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_000408 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -15 and common difference 12. Find the sum of its first 12 terms. | {
"A": "306",
"B": "611",
"C": "612",
"D": "459"
} | C | 612 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-15, d=12, n=12: Sₙ=12/2[2(-15)+(12−1)(12)]=612. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 612, not 306.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 612, not 611.",
"C": "Correct. The worked calculation gives 612.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003832 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block initially moves at 9 m s⁻¹. A constant net force does 23 N of work over 14 m in the direction of motion. Find its final kinetic energy. | {
"A": "524.5 J",
"B": "522.5 J",
"C": "523.5 J",
"D": "262.25 J"
} | A | 524.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(5)(9)²+(23)(14)=524.5 J. | {
"A": "Correct. The worked calculation gives 524.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 524.5 J, not 522.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 524.5 J, not 523.5 J.",
"D": "Incorrect. Substituting the stated va... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006826 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 12 mol H₂ and 28 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "18 mol",
"B": "14 mol",
"C": "9 mol",
"D": "12 mol"
} | D | 12 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 12 mol H₂O; O₂ can produce 56 mol H₂O. The limiting condition is H₂; product=12 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 18 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 14 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 9 mol.",
... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003812 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 13 kg block initially moves at 2 m s⁻¹. A constant net force does 18 N of work over 9 m in the direction of motion. Find its final kinetic energy. | {
"A": "94 J",
"B": "282 J",
"C": "188 J",
"D": "187 J"
} | C | 188 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(13)(2)²+(18)(9)=188 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 188 J, not 94 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 188 J, not 282 J.",
"C": "Correct. The worked calculation gives 188 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_009843 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(Cl)_2]^+3, each Cl ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "6",
"B": "5",
"C": "7",
"D": "2"
} | B | 5 | Let the formal oxidation state of Pt be x. Charge balance gives x+(2)(−1)=+3; hence x=3+2=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 6.",
"B": "Correct. The worked calculation gives 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_002282 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 12 blue and 8 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.67077",
"B": "2.33538",
"C": "0.33538",
"D": "0.16769"
} | C | 0.33538 | Favourable pairs = C(6,2)+C(12,2)+C(8,2)=109. Total pairs=C(26,2)=325. Therefore P=109/325=0.33538. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33538, not 0.67077.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33538, not 2.33538.",
"C": "Correct. The worked calculation gives 0.33538.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008742 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.56 mol L⁻¹ and initially B is absent. At equilibrium, 64% of A has dissociated at constant volume. Find K_c. | {
"A": "10.09973",
"B": "8.09973",
"C": "7.09973",
"D": "10.6496"
} | C | 7.09973 | Let α=0.64. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.56)(0.64)²/(1−0.64)=7.09973. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.09973, not 10.09973.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.09973, not 8.09973.",
"C": "Correct. The worked calculation gives 7.09973.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004974 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 12 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.39286 A",
"B": "0.78571 A",
"C": "0.58929 A",
"D": "1.78571 A"
} | B | 0.78571 A | Series branch resistance=13+8=21 Ω. Parallel equivalent R_eq=(21×12)/(21+12)=7.63636 Ω. Total current I=V/R_eq=6/7.63636=0.78571 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.78571 A, not 0.39286 A.",
"B": "Correct. The worked calculation gives 0.78571 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.78571 A, not 0.58929 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_004378 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 2 m is acted on by a constant torque of 63 N m about its central axis. Find its angular acceleration. | {
"A": "7.875 rad s⁻²",
"B": "3.9375 rad s⁻²",
"C": "4.9375 rad s⁻²",
"D": "5.90625 rad s⁻²"
} | B | 3.9375 rad s⁻² | For a solid disc, I=½MR²=½(8)(2)²=16 kg m². Using τ=Iα, α=63/16=3.9375 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.9375 rad s⁻², not 7.875 rad s⁻².",
"B": "Correct. The worked calculation gives 3.9375 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.9375 rad s⁻², not 4.9375 rad s⁻².",
"D": "Inc... | [
"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_009130 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.93 V, transfers 1 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.5692 V",
"B": "1.2846 V",
"C": "3.2846 V",
"D": "2.2846 V"
} | B | 1.2846 V | Apply the Nernst equation: E=0.93−(0.0591/1)(-6)=1.2846 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.2846 V, not 2.5692 V.",
"B": "Correct. The worked calculation gives 1.2846 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2846 V, not 3.2846 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_008675 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.43 mol L⁻¹ and initially B is absent. At equilibrium, 55% of A has dissociated at constant volume. Find K_c. | {
"A": "1.92256",
"B": "3.84511",
"C": "6.84511",
"D": "2.84511"
} | B | 3.84511 | Let α=0.55. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.43)(0.55)²/(1−0.55)=3.84511. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.84511, not 1.92256.",
"B": "Correct. The worked calculation gives 3.84511.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.84511, not 6.84511.",
"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_000987 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio -2. What is the sum of its first 8 terms? | {
"A": "-68",
"B": "-85",
"C": "-102",
"D": "-83"
} | B | -85 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(-2^8−1)/(-2−1)=-85. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -85, not -68.",
"B": "Correct. The worked calculation gives -85.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -85, not -102.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_001033 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ +4x² +9x+7. Evaluate f′(5). | {
"A": "349",
"B": "347",
"C": "174.5",
"D": "261.75"
} | A | 349 | Differentiate: f′(x)=3(4)x²+2(4)x+(9). At x=5, f′(5)=3(4)(5)²+2(4)(5)+(9)=349. | {
"A": "Correct. The worked calculation gives 349.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 349, not 347.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 349, not 174.5.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000909 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio -2. What is the sum of its first 11 terms? | {
"A": "6831",
"B": "6830",
"C": "6828",
"D": "5464"
} | B | 6830 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(-2^11−1)/(-2−1)=6830. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6830, not 6831.",
"B": "Correct. The worked calculation gives 6830.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6830, not 6828.",
"D": "Incorrect. Substituting the stated values into the g... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001593 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (0x² +0x +2) dx. | {
"A": "8",
"B": "-6",
"C": "3",
"D": "6"
} | D | 6 | An antiderivative is (0/3)x³+(0/2)x²+(2)x. Evaluating between 0 and 3 gives (0/3)(3)³+(0/2)(3)²+(2)(3)=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not -6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"D": "Correct. The worked c... | [
"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_003376 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 31 m s⁻¹ at 50° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "92.64003 m",
"B": "75.71202 m",
"C": "113.56803 m",
"D": "94.64003 m"
} | D | 94.64003 m | Range R=u²sin(2θ)/g. Substituting u=31, θ=50° and g=10 gives R=(31)²sin(100°)/10=94.64003 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 94.64003 m, not 92.64003 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 94.64003 m, not 75.71202 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 94.640... | [
"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_003401 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 67 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "421.82802 m",
"B": "419.82802 m",
"C": "423.82802 m",
"D": "210.91401 m"
} | A | 421.82802 m | Range R=u²sin(2θ)/g. Substituting u=67, θ=55° and g=10 gives R=(67)²sin(110°)/10=421.82802 m. | {
"A": "Correct. The worked calculation gives 421.82802 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 421.82802 m, not 419.82802 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 421.82802 m, not 423.82802 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005406 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 1 μF capacitor is charged to a potential difference of 27 V. Calculate the energy stored, expressed in μJ. | {
"A": "364.5 μJ",
"B": "546.75 μJ",
"C": "365.5 μJ",
"D": "273.375 μJ"
} | A | 364.5 μJ | U=½CV². Since C=1 μF, U in μJ is ½×1×(27)²=364.5 μJ. | {
"A": "Correct. The worked calculation gives 364.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 364.5 μJ, not 546.75 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 364.5 μJ, not 365.5 μJ.",
"D": "Incorrect. Substituting the sta... | [
"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_008460 | 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 0.89 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": "-0.22 K",
"B": "4.78 K",
"C": "1.335 K",
"D": "1.78 K"
} | D | 1.78 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×0.89=1.78 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.78 K, not -0.22 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.78 K, not 4.78 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.78 K, not 1.335 K."... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006367 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 15 kg is attached to an ideal spring of force constant 62 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.98374 s",
"B": "-0.01626 s",
"C": "1.98374 s",
"D": "-1.01626 s"
} | A | 0.98374 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(15/62)=0.98374 s. | {
"A": "Correct. The worked calculation gives 0.98374 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.98374 s, not -0.01626 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.98374 s, not 1.98374 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_007403 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 73 mL of 0.10 M HCl is mixed with 17 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-1.20605",
"B": "0.60303",
"C": "1.20605",
"D": "0.90454"
} | C | 1.20605 | Excess H⁺ moles=0.10×(73−17)/1000=0.005600 mol. Total volume=0.090 L, so [H⁺]=0.062222 M and pH=−log₁₀[H⁺]=1.20605. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.20605, not -1.20605.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.20605, not 0.60303.",
"C": "Correct. The worked calculation gives 1.20605.",
"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_007376 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 14 mL of 0.10 M HCl is mixed with 25 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.45033",
"B": "-12.45033",
"C": "9.33775",
"D": "24.90066"
} | A | 12.45033 | Excess OH⁻ moles=0.10×(25−14)/1000=0.001100 mol. Total volume=0.039 L, so [OH⁻]=0.028205 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.45033. | {
"A": "Correct. The worked calculation gives 12.45033.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.45033, not -12.45033.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.45033, not 9.33775.",
"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_000695 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio -3. What is the sum of its first 6 terms? | {
"A": "-1911",
"B": "-637",
"C": "-1274",
"D": "-1273"
} | C | -1274 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(-3^6−1)/(-3−1)=-1274. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1274, not -1911.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1274, not -637.",
"C": "Correct. The worked calculation gives -1274.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_003586 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 118 m s⁻¹ at 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "2056.86947 m",
"B": "1371.24632 m",
"C": "1370.24632 m",
"D": "1096.99705 m"
} | B | 1371.24632 m | Range R=u²sin(2θ)/g. Substituting u=118, θ=40° and g=10 gives R=(118)²sin(80°)/10=1371.24632 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1371.24632 m, not 2056.86947 m.",
"B": "Correct. The worked calculation gives 1371.24632 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1371.24632 m, not 1370.24632 m.",
"D": "Incorrect. S... | [
"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_004280 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.16. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "30.208 N",
"B": "37.76 N",
"C": "4.776 N",
"D": "38.76 N"
} | B | 37.76 N | Net force=mg(sinθ−μcosθ)=8×10×(0.6−0.16×0.8)=37.76 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 37.76 N, not 30.208 N.",
"B": "Correct. The worked calculation gives 37.76 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 37.76 N, not 4.776 N.",
"D": "Incorrect. Substituting the stated v... | [
"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_003641 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 21 m s⁻¹ at 65° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "4.37826 m",
"B": "33.78256 m",
"C": "31.78256 m",
"D": "67.56512 m"
} | B | 33.78256 m | Range R=u²sin(2θ)/g. Substituting u=21, θ=65° and g=10 gives R=(21)²sin(130°)/10=33.78256 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33.78256 m, not 4.37826 m.",
"B": "Correct. The worked calculation gives 33.78256 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 33.78256 m, not 31.78256 m.",
"D": "Incorrect. Substituting... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005438 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 74 μF capacitor is charged to a potential difference of 22 V. Calculate the energy stored, expressed in μJ. | {
"A": "17908 μJ",
"B": "17906 μJ",
"C": "13431 μJ",
"D": "21489.6 μJ"
} | A | 17908 μJ | U=½CV². Since C=74 μF, U in μJ is ½×74×(22)²=17908 μJ. | {
"A": "Correct. The worked calculation gives 17908 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17908 μJ, not 17906 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17908 μJ, not 13431 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_008682 | 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 0.97 mol L⁻¹ and initially B is absent. At equilibrium, 57% of A has dissociated at constant volume. Find K_c. | {
"A": "2.93166",
"B": "4.93166",
"C": "1.29317",
"D": "-2.93166"
} | A | 2.93166 | Let α=0.57. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.97)(0.57)²/(1−0.57)=2.93166. | {
"A": "Correct. The worked calculation gives 2.93166.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.93166, not 4.93166.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.93166, not 1.29317.",
"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_009419 | 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_8H_11N_1X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "4",
"B": "1",
"C": "1.2",
"D": "2"
} | D | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×8+2+1−11−4)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.2.",
"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_002855 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-5, 1, 2) and v=(-5, 3, 4), calculate u·v. | {
"A": "72",
"B": "36",
"C": "43.2",
"D": "37"
} | B | 36 | The dot product is the sum of corresponding component products: (-5)(-5)+(1)(3)+(2)(4)=36. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 36, not 72.",
"B": "Correct. The worked calculation gives 36.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 36, not 43.2.",
"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_004918 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 17 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "-0.54412 A",
"B": "1.45588 A",
"C": "1.14559 A",
"D": "4.45588 A"
} | B | 1.45588 A | Series branch resistance=8+8=16 Ω. Parallel equivalent R_eq=(16×17)/(16+17)=8.24242 Ω. Total current I=V/R_eq=12/8.24242=1.45588 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.45588 A, not -0.54412 A.",
"B": "Correct. The worked calculation gives 1.45588 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.45588 A, not 1.14559 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009752 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(OH)_4]^+0, each OH ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "4",
"B": "1.4",
"C": "3",
"D": "5"
} | A | 4 | Let the formal oxidation state of Pt be x. Charge balance gives x+(4)(−1)=+0; hence x=0+4=+4. | {
"A": "Correct. The worked calculation gives 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 3.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_006912 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 48 mol H₂ and 10 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "10 mol",
"B": "15 mol",
"C": "19 mol",
"D": "20 mol"
} | D | 20 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 48 mol H₂O; O₂ can produce 20 mol H₂O. The limiting condition is O₂; product=20 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20 mol, not 10 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20 mol, not 15 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20 mol, not 19 mol.",
... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004416 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 4 m is acted on by a constant torque of 99 N m about its central axis. Find its angular acceleration. | {
"A": "0.475 rad s⁻²",
"B": "2.475 rad s⁻²",
"C": "4.95 rad s⁻²",
"D": "4.475 rad s⁻²"
} | B | 2.475 rad s⁻² | For a solid disc, I=½MR²=½(5)(4)²=40 kg m². Using τ=Iα, α=99/40=2.475 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.475 rad s⁻², not 0.475 rad s⁻².",
"B": "Correct. The worked calculation gives 2.475 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.475 rad s⁻², not 4.95 rad s⁻².",
"D": "Incorrec... | [
"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_005791 | 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 1.5 atm at 274 K. What is its pressure at 678 K? | {
"A": "2.71168 atm",
"B": "3.71168 atm",
"C": "-3.71168 atm",
"D": "1.37117 atm"
} | B | 3.71168 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.5)(678)/(274)=3.71168 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.71168 atm, not 2.71168 atm.",
"B": "Correct. The worked calculation gives 3.71168 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.71168 atm, not -3.71168 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_002989 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, 7, -1) and v=(-2, 5, -2), calculate u·v. | {
"A": "14.5",
"B": "30",
"C": "29",
"D": "34.8"
} | C | 29 | The dot product is the sum of corresponding component products: (4)(-2)+(7)(5)+(-1)(-2)=29. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 29, not 14.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 29, not 30.",
"C": "Correct. The worked calculation gives 29.",
"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_005807 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.8 atm at 391 K. What is its pressure at 547 K? | {
"A": "7.83427 atm",
"B": "2.93785 atm",
"C": "3.91714 atm",
"D": "5.8757 atm"
} | C | 3.91714 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.8)(547)/(391)=3.91714 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.91714 atm, not 7.83427 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.91714 atm, not 2.93785 atm.",
"C": "Correct. The worked calculation gives 3.91714 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_007997 | 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 25 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "3.125 mmol L⁻¹",
"B": "5.125 mmol L⁻¹",
"C": "-3.125 mmol L⁻¹",
"D": "4.6875 mmol L⁻¹"
} | A | 3.125 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=25/2^3=3.125 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 3.125 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.125 mmol L⁻¹, not 5.125 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.125 mmol L⁻¹, not -3.125 mmol L⁻¹.",
"D": "I... | [
"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_004676 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 5 Ω and 3 Ω are connected in series; this combination is connected in parallel with a 9 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "11.33333 A",
"B": "5.66667 A",
"C": "-5.66667 A",
"D": "4.66667 A"
} | B | 5.66667 A | Series branch resistance=5+3=8 Ω. Parallel equivalent R_eq=(8×9)/(8+9)=4.23529 Ω. Total current I=V/R_eq=24/4.23529=5.66667 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.66667 A, not 11.33333 A.",
"B": "Correct. The worked calculation gives 5.66667 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.66667 A, not -5.66667 A.",
"D": "Incorrect. Substituting t... | [
"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_002627 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, 5], [5, 8]]. | {
"A": "12",
"B": "15",
"C": "30",
"D": "7.5"
} | B | 15 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(8)−(5)(5)=15. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15, not 12.",
"B": "Correct. The worked calculation gives 15.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15, not 30.",
"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_000498 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 25 and common difference 8. Find the sum of its first 23 terms. | {
"A": "1949.25",
"B": "-2599",
"C": "2599",
"D": "3898.5"
} | C | 2599 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=25, d=8, n=23: Sₙ=23/2[2(25)+(23−1)(8)]=2599. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2599, not 1949.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2599, not -2599.",
"C": "Correct. The worked calculation gives 2599.",
"D": "Incorrect. Substituting the stated values into 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_001990 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 12 elements can be selected from a set of 35 distinct elements? | {
"A": "-834451800",
"B": "834451799",
"C": "83445181",
"D": "834451800"
} | D | 834451800 | Order does not matter, so the count is C(35,12)=35!/[12!(23)!]=834451800. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 834451800, not -834451800.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 834451800, not 834451799.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 834451800... | [
"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_005295 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +2 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "1.72 N",
"B": "5.4 N",
"C": "7.2 N",
"D": "9.2 N"
} | C | 7.2 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(2×10⁻⁶)/(10×10⁻²)²=7.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.2 N, not 1.72 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.2 N, not 5.4 N.",
"C": "Correct. The worked calculation gives 7.2 N.",
"D": "Incorrect. Substituting the stated values into... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004248 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 28 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.19. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "250.88 N",
"B": "123.44 N",
"C": "188.16 N",
"D": "125.44 N"
} | D | 125.44 N | Net force=mg(sinθ−μcosθ)=28×10×(0.6−0.19×0.8)=125.44 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 125.44 N, not 250.88 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 125.44 N, not 123.44 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 125.44 N, not ... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002658 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, 6], [2, 8]]. | {
"A": "38",
"B": "36",
"C": "28.8",
"D": "43.2"
} | B | 36 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(8)−(6)(2)=36. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 36, not 38.",
"B": "Correct. The worked calculation gives 36.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 36, not 28.8.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009724 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(OH)_2]^-4, each OH ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "-1.5",
"B": "-2",
"C": "-4",
"D": "0"
} | B | -2 | Let the formal oxidation state of Co be x. Charge balance gives x+(2)(−1)=-4; hence x=-4+2=-2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2, not -1.5.",
"B": "Correct. The worked calculation gives -2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2, not -4.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"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_001240 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ +3x² +1x+7. Evaluate f′(3). | {
"A": "152",
"B": "115.5",
"C": "16.4",
"D": "154"
} | D | 154 | Differentiate: f′(x)=3(5)x²+2(3)x+(1). At x=3, f′(3)=3(5)(3)²+2(3)(3)+(1)=154. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 154, not 152.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 154, not 115.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 154, not 16.4.",
"D": "Correct... | [
"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_000099 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +6x +11=0, let its roots be α and β. What is α²+β²? | {
"A": "0.04",
"B": "-2.96",
"C": "2.96",
"D": "-4.44"
} | B | -2.96 | By Vieta's relations, α+β = -6/5 and αβ = 11/5. Then α²+β²=(α+β)²−2αβ = (-6/5)²−2(11/5) = -2.96. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2.96, not 0.04.",
"B": "Correct. The worked calculation gives -2.96.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2.96, not 2.96.",
"D": "Incorrect. Substituting the stated values into th... | [
"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_004897 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 6 Ω and 12 Ω are connected in series; this combination is connected in parallel with a 16 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.0625 A",
"B": "3.0625 A",
"C": "2.125 A",
"D": "-1.0625 A"
} | A | 1.0625 A | Series branch resistance=6+12=18 Ω. Parallel equivalent R_eq=(18×16)/(18+16)=8.47059 Ω. Total current I=V/R_eq=9/8.47059=1.0625 A. | {
"A": "Correct. The worked calculation gives 1.0625 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0625 A, not 3.0625 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0625 A, not 2.125 A.",
"D": "Incorrect. Substituting the state... | [
"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_002363 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, -8], [7, -7]]. | {
"A": "51",
"B": "5.9",
"C": "49",
"D": "39.2"
} | C | 49 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(-7)−(-8)(7)=49. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 49, not 51.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 49, not 5.9.",
"C": "Correct. The worked calculation gives 49.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001298 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ -9x² +11x+7. Evaluate f′(-1). | {
"A": "16",
"B": "14",
"C": "2.4",
"D": "28"
} | B | 14 | Differentiate: f′(x)=3(-5)x²+2(-9)x+(11). At x=-1, f′(-1)=3(-5)(-1)²+2(-9)(-1)+(11)=14. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14, not 16.",
"B": "Correct. The worked calculation gives 14.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14, not 2.4.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"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_001863 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 6 elements can be selected from a set of 33 distinct elements? | {
"A": "1107569",
"B": "2215136",
"C": "553784",
"D": "1107568"
} | D | 1107568 | Order does not matter, so the count is C(33,6)=33!/[6!(27)!]=1107568. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1107568, not 1107569.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1107568, not 2215136.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1107568, not 55378... | [
"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_007704 | 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 20 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "7 mmol L⁻¹",
"B": "5 mmol L⁻¹",
"C": "3 mmol L⁻¹",
"D": "10 mmol L⁻¹"
} | B | 5 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=20/2^2=5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5 mmol L⁻¹, not 7 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5 mmol L⁻¹, not 3 mmol L⁻¹.",
"D": "Incorrect. Substitutin... | [
"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_000851 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio -3. What is the sum of its first 6 terms? | {
"A": "-546",
"B": "-364",
"C": "-273",
"D": "-365"
} | B | -364 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(-3^6−1)/(-3−1)=-364. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -364, not -546.",
"B": "Correct. The worked calculation gives -364.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -364, not -273.",
"D": "Incorrect. Substituting the stated values into the g... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007818 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 90 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "8.4375 mmol L⁻¹",
"B": "22.5 mmol L⁻¹",
"C": "16.875 mmol L⁻¹",
"D": "11.25 mmol L⁻¹"
} | D | 11.25 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=90/2^3=11.25 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.25 mmol L⁻¹, not 8.4375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.25 mmol L⁻¹, not 22.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relat... | [
"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_009426 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_7H_4N_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "6",
"B": "4",
"C": "3.5",
"D": "7"
} | D | 7 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+2−4−0)/2=7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 3.5.",
"D": "Correct. The worked ... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006922 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 27 mol H₂ and 13 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "31.2 mol",
"B": "52 mol",
"C": "26 mol",
"D": "13 mol"
} | C | 26 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 27 mol H₂O; O₂ can produce 26 mol H₂O. The limiting condition is O₂; product=26 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 31.2 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 52 mol.",
"C": "Correct. The worked calculation gives 26 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_008772 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.52 mol L⁻¹ and initially B is absent. At equilibrium, 44% of A has dissociated at constant volume. Find K_c. | {
"A": "3.10194",
"B": "1.57646",
"C": "0.10194",
"D": "2.10194"
} | D | 2.10194 | Let α=0.44. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.52)(0.44)²/(1−0.44)=2.10194. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.10194, not 3.10194.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.10194, not 1.57646.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.10194, not 0.101... | [
"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_005905 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.1 atm at 285 K. What is its pressure at 732 K? | {
"A": "4.04526 atm",
"B": "5.39368 atm",
"C": "7.39368 atm",
"D": "6.39368 atm"
} | B | 5.39368 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.1)(732)/(285)=5.39368 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.39368 atm, not 4.04526 atm.",
"B": "Correct. The worked calculation gives 5.39368 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.39368 atm, not 7.39368 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_007030 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 10 mol of gas at 627 K and 1.6 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "321.56087 L",
"B": "257.24869 L",
"C": "33.15609 L",
"D": "323.56087 L"
} | A | 321.56087 L | PV=nRT, so V=nRT/P=(10)(0.082057)(627)/(1.6)=321.56087 L. | {
"A": "Correct. The worked calculation gives 321.56087 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 321.56087 L, not 257.24869 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 321.56087 L, not 33.15609 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_008391 | 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 1.96 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "2.2932 K",
"B": "6.0576 K",
"C": "3.0576 K",
"D": "0.0576 K"
} | C | 3.0576 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.52×1.96=3.0576 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.0576 K, not 2.2932 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.0576 K, not 6.0576 K.",
"C": "Correct. The worked calculation gives 3.0576 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_000192 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 -18x -9=0, let its roots be α and β. What is α²+β²? | {
"A": "23.75",
"B": "24.75",
"C": "49.5",
"D": "26.75"
} | B | 24.75 | By Vieta's relations, α+β = 18/4 and αβ = -9/4. Then α²+β²=(α+β)²−2αβ = (18/4)²−2(-9/4) = 24.75. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24.75, not 23.75.",
"B": "Correct. The worked calculation gives 24.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24.75, not 49.5.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_004174 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 42 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.44. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "78.12 N",
"B": "104.16 N",
"C": "11.416 N",
"D": "156.24 N"
} | B | 104.16 N | Net force=mg(sinθ−μcosθ)=42×10×(0.6−0.44×0.8)=104.16 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 104.16 N, not 78.12 N.",
"B": "Correct. The worked calculation gives 104.16 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 104.16 N, not 11.416 N.",
"D": "Incorrect. Substituting the state... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004977 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 2 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.325 A",
"B": "5.25 A",
"C": "1.625 A",
"D": "3.25 A"
} | D | 3.25 A | Series branch resistance=10+14=24 Ω. Parallel equivalent R_eq=(24×2)/(24+2)=1.84615 Ω. Total current I=V/R_eq=6/1.84615=3.25 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.25 A, not 1.325 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.25 A, not 5.25 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.25 A, not 1.625 A."... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006202 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 41 cm in front of a thin convex lens of focal length 14 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.51852",
"B": "1.03704",
"C": "0.51852",
"D": "3.51852"
} | C | 0.51852 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(41)(14)/(41−14)=21.25926 cm. Thus |m|=v/u=21.25926/41=0.51852. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.51852, not 1.51852.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.51852, not 1.03704.",
"C": "Correct. The worked calculation gives 0.51852.",
"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_007310 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 16 mol of gas at 646 K and 1.9 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "535.6681 L",
"B": "448.39008 L",
"C": "446.39008 L",
"D": "444.39008 L"
} | C | 446.39008 L | PV=nRT, so V=nRT/P=(16)(0.082057)(646)/(1.9)=446.39008 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 446.39008 L, not 535.6681 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 446.39008 L, not 448.39008 L.",
"C": "Correct. The worked calculation gives 446.39008 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_005244 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +8 μC and +5 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "30.75207 N",
"B": "29.75207 N",
"C": "28.75207 N",
"D": "23.80165 N"
} | B | 29.75207 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(8×10⁻⁶)(5×10⁻⁶)/(11×10⁻²)²=29.75207 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 29.75207 N, not 30.75207 N.",
"B": "Correct. The worked calculation gives 29.75207 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29.75207 N, not 28.75207 N.",
"D": "Incorrect. Substitutin... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009641 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_6H_8N_2X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "-1",
"B": "4",
"C": "1",
"D": "2"
} | D | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+2−8−4)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not -1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"D": "Correct. The worked c... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009141 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.11 V, transfers 3 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.1494 V",
"B": "0.86205 V",
"C": "1.7241 V",
"D": "-1.8506 V"
} | A | 1.1494 V | Apply the Nernst equation: E=1.11−(0.0591/3)(-2)=1.1494 V. | {
"A": "Correct. The worked calculation gives 1.1494 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1494 V, not 0.86205 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1494 V, not 1.7241 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_002284 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 7 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.16452",
"B": "-0.67097",
"C": "0.32903",
"D": "-2.67097"
} | C | 0.32903 | Favourable pairs = C(12,2)+C(7,2)+C(12,2)=153. Total pairs=C(31,2)=465. Therefore P=153/465=0.32903. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32903, not 0.16452.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32903, not -0.67097.",
"C": "Correct. The worked calculation gives 0.32903.",
"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_000846 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio 5. What is the sum of its first 11 terms? | {
"A": "36621093",
"B": "24414060",
"C": "-24414062",
"D": "24414062"
} | D | 24414062 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(5^11−1)/(5−1)=24414062. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24414062, not 36621093.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24414062, not 24414060.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24414062, 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_000767 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 4. What is the sum of its first 6 terms? | {
"A": "20475",
"B": "13650",
"C": "10237.5",
"D": "13649"
} | B | 13650 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(4^6−1)/(4−1)=13650. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13650, not 20475.",
"B": "Correct. The worked calculation gives 13650.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13650, not 10237.5.",
"D": "Incorrect. Substituting the stated values int... | [
"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_007896 | 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 11 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "2.34375 mmol L⁻¹",
"B": "-0.65625 mmol L⁻¹",
"C": "0.34375 mmol L⁻¹",
"D": "3.34375 mmol L⁻¹"
} | C | 0.34375 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=11/2^5=0.34375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34375 mmol L⁻¹, not 2.34375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34375 mmol L⁻¹, not -0.65625 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.34375 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_008575 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.55 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.209 K",
"B": "2.418 K",
"C": "3.418 K",
"D": "-0.582 K"
} | B | 2.418 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.52×1.55=2.418 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.418 K, not 1.209 K.",
"B": "Correct. The worked calculation gives 2.418 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.418 K, not 3.418 K.",
"D": "Incorrect. Substituting the stated va... | [
"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_002402 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 6], [2, 7]]. | {
"A": "16",
"B": "24",
"C": "12",
"D": "-16"
} | A | 16 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(7)−(6)(2)=16. | {
"A": "Correct. The worked calculation gives 16.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16, not 24.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16, not 12.",
"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_004543 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 10 kg and radius 1 m is acted on by a constant torque of 76 N m about its central axis. Find its angular acceleration. | {
"A": "15.2 rad s⁻²",
"B": "18.24 rad s⁻²",
"C": "11.4 rad s⁻²",
"D": "22.8 rad s⁻²"
} | A | 15.2 rad s⁻² | For a solid disc, I=½MR²=½(10)(1)²=5 kg m². Using τ=Iα, α=76/5=15.2 rad s⁻². | {
"A": "Correct. The worked calculation gives 15.2 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15.2 rad s⁻², not 18.24 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15.2 rad s⁻², not 11.4 rad s⁻².",
"D": "Incorrect. ... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001873 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 88 distinct elements? | {
"A": "64276915527",
"B": "-64276915527",
"C": "64276915525",
"D": "64276915526"
} | A | 64276915527 | Order does not matter, so the count is C(88,8)=88!/[8!(80)!]=64276915527. | {
"A": "Correct. The worked calculation gives 64276915527.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 64276915527, not -64276915527.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 64276915527, not 64276915525.",
"D": "Incorrect. Subst... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007508 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 98 mL of 0.10 M HCl is mixed with 71 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.69478",
"B": "0.89826",
"C": "1.79652",
"D": "1.34739"
} | C | 1.79652 | Excess H⁺ moles=0.10×(98−71)/1000=0.002700 mol. Total volume=0.169 L, so [H⁺]=0.015976 M and pH=−log₁₀[H⁺]=1.79652. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.79652, not 2.69478.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.79652, not 0.89826.",
"C": "Correct. The worked calculation gives 1.79652.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005022 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +3 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "153.875 N",
"B": "-151.875 N",
"C": "151.875 N",
"D": "182.25 N"
} | C | 151.875 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(3×10⁻⁶)/(4×10⁻²)²=151.875 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 151.875 N, not 153.875 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 151.875 N, not -151.875 N.",
"C": "Correct. The worked calculation gives 151.875 N.",
"D": "Incorrect. Substituting th... | [
"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_004773 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 5 Ω are connected in series; this combination is connected in parallel with a 14 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.72857 A",
"B": "0.48571 A",
"C": "2.48571 A",
"D": "-2.48571 A"
} | C | 2.48571 A | Series branch resistance=10+5=15 Ω. Parallel equivalent R_eq=(15×14)/(15+14)=7.24138 Ω. Total current I=V/R_eq=18/7.24138=2.48571 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.48571 A, not 3.72857 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.48571 A, not 0.48571 A.",
"C": "Correct. The worked calculation gives 2.48571 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_007590 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 21 mL of 0.10 M HCl is mixed with 14 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.69897",
"B": "3.39794",
"C": "3.69897",
"D": "0.84949"
} | A | 1.69897 | Excess H⁺ moles=0.10×(21−14)/1000=0.000700 mol. Total volume=0.035 L, so [H⁺]=0.020000 M and pH=−log₁₀[H⁺]=1.69897. | {
"A": "Correct. The worked calculation gives 1.69897.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.69897, not 3.39794.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.69897, not 3.69897.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008649 | 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 0.19 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.29184 K",
"B": "-0.70816 K",
"C": "1.02918 K",
"D": "1.29184 K"
} | A | 0.29184 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.512×0.19=0.29184 K. | {
"A": "Correct. The worked calculation gives 0.29184 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29184 K, not -0.70816 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29184 K, not 1.02918 K.",
"D": "Incorrect. Substituting th... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008044 | 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 15 A for 14997 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": "76.01369 g",
"B": "74.01369 g",
"C": "148.02738 g",
"D": "73.01369 g"
} | B | 74.01369 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×15×14997/(2×96500)=74.01369 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 74.01369 g, not 76.01369 g.",
"B": "Correct. The worked calculation gives 74.01369 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 74.01369 g, not 148.02738 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003408 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 44 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "19.19245 m",
"B": "179.92449 m",
"C": "181.92449 m",
"D": "145.53959 m"
} | C | 181.92449 m | Range R=u²sin(2θ)/g. Substituting u=44, θ=55° and g=10 gives R=(44)²sin(110°)/10=181.92449 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 181.92449 m, not 19.19245 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 181.92449 m, not 179.92449 m.",
"C": "Correct. The worked calculation gives 181.92449 m.",
"D": "Incorrect. Substit... | [
"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_004100 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 33 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.22. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "137.92 N",
"B": "139.92 N",
"C": "279.84 N",
"D": "104.94 N"
} | B | 139.92 N | Net force=mg(sinθ−μcosθ)=33×10×(0.6−0.22×0.8)=139.92 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 139.92 N, not 137.92 N.",
"B": "Correct. The worked calculation gives 139.92 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 139.92 N, not 279.84 N.",
"D": "Incorrect. Substituting the stat... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001920 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 4 elements can be selected from a set of 23 distinct elements? | {
"A": "13282.5",
"B": "8855",
"C": "4427.5",
"D": "-8855"
} | B | 8855 | Order does not matter, so the count is C(23,4)=23!/[4!(19)!]=8855. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8855, not 13282.5.",
"B": "Correct. The worked calculation gives 8855.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8855, not 4427.5.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_007497 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 36 mL of 0.10 M HCl is mixed with 24 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "3.39794",
"B": "-1.30103",
"C": "1.69897",
"D": "3.69897"
} | C | 1.69897 | Excess H⁺ moles=0.10×(36−24)/1000=0.001200 mol. Total volume=0.060 L, so [H⁺]=0.020000 M and pH=−log₁₀[H⁺]=1.69897. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.69897, not 3.39794.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.69897, not -1.30103.",
"C": "Correct. The worked calculation gives 1.69897.",
"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_002158 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 9 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-1.66667",
"B": "0.33333",
"C": "-0.66667",
"D": "0.66667"
} | B | 0.33333 | Favourable pairs = C(12,2)+C(9,2)+C(6,2)=117. Total pairs=C(27,2)=351. Therefore P=117/351=0.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not -1.66667.",
"B": "Correct. The worked calculation gives 0.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not -0.66667.",
"D": "Incorrect. Substituting the stated ... | [
"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_001715 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 6 elements can be selected from a set of 15 distinct elements? | {
"A": "6006",
"B": "-5005",
"C": "5004",
"D": "5005"
} | D | 5005 | Order does not matter, so the count is C(15,6)=15!/[6!(9)!]=5005. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5005, not 6006.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5005, not -5005.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5005, not 5004.",
"D": "Cor... | [
"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_007885 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 92 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "14.5 mmol L⁻¹",
"B": "-11.5 mmol L⁻¹",
"C": "8.625 mmol L⁻¹",
"D": "11.5 mmol L⁻¹"
} | D | 11.5 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=92/2^3=11.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.5 mmol L⁻¹, not 14.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.5 mmol L⁻¹, not -11.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation... | [
"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_001980 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 32 distinct elements? | {
"A": "15777450",
"B": "1051831",
"C": "10518301",
"D": "10518300"
} | D | 10518300 | Order does not matter, so the count is C(32,8)=32!/[8!(24)!]=10518300. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10518300, not 15777450.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10518300, not 1051831.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10518300, not 1... | [
"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_006979 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 27 mol H₂ and 5 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "10 mol",
"B": "13 mol",
"C": "2 mol",
"D": "-10 mol"
} | A | 10 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 27 mol H₂O; O₂ can produce 10 mol H₂O. The limiting condition is O₂; product=10 mol. | {
"A": "Correct. The worked calculation gives 10 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 13 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 2 mol.",
"D": "Incorrect. Substituting the stated values i... | [
"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_000739 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 12 and common ratio 2. What is the sum of its first 6 terms? | {
"A": "754",
"B": "76.6",
"C": "756",
"D": "1512"
} | C | 756 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=12(2^6−1)/(2−1)=756. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 756, not 754.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 756, not 76.6.",
"C": "Correct. The worked calculation gives 756.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_009413 | 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_18H_23N_1X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "4.5",
"B": "7",
"C": "6",
"D": "9"
} | C | 6 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+1−23−4)/2=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 7.",
"C": "Correct. The worked calculation gives 6.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_007496 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 50 mL of 0.10 M HCl is mixed with 79 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "14.35181",
"B": "-12.35181",
"C": "12.35181",
"D": "24.70362"
} | C | 12.35181 | Excess OH⁻ moles=0.10×(79−50)/1000=0.002900 mol. Total volume=0.129 L, so [OH⁻]=0.022481 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.35181. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.35181, not 14.35181.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.35181, not -12.35181.",
"C": "Correct. The worked calculation gives 12.35181.",
"D": "Incorrect. Substituting the sta... | [
"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_006353 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 1 kg is attached to an ideal spring of force constant 360 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.89459 s",
"B": "0.0527 s",
"C": "0.10541 s",
"D": "0.15811 s"
} | C | 0.10541 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(1/360)=0.10541 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.10541 s, not -0.89459 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.10541 s, not 0.0527 s.",
"C": "Correct. The worked calculation gives 0.10541 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_005868 | 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 3.3 atm at 203 K. What is its pressure at 261 K? | {
"A": "2.12143 atm",
"B": "3.24286 atm",
"C": "8.48571 atm",
"D": "4.24286 atm"
} | D | 4.24286 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.3)(261)/(203)=4.24286 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.24286 atm, not 2.12143 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.24286 atm, not 3.24286 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.... | [
"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_005242 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +1 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "2.44444 N",
"B": "4.44444 N",
"C": "3.33333 N",
"D": "7.44444 N"
} | B | 4.44444 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(1×10⁻⁶)/(9×10⁻²)²=4.44444 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.44444 N, not 2.44444 N.",
"B": "Correct. The worked calculation gives 4.44444 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.44444 N, not 3.33333 N.",
"D": "Incorrect. Substituting the... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009866 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(OH)_3]^-4, each OH ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "-2",
"B": "-1.5",
"C": "-1",
"D": "1"
} | C | -1 | Let the formal oxidation state of Ni be x. Charge balance gives x+(3)(−1)=-4; hence x=-4+3=-1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1, not -1.5.",
"C": "Correct. The worked calculation gives -1.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005215 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +1 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "-0.2 N",
"B": "0.8 N",
"C": "1.8 N",
"D": "-1.2 N"
} | C | 1.8 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(1×10⁻⁶)/(10×10⁻²)²=1.8 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.8 N, not -0.2 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.8 N, not 0.8 N.",
"C": "Correct. The worked calculation gives 1.8 N.",
"D": "Incorrect. Substituting the stated values into... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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