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_008314 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 10 A for 4298 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": "15.14109 g",
"B": "11.14109 g",
"C": "21.21163 g",
"D": "14.14109 g"
} | D | 14.14109 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×10×4298/(2×96500)=14.14109 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14.14109 g, not 15.14109 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14.14109 g, not 11.14109 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14.141... | [
"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_007327 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 8 mol of gas at 306 K and 2.5 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "9.03502 L",
"B": "60.26266 L",
"C": "80.35021 L",
"D": "96.42026 L"
} | C | 80.35021 L | PV=nRT, so V=nRT/P=(8)(0.082057)(306)/(2.5)=80.35021 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 80.35021 L, not 9.03502 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 80.35021 L, not 60.26266 L.",
"C": "Correct. The worked calculation gives 80.35021 L.",
"D": "Incorrect. Substituting... | [
"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_000902 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio 4. What is the sum of its first 11 terms? | {
"A": "2796201",
"B": "3355442.4",
"C": "2796202",
"D": "2796204"
} | C | 2796202 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(4^11−1)/(4−1)=2796202. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2796202, not 2796201.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2796202, not 3355442.4.",
"C": "Correct. The worked calculation gives 2796202.",
"D": "Incorrect. Substituting the stated ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008986 | 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 1.46 mol L⁻¹ and initially B is absent. At equilibrium, 70% of A has dissociated at constant volume. Find K_c. | {
"A": "7.53867",
"B": "4.76933",
"C": "12.53867",
"D": "9.53867"
} | D | 9.53867 | Let α=0.7. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.46)(0.7)²/(1−0.7)=9.53867. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.53867, not 7.53867.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.53867, not 4.76933.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.53867, not 12.53... | [
"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_006100 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 78 cm in front of a thin convex lens of focal length 27 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.52941",
"B": "3.52941",
"C": "-0.47059",
"D": "-1.47059"
} | A | 0.52941 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(78)(27)/(78−27)=41.29412 cm. Thus |m|=v/u=41.29412/78=0.52941. | {
"A": "Correct. The worked calculation gives 0.52941.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.52941, not 3.52941.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.52941, not -0.47059.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003306 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-9+3i)/(1+6i). What is Re(z), the real part of z? | {
"A": "0.36486",
"B": "0.18243",
"C": "0.24324",
"D": "0.12162"
} | C | 0.24324 | Multiply numerator and denominator by the conjugate (1-6i). Then Re(z)=(ac+bd)/(c²+d²)=((-9)(1)+(3)(6))/(1²+(6)²)=0.24324. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.24324, not 0.36486.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.24324, not 0.18243.",
"C": "Correct. The worked calculation gives 0.24324.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001484 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (-3x² +1x +2) dx. | {
"A": "-3",
"B": "-4",
"C": "0.8",
"D": "-2"
} | D | -2 | An antiderivative is (-3/3)x³+(1/2)x²+(2)x. Evaluating between 0 and 2 gives (-3/3)(2)³+(1/2)(2)²+(2)(2)=-2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2, not -3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2, not -4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2, not 0.8.",
"D": "Correct. The wo... | [
"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_006264 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 50 cm in front of a thin convex lens of focal length 25 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.75",
"B": "0.5",
"C": "1",
"D": "3"
} | C | 1 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(50)(25)/(50−25)=50 cm. Thus |m|=v/u=50/50=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.5.",
"C": "Correct. The worked calculation gives 1.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_004503 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 15 kg and radius 1 m is acted on by a constant torque of 10 N m about its central axis. Find its angular acceleration. | {
"A": "1.33333 rad s⁻²",
"B": "4.33333 rad s⁻²",
"C": "3.33333 rad s⁻²",
"D": "-1.66667 rad s⁻²"
} | A | 1.33333 rad s⁻² | For a solid disc, I=½MR²=½(15)(1)²=7.5 kg m². Using τ=Iα, α=10/7.5=1.33333 rad s⁻². | {
"A": "Correct. The worked calculation gives 1.33333 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.33333 rad s⁻², not 4.33333 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.33333 rad s⁻², not 3.33333 rad s⁻².",
"D"... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007716 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 12 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "1.00469 mmol L⁻¹",
"B": "0.04688 mmol L⁻¹",
"C": "0.02344 mmol L⁻¹",
"D": "0.09375 mmol L⁻¹"
} | B | 0.04688 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=12/2^8=0.04688 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.04688 mmol L⁻¹, not 1.00469 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 0.04688 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.04688 mmol L⁻¹, not 0.02344 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_000356 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 23 and common difference 8. Find the sum of its first 27 terms. | {
"A": "343.9",
"B": "3431",
"C": "1714.5",
"D": "3429"
} | D | 3429 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=23, d=8, n=27: Sₙ=27/2[2(23)+(27−1)(8)]=3429. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3429, not 343.9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3429, not 3431.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3429, not 1714.5.",
"D": "C... | [
"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_004343 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 9 kg and radius 3 m is acted on by a constant torque of 38 N m about its central axis. Find its angular acceleration. | {
"A": "0.7037 rad s⁻²",
"B": "0.93827 rad s⁻²",
"C": "1.93827 rad s⁻²",
"D": "-2.06173 rad s⁻²"
} | B | 0.93827 rad s⁻² | For a solid disc, I=½MR²=½(9)(3)²=40.5 kg m². Using τ=Iα, α=38/40.5=0.93827 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.93827 rad s⁻², not 0.7037 rad s⁻².",
"B": "Correct. The worked calculation gives 0.93827 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.93827 rad s⁻², not 1.93827 rad s⁻².",
"D":... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000402 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -13 and common difference 8. Find the sum of its first 22 terms. | {
"A": "2343",
"B": "1249.6",
"C": "1562",
"D": "1560"
} | C | 1562 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-13, d=8, n=22: Sₙ=22/2[2(-13)+(22−1)(8)]=1562. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1562, not 2343.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1562, not 1249.6.",
"C": "Correct. The worked calculation gives 1562.",
"D": "Incorrect. Substituting the stated values into the... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009345 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_13H_20. Treat X as the total number of monovalent halogen atoms. | {
"A": "4",
"B": "8",
"C": "1",
"D": "1.4"
} | A | 4 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×13+2+0−20−0)/2=4. | {
"A": "Correct. The worked calculation gives 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001042 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ -4x² +10x+7. Evaluate f′(-3). | {
"A": "195",
"B": "196",
"C": "147",
"D": "98"
} | B | 196 | Differentiate: f′(x)=3(6)x²+2(-4)x+(10). At x=-3, f′(-3)=3(6)(-3)²+2(-4)(-3)+(10)=196. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 196, not 195.",
"B": "Correct. The worked calculation gives 196.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 196, not 147.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008872 | 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, 59% of A has dissociated at constant volume. Find K_c. | {
"A": "0.29421",
"B": "6.29421",
"C": "6.58843",
"D": "3.29421"
} | D | 3.29421 | Let α=0.59. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.97)(0.59)²/(1−0.59)=3.29421. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.29421, not 0.29421.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.29421, not 6.29421.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.29421, not 6.588... | [
"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_001984 | 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 56 distinct elements? | {
"A": "440748",
"B": "367290",
"C": "367289",
"D": "-367290"
} | B | 367290 | Order does not matter, so the count is C(56,4)=56!/[4!(52)!]=367290. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 367290, not 440748.",
"B": "Correct. The worked calculation gives 367290.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 367290, not 367289.",
"D": "Incorrect. Substituting the stated values ... | [
"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_004002 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 9 m s⁻¹. A constant net force does 21 N of work over 17 m in the direction of motion. Find its final kinetic energy. | {
"A": "521 J",
"B": "519 J",
"C": "52.9 J",
"D": "517 J"
} | B | 519 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(9)²+(21)(17)=519 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 519 J, not 521 J.",
"B": "Correct. The worked calculation gives 519 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 519 J, not 52.9 J.",
"D": "Incorrect. Substituting the stated values into... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009339 | 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_14X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "7",
"B": "2",
"C": "15",
"D": "10"
} | D | 10 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+0−14−4)/2=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 15.",
"D": "Correct. The worke... | [
"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_009465 | 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_10X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "10",
"B": "18",
"C": "12",
"D": "9"
} | C | 12 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+0−10−4)/2=12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12, not 10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12, not 18.",
"C": "Correct. The worked calculation gives 12.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005352 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 30 μF capacitor is charged to a potential difference of 2 V. Calculate the energy stored, expressed in μJ. | {
"A": "61 μJ",
"B": "60 μJ",
"C": "7 μJ",
"D": "62 μJ"
} | B | 60 μJ | U=½CV². Since C=30 μF, U in μJ is ½×30×(2)²=60 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 60 μJ, not 61 μJ.",
"B": "Correct. The worked calculation gives 60 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 60 μJ, not 7 μJ.",
"D": "Incorrect. Substituting the stated values into t... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008792 | 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 0.61 mol L⁻¹ and initially B is absent. At equilibrium, 58% of A has dissociated at constant volume. Find K_c. | {
"A": "1.95432",
"B": "3.95432",
"C": "2.93149",
"D": "-1.95432"
} | A | 1.95432 | Let α=0.58. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.61)(0.58)²/(1−0.58)=1.95432. | {
"A": "Correct. The worked calculation gives 1.95432.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.95432, not 3.95432.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.95432, not 2.93149.",
"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_002977 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-2, -5, 2) and v=(-4, 8, 9), calculate u·v. | {
"A": "-21",
"B": "-16",
"C": "-14",
"D": "14"
} | C | -14 | The dot product is the sum of corresponding component products: (-2)(-4)+(-5)(8)+(2)(9)=-14. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -14, not -21.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -14, not -16.",
"C": "Correct. The worked calculation gives -14.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_003452 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 96 m s⁻¹ at 50° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "726.07906 m",
"B": "91.75988 m",
"C": "907.59883 m",
"D": "1089.11859 m"
} | C | 907.59883 m | Range R=u²sin(2θ)/g. Substituting u=96, θ=50° and g=10 gives R=(96)²sin(100°)/10=907.59883 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 907.59883 m, not 726.07906 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 907.59883 m, not 91.75988 m.",
"C": "Correct. The worked calculation gives 907.59883 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_005118 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +8 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "405 N",
"B": "270 N",
"C": "271 N",
"D": "269 N"
} | B | 270 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(8×10⁻⁶)/(4×10⁻²)²=270 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 270 N, not 405 N.",
"B": "Correct. The worked calculation gives 270 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 270 N, not 271 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_008681 | 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 1.84 mol L⁻¹ and initially B is absent. At equilibrium, 11% of A has dissociated at constant volume. Find K_c. | {
"A": "3.10006",
"B": "0.05003",
"C": "0.10006",
"D": "-0.10006"
} | C | 0.10006 | Let α=0.11. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.84)(0.11)²/(1−0.11)=0.10006. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.10006, not 3.10006.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.10006, not 0.05003.",
"C": "Correct. The worked calculation gives 0.10006.",
"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_007730 | 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 26 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "8.5 mmol L⁻¹",
"B": "9.5 mmol L⁻¹",
"C": "9.75 mmol L⁻¹",
"D": "6.5 mmol L⁻¹"
} | D | 6.5 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=26/2^2=6.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.5 mmol L⁻¹, not 8.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.5 mmol L⁻¹, not 9.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation give... | [
"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_002451 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, -6], [6, -4]]. | {
"A": "4",
"B": "2",
"C": "6",
"D": "3"
} | A | 4 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(-4)−(-6)(6)=4. | {
"A": "Correct. The worked calculation gives 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 6.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001749 | 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 68 distinct elements? | {
"A": "610788.75",
"B": "814385",
"C": "814383",
"D": "814387"
} | B | 814385 | Order does not matter, so the count is C(68,4)=68!/[4!(64)!]=814385. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 814385, not 610788.75.",
"B": "Correct. The worked calculation gives 814385.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 814385, not 814383.",
"D": "Incorrect. Substituting the stated valu... | [
"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_002091 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 6 blue and 10 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.33333",
"B": "0.66667",
"C": "3.33333",
"D": "1.33333"
} | A | 0.33333 | Favourable pairs = C(12,2)+C(6,2)+C(10,2)=126. Total pairs=C(28,2)=378. Therefore P=126/378=0.33333. | {
"A": "Correct. The worked calculation gives 0.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not 0.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not 3.33333.",
"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_007732 | 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 86 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "-10.75 mmol L⁻¹",
"B": "10.75 mmol L⁻¹",
"C": "8.0625 mmol L⁻¹",
"D": "5.375 mmol L⁻¹"
} | B | 10.75 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=86/2^3=10.75 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.75 mmol L⁻¹, not -10.75 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 10.75 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10.75 mmol L⁻¹, not 8.0625 mmol L⁻¹.",
"D": "... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004285 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.30. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "43.2 N",
"B": "64.8 N",
"C": "5.32 N",
"D": "-43.2 N"
} | A | 43.2 N | Net force=mg(sinθ−μcosθ)=12×10×(0.6−0.30×0.8)=43.2 N. | {
"A": "Correct. The worked calculation gives 43.2 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 43.2 N, not 64.8 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 43.2 N, not 5.32 N.",
"D": "Incorrect. Substituting the stated values ... | [
"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_005543 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 3 μF capacitor is charged to a potential difference of 17 V. Calculate the energy stored, expressed in μJ. | {
"A": "434.5 μJ",
"B": "433.5 μJ",
"C": "346.8 μJ",
"D": "650.25 μJ"
} | B | 433.5 μJ | U=½CV². Since C=3 μF, U in μJ is ½×3×(17)²=433.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 433.5 μJ, not 434.5 μJ.",
"B": "Correct. The worked calculation gives 433.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 433.5 μJ, not 346.8 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_008067 | 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 28824 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": "140.25316 g",
"B": "71.12658 g",
"C": "-142.25316 g",
"D": "142.25316 g"
} | D | 142.25316 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×15×28824/(2×96500)=142.25316 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 142.25316 g, not 140.25316 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 142.25316 g, not 71.12658 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 142... | [
"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_003949 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 13 kg block initially moves at 0 m s⁻¹. A constant net force does 21 N of work over 16 m in the direction of motion. Find its final kinetic energy. | {
"A": "252 J",
"B": "335 J",
"C": "672 J",
"D": "336 J"
} | D | 336 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(13)(0)²+(21)(16)=336 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 336 J, not 252 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 336 J, not 335 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 336 J, not 672 J.",
"D":... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003073 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(2-14i)/(7+9i). What is Re(z), the real part of z? | {
"A": "-2.86154",
"B": "-1.86154",
"C": "-0.86154",
"D": "-1.72308"
} | C | -0.86154 | Multiply numerator and denominator by the conjugate (7-9i). Then Re(z)=(ac+bd)/(c²+d²)=((2)(7)+(-14)(9))/(7²+(9)²)=-0.86154. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.86154, not -2.86154.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.86154, not -1.86154.",
"C": "Correct. The worked calculation gives -0.86154.",
"D": "Incorrect. Substituting the stat... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004906 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 6 Ω are connected in series; this combination is connected in parallel with a 12 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "7.57143 A",
"B": "5.57143 A",
"C": "8.35714 A",
"D": "4.57143 A"
} | B | 5.57143 A | Series branch resistance=8+6=14 Ω. Parallel equivalent R_eq=(14×12)/(14+12)=6.46154 Ω. Total current I=V/R_eq=36/6.46154=5.57143 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.57143 A, not 7.57143 A.",
"B": "Correct. The worked calculation gives 5.57143 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.57143 A, not 8.35714 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_004227 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 35 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.13. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "260.4 N",
"B": "208.32 N",
"C": "18.36 N",
"D": "173.6 N"
} | D | 173.6 N | Net force=mg(sinθ−μcosθ)=35×10×(0.6−0.13×0.8)=173.6 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 173.6 N, not 260.4 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 173.6 N, not 208.32 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 173.6 N, not 18.3... | [
"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_001849 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 11 elements can be selected from a set of 90 distinct elements? | {
"A": "-41604694413840",
"B": "41604694413840",
"C": "31203520810380",
"D": "4160469441385"
} | B | 41604694413840 | Order does not matter, so the count is C(90,11)=90!/[11!(79)!]=41604694413840. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 41604694413840, not -41604694413840.",
"B": "Correct. The worked calculation gives 41604694413840.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 41604694413840, not 31203520810380.",
"D": "I... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004098 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 46 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.13. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "114.08 N",
"B": "228.16 N",
"C": "229.16 N",
"D": "227.16 N"
} | B | 228.16 N | Net force=mg(sinθ−μcosθ)=46×10×(0.6−0.13×0.8)=228.16 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 228.16 N, not 114.08 N.",
"B": "Correct. The worked calculation gives 228.16 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 228.16 N, not 229.16 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_008778 | 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 0.74 mol L⁻¹ and initially B is absent. At equilibrium, 23% of A has dissociated at constant volume. Find K_c. | {
"A": "0.15252",
"B": "-1.79664",
"C": "1.02034",
"D": "0.20336"
} | D | 0.20336 | Let α=0.23. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.74)(0.23)²/(1−0.23)=0.20336. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.20336, not 0.15252.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.20336, not -1.79664.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.20336, not 1.02... | [
"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_009757 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(OH)_3]^+0, each OH ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "3",
"B": "0",
"C": "6",
"D": "-3"
} | A | 3 | Let the formal oxidation state of Mn be x. Charge balance gives x+(3)(−1)=+0; hence x=0+3=+3. | {
"A": "Correct. The worked calculation gives 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 0.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"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_003103 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(0-14i)/(1+3i). What is Re(z), the real part of z? | {
"A": "-3.15",
"B": "-4.2",
"C": "4.2",
"D": "-3.2"
} | B | -4.2 | Multiply numerator and denominator by the conjugate (1-3i). Then Re(z)=(ac+bd)/(c²+d²)=((0)(1)+(-14)(3))/(1²+(3)²)=-4.2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4.2, not -3.15.",
"B": "Correct. The worked calculation gives -4.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -4.2, not 4.2.",
"D": "Incorrect. Substituting the stated values into the g... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008573 | 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 0.79 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": "3.21344 K",
"B": "4.21344 K",
"C": "-1.78656 K",
"D": "1.21344 K"
} | D | 1.21344 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.512×0.79=1.21344 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.21344 K, not 3.21344 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.21344 K, not 4.21344 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.21344 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_008593 | 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 1.78 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": "1.7768 K",
"B": "5.5536 K",
"C": "2.7768 K",
"D": "1.27768 K"
} | C | 2.7768 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.52×1.78=2.7768 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.7768 K, not 1.7768 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.7768 K, not 5.5536 K.",
"C": "Correct. The worked calculation gives 2.7768 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_003867 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 3 m s⁻¹. A constant net force does 10 N of work over 3 m in the direction of motion. Find its final kinetic energy. | {
"A": "71.5 J",
"B": "52.875 J",
"C": "141 J",
"D": "70.5 J"
} | D | 70.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(3)²+(10)(3)=70.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 70.5 J, not 71.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 70.5 J, not 52.875 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 70.5 J, not 141 J.",... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008671 | 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 0.45 mol L⁻¹ and initially B is absent. At equilibrium, 31% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.7493",
"B": "0.2507",
"C": "-0.2507",
"D": "-1.7493"
} | B | 0.2507 | Let α=0.31. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.45)(0.31)²/(1−0.31)=0.2507. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.2507, not -0.7493.",
"B": "Correct. The worked calculation gives 0.2507.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.2507, not -0.2507.",
"D": "Incorrect. Substituting the stated value... | [
"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_005668 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 62 μF capacitor is charged to a potential difference of 25 V. Calculate the energy stored, expressed in μJ. | {
"A": "19375 μJ",
"B": "1938.5 μJ",
"C": "-19375 μJ",
"D": "29062.5 μJ"
} | A | 19375 μJ | U=½CV². Since C=62 μF, U in μJ is ½×62×(25)²=19375 μJ. | {
"A": "Correct. The worked calculation gives 19375 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19375 μJ, not 1938.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19375 μJ, not -19375 μJ.",
"D": "Incorrect. Substituting the st... | [
"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_002980 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-4, 5, 7) and v=(2, -1, 2), calculate u·v. | {
"A": "1.5",
"B": "1.1",
"C": "0.5",
"D": "1"
} | D | 1 | The dot product is the sum of corresponding component products: (-4)(2)+(5)(-1)+(7)(2)=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.5.",
"D": "Correct. The wor... | [
"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_005742 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.4 atm at 181 K. What is its pressure at 536 K? | {
"A": "14.02983 atm",
"B": "13.02983 atm",
"C": "2.30298 atm",
"D": "-13.02983 atm"
} | B | 13.02983 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.4)(536)/(181)=13.02983 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13.02983 atm, not 14.02983 atm.",
"B": "Correct. The worked calculation gives 13.02983 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13.02983 atm, not 2.30298 atm.",
"D": "Incorrect. Su... | [
"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_008000 | 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 79 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "-2.69141 mmol L⁻¹",
"B": "0.46289 mmol L⁻¹",
"C": "0.30859 mmol L⁻¹",
"D": "-0.30859 mmol L⁻¹"
} | C | 0.30859 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=79/2^8=0.30859 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30859 mmol L⁻¹, not -2.69141 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30859 mmol L⁻¹, not 0.46289 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.30859 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_005887 | 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 3.9 atm at 322 K. What is its pressure at 711 K? | {
"A": "5.61149 atm",
"B": "8.61149 atm",
"C": "4.30575 atm",
"D": "12.91724 atm"
} | B | 8.61149 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.9)(711)/(322)=8.61149 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.61149 atm, not 5.61149 atm.",
"B": "Correct. The worked calculation gives 8.61149 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.61149 atm, not 4.30575 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_004405 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 3 m is acted on by a constant torque of 54 N m about its central axis. Find its angular acceleration. | {
"A": "0.5 rad s⁻²",
"B": "1.5 rad s⁻²",
"C": "-0.5 rad s⁻²",
"D": "0.75 rad s⁻²"
} | B | 1.5 rad s⁻² | For a solid disc, I=½MR²=½(8)(3)²=36 kg m². Using τ=Iα, α=54/36=1.5 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.5 rad s⁻², not 0.5 rad s⁻².",
"B": "Correct. The worked calculation gives 1.5 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.5 rad s⁻², not -0.5 rad s⁻².",
"D": "Incorrect. Subst... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001414 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (0x² -8x +7) dx. | {
"A": "-2",
"B": "-3",
"C": "-4",
"D": "-1"
} | A | -2 | An antiderivative is (0/3)x³+(-8/2)x²+(7)x. Evaluating between 0 and 2 gives (0/3)(2)³+(-8/2)(2)²+(7)(2)=-2. | {
"A": "Correct. The worked calculation gives -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2, not -3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2, not -4.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_005198 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +7 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "1419.5 N",
"B": "1417.5 N",
"C": "1063.125 N",
"D": "2126.25 N"
} | B | 1417.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(7×10⁻⁶)/(2×10⁻²)²=1417.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1417.5 N, not 1419.5 N.",
"B": "Correct. The worked calculation gives 1417.5 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1417.5 N, not 1063.125 N.",
"D": "Incorrect. Substituting the st... | [
"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_002098 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 3 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.46154",
"B": "2.30769",
"C": "0.30769",
"D": "-0.69231"
} | C | 0.30769 | Favourable pairs = C(5,2)+C(3,2)+C(6,2)=28. Total pairs=C(14,2)=91. Therefore P=28/91=0.30769. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not 0.46154.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not 2.30769.",
"C": "Correct. The worked calculation gives 0.30769.",
"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_000339 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 24 and common difference 9. Find the sum of its first 32 terms. | {
"A": "5233",
"B": "5232",
"C": "5231",
"D": "4185.6"
} | B | 5232 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=24, d=9, n=32: Sₙ=32/2[2(24)+(32−1)(9)]=5232. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5232, not 5233.",
"B": "Correct. The worked calculation gives 5232.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5232, not 5231.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003407 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 13 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "11.94615 m",
"B": "10.94615 m",
"C": "12.94615 m",
"D": "13.94615 m"
} | C | 12.94615 m | Range R=u²sin(2θ)/g. Substituting u=13, θ=25° and g=10 gives R=(13)²sin(50°)/10=12.94615 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.94615 m, not 11.94615 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.94615 m, not 10.94615 m.",
"C": "Correct. The worked calculation gives 12.94615 m.",
"D": "Incorrect. Substitutin... | [
"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_003267 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(8-2i)/(8+9i). What is Re(z), the real part of z? | {
"A": "2.31724",
"B": "-0.31724",
"C": "-2.68276",
"D": "0.31724"
} | D | 0.31724 | Multiply numerator and denominator by the conjugate (8-9i). Then Re(z)=(ac+bd)/(c²+d²)=((8)(8)+(-2)(9))/(8²+(9)²)=0.31724. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31724, not 2.31724.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31724, not -0.31724.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31724, not -2.6... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007181 | 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 311 K and 2.28 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "177.0858 L",
"B": "358.17161 L",
"C": "179.0858 L",
"D": "214.90296 L"
} | C | 179.0858 L | PV=nRT, so V=nRT/P=(16)(0.082057)(311)/(2.28)=179.0858 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 179.0858 L, not 177.0858 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 179.0858 L, not 358.17161 L.",
"C": "Correct. The worked calculation gives 179.0858 L.",
"D": "Incorrect. Substituti... | [
"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_001291 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ -9x² -1x+7. Evaluate f′(2). | {
"A": "17.5",
"B": "4.5",
"C": "33",
"D": "35"
} | D | 35 | Differentiate: f′(x)=3(6)x²+2(-9)x+(-1). At x=2, f′(2)=3(6)(2)²+2(-9)(2)+(-1)=35. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 35, not 17.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 35, not 4.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 35, not 33.",
"D": "Correct. The ... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001666 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (-2x² +8x -2) dx. | {
"A": "6",
"B": "9",
"C": "24",
"D": "12"
} | D | 12 | An antiderivative is (-2/3)x³+(8/2)x²+(-2)x. Evaluating between 0 and 3 gives (-2/3)(3)³+(8/2)(3)²+(-2)(3)=12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12, not 9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12, not 24.",
"D": "Correct. The worke... | [
"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_005328 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +4 μC are separated by 5 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "23.04 N",
"B": "28.8 N",
"C": "21.6 N",
"D": "14.4 N"
} | B | 28.8 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(4×10⁻⁶)/(5×10⁻²)²=28.8 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28.8 N, not 23.04 N.",
"B": "Correct. The worked calculation gives 28.8 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28.8 N, not 21.6 N.",
"D": "Incorrect. Substituting the stated values... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003054 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-12-8i)/(11+5i). What is Re(z), the real part of z? | {
"A": "-1.17808",
"B": "-0.58904",
"C": "-3.17808",
"D": "-4.17808"
} | A | -1.17808 | Multiply numerator and denominator by the conjugate (11-5i). Then Re(z)=(ac+bd)/(c²+d²)=((-12)(11)+(-8)(5))/(11²+(5)²)=-1.17808. | {
"A": "Correct. The worked calculation gives -1.17808.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.17808, not -0.58904.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.17808, not -3.17808.",
"D": "Incorrect. Substituting the stat... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005799 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.6 atm at 262 K. What is its pressure at 557 K? | {
"A": "-0.72443 atm",
"B": "1.27557 atm",
"C": "3.27557 atm",
"D": "2.55115 atm"
} | B | 1.27557 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.6)(557)/(262)=1.27557 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.27557 atm, not -0.72443 atm.",
"B": "Correct. The worked calculation gives 1.27557 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.27557 atm, not 3.27557 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_000297 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 -16x +11=0, let its roots be α and β. What is α²+β²? | {
"A": "13.5",
"B": "21",
"C": "10.5",
"D": "15.75"
} | C | 10.5 | By Vieta's relations, α+β = 16/4 and αβ = 11/4. Then α²+β²=(α+β)²−2αβ = (16/4)²−2(11/4) = 10.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.5, not 13.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.5, not 21.",
"C": "Correct. The worked calculation gives 10.5.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_001872 | 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 78 distinct elements? | {
"A": "43430966148115",
"B": "43430966148114",
"C": "43430966148113",
"D": "65146449222172.5"
} | A | 43430966148115 | Order does not matter, so the count is C(78,12)=78!/[12!(66)!]=43430966148115. | {
"A": "Correct. The worked calculation gives 43430966148115.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 43430966148115, not 43430966148114.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 43430966148115, not 43430966148113.",
"D": "In... | [
"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_009700 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(OH)_5]^-4, each OH ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "2",
"B": "1.1",
"C": "-2",
"D": "1"
} | D | 1 | Let the formal oxidation state of Cu be x. Charge balance gives x+(5)(−1)=-4; hence x=-4+5=+1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not -2.",
"D": "Correct. The worked... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001878 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 7 elements can be selected from a set of 63 distinct elements? | {
"A": "553270672",
"B": "553270669",
"C": "553270671",
"D": "414953003.25"
} | C | 553270671 | Order does not matter, so the count is C(63,7)=63!/[7!(56)!]=553270671. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 553270671, not 553270672.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 553270671, not 553270669.",
"C": "Correct. The worked calculation gives 553270671.",
"D": "Incorrect. Substituting the... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000188 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 -6x -1=0, let its roots be α and β. What is α²+β²? | {
"A": "1.84",
"B": "4.84",
"C": "3.84",
"D": "-1.16"
} | A | 1.84 | By Vieta's relations, α+β = 6/5 and αβ = -1/5. Then α²+β²=(α+β)²−2αβ = (6/5)²−2(-1/5) = 1.84. | {
"A": "Correct. The worked calculation gives 1.84.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.84, not 4.84.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.84, not 3.84.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_004995 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 16 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.375 A",
"B": "1.3375 A",
"C": "6.75 A",
"D": "1.375 A"
} | A | 3.375 A | Series branch resistance=4+4=8 Ω. Parallel equivalent R_eq=(8×16)/(8+16)=5.33333 Ω. Total current I=V/R_eq=18/5.33333=3.375 A. | {
"A": "Correct. The worked calculation gives 3.375 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.375 A, not 1.3375 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.375 A, not 6.75 A.",
"D": "Incorrect. Substituting the stated va... | [
"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_005221 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +1 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "-157.5 N",
"B": "315 N",
"C": "157.5 N",
"D": "159.5 N"
} | C | 157.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(1×10⁻⁶)/(2×10⁻²)²=157.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 157.5 N, not -157.5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 157.5 N, not 315 N.",
"C": "Correct. The worked calculation gives 157.5 N.",
"D": "Incorrect. Substituting the stated val... | [
"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_006419 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 14 kg is attached to an ideal spring of force constant 369 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.61043 s",
"B": "2.38957 s",
"C": "0.77913 s",
"D": "0.38957 s"
} | D | 0.38957 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(14/369)=0.38957 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.38957 s, not -0.61043 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.38957 s, not 2.38957 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.38957 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002058 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 7 red, 5 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.4625",
"B": "0.15417",
"C": "0.30833",
"D": "1.03083"
} | C | 0.30833 | Favourable pairs = C(7,2)+C(5,2)+C(4,2)=37. Total pairs=C(16,2)=120. Therefore P=37/120=0.30833. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30833, not 0.4625.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30833, not 0.15417.",
"C": "Correct. The worked calculation gives 0.30833.",
"D": "Incorrect. Substituting the stated val... | [
"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_009731 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(CN)_4]^-1, each CN ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "6",
"B": "4",
"C": "0",
"D": "3"
} | D | 3 | Let the formal oxidation state of Fe be x. Charge balance gives x+(4)(−1)=-1; hence x=-1+4=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 0.",
"D": "Correct. The worked ca... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000073 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +7x +11=0, let its roots be α and β. What is α²+β²? | {
"A": "-4.88",
"B": "0.56",
"C": "2.44",
"D": "-2.44"
} | D | -2.44 | By Vieta's relations, α+β = -7/5 and αβ = 11/5. Then α²+β²=(α+β)²−2αβ = (-7/5)²−2(11/5) = -2.44. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2.44, not -4.88.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2.44, not 0.56.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2.44, not 2.44.",
"D": "... | [
"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_001581 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (6x² +8x +0) dx. | {
"A": "1.6",
"B": "6",
"C": "12",
"D": "5"
} | B | 6 | An antiderivative is (6/3)x³+(8/2)x²+(0)x. Evaluating between 0 and 1 gives (6/3)(1)³+(8/2)(1)²+(0)(1)=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 1.6.",
"B": "Correct. The worked calculation gives 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 12.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"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_005169 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +1 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "15 N",
"B": "30 N",
"C": "20 N",
"D": "-20 N"
} | C | 20 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(1×10⁻⁶)/(3×10⁻²)²=20 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20 N, not 15 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20 N, not 30 N.",
"C": "Correct. The worked calculation gives 20 N.",
"D": "Incorrect. Substituting the stated values into the g... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006300 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 73 cm in front of a thin convex lens of focal length 22 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.43137",
"B": "-0.56863",
"C": "0.21569",
"D": "0.32353"
} | A | 0.43137 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(73)(22)/(73−22)=31.4902 cm. Thus |m|=v/u=31.4902/73=0.43137. | {
"A": "Correct. The worked calculation gives 0.43137.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.43137, not -0.56863.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.43137, not 0.21569.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000698 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 5. What is the sum of its first 5 terms? | {
"A": "7810",
"B": "7812",
"C": "7809",
"D": "5857.5"
} | A | 7810 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(5^5−1)/(5−1)=7810. | {
"A": "Correct. The worked calculation gives 7810.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7810, not 7812.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7810, not 7809.",
"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_007842 | 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 26 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "-13 mmol L⁻¹",
"B": "2.3 mmol L⁻¹",
"C": "15 mmol L⁻¹",
"D": "13 mmol L⁻¹"
} | D | 13 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=26/2^1=13 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13 mmol L⁻¹, not -13 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13 mmol L⁻¹, not 2.3 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives ... | [
"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_006637 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 6 kg is attached to an ideal spring of force constant 644 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.14479 s",
"B": "-0.80695 s",
"C": "1.0193 s",
"D": "0.19305 s"
} | D | 0.19305 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(6/644)=0.19305 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.19305 s, not 0.14479 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.19305 s, not -0.80695 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.19305 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008549 | 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 1.2 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.248 K",
"B": "4.248 K",
"C": "3.248 K",
"D": "2.496 K"
} | A | 1.248 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×1.2=1.248 K. | {
"A": "Correct. The worked calculation gives 1.248 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.248 K, not 4.248 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.248 K, not 3.248 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_005424 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 14 μF capacitor is charged to a potential difference of 8 V. Calculate the energy stored, expressed in μJ. | {
"A": "448 μJ",
"B": "450 μJ",
"C": "449 μJ",
"D": "-448 μJ"
} | A | 448 μJ | U=½CV². Since C=14 μF, U in μJ is ½×14×(8)²=448 μJ. | {
"A": "Correct. The worked calculation gives 448 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 448 μJ, not 450 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 448 μJ, not 449 μJ.",
"D": "Incorrect. Substituting the stated values ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007653 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 10 mL of 0.10 M HCl is mixed with 89 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "6.451",
"B": "2.2902",
"C": "9.67649",
"D": "12.90199"
} | D | 12.90199 | Excess OH⁻ moles=0.10×(89−10)/1000=0.007900 mol. Total volume=0.099 L, so [OH⁻]=0.079798 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.90199. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.90199, not 6.451.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.90199, not 2.2902.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.90199, not 9.676... | [
"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_008180 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 14 A for 21314 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": "-98.17692 g",
"B": "98.17692 g",
"C": "73.63269 g",
"D": "117.81231 g"
} | B | 98.17692 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×21314/(2×96500)=98.17692 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 98.17692 g, not -98.17692 g.",
"B": "Correct. The worked calculation gives 98.17692 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 98.17692 g, not 73.63269 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_006191 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 36 cm in front of a thin convex lens of focal length 29 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-4.14286",
"B": "6.21429",
"C": "3.14286",
"D": "4.14286"
} | D | 4.14286 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(36)(29)/(36−29)=149.14286 cm. Thus |m|=v/u=149.14286/36=4.14286. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.14286, not -4.14286.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.14286, not 6.21429.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.14286, not 3.14... | [
"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_003142 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-6-13i)/(5+11i). What is Re(z), the real part of z? | {
"A": "-2.18493",
"B": "-1.18493",
"C": "0.88151",
"D": "-0.8887"
} | B | -1.18493 | Multiply numerator and denominator by the conjugate (5-11i). Then Re(z)=(ac+bd)/(c²+d²)=((-6)(5)+(-13)(11))/(5²+(11)²)=-1.18493. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.18493, not -2.18493.",
"B": "Correct. The worked calculation gives -1.18493.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.18493, not 0.88151.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007199 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 13 mol of gas at 266 K and 2.9 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "97.8459 L",
"B": "195.6918 L",
"C": "-97.8459 L",
"D": "98.8459 L"
} | A | 97.8459 L | PV=nRT, so V=nRT/P=(13)(0.082057)(266)/(2.9)=97.8459 L. | {
"A": "Correct. The worked calculation gives 97.8459 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 97.8459 L, not 195.6918 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 97.8459 L, not -97.8459 L.",
"D": "Incorrect. Substituting t... | [
"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_001997 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 2 elements can be selected from a set of 28 distinct elements? | {
"A": "283.5",
"B": "38.8",
"C": "378",
"D": "-378"
} | C | 378 | Order does not matter, so the count is C(28,2)=28!/[2!(26)!]=378. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 378, not 283.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 378, not 38.8.",
"C": "Correct. The worked calculation gives 378.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_003684 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 1 m s⁻¹. A constant net force does 12 N of work over 7 m in the direction of motion. Find its final kinetic energy. | {
"A": "89.5 J",
"B": "91.5 J",
"C": "88.5 J",
"D": "107.4 J"
} | A | 89.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(1)²+(12)(7)=89.5 J. | {
"A": "Correct. The worked calculation gives 89.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 89.5 J, not 91.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 89.5 J, not 88.5 J.",
"D": "Incorrect. Substituting the stated values ... | [
"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_004733 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 12 Ω and 9 Ω are connected in series; this combination is connected in parallel with a 2 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "-19.71429 A",
"B": "20.71429 A",
"C": "17.71429 A",
"D": "19.71429 A"
} | D | 19.71429 A | Series branch resistance=12+9=21 Ω. Parallel equivalent R_eq=(21×2)/(21+2)=1.82609 Ω. Total current I=V/R_eq=36/1.82609=19.71429 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19.71429 A, not -19.71429 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19.71429 A, not 20.71429 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19.71... | [
"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_006333 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 127 cm in front of a thin convex lens of focal length 29 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "3.29592",
"B": "-2.70408",
"C": "0.59184",
"D": "0.29592"
} | D | 0.29592 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(127)(29)/(127−29)=37.58163 cm. Thus |m|=v/u=37.58163/127=0.29592. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29592, not 3.29592.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29592, not -2.70408.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29592, not 0.59... | [
"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_003413 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 99 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "848.7915 m",
"B": "849.7915 m",
"C": "1018.5498 m",
"D": "-848.7915 m"
} | A | 848.7915 m | Range R=u²sin(2θ)/g. Substituting u=99, θ=60° and g=10 gives R=(99)²sin(120°)/10=848.7915 m. | {
"A": "Correct. The worked calculation gives 848.7915 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 848.7915 m, not 849.7915 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 848.7915 m, not 1018.5498 m.",
"D": "Incorrect. Substituti... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007922 | 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 17 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "4.25 mmol L⁻¹",
"B": "2.25 mmol L⁻¹",
"C": "7.25 mmol L⁻¹",
"D": "1.425 mmol L⁻¹"
} | A | 4.25 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=17/2^2=4.25 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 4.25 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.25 mmol L⁻¹, not 2.25 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.25 mmol L⁻¹, not 7.25 mmol L⁻¹.",
"D": "Incorre... | [
"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_004852 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 13 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.83258 A",
"B": "2.22172 A",
"C": "1.22172 A",
"D": "1.12217 A"
} | C | 1.22172 A | Series branch resistance=13+4=17 Ω. Parallel equivalent R_eq=(17×13)/(17+13)=7.36667 Ω. Total current I=V/R_eq=9/7.36667=1.22172 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.22172 A, not 1.83258 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.22172 A, not 2.22172 A.",
"C": "Correct. The worked calculation gives 1.22172 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_008895 | 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 0.28 mol L⁻¹ and initially B is absent. At equilibrium, 80% of A has dissociated at constant volume. Find K_c. | {
"A": "1.584",
"B": "3.584",
"C": "2.584",
"D": "1.3584"
} | B | 3.584 | Let α=0.8. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.28)(0.8)²/(1−0.8)=3.584. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.584, not 1.584.",
"B": "Correct. The worked calculation gives 3.584.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.584, not 2.584.",
"D": "Incorrect. Substituting the stated values into ... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008746 | 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 1.93 mol L⁻¹ and initially B is absent. At equilibrium, 35% of A has dissociated at constant volume. Find K_c. | {
"A": "2.45492",
"B": "1.45492",
"C": "0.72746",
"D": "4.45492"
} | B | 1.45492 | Let α=0.35. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.93)(0.35)²/(1−0.35)=1.45492. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.45492, not 2.45492.",
"B": "Correct. The worked calculation gives 1.45492.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.45492, not 0.72746.",
"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_003666 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 57 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "162.45 m",
"B": "326.9 m",
"C": "323.9 m",
"D": "324.9 m"
} | D | 324.9 m | Range R=u²sin(2θ)/g. Substituting u=57, θ=45° and g=10 gives R=(57)²sin(90°)/10=324.9 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 324.9 m, not 162.45 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 324.9 m, not 326.9 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 324.9 m, not 323.... | [
"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_008114 | 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 2 A for 790 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": "-1.48016 g",
"B": "0.51984 g",
"C": "2.51984 g",
"D": "1.51984 g"
} | B | 0.51984 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×2×790/(2×96500)=0.51984 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.51984 g, not -1.48016 g.",
"B": "Correct. The worked calculation gives 0.51984 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.51984 g, not 2.51984 g.",
"D": "Incorrect. Substituting th... | [
"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 |
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