [
"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_006291 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 27 cm in front of a thin convex lens of focal length 12 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.8",
"B": "-1.2",
"C": "0.8",
"D": "-2.2"
} | C | 0.8 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(27)(12)/(27−12)=21.6 cm. Thus |m|=v/u=21.6/27=0.8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8, not -0.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8, not -1.2.",
"C": "Correct. The worked calculation gives 0.8.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_003062 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-13+5i)/(11+6i). What is Re(z), the real part of z? | {
"A": "-0.71975",
"B": "0.28025",
"C": "-1.71975",
"D": "-0.53981"
} | A | -0.71975 | Multiply numerator and denominator by the conjugate (11-6i). Then Re(z)=(ac+bd)/(c²+d²)=((-13)(11)+(5)(6))/(11²+(6)²)=-0.71975. | {
"A": "Correct. The worked calculation gives -0.71975.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.71975, not 0.28025.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.71975, not -1.71975.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003983 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block initially moves at 7 m s⁻¹. A constant net force does 20 N of work over 13 m in the direction of motion. Find its final kinetic energy. | {
"A": "405 J",
"B": "305.25 J",
"C": "407 J",
"D": "409 J"
} | C | 407 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(6)(7)²+(20)(13)=407 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 407 J, not 405 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 407 J, not 305.25 J.",
"C": "Correct. The worked calculation gives 407 J.",
"D": "Incorrect. Substituting the stated values in... | [
"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_009703 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(Cl)_6]^+0, each Cl ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "5",
"B": "3",
"C": "7",
"D": "6"
} | D | 6 | Let the formal oxidation state of Cr be x. Charge balance gives x+(6)(−1)=+0; hence x=0+6=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 7.",
"D": "Correct. The worked ca... | [
"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_008424 | 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 1.89 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": "7.56 K",
"B": "5.78 K",
"C": "3.78 K",
"D": "1.89 K"
} | C | 3.78 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×1.89=3.78 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.78 K, not 7.56 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.78 K, not 5.78 K.",
"C": "Correct. The worked calculation gives 3.78 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_002501 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, -3], [8, 0]]. | {
"A": "36",
"B": "18",
"C": "24",
"D": "26"
} | C | 24 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(0)−(-3)(8)=24. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24, not 36.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24, not 18.",
"C": "Correct. The worked calculation gives 24.",
"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_009821 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(CN)_2]^+0, each CN ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "-2",
"B": "2",
"C": "5",
"D": "1"
} | B | 2 | Let the formal oxidation state of Mn be x. Charge balance gives x+(2)(−1)=+0; hence x=0+2=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 5.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007651 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 71 mL of 0.10 M HCl is mixed with 21 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-1.73518",
"B": "2.26482",
"C": "1.26482",
"D": "0.26482"
} | C | 1.26482 | Excess H⁺ moles=0.10×(71−21)/1000=0.005000 mol. Total volume=0.092 L, so [H⁺]=0.054348 M and pH=−log₁₀[H⁺]=1.26482. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.26482, not -1.73518.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.26482, not 2.26482.",
"C": "Correct. The worked calculation gives 1.26482.",
"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_004113 | 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 0.22. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "31.8 N",
"B": "76.32 N",
"C": "47.7 N",
"D": "63.6 N"
} | D | 63.6 N | Net force=mg(sinθ−μcosθ)=15×10×(0.6−0.22×0.8)=63.6 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 63.6 N, not 31.8 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 63.6 N, not 76.32 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 63.6 N, not 47.7 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_001714 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 3 elements can be selected from a set of 17 distinct elements? | {
"A": "544",
"B": "-680",
"C": "680",
"D": "679"
} | C | 680 | Order does not matter, so the count is C(17,3)=17!/[3!(14)!]=680. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 680, not 544.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 680, not -680.",
"C": "Correct. The worked calculation gives 680.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_001266 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ -7x² -10x+7. Evaluate f′(-4). | {
"A": "-109.5",
"B": "-146",
"C": "-292",
"D": "-73"
} | B | -146 | Differentiate: f′(x)=3(-4)x²+2(-7)x+(-10). At x=-4, f′(-4)=3(-4)(-4)²+2(-7)(-4)+(-10)=-146. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -146, not -109.5.",
"B": "Correct. The worked calculation gives -146.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -146, not -292.",
"D": "Incorrect. Substituting the stated values into the... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007584 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 39 mL of 0.10 M HCl is mixed with 72 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "15.47319",
"B": "10.47319",
"C": "9.47319",
"D": "12.47319"
} | D | 12.47319 | Excess OH⁻ moles=0.10×(72−39)/1000=0.003300 mol. Total volume=0.111 L, so [OH⁻]=0.029730 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.47319. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.47319, not 15.47319.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.47319, not 10.47319.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.47319, 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_005256 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +3 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "-24.3 N",
"B": "22.3 N",
"C": "24.3 N",
"D": "36.45 N"
} | C | 24.3 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(3×10⁻⁶)/(10×10⁻²)²=24.3 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24.3 N, not -24.3 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24.3 N, not 22.3 N.",
"C": "Correct. The worked calculation gives 24.3 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_009180 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.33 V, transfers 2 electrons, and has reaction quotient Q=10^0. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.33 V",
"B": "1.33 V",
"C": "3.33 V",
"D": "0.665 V"
} | B | 1.33 V | Apply the Nernst equation: E=1.33−(0.0591/2)(0)=1.33 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.33 V, not -1.33 V.",
"B": "Correct. The worked calculation gives 1.33 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.33 V, not 3.33 V.",
"D": "Incorrect. Substituting the stated values... | [
"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_009299 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.44 V, transfers 1 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.0854 V",
"B": "4.0854 V",
"C": "0.81405 V",
"D": "0.0854 V"
} | A | 1.0854 V | Apply the Nernst equation: E=1.44−(0.0591/1)(6)=1.0854 V. | {
"A": "Correct. The worked calculation gives 1.0854 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0854 V, not 4.0854 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0854 V, not 0.81405 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_008874 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.66 mol L⁻¹ and initially B is absent. At equilibrium, 18% of A has dissociated at constant volume. Find K_c. | {
"A": "0.20862",
"B": "0.10431",
"C": "0.05216",
"D": "-1.89569"
} | B | 0.10431 | Let α=0.18. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.66)(0.18)²/(1−0.18)=0.10431. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.10431, not 0.20862.",
"B": "Correct. The worked calculation gives 0.10431.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.10431, not 0.05216.",
"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_009083 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.01 V, transfers 3 electrons, and has reaction quotient Q=10^1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.9903 V",
"B": "2.9903 V",
"C": "0.9903 V",
"D": "3.9903 V"
} | C | 0.9903 V | Apply the Nernst equation: E=1.01−(0.0591/3)(1)=0.9903 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9903 V, not -0.9903 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9903 V, not 2.9903 V.",
"C": "Correct. The worked calculation gives 0.9903 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_002577 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, 1], [6, -6]]. | {
"A": "48",
"B": "-24",
"C": "-57.6",
"D": "-48"
} | D | -48 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(-6)−(1)(6)=-48. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -48, not 48.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -48, not -24.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -48, not -57.6.",
"D": "Correct. ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007617 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 47 mL of 0.10 M HCl is mixed with 37 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "4.92428",
"B": "1.19243",
"C": "2.88642",
"D": "1.92428"
} | D | 1.92428 | Excess H⁺ moles=0.10×(47−37)/1000=0.001000 mol. Total volume=0.084 L, so [H⁺]=0.011905 M and pH=−log₁₀[H⁺]=1.92428. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.92428, not 4.92428.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.92428, not 1.19243.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.92428, not 2.886... | [
"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_006080 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 100 cm in front of a thin convex lens of focal length 22 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.28205",
"B": "-0.71795",
"C": "1.02821",
"D": "1.28205"
} | A | 0.28205 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(100)(22)/(100−22)=28.20513 cm. Thus |m|=v/u=28.20513/100=0.28205. | {
"A": "Correct. The worked calculation gives 0.28205.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.28205, not -0.71795.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.28205, not 1.02821.",
"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_002640 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -5], [2, -7]]. | {
"A": "-24",
"B": "-27",
"C": "-25",
"D": "25"
} | C | -25 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(-7)−(-5)(2)=-25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -25, not -24.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -25, not -27.",
"C": "Correct. The worked calculation gives -25.",
"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_007038 | 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 526 K and 0.36 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "809.28716 L",
"B": "863.23964 L",
"C": "1078.04955 L",
"D": "1079.04955 L"
} | D | 1079.04955 L | PV=nRT, so V=nRT/P=(9)(0.082057)(526)/(0.36)=1079.04955 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1079.04955 L, not 809.28716 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1079.04955 L, not 863.23964 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives ... | [
"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_003740 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 12 m s⁻¹. A constant net force does 12 N of work over 6 m in the direction of motion. Find its final kinetic energy. | {
"A": "360 J",
"B": "432 J",
"C": "37 J",
"D": "361 J"
} | A | 360 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(12)²+(12)(6)=360 J. | {
"A": "Correct. The worked calculation gives 360 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 360 J, not 432 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 360 J, not 37 J.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_001099 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=2x³ -10x² +5x+7. Evaluate f′(-2). | {
"A": "103.5",
"B": "71",
"C": "70",
"D": "69"
} | D | 69 | Differentiate: f′(x)=3(2)x²+2(-10)x+(5). At x=-2, f′(-2)=3(2)(-2)²+2(-10)(-2)+(5)=69. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 69, not 103.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 69, not 71.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 69, not 70.",
"D": "Correct. The ... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001787 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 7 elements can be selected from a set of 64 distinct elements? | {
"A": "621216193",
"B": "621216192",
"C": "745459430.4",
"D": "621216194"
} | B | 621216192 | Order does not matter, so the count is C(64,7)=64!/[7!(57)!]=621216192. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 621216192, not 621216193.",
"B": "Correct. The worked calculation gives 621216192.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 621216192, not 745459430.4.",
"D": "Incorrect. Substituting t... | [
"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_007426 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 54 mL of 0.10 M HCl is mixed with 84 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.33724",
"B": "15.33724",
"C": "10.33724",
"D": "2.23372"
} | A | 12.33724 | Excess OH⁻ moles=0.10×(84−54)/1000=0.003000 mol. Total volume=0.138 L, so [OH⁻]=0.021739 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.33724. | {
"A": "Correct. The worked calculation gives 12.33724.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.33724, not 15.33724.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.33724, not 10.33724.",
"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_009291 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.12 V, transfers 1 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.4746 V",
"B": "0.7373 V",
"C": "4.4746 V",
"D": "2.4746 V"
} | A | 1.4746 V | Apply the Nernst equation: E=1.12−(0.0591/1)(-6)=1.4746 V. | {
"A": "Correct. The worked calculation gives 1.4746 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4746 V, not 0.7373 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.4746 V, not 4.4746 V.",
"D": "Incorrect. Substituting the stat... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004843 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 3 Ω and 5 Ω are connected in series; this combination is connected in parallel with a 10 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "12.15 A",
"B": "1.81 A",
"C": "8.1 A",
"D": "5.1 A"
} | C | 8.1 A | Series branch resistance=3+5=8 Ω. Parallel equivalent R_eq=(8×10)/(8+10)=4.44444 Ω. Total current I=V/R_eq=36/4.44444=8.1 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.1 A, not 12.15 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.1 A, not 1.81 A.",
"C": "Correct. The worked calculation gives 8.1 A.",
"D": "Incorrect. Substituting the stated values in... | [
"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_003709 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 3 m s⁻¹. A constant net force does 17 N of work over 5 m in the direction of motion. Find its final kinetic energy. | {
"A": "115.5 J",
"B": "12.65 J",
"C": "93.2 J",
"D": "116.5 J"
} | D | 116.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(3)²+(17)(5)=116.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 116.5 J, not 115.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 116.5 J, not 12.65 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 116.5 J, not 93.2 ... | [
"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_009733 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(Cl)_3]^+1, each Cl ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "4",
"B": "-4",
"C": "8",
"D": "5"
} | A | 4 | Let the formal oxidation state of Mn be x. Charge balance gives x+(3)(−1)=+1; hence x=1+3=+4. | {
"A": "Correct. The worked calculation gives 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not -4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 8.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002084 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 10 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.53",
"B": "0.35333",
"C": "-2.64667",
"D": "-1.64667"
} | B | 0.35333 | Favourable pairs = C(4,2)+C(10,2)+C(11,2)=106. Total pairs=C(25,2)=300. Therefore P=106/300=0.35333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35333, not 0.53.",
"B": "Correct. The worked calculation gives 0.35333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35333, not -2.64667.",
"D": "Incorrect. Substituting the stated valu... | [
"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_004883 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 11 Ω and 2 Ω are connected in series; this combination is connected in parallel with a 5 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "8.64615 A",
"B": "3.64615 A",
"C": "6.64615 A",
"D": "13.29231 A"
} | C | 6.64615 A | Series branch resistance=11+2=13 Ω. Parallel equivalent R_eq=(13×5)/(13+5)=3.61111 Ω. Total current I=V/R_eq=24/3.61111=6.64615 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.64615 A, not 8.64615 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.64615 A, not 3.64615 A.",
"C": "Correct. The worked calculation gives 6.64615 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_005939 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.2 atm at 249 K. What is its pressure at 605 K? | {
"A": "0.48594 atm",
"B": "3.48594 atm",
"C": "-2.51406 atm",
"D": "0.72892 atm"
} | A | 0.48594 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.2)(605)/(249)=0.48594 atm. | {
"A": "Correct. The worked calculation gives 0.48594 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.48594 atm, not 3.48594 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.48594 atm, not -2.51406 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005469 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 56 μF capacitor is charged to a potential difference of 30 V. Calculate the energy stored, expressed in μJ. | {
"A": "25200 μJ",
"B": "50400 μJ",
"C": "12600 μJ",
"D": "2521 μJ"
} | A | 25200 μJ | U=½CV². Since C=56 μF, U in μJ is ½×56×(30)²=25200 μJ. | {
"A": "Correct. The worked calculation gives 25200 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 25200 μJ, not 50400 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 25200 μJ, not 12600 μJ.",
"D": "Incorrect. Substituting the stat... | [
"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_001180 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ -7x² +9x+7. Evaluate f′(-3). | {
"A": "-82",
"B": "-83",
"C": "-63",
"D": "-84"
} | D | -84 | Differentiate: f′(x)=3(-5)x²+2(-7)x+(9). At x=-3, f′(-3)=3(-5)(-3)²+2(-7)(-3)+(9)=-84. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -84, not -82.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -84, not -83.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -84, not -63.",
"D": "Correct. T... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001382 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (1x² +6x +1) dx. | {
"A": "296.53333",
"B": "368.66667",
"C": "370.66667",
"D": "-370.66667"
} | C | 370.66667 | An antiderivative is (1/3)x³+(6/2)x²+(1)x. Evaluating between 0 and 8 gives (1/3)(8)³+(6/2)(8)²+(1)(8)=370.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 370.66667, not 296.53333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 370.66667, not 368.66667.",
"C": "Correct. The worked calculation gives 370.66667.",
"D": "Incorrect. Substituting the... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008646 | 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 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "2.9936 K",
"B": "2.9952 K",
"C": "3.9936 K",
"D": "1.9968 K"
} | C | 3.9936 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.52×1.92=3.9936 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.9936 K, not 2.9936 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.9936 K, not 2.9952 K.",
"C": "Correct. The worked calculation gives 3.9936 K.",
"D": "Incorrect. Substituting the stat... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006867 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 34 mol H₂ and 33 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "36 mol",
"B": "34 mol",
"C": "35 mol",
"D": "33 mol"
} | B | 34 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 34 mol H₂O; O₂ can produce 66 mol H₂O. The limiting condition is H₂; product=34 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 34 mol, not 36 mol.",
"B": "Correct. The worked calculation gives 34 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 34 mol, not 35 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_000074 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +3x +10=0, let its roots be α and β. What is α²+β²? | {
"A": "-4.25",
"B": "0.43333",
"C": "-7.66667",
"D": "-5.66667"
} | D | -5.66667 | By Vieta's relations, α+β = -3/3 and αβ = 10/3. Then α²+β²=(α+β)²−2αβ = (-3/3)²−2(10/3) = -5.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -5.66667, not -4.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -5.66667, not 0.43333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -5.66667, not -7.6... | [
"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_009019 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.45 V, transfers 2 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.6636 V",
"B": "1.3318 V",
"C": "-1.6682 V",
"D": "-0.6682 V"
} | B | 1.3318 V | Apply the Nernst equation: E=1.45−(0.0591/2)(4)=1.3318 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.3318 V, not 2.6636 V.",
"B": "Correct. The worked calculation gives 1.3318 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.3318 V, not -1.6682 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_006476 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 11 kg is attached to an ideal spring of force constant 739 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.36601 s",
"B": "0.24401 s",
"C": "1.24401 s",
"D": "-0.75599 s"
} | B | 0.24401 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(11/739)=0.24401 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.24401 s, not 0.36601 s.",
"B": "Correct. The worked calculation gives 0.24401 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.24401 s, not 1.24401 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007894 | 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 82 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "10.25 mmol L⁻¹",
"B": "11.25 mmol L⁻¹",
"C": "20.5 mmol L⁻¹",
"D": "5.125 mmol L⁻¹"
} | A | 10.25 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=82/2^3=10.25 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 10.25 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.25 mmol L⁻¹, not 11.25 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10.25 mmol L⁻¹, not 20.5 mmol L⁻¹.",
"D": "Inc... | [
"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_004637 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 12 kg and radius 2 m is acted on by a constant torque of 94 N m about its central axis. Find its angular acceleration. | {
"A": "5.875 rad s⁻²",
"B": "3.91667 rad s⁻²",
"C": "1.95833 rad s⁻²",
"D": "1.39167 rad s⁻²"
} | B | 3.91667 rad s⁻² | For a solid disc, I=½MR²=½(12)(2)²=24 kg m². Using τ=Iα, α=94/24=3.91667 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.91667 rad s⁻², not 5.875 rad s⁻².",
"B": "Correct. The worked calculation gives 3.91667 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.91667 rad s⁻², not 1.95833 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_004516 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 15 kg and radius 2 m is acted on by a constant torque of 74 N m about its central axis. Find its angular acceleration. | {
"A": "4.46667 rad s⁻²",
"B": "-2.46667 rad s⁻²",
"C": "1.24667 rad s⁻²",
"D": "2.46667 rad s⁻²"
} | D | 2.46667 rad s⁻² | For a solid disc, I=½MR²=½(15)(2)²=30 kg m². Using τ=Iα, α=74/30=2.46667 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.46667 rad s⁻², not 4.46667 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.46667 rad s⁻², not -2.46667 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing ... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000895 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio -3. What is the sum of its first 8 terms? | {
"A": "-3280",
"B": "-5248",
"C": "-6561",
"D": "-6560"
} | D | -6560 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(-3^8−1)/(-3−1)=-6560. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -6560, not -3280.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -6560, not -5248.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -6560, not -6561.",
"D":... | [
"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_003826 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block initially moves at 11 m s⁻¹. A constant net force does 22 N of work over 10 m in the direction of motion. Find its final kinetic energy. | {
"A": "1069 J",
"B": "1067 J",
"C": "1600.5 J",
"D": "853.6 J"
} | B | 1067 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(14)(11)²+(22)(10)=1067 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1067 J, not 1069 J.",
"B": "Correct. The worked calculation gives 1067 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1067 J, not 1600.5 J.",
"D": "Incorrect. Substituting the stated value... | [
"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_008377 | 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 0.9 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.4608 K",
"B": "-2.5392 K",
"C": "0.3456 K",
"D": "-0.5392 K"
} | A | 0.4608 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.512×0.9=0.4608 K. | {
"A": "Correct. The worked calculation gives 0.4608 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.4608 K, not -2.5392 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.4608 K, not 0.3456 K.",
"D": "Incorrect. Substituting the sta... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000352 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -6 and common difference 3. Find the sum of its first 25 terms. | {
"A": "752",
"B": "751",
"C": "900",
"D": "750"
} | D | 750 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-6, d=3, n=25: Sₙ=25/2[2(-6)+(25−1)(3)]=750. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 750, not 752.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 750, not 751.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 750, not 900.",
"D": "Correct. T... | [
"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_004750 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 6 Ω and 15 Ω are connected in series; this combination is connected in parallel with a 10 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.98571 A",
"B": "2.65714 A",
"C": "4.65714 A",
"D": "1.26571 A"
} | B | 2.65714 A | Series branch resistance=6+15=21 Ω. Parallel equivalent R_eq=(21×10)/(21+10)=6.77419 Ω. Total current I=V/R_eq=18/6.77419=2.65714 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.65714 A, not 3.98571 A.",
"B": "Correct. The worked calculation gives 2.65714 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.65714 A, not 4.65714 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_009370 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_3H_8N_1X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "1",
"B": "-2",
"C": "-1",
"D": "0"
} | D | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×3+2+1−8−1)/2=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not -1.",
"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_003343 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 78 m s⁻¹ at 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "599.15704 m",
"B": "1198.31407 m",
"C": "600.15704 m",
"D": "898.73556 m"
} | A | 599.15704 m | Range R=u²sin(2θ)/g. Substituting u=78, θ=40° and g=10 gives R=(78)²sin(80°)/10=599.15704 m. | {
"A": "Correct. The worked calculation gives 599.15704 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 599.15704 m, not 1198.31407 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 599.15704 m, not 600.15704 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_003768 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block initially moves at 2 m s⁻¹. A constant net force does 20 N of work over 17 m in the direction of motion. Find its final kinetic energy. | {
"A": "736 J",
"B": "368 J",
"C": "294.4 J",
"D": "366 J"
} | B | 368 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(14)(2)²+(20)(17)=368 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 368 J, not 736 J.",
"B": "Correct. The worked calculation gives 368 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 368 J, not 294.4 J.",
"D": "Incorrect. Substituting the stated values int... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006691 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 40 mol H₂ and 25 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "40 mol",
"B": "38 mol",
"C": "60 mol",
"D": "48 mol"
} | A | 40 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 40 mol H₂O; O₂ can produce 50 mol H₂O. The limiting condition is H₂; product=40 mol. | {
"A": "Correct. The worked calculation gives 40 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 40 mol, not 38 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 40 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_006621 | 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 426 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.61285 s",
"B": "1.03064 s",
"C": "-0.69357 s",
"D": "0.30643 s"
} | D | 0.30643 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(10/426)=0.30643 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30643 s, not 0.61285 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30643 s, not 1.03064 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30643 s,... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000958 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio -2. What is the sum of its first 9 terms? | {
"A": "2257.2",
"B": "1881",
"C": "1879",
"D": "940.5"
} | B | 1881 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(-2^9−1)/(-2−1)=1881. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1881, not 2257.2.",
"B": "Correct. The worked calculation gives 1881.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1881, not 1879.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_000947 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio 2. What is the sum of its first 7 terms? | {
"A": "1016",
"B": "1219.2",
"C": "102.6",
"D": "762"
} | A | 1016 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(2^7−1)/(2−1)=1016. | {
"A": "Correct. The worked calculation gives 1016.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1016, not 1219.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1016, not 102.6.",
"D": "Incorrect. Substituting the stated values into th... | [
"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_006010 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 25 cm in front of a thin convex lens of focal length 15 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-1.5",
"B": "2.25",
"C": "1.5",
"D": "1.125"
} | C | 1.5 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(25)(15)/(25−15)=37.5 cm. Thus |m|=v/u=37.5/25=1.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.5, not -1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.5, not 2.25.",
"C": "Correct. The worked calculation gives 1.5.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_005125 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +9 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "50 N",
"B": "100 N",
"C": "-50 N",
"D": "6 N"
} | A | 50 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(9×10⁻⁶)/(9×10⁻²)²=50 N. | {
"A": "Correct. The worked calculation gives 50 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 50 N, not 100 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 50 N, not -50 N.",
"D": "Incorrect. Substituting the stated values into 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_004118 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 26 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.34. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "63.96 N",
"B": "85.28 N",
"C": "9.528 N",
"D": "-85.28 N"
} | B | 85.28 N | Net force=mg(sinθ−μcosθ)=26×10×(0.6−0.34×0.8)=85.28 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 85.28 N, not 63.96 N.",
"B": "Correct. The worked calculation gives 85.28 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 85.28 N, not 9.528 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001126 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-1x³ -2x² -4x+7. Evaluate f′(0). | {
"A": "-6",
"B": "-2",
"C": "-4",
"D": "-3"
} | C | -4 | Differentiate: f′(x)=3(-1)x²+2(-2)x+(-4). At x=0, f′(0)=3(-1)(0)²+2(-2)(0)+(-4)=-4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4, not -6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -4, not -2.",
"C": "Correct. The worked calculation gives -4.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000324 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -8x -8=0, let its roots be α and β. What is α²+β²? | {
"A": "18",
"B": "24",
"C": "-24",
"D": "3.4"
} | B | 24 | By Vieta's relations, α+β = 8/2 and αβ = -8/2. Then α²+β²=(α+β)²−2αβ = (8/2)²−2(-8/2) = 24. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24, not 18.",
"B": "Correct. The worked calculation gives 24.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24, not -24.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"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_002009 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 12 blue and 5 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "3.39048",
"B": "-0.60952",
"C": "0.39048",
"D": "-2.60952"
} | C | 0.39048 | Favourable pairs = C(4,2)+C(12,2)+C(5,2)=82. Total pairs=C(21,2)=210. Therefore P=82/210=0.39048. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.39048, not 3.39048.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.39048, not -0.60952.",
"C": "Correct. The worked calculation gives 0.39048.",
"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_002190 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 10 blue and 5 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-2.67194",
"B": "0.16403",
"C": "2.32806",
"D": "0.32806"
} | D | 0.32806 | Favourable pairs = C(8,2)+C(10,2)+C(5,2)=83. Total pairs=C(23,2)=253. Therefore P=83/253=0.32806. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32806, not -2.67194.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32806, not 0.16403.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32806, not 2.32... | [
"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_000916 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio 4. What is the sum of its first 5 terms? | {
"A": "3751",
"B": "5626.5",
"C": "2813.25",
"D": "7502"
} | A | 3751 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(4^5−1)/(4−1)=3751. | {
"A": "Correct. The worked calculation gives 3751.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3751, not 5626.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3751, not 2813.25.",
"D": "Incorrect. Substituting the stated values into ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003076 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(4+0i)/(8+6i). What is Re(z), the real part of z? | {
"A": "-2.68",
"B": "3.32",
"C": "0.32",
"D": "-0.68"
} | C | 0.32 | Multiply numerator and denominator by the conjugate (8-6i). Then Re(z)=(ac+bd)/(c²+d²)=((4)(8)+(0)(6))/(8²+(6)²)=0.32. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32, not -2.68.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32, not 3.32.",
"C": "Correct. The worked calculation gives 0.32.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_008222 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 10 A for 21936 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": "73.17285 g",
"B": "36.08642 g",
"C": "72.17285 g",
"D": "108.25927 g"
} | C | 72.17285 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×10×21936/(2×96500)=72.17285 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 72.17285 g, not 73.17285 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 72.17285 g, not 36.08642 g.",
"C": "Correct. The worked calculation gives 72.17285 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006341 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 20 kg is attached to an ideal spring of force constant 395 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.45004 s",
"B": "0.45004 s",
"C": "-0.54996 s",
"D": "1.45004 s"
} | B | 0.45004 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(20/395)=0.45004 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.45004 s, not -0.45004 s.",
"B": "Correct. The worked calculation gives 0.45004 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.45004 s, not -0.54996 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_002345 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, 6], [3, 3]]. | {
"A": "4.5",
"B": "4",
"C": "9",
"D": "6"
} | D | 6 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(3)−(6)(3)=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"D": "Correct. The worked ... | [
"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_006516 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 23 kg is attached to an ideal spring of force constant 118 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.88298 s",
"B": "0.88298 s",
"C": "-0.88298 s",
"D": "-2.11702 s"
} | B | 0.88298 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(23/118)=0.88298 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.88298 s, not 1.88298 s.",
"B": "Correct. The worked calculation gives 0.88298 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.88298 s, not -0.88298 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_001391 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (3x² -5x -4) dx. | {
"A": "-9",
"B": "-10",
"C": "-7.5",
"D": "-7"
} | B | -10 | An antiderivative is (3/3)x³+(-5/2)x²+(-4)x. Evaluating between 0 and 2 gives (3/3)(2)³+(-5/2)(2)²+(-4)(2)=-10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -10, not -9.",
"B": "Correct. The worked calculation gives -10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -10, not -7.5.",
"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_005852 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.7 atm at 437 K. What is its pressure at 700 K? | {
"A": "7.92677 atm",
"B": "5.92677 atm",
"C": "1.59268 atm",
"D": "11.85355 atm"
} | B | 5.92677 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.7)(700)/(437)=5.92677 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.92677 atm, not 7.92677 atm.",
"B": "Correct. The worked calculation gives 5.92677 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.92677 atm, not 1.59268 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006063 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 48 cm in front of a thin convex lens of focal length 15 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.34091",
"B": "0.90909",
"C": "0.45455",
"D": "2.45455"
} | C | 0.45455 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(48)(15)/(48−15)=21.81818 cm. Thus |m|=v/u=21.81818/48=0.45455. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.45455, not 0.34091.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.45455, not 0.90909.",
"C": "Correct. The worked calculation gives 0.45455.",
"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_000736 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio 4. What is the sum of its first 12 terms? | {
"A": "100663290",
"B": "50331647",
"C": "50331645",
"D": "5033165.5"
} | C | 50331645 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(4^12−1)/(4−1)=50331645. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 50331645, not 100663290.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 50331645, not 50331647.",
"C": "Correct. The worked calculation gives 50331645.",
"D": "Incorrect. Substituting the sta... | [
"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_006989 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 21 mol H₂ and 33 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "21 mol",
"B": "-21 mol",
"C": "3.1 mol",
"D": "31.5 mol"
} | A | 21 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 21 mol H₂O; O₂ can produce 66 mol H₂O. The limiting condition is H₂; product=21 mol. | {
"A": "Correct. The worked calculation gives 21 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21 mol, not -21 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21 mol, not 3.1 mol.",
"D": "Incorrect. Substituting the stated value... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003997 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block initially moves at 10 m s⁻¹. A constant net force does 12 N of work over 3 m in the direction of motion. Find its final kinetic energy. | {
"A": "272 J",
"B": "-136 J",
"C": "102 J",
"D": "136 J"
} | D | 136 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(2)(10)²+(12)(3)=136 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 136 J, not 272 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 136 J, not -136 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 136 J, not 102 J.",
"D"... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000809 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio 4. What is the sum of its first 10 terms? | {
"A": "2446675",
"B": "1223337.5",
"C": "2446674",
"D": "2936010"
} | A | 2446675 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(4^10−1)/(4−1)=2446675. | {
"A": "Correct. The worked calculation gives 2446675.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2446675, not 1223337.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2446675, not 2446674.",
"D": "Incorrect. Substituting the stated ... | [
"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_004997 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 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": "1.28571 A",
"B": "2.28571 A",
"C": "3.28571 A",
"D": "-1.28571 A"
} | A | 1.28571 A | Series branch resistance=9+12=21 Ω. Parallel equivalent R_eq=(21×6)/(21+6)=4.66667 Ω. Total current I=V/R_eq=6/4.66667=1.28571 A. | {
"A": "Correct. The worked calculation gives 1.28571 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.28571 A, not 2.28571 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.28571 A, not 3.28571 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_002876 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-5, 1, 8) and v=(-2, -7, 5), calculate u·v. | {
"A": "5.3",
"B": "44",
"C": "43",
"D": "21.5"
} | C | 43 | The dot product is the sum of corresponding component products: (-5)(-2)+(1)(-7)+(8)(5)=43. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 43, not 5.3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 43, not 44.",
"C": "Correct. The worked calculation gives 43.",
"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_001300 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=1x³ +5x² +8x+7. Evaluate f′(-1). | {
"A": "-1",
"B": "1.5",
"C": "1",
"D": "-2"
} | C | 1 | Differentiate: f′(x)=3(1)x²+2(5)x+(8). At x=-1, f′(-1)=3(1)(-1)²+2(5)(-1)+(8)=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not -1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.5.",
"C": "Correct. The worked calculation gives 1.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007870 | 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 21 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "10.5 mmol L⁻¹",
"B": "9.5 mmol L⁻¹",
"C": "7.5 mmol L⁻¹",
"D": "5.25 mmol L⁻¹"
} | A | 10.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=21/2^1=10.5 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 10.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.5 mmol L⁻¹, not 9.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10.5 mmol L⁻¹, not 7.5 mmol L⁻¹.",
"D": "Incorrect... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001653 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (0x² +8x -3) dx. | {
"A": "-10",
"B": "5",
"C": "13",
"D": "10"
} | D | 10 | An antiderivative is (0/3)x³+(8/2)x²+(-3)x. Evaluating between 0 and 2 gives (0/3)(2)³+(8/2)(2)²+(-3)(2)=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not -10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 13.",
"D": "Correct. The wor... | [
"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_009219 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.09 V, transfers 3 electrons, and has reaction quotient Q=10^3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.0309 V",
"B": "1.54635 V",
"C": "3.0309 V",
"D": "4.0309 V"
} | A | 1.0309 V | Apply the Nernst equation: E=1.09−(0.0591/3)(3)=1.0309 V. | {
"A": "Correct. The worked calculation gives 1.0309 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0309 V, not 1.54635 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0309 V, not 3.0309 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_002069 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 9 blue and 7 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.24405",
"B": "-1.6746",
"C": "0.3254",
"D": "3.3254"
} | C | 0.3254 | Favourable pairs = C(12,2)+C(9,2)+C(7,2)=123. Total pairs=C(28,2)=378. Therefore P=123/378=0.3254. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3254, not 0.24405.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3254, not -1.6746.",
"C": "Correct. The worked calculation gives 0.3254.",
"D": "Incorrect. Substituting the stated value... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007758 | 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 65 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "0.25391 mmol L⁻¹",
"B": "3.25391 mmol L⁻¹",
"C": "0.38086 mmol L⁻¹",
"D": "0.50781 mmol L⁻¹"
} | A | 0.25391 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=65/2^8=0.25391 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 0.25391 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25391 mmol L⁻¹, not 3.25391 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25391 mmol L⁻¹, not 0.38086 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_000447 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 12 and common difference 13. Find the sum of its first 33 terms. | {
"A": "5808",
"B": "10890",
"C": "7260",
"D": "5445"
} | C | 7260 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=12, d=13, n=33: Sₙ=33/2[2(12)+(33−1)(13)]=7260. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7260, not 5808.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7260, not 10890.",
"C": "Correct. The worked calculation gives 7260.",
"D": "Incorrect. Substituting the stated values into the ... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002725 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-5, 9, 4) and v=(-7, 6, -3), calculate u·v. | {
"A": "75",
"B": "77",
"C": "-77",
"D": "154"
} | B | 77 | The dot product is the sum of corresponding component products: (-5)(-7)+(9)(6)+(4)(-3)=77. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 77, not 75.",
"B": "Correct. The worked calculation gives 77.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 77, not -77.",
"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_007923 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 23 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "2.08984 mmol L⁻¹",
"B": "-0.91016 mmol L⁻¹",
"C": "0.08984 mmol L⁻¹",
"D": "-0.08984 mmol L⁻¹"
} | C | 0.08984 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=23/2^8=0.08984 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.08984 mmol L⁻¹, not 2.08984 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.08984 mmol L⁻¹, not -0.91016 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.08984 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_005800 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.6 atm at 270 K. What is its pressure at 448 K? | {
"A": "1.65481 atm",
"B": "-2.65481 atm",
"C": "2.65481 atm",
"D": "0.65481 atm"
} | C | 2.65481 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.6)(448)/(270)=2.65481 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.65481 atm, not 1.65481 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.65481 atm, not -2.65481 atm.",
"C": "Correct. The worked calculation gives 2.65481 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006592 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 6 kg is attached to an ideal spring of force constant 1105 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.14738 s",
"B": "0.14738 s",
"C": "0.22106 s",
"D": "0.11053 s"
} | B | 0.14738 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(6/1105)=0.14738 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.14738 s, not -0.14738 s.",
"B": "Correct. The worked calculation gives 0.14738 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.14738 s, not 0.22106 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_007198 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 5 mol of gas at 307 K and 0.95 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "66.29342 L",
"B": "198.88026 L",
"C": "132.58684 L",
"D": "134.58684 L"
} | C | 132.58684 L | PV=nRT, so V=nRT/P=(5)(0.082057)(307)/(0.95)=132.58684 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 132.58684 L, not 66.29342 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 132.58684 L, not 198.88026 L.",
"C": "Correct. The worked calculation gives 132.58684 L.",
"D": "Incorrect. Substit... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004801 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 15 Ω and 6 Ω are connected in series; this combination is connected in parallel with a 3 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "8.42857 A",
"B": "17.14286 A",
"C": "11.42857 A",
"D": "22.85714 A"
} | C | 11.42857 A | Series branch resistance=15+6=21 Ω. Parallel equivalent R_eq=(21×3)/(21+3)=2.625 Ω. Total current I=V/R_eq=30/2.625=11.42857 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.42857 A, not 8.42857 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.42857 A, not 17.14286 A.",
"C": "Correct. The worked calculation gives 11.42857 A.",
"D": "Incorrect. Substituting... | [
"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_007434 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 28 mL of 0.10 M HCl is mixed with 21 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "4.8451",
"B": "1.8451",
"C": "-0.1549",
"D": "2.8451"
} | B | 1.8451 | Excess H⁺ moles=0.10×(28−21)/1000=0.000700 mol. Total volume=0.049 L, so [H⁺]=0.014286 M and pH=−log₁₀[H⁺]=1.8451. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.8451, not 4.8451.",
"B": "Correct. The worked calculation gives 1.8451.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.8451, not -0.1549.",
"D": "Incorrect. Substituting the stated values... | [
"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_009561 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_16H_18. Treat X as the total number of monovalent halogen atoms. | {
"A": "8",
"B": "6",
"C": "11",
"D": "-8"
} | A | 8 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×16+2+0−18−0)/2=8. | {
"A": "Correct. The worked calculation gives 8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 11.",
"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_009704 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(OH)_4]^-1, each OH ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "1.3",
"B": "3",
"C": "4.5",
"D": "-3"
} | B | 3 | Let the formal oxidation state of Ni 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 1.3.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.5.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_009124 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.40 V, transfers 3 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.6985 V",
"B": "2.603 V",
"C": "1.3015 V",
"D": "1.95225 V"
} | C | 1.3015 V | Apply the Nernst equation: E=1.40−(0.0591/3)(5)=1.3015 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.3015 V, not -0.6985 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.3015 V, not 2.603 V.",
"C": "Correct. The worked calculation gives 1.3015 V.",
"D": "Incorrect. Substituting the stat... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001810 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 7 elements can be selected from a set of 55 distinct elements? | {
"A": "202927725",
"B": "101463862.5",
"C": "202927727",
"D": "202927726"
} | A | 202927725 | Order does not matter, so the count is C(55,7)=55!/[7!(48)!]=202927725. | {
"A": "Correct. The worked calculation gives 202927725.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 202927725, not 101463862.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 202927725, not 202927727.",
"D": "Incorrect. Substituting t... | [
"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_008204 | 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 9 A for 4249 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "2.25819 g",
"B": "11.58188 g",
"C": "12.58188 g",
"D": "18.87283 g"
} | C | 12.58188 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×9×4249/(2×96500)=12.58188 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.58188 g, not 2.25819 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.58188 g, not 11.58188 g.",
"C": "Correct. The worked calculation gives 12.58188 g.",
"D": "Incorrect. Substituting... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001190 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=7x³ +2x² +9x+7. Evaluate f′(-2). | {
"A": "127.5",
"B": "87",
"C": "84",
"D": "85"
} | D | 85 | Differentiate: f′(x)=3(7)x²+2(2)x+(9). At x=-2, f′(-2)=3(7)(-2)²+2(2)(-2)+(9)=85. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 85, not 127.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 85, not 87.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 85, not 84.",
"D": "Correct. The ... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003004 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-5, 8, -2) and v=(7, -6, -2), calculate u·v. | {
"A": "-79",
"B": "-59.25",
"C": "-39.5",
"D": "-81"
} | A | -79 | The dot product is the sum of corresponding component products: (-5)(7)+(8)(-6)+(-2)(-2)=-79. | {
"A": "Correct. The worked calculation gives -79.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -79, not -59.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -79, not -39.5.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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 |
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