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_003011 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(4+0i)/(3+12i). What is Re(z), the real part of z? | {
"A": "0.07843",
"B": "0.05882",
"C": "-2.92157",
"D": "3.07843"
} | A | 0.07843 | Multiply numerator and denominator by the conjugate (3-12i). Then Re(z)=(ac+bd)/(c²+d²)=((4)(3)+(0)(12))/(3²+(12)²)=0.07843. | {
"A": "Correct. The worked calculation gives 0.07843.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.07843, not 0.05882.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.07843, not -2.92157.",
"D": "Incorrect. Substituting the stated v... | [
"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_007056 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 10 mol of gas at 280 K and 0.68 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "337.88176 L",
"B": "506.82265 L",
"C": "168.94088 L",
"D": "270.30541 L"
} | A | 337.88176 L | PV=nRT, so V=nRT/P=(10)(0.082057)(280)/(0.68)=337.88176 L. | {
"A": "Correct. The worked calculation gives 337.88176 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 337.88176 L, not 506.82265 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 337.88176 L, not 168.94088 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006639 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 1 kg is attached to an ideal spring of force constant 734 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.07382 s",
"B": "-0.07382 s",
"C": "1.07382 s",
"D": "2.07382 s"
} | A | 0.07382 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(1/734)=0.07382 s. | {
"A": "Correct. The worked calculation gives 0.07382 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.07382 s, not -0.07382 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.07382 s, not 1.07382 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004389 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 2 m is acted on by a constant torque of 56 N m about its central axis. Find its angular acceleration. | {
"A": "4 rad s⁻²",
"B": "8 rad s⁻²",
"C": "6 rad s⁻²",
"D": "2 rad s⁻²"
} | A | 4 rad s⁻² | For a solid disc, I=½MR²=½(7)(2)²=14 kg m². Using τ=Iα, α=56/14=4 rad s⁻². | {
"A": "Correct. The worked calculation gives 4 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4 rad s⁻², not 8 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4 rad s⁻², not 6 rad s⁻².",
"D": "Incorrect. Substituting the... | [
"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_005467 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 22 μF capacitor is charged to a potential difference of 38 V. Calculate the energy stored, expressed in μJ. | {
"A": "31768 μJ",
"B": "15885 μJ",
"C": "15884 μJ",
"D": "7942 μJ"
} | C | 15884 μJ | U=½CV². Since C=22 μF, U in μJ is ½×22×(38)²=15884 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15884 μJ, not 31768 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15884 μJ, not 15885 μJ.",
"C": "Correct. The worked calculation gives 15884 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_002031 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 9 blue and 8 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.3202",
"B": "0.4803",
"C": "1.03202",
"D": "0.3202"
} | D | 0.3202 | Favourable pairs = C(12,2)+C(9,2)+C(8,2)=130. Total pairs=C(29,2)=406. Therefore P=130/406=0.3202. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3202, not -0.3202.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3202, not 0.4803.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3202, not 1.03202."... | [
"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_004649 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 3 kg and radius 6 m is acted on by a constant torque of 85 N m about its central axis. Find its angular acceleration. | {
"A": "-1.42593 rad s⁻²",
"B": "-1.57407 rad s⁻²",
"C": "2.36111 rad s⁻²",
"D": "1.57407 rad s⁻²"
} | D | 1.57407 rad s⁻² | For a solid disc, I=½MR²=½(3)(6)²=54 kg m². Using τ=Iα, α=85/54=1.57407 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.57407 rad s⁻², not -1.42593 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.57407 rad s⁻², not -1.57407 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000535 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 7 and common difference 9. Find the sum of its first 23 terms. | {
"A": "-2438",
"B": "2925.6",
"C": "1219",
"D": "2438"
} | D | 2438 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=7, d=9, n=23: Sₙ=23/2[2(7)+(23−1)(9)]=2438. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2438, not -2438.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2438, not 2925.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2438, not 1219.",
"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_002932 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, 6, 7) and v=(-1, 5, -5), calculate u·v. | {
"A": "-5",
"B": "-6",
"C": "-8",
"D": "0.4"
} | B | -6 | The dot product is the sum of corresponding component products: (1)(-1)+(6)(5)+(7)(-5)=-6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -6, not -5.",
"B": "Correct. The worked calculation gives -6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -6, not -8.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004146 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 37 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.18. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "134.976 N",
"B": "84.36 N",
"C": "-168.72 N",
"D": "168.72 N"
} | D | 168.72 N | Net force=mg(sinθ−μcosθ)=37×10×(0.6−0.18×0.8)=168.72 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 168.72 N, not 134.976 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 168.72 N, not 84.36 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 168.72 N, not ... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009337 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_3H_2N_1X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "2",
"B": "-2",
"C": "1",
"D": "4"
} | A | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×3+2+1−2−3)/2=2. | {
"A": "Correct. The worked calculation gives 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009443 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_8H_13X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "1.2",
"B": "2",
"C": "1",
"D": "4"
} | B | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×8+2+0−13−1)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.2.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003015 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-14-9i)/(4+2i). What is Re(z), the real part of z? | {
"A": "-5.55",
"B": "-3.7",
"C": "-5.7",
"D": "-7.4"
} | B | -3.7 | Multiply numerator and denominator by the conjugate (4-2i). Then Re(z)=(ac+bd)/(c²+d²)=((-14)(4)+(-9)(2))/(4²+(2)²)=-3.7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -3.7, not -5.55.",
"B": "Correct. The worked calculation gives -3.7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -3.7, not -5.7.",
"D": "Incorrect. Substituting the stated values into the ... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004149 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 50 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.26. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "392 N",
"B": "156.8 N",
"C": "196 N",
"D": "197 N"
} | C | 196 N | Net force=mg(sinθ−μcosθ)=50×10×(0.6−0.26×0.8)=196 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 196 N, not 392 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 196 N, not 156.8 N.",
"C": "Correct. The worked calculation gives 196 N.",
"D": "Incorrect. Substituting the stated values int... | [
"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_001608 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (2x² +7x +0) dx. | {
"A": "565.33333",
"B": "57.53333",
"C": "848",
"D": "566.33333"
} | A | 565.33333 | An antiderivative is (2/3)x³+(7/2)x²+(0)x. Evaluating between 0 and 8 gives (2/3)(8)³+(7/2)(8)²+(0)(8)=565.33333. | {
"A": "Correct. The worked calculation gives 565.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 565.33333, not 57.53333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 565.33333, not 848.",
"D": "Incorrect. Substituting the stated... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004141 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 40 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.24. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "164.2 N",
"B": "-163.2 N",
"C": "244.8 N",
"D": "163.2 N"
} | D | 163.2 N | Net force=mg(sinθ−μcosθ)=40×10×(0.6−0.24×0.8)=163.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 163.2 N, not 164.2 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 163.2 N, not -163.2 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 163.2 N, not 244.... | [
"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_005897 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.2 atm at 190 K. What is its pressure at 624 K? | {
"A": "1.94105 atm",
"B": "3.94105 atm",
"C": "1.97053 atm",
"D": "5.91158 atm"
} | B | 3.94105 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.2)(624)/(190)=3.94105 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.94105 atm, not 1.94105 atm.",
"B": "Correct. The worked calculation gives 3.94105 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.94105 atm, not 1.97053 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_002356 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, 3], [7, 4]]. | {
"A": "5.5",
"B": "11",
"C": "8",
"D": "13"
} | B | 11 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(4)−(3)(7)=11. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11, not 5.5.",
"B": "Correct. The worked calculation gives 11.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11, not 8.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002171 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 5 blue and 5 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.28571",
"B": "2.28571",
"C": "-2.71429",
"D": "1.02857"
} | A | 0.28571 | Favourable pairs = C(5,2)+C(5,2)+C(5,2)=30. Total pairs=C(15,2)=105. Therefore P=30/105=0.28571. | {
"A": "Correct. The worked calculation gives 0.28571.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.28571, not 2.28571.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.28571, not -2.71429.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004410 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 6 m is acted on by a constant torque of 92 N m about its central axis. Find its angular acceleration. | {
"A": "1.27778 rad s⁻²",
"B": "0.63889 rad s⁻²",
"C": "-2.36111 rad s⁻²",
"D": "1.63889 rad s⁻²"
} | B | 0.63889 rad s⁻² | For a solid disc, I=½MR²=½(8)(6)²=144 kg m². Using τ=Iα, α=92/144=0.63889 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.63889 rad s⁻², not 1.27778 rad s⁻².",
"B": "Correct. The worked calculation gives 0.63889 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.63889 rad s⁻², not -2.36111 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_002912 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-7, -6, 8) and v=(-6, -2, 8), calculate u·v. | {
"A": "120",
"B": "118",
"C": "236",
"D": "12.8"
} | B | 118 | The dot product is the sum of corresponding component products: (-7)(-6)+(-6)(-2)+(8)(8)=118. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 118, not 120.",
"B": "Correct. The worked calculation gives 118.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 118, not 236.",
"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_003128 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-6+14i)/(8+9i). What is Re(z), the real part of z? | {
"A": "0.40345",
"B": "0.53793",
"C": "1.07586",
"D": "-0.46207"
} | B | 0.53793 | Multiply numerator and denominator by the conjugate (8-9i). Then Re(z)=(ac+bd)/(c²+d²)=((-6)(8)+(14)(9))/(8²+(9)²)=0.53793. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.53793, not 0.40345.",
"B": "Correct. The worked calculation gives 0.53793.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.53793, not 1.07586.",
"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_006446 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 22 kg is attached to an ideal spring of force constant 134 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.18962 s",
"B": "-2.18962 s",
"C": "0.81038 s",
"D": "3.81038 s"
} | C | 0.81038 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(22/134)=0.81038 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.81038 s, not -0.18962 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.81038 s, not -2.18962 s.",
"C": "Correct. The worked calculation gives 0.81038 s.",
"D": "Incorrect. Substituting t... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003456 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 55 m s⁻¹ at 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "595.80869 m",
"B": "298.90435 m",
"C": "297.90435 m",
"D": "238.32348 m"
} | C | 297.90435 m | Range R=u²sin(2θ)/g. Substituting u=55, θ=40° and g=10 gives R=(55)²sin(80°)/10=297.90435 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 297.90435 m, not 595.80869 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 297.90435 m, not 298.90435 m.",
"C": "Correct. The worked calculation gives 297.90435 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001861 | 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 62 distinct elements? | {
"A": "-491796152",
"B": "491796154",
"C": "491796152",
"D": "49179616.2"
} | C | 491796152 | Order does not matter, so the count is C(62,7)=62!/[7!(55)!]=491796152. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 491796152, not -491796152.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 491796152, not 491796154.",
"C": "Correct. The worked calculation gives 491796152.",
"D": "Incorrect. Substituting th... | [
"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_000439 | 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 12 terms. | {
"A": "684",
"B": "-684",
"C": "1026",
"D": "682"
} | A | 684 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=13, d=8, n=12: Sₙ=12/2[2(13)+(12−1)(8)]=684. | {
"A": "Correct. The worked calculation gives 684.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 684, not -684.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 684, not 1026.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_007769 | 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 71 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "1.10938 mmol L⁻¹",
"B": "-2.21875 mmol L⁻¹",
"C": "-0.78125 mmol L⁻¹",
"D": "2.21875 mmol L⁻¹"
} | D | 2.21875 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=71/2^5=2.21875 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.21875 mmol L⁻¹, not 1.10938 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.21875 mmol L⁻¹, not -2.21875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the govern... | [
"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_008722 | 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 1.34 mol L⁻¹ and initially B is absent. At equilibrium, 65% of A has dissociated at constant volume. Find K_c. | {
"A": "-6.47029",
"B": "6.47029",
"C": "8.47029",
"D": "5.47029"
} | B | 6.47029 | Let α=0.65. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.34)(0.65)²/(1−0.65)=6.47029. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.47029, not -6.47029.",
"B": "Correct. The worked calculation gives 6.47029.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.47029, not 8.47029.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005605 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 53 μF capacitor is charged to a potential difference of 27 V. Calculate the energy stored, expressed in μJ. | {
"A": "15454.8 μJ",
"B": "19318.5 μJ",
"C": "19319.5 μJ",
"D": "38637 μJ"
} | B | 19318.5 μJ | U=½CV². Since C=53 μF, U in μJ is ½×53×(27)²=19318.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19318.5 μJ, not 15454.8 μJ.",
"B": "Correct. The worked calculation gives 19318.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19318.5 μJ, not 19319.5 μJ.",
"D": "Incorrect. Substitutin... | [
"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_005715 | 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 200 K. What is its pressure at 378 K? | {
"A": "-8.316 atm",
"B": "1.8316 atm",
"C": "11.316 atm",
"D": "8.316 atm"
} | D | 8.316 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.4)(378)/(200)=8.316 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.316 atm, not -8.316 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.316 atm, not 1.8316 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.316 at... | [
"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_001669 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (-1x² +8x +4) dx. | {
"A": "58.66667",
"B": "59.66667",
"C": "6.86667",
"D": "56.66667"
} | A | 58.66667 | An antiderivative is (-1/3)x³+(8/2)x²+(4)x. Evaluating between 0 and 4 gives (-1/3)(4)³+(8/2)(4)²+(4)(4)=58.66667. | {
"A": "Correct. The worked calculation gives 58.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 58.66667, not 59.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 58.66667, not 6.86667.",
"D": "Incorrect. Substituting the state... | [
"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_008783 | 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 1.22 mol L⁻¹ and initially B is absent. At equilibrium, 70% of A has dissociated at constant volume. Find K_c. | {
"A": "4.97067",
"B": "5.978",
"C": "7.97067",
"D": "1.79707"
} | C | 7.97067 | Let α=0.7. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.22)(0.7)²/(1−0.7)=7.97067. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.97067, not 4.97067.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.97067, not 5.978.",
"C": "Correct. The worked calculation gives 7.97067.",
"D": "Incorrect. Substituting the stated valu... | [
"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_008353 | 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 0.86 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "4.7888 K",
"B": "2.7888 K",
"C": "0.8944 K",
"D": "1.7888 K"
} | D | 1.7888 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.52×0.86=1.7888 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.7888 K, not 4.7888 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.7888 K, not 2.7888 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.7888 K, not ... | [
"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_000162 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 +6x -10=0, let its roots be α and β. What is α²+β²? | {
"A": "7.18367",
"B": "5.59184",
"C": "5.38776",
"D": "3.59184"
} | D | 3.59184 | By Vieta's relations, α+β = -6/7 and αβ = -10/7. Then α²+β²=(α+β)²−2αβ = (-6/7)²−2(-10/7) = 3.59184. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.59184, not 7.18367.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.59184, not 5.59184.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.59184, not 5.387... | [
"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_007536 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 84 mL of 0.10 M HCl is mixed with 58 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-0.26269",
"B": "2.73731",
"C": "1.73731",
"D": "2.60597"
} | C | 1.73731 | Excess H⁺ moles=0.10×(84−58)/1000=0.002600 mol. Total volume=0.142 L, so [H⁺]=0.018310 M and pH=−log₁₀[H⁺]=1.73731. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.73731, not -0.26269.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.73731, not 2.73731.",
"C": "Correct. The worked calculation gives 1.73731.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009588 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_10H_5N_2X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "6.75",
"B": "13.5",
"C": "9",
"D": "11"
} | C | 9 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×10+2+2−5−1)/2=9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9, not 6.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9, not 13.5.",
"C": "Correct. The worked calculation gives 9.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002494 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, 8], [8, -6]]. | {
"A": "-75.2",
"B": "-47",
"C": "-94",
"D": "-141"
} | C | -94 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(-6)−(8)(8)=-94. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -94, not -75.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -94, not -47.",
"C": "Correct. The worked calculation gives -94.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_006891 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 31 mol H₂ and 33 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "23.25 mol",
"B": "33 mol",
"C": "37.2 mol",
"D": "31 mol"
} | D | 31 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 31 mol H₂O; O₂ can produce 66 mol H₂O. The limiting condition is H₂; product=31 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 31 mol, not 23.25 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 31 mol, not 33 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 31 mol, not 37.2 mo... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008119 | 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 25417 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": "16.72518 g",
"B": "8.36259 g",
"C": "20.07021 g",
"D": "18.72518 g"
} | A | 16.72518 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×2×25417/(2×96500)=16.72518 g. | {
"A": "Correct. The worked calculation gives 16.72518 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16.72518 g, not 8.36259 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16.72518 g, not 20.07021 g.",
"D": "Incorrect. Substituting... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003079 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(5-1i)/(8+2i). What is Re(z), the real part of z? | {
"A": "0.83824",
"B": "-1.44118",
"C": "0.55882",
"D": "1.05588"
} | C | 0.55882 | Multiply numerator and denominator by the conjugate (8-2i). Then Re(z)=(ac+bd)/(c²+d²)=((5)(8)+(-1)(2))/(8²+(2)²)=0.55882. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.55882, not 0.83824.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.55882, not -1.44118.",
"C": "Correct. The worked calculation gives 0.55882.",
"D": "Incorrect. Substituting the stated v... | [
"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_003806 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 12 m s⁻¹. A constant net force does 20 N of work over 13 m in the direction of motion. Find its final kinetic energy. | {
"A": "1052 J",
"B": "789 J",
"C": "2104 J",
"D": "841.6 J"
} | A | 1052 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(12)²+(20)(13)=1052 J. | {
"A": "Correct. The worked calculation gives 1052 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1052 J, not 789 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1052 J, not 2104 J.",
"D": "Incorrect. Substituting the stated values i... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006869 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 1 mol H₂ and 1 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "0.75 mol",
"B": "-1 mol",
"C": "1.1 mol",
"D": "1 mol"
} | D | 1 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 1 mol H₂O; O₂ can produce 2 mol H₂O. The limiting condition is H₂; product=1 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1 mol, not 0.75 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1 mol, not -1 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1 mol, not 1.1 mol.",
... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005637 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 8 μF capacitor is charged to a potential difference of 38 V. Calculate the energy stored, expressed in μJ. | {
"A": "4620.8 μJ",
"B": "5778 μJ",
"C": "5776 μJ",
"D": "5777 μJ"
} | C | 5776 μJ | U=½CV². Since C=8 μF, U in μJ is ½×8×(38)²=5776 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5776 μJ, not 4620.8 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5776 μJ, not 5778 μJ.",
"C": "Correct. The worked calculation gives 5776 μJ.",
"D": "Incorrect. Substituting the stated ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008791 | 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 1.4 mol L⁻¹ and initially B is absent. At equilibrium, 47% of A has dissociated at constant volume. Find K_c. | {
"A": "4.66808",
"B": "0.33404",
"C": "2.33404",
"D": "-2.33404"
} | C | 2.33404 | Let α=0.47. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.4)(0.47)²/(1−0.47)=2.33404. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.33404, not 4.66808.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.33404, not 0.33404.",
"C": "Correct. The worked calculation gives 2.33404.",
"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_001762 | 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 60 distinct elements? | {
"A": "2099038267462.5",
"B": "2798717689950",
"C": "1399358844977",
"D": "1399358844975"
} | D | 1399358844975 | Order does not matter, so the count is C(60,12)=60!/[12!(48)!]=1399358844975. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1399358844975, not 2099038267462.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1399358844975, not 2798717689950.",
"C": "Incorrect. Substituting the stated values into the governing relatio... | [
"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_007269 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 20 mol of gas at 620 K and 2.99 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "510.45492 L",
"B": "255.22746 L",
"C": "170.15164 L",
"D": "340.30328 L"
} | D | 340.30328 L | PV=nRT, so V=nRT/P=(20)(0.082057)(620)/(2.99)=340.30328 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 340.30328 L, not 510.45492 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 340.30328 L, not 255.22746 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 34... | [
"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_002215 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 7 blue and 9 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.15584",
"B": "0.31169",
"C": "3.31169",
"D": "0.23377"
} | B | 0.31169 | Favourable pairs = C(6,2)+C(7,2)+C(9,2)=72. Total pairs=C(22,2)=231. Therefore P=72/231=0.31169. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31169, not 0.15584.",
"B": "Correct. The worked calculation gives 0.31169.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31169, not 3.31169.",
"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_005838 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.2 atm at 405 K. What is its pressure at 661 K? | {
"A": "1.79531 atm",
"B": "3.59062 atm",
"C": "1.59062 atm",
"D": "5.59062 atm"
} | B | 3.59062 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.2)(661)/(405)=3.59062 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.59062 atm, not 1.79531 atm.",
"B": "Correct. The worked calculation gives 3.59062 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.59062 atm, not 1.59062 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_007942 | 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 60 minutes? | {
"A": "10.875 mmol L⁻¹",
"B": "9.875 mmol L⁻¹",
"C": "8.875 mmol L⁻¹",
"D": "11.875 mmol L⁻¹"
} | B | 9.875 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=79/2^3=9.875 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.875 mmol L⁻¹, not 10.875 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 9.875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.875 mmol L⁻¹, not 8.875 mmol L⁻¹.",
"D": "I... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005872 | 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 199 K. What is its pressure at 753 K? | {
"A": "14.75729 atm",
"B": "11.06796 atm",
"C": "22.13593 atm",
"D": "12.75729 atm"
} | A | 14.75729 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.9)(753)/(199)=14.75729 atm. | {
"A": "Correct. The worked calculation gives 14.75729 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14.75729 atm, not 11.06796 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14.75729 atm, not 22.13593 atm.",
"D": "Incorrect. S... | [
"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_002323 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 7 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": "2.31429",
"B": "0.31429",
"C": "-2.68571",
"D": "0.23571"
} | B | 0.31429 | Favourable pairs = C(4,2)+C(7,2)+C(4,2)=33. Total pairs=C(15,2)=105. Therefore P=33/105=0.31429. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31429, not 2.31429.",
"B": "Correct. The worked calculation gives 0.31429.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31429, not -2.68571.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001673 | 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 58 distinct elements? | {
"A": "424271",
"B": "424272",
"C": "42428",
"D": "424270"
} | D | 424270 | Order does not matter, so the count is C(58,4)=58!/[4!(54)!]=424270. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 424270, not 424271.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 424270, not 424272.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 424270, not 42428.",
... | [
"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_000997 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio 5. What is the sum of its first 7 terms? | {
"A": "-19531",
"B": "19531",
"C": "9765.5",
"D": "19532"
} | B | 19531 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(5^7−1)/(5−1)=19531. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19531, not -19531.",
"B": "Correct. The worked calculation gives 19531.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19531, not 9765.5.",
"D": "Incorrect. Substituting the stated values int... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000882 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio 3. What is the sum of its first 9 terms? | {
"A": "54125.5",
"B": "108253",
"C": "108251",
"D": "216502"
} | C | 108251 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(3^9−1)/(3−1)=108251. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 108251, not 54125.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 108251, not 108253.",
"C": "Correct. The worked calculation gives 108251.",
"D": "Incorrect. Substituting the stated values... | [
"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_006372 | 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 38 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.20528 s",
"B": "0.79472 s",
"C": "2.79472 s",
"D": "1.07947 s"
} | B | 0.79472 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(6/38)=0.79472 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.79472 s, not -2.20528 s.",
"B": "Correct. The worked calculation gives 0.79472 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.79472 s, not 2.79472 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006278 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 37 cm in front of a thin convex lens of focal length 10 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.37037",
"B": "-2.62963",
"C": "0.27778",
"D": "0.37037"
} | D | 0.37037 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(37)(10)/(37−10)=13.7037 cm. Thus |m|=v/u=13.7037/37=0.37037. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.37037, not 1.37037.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.37037, not -2.62963.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.37037, not 0.27... | [
"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_006388 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 15 kg is attached to an ideal spring of force constant 658 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.30197 s",
"B": "-0.69803 s",
"C": "-2.69803 s",
"D": "-1.69803 s"
} | A | 0.30197 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(15/658)=0.30197 s. | {
"A": "Correct. The worked calculation gives 0.30197 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30197 s, not -0.69803 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30197 s, not -2.69803 s.",
"D": "Incorrect. Substituting t... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003365 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 116 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1165.32378 m",
"B": "1166.32378 m",
"C": "1747.98567 m",
"D": "873.99284 m"
} | A | 1165.32378 m | Range R=u²sin(2θ)/g. Substituting u=116, θ=60° and g=10 gives R=(116)²sin(120°)/10=1165.32378 m. | {
"A": "Correct. The worked calculation gives 1165.32378 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1165.32378 m, not 1166.32378 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1165.32378 m, not 1747.98567 m.",
"D": "Incorrect. S... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008048 | 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 13 A for 29713 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": "129.08851 g",
"B": "254.17701 g",
"C": "101.6708 g",
"D": "127.08851 g"
} | D | 127.08851 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×29713/(2×96500)=127.08851 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 127.08851 g, not 129.08851 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 127.08851 g, not 254.17701 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12... | [
"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_000258 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 -11x -12=0, let its roots be α and β. What is α²+β²? | {
"A": "6.89796",
"B": "2.89796",
"C": "5.89796",
"D": "1.5898"
} | C | 5.89796 | By Vieta's relations, α+β = 11/7 and αβ = -12/7. Then α²+β²=(α+β)²−2αβ = (11/7)²−2(-12/7) = 5.89796. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.89796, not 6.89796.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.89796, not 2.89796.",
"C": "Correct. The worked calculation gives 5.89796.",
"D": "Incorrect. Substituting the stated va... | [
"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_001569 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (4x² +2x +6) dx. | {
"A": "100.26667",
"B": "125.33333",
"C": "94",
"D": "124.33333"
} | B | 125.33333 | An antiderivative is (4/3)x³+(2/2)x²+(6)x. Evaluating between 0 and 4 gives (4/3)(4)³+(2/2)(4)²+(6)(4)=125.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 125.33333, not 100.26667.",
"B": "Correct. The worked calculation gives 125.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 125.33333, not 94.",
"D": "Incorrect. Substituting the stated... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001061 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ +4x² +10x+7. Evaluate f′(4). | {
"A": "-112.5",
"B": "-120",
"C": "-150",
"D": "-148"
} | C | -150 | Differentiate: f′(x)=3(-4)x²+2(4)x+(10). At x=4, f′(4)=3(-4)(4)²+2(4)(4)+(10)=-150. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -150, not -112.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -150, not -120.",
"C": "Correct. The worked calculation gives -150.",
"D": "Incorrect. Substituting the stated values into the... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000318 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 +6x -6=0, let its roots be α and β. What is α²+β²? | {
"A": "1.5",
"B": "2.25",
"C": "2",
"D": "3"
} | D | 3 | By Vieta's relations, α+β = -6/6 and αβ = -6/6. Then α²+β²=(α+β)²−2αβ = (-6/6)²−2(-6/6) = 3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.",
"D": "Correct. The work... | [
"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_001919 | 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 68 distinct elements? | {
"A": "5461519216998",
"B": "7282025622664",
"C": "10923038433996",
"D": "728202562267.40002"
} | B | 7282025622664 | Order does not matter, so the count is C(68,12)=68!/[12!(56)!]=7282025622664. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7282025622664, not 5461519216998.",
"B": "Correct. The worked calculation gives 7282025622664.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7282025622664, not 10923038433996.",
"D": "Incorr... | [
"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_006720 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 8 mol H₂ and 25 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "16 mol",
"B": "5 mol",
"C": "8 mol",
"D": "11 mol"
} | C | 8 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 8 mol H₂O; O₂ can produce 50 mol H₂O. The limiting condition is H₂; product=8 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8 mol, not 16 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8 mol, not 5 mol.",
"C": "Correct. The worked calculation gives 8 mol.",
"D": "Incorrect. Substituting the stated values into... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009189 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.81 V, transfers 2 electrons, and has reaction quotient Q=10^-4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.9282 V",
"B": "0.69615 V",
"C": "1.09282 V",
"D": "0.4641 V"
} | A | 0.9282 V | Apply the Nernst equation: E=0.81−(0.0591/2)(-4)=0.9282 V. | {
"A": "Correct. The worked calculation gives 0.9282 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9282 V, not 0.69615 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9282 V, not 1.09282 V.",
"D": "Incorrect. Substituting the st... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003216 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(0-7i)/(6+2i). What is Re(z), the real part of z? | {
"A": "-1.35",
"B": "-0.35",
"C": "-3.35",
"D": "0.965"
} | B | -0.35 | Multiply numerator and denominator by the conjugate (6-2i). Then Re(z)=(ac+bd)/(c²+d²)=((0)(6)+(-7)(2))/(6²+(2)²)=-0.35. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.35, not -1.35.",
"B": "Correct. The worked calculation gives -0.35.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.35, not -3.35.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_006820 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 22 mol H₂ and 14 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "-22 mol",
"B": "17.6 mol",
"C": "22 mol",
"D": "3.2 mol"
} | C | 22 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 22 mol H₂O; O₂ can produce 28 mol H₂O. The limiting condition is H₂; product=22 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22 mol, not -22 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22 mol, not 17.6 mol.",
"C": "Correct. The worked calculation gives 22 mol.",
"D": "Incorrect. Substituting the stated valu... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003233 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-8+15i)/(7+3i). What is Re(z), the real part of z? | {
"A": "-0.14224",
"B": "-1.18966",
"C": "2.81034",
"D": "-0.18966"
} | D | -0.18966 | Multiply numerator and denominator by the conjugate (7-3i). Then Re(z)=(ac+bd)/(c²+d²)=((-8)(7)+(15)(3))/(7²+(3)²)=-0.18966. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.18966, not -0.14224.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.18966, not -1.18966.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.18966, not ... | [
"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_003188 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(15+4i)/(3+12i). What is Re(z), the real part of z? | {
"A": "1.21569",
"B": "1.60784",
"C": "0.60784",
"D": "-0.60784"
} | C | 0.60784 | Multiply numerator and denominator by the conjugate (3-12i). Then Re(z)=(ac+bd)/(c²+d²)=((15)(3)+(4)(12))/(3²+(12)²)=0.60784. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.60784, not 1.21569.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.60784, not 1.60784.",
"C": "Correct. The worked calculation gives 0.60784.",
"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_006999 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 34 mol H₂ and 25 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "33 mol",
"B": "32 mol",
"C": "34 mol",
"D": "36 mol"
} | C | 34 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 34 mol H₂O; O₂ can produce 50 mol H₂O. The limiting condition is H₂; product=34 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 34 mol, not 33 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 34 mol, not 32 mol.",
"C": "Correct. The worked calculation gives 34 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002660 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -8], [5, -1]]. | {
"A": "42",
"B": "37",
"C": "4.5",
"D": "35"
} | D | 35 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(-1)−(-8)(5)=35. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 35, not 42.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 35, not 37.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 35, not 4.5.",
"D": "Correct. The wo... | [
"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_009573 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_10H_1N_3X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "20",
"B": "10",
"C": "7.5",
"D": "7"
} | B | 10 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×10+2+3−1−4)/2=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 20.",
"B": "Correct. The worked calculation gives 10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 7.5.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003770 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 1 m s⁻¹. A constant net force does 18 N of work over 8 m in the direction of motion. Find its final kinetic energy. | {
"A": "111 J",
"B": "-148 J",
"C": "148 J",
"D": "177.6 J"
} | C | 148 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(1)²+(18)(8)=148 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 148 J, not 111 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 148 J, not -148 J.",
"C": "Correct. The worked calculation gives 148 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_003587 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 95 m s⁻¹ at 35° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "678.45807 m",
"B": "85.80726 m",
"C": "848.07259 m",
"D": "849.07259 m"
} | C | 848.07259 m | Range R=u²sin(2θ)/g. Substituting u=95, θ=35° and g=10 gives R=(95)²sin(70°)/10=848.07259 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 848.07259 m, not 678.45807 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 848.07259 m, not 85.80726 m.",
"C": "Correct. The worked calculation gives 848.07259 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_009471 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_17H_27N_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "6",
"B": "3",
"C": "-5",
"D": "5"
} | D | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×17+2+1−27−0)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not -5.",
"D": "Correct. The worked c... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000037 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +5x +10=0, let its roots be α and β. What is α²+β²? | {
"A": "-3.88889",
"B": "-7.77778",
"C": "-0.88889",
"D": "0.61111"
} | A | -3.88889 | By Vieta's relations, α+β = -5/3 and αβ = 10/3. Then α²+β²=(α+β)²−2αβ = (-5/3)²−2(10/3) = -3.88889. | {
"A": "Correct. The worked calculation gives -3.88889.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -3.88889, not -7.77778.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -3.88889, not -0.88889.",
"D": "Incorrect. Substituting the stat... | [
"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_001434 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (4x² +5x +4) dx. | {
"A": "141.33333",
"B": "-141.33333",
"C": "139.33333",
"D": "212"
} | A | 141.33333 | An antiderivative is (4/3)x³+(5/2)x²+(4)x. Evaluating between 0 and 4 gives (4/3)(4)³+(5/2)(4)²+(4)(4)=141.33333. | {
"A": "Correct. The worked calculation gives 141.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 141.33333, not -141.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 141.33333, not 139.33333.",
"D": "Incorrect. Substituting th... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000491 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -2 and common difference 10. Find the sum of its first 13 terms. | {
"A": "754",
"B": "1508",
"C": "752",
"D": "1131"
} | A | 754 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-2, d=10, n=13: Sₙ=13/2[2(-2)+(13−1)(10)]=754. | {
"A": "Correct. The worked calculation gives 754.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 754, not 1508.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 754, not 752.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_008163 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 11 A for 9716 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": "70.32773 g",
"B": "52.7458 g",
"C": "37.16387 g",
"D": "35.16387 g"
} | D | 35.16387 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×9716/(2×96500)=35.16387 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 35.16387 g, not 70.32773 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 35.16387 g, not 52.7458 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 35.1638... | [
"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_004961 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 5 Ω are connected in series; this combination is connected in parallel with a 17 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.51471 A",
"B": "3.02941 A",
"C": "-1.02941 A",
"D": "1.02941 A"
} | D | 1.02941 A | Series branch resistance=13+5=18 Ω. Parallel equivalent R_eq=(18×17)/(18+17)=8.74286 Ω. Total current I=V/R_eq=9/8.74286=1.02941 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.02941 A, not 0.51471 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.02941 A, not 3.02941 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.02941 A,... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000186 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 -6x -5=0, let its roots be α and β. What is α²+β²? | {
"A": "2.66667",
"B": "1.33333",
"C": "4.66667",
"D": "0.66667"
} | A | 2.66667 | By Vieta's relations, α+β = 6/6 and αβ = -5/6. Then α²+β²=(α+β)²−2αβ = (6/6)²−2(-5/6) = 2.66667. | {
"A": "Correct. The worked calculation gives 2.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.66667, not 1.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.66667, not 4.66667.",
"D": "Incorrect. Substituting the stated va... | [
"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_008984 | 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, 61% of A has dissociated at constant volume. Find K_c. | {
"A": "-1.06859",
"B": "1.10686",
"C": "1.06859",
"D": "1.60289"
} | C | 1.06859 | Let α=0.61. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.28)(0.61)²/(1−0.61)=1.06859. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.06859, not -1.06859.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.06859, not 1.10686.",
"C": "Correct. The worked calculation gives 1.06859.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002844 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(6, 8, 1) and v=(0, -6, -1), calculate u·v. | {
"A": "-49",
"B": "-3.9",
"C": "-39.2",
"D": "-48"
} | A | -49 | The dot product is the sum of corresponding component products: (6)(0)+(8)(-6)+(1)(-1)=-49. | {
"A": "Correct. The worked calculation gives -49.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -49, not -3.9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -49, not -39.2.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_002881 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(5, 6, 9) and v=(0, -2, -6), calculate u·v. | {
"A": "-66",
"B": "66",
"C": "-132",
"D": "-68"
} | A | -66 | The dot product is the sum of corresponding component products: (5)(0)+(6)(-2)+(9)(-6)=-66. | {
"A": "Correct. The worked calculation gives -66.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -66, not 66.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -66, not -132.",
"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_002798 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-4, 7, 1) and v=(3, 4, 4), calculate u·v. | {
"A": "-20",
"B": "20",
"C": "3",
"D": "24"
} | B | 20 | The dot product is the sum of corresponding component products: (-4)(3)+(7)(4)+(1)(4)=20. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20, not -20.",
"B": "Correct. The worked calculation gives 20.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20, not 3.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000444 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -20 and common difference 6. Find the sum of its first 30 terms. | {
"A": "2412",
"B": "1507.5",
"C": "2010",
"D": "1608"
} | C | 2010 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-20, d=6, n=30: Sₙ=30/2[2(-20)+(30−1)(6)]=2010. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2010, not 2412.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2010, not 1507.5.",
"C": "Correct. The worked calculation gives 2010.",
"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_005776 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.8 atm at 248 K. What is its pressure at 716 K? | {
"A": "10.39355 atm",
"B": "15.85806 atm",
"C": "13.85806 atm",
"D": "10.85806 atm"
} | C | 13.85806 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.8)(716)/(248)=13.85806 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13.85806 atm, not 10.39355 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13.85806 atm, not 15.85806 atm.",
"C": "Correct. The worked calculation gives 13.85806 atm.",
"D": "Incorrect. S... | [
"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_008699 | 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 0.37 mol L⁻¹ and initially B is absent. At equilibrium, 79% of A has dissociated at constant volume. Find K_c. | {
"A": "-4.39842",
"B": "3.39842",
"C": "4.39842",
"D": "3.29881"
} | C | 4.39842 | Let α=0.79. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.37)(0.79)²/(1−0.79)=4.39842. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.39842, not -4.39842.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.39842, not 3.39842.",
"C": "Correct. The worked calculation gives 4.39842.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008401 | 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 0.76 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.16736 K",
"B": "1.11674 K",
"C": "2.33472 K",
"D": "-0.83264 K"
} | A | 1.16736 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.512×0.76=1.16736 K. | {
"A": "Correct. The worked calculation gives 1.16736 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.16736 K, not 1.11674 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.16736 K, not 2.33472 K.",
"D": "Incorrect. Substituting the... | [
"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_003183 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(6-15i)/(8+1i). What is Re(z), the real part of z? | {
"A": "-0.49231",
"B": "3.50769",
"C": "0.38077",
"D": "0.50769"
} | D | 0.50769 | Multiply numerator and denominator by the conjugate (8-1i). Then Re(z)=(ac+bd)/(c²+d²)=((6)(8)+(-15)(1))/(8²+(1)²)=0.50769. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.50769, not -0.49231.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.50769, not 3.50769.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.50769, not 0.38... | [
"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_005409 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 9 μF capacitor is charged to a potential difference of 8 V. Calculate the energy stored, expressed in μJ. | {
"A": "288 μJ",
"B": "286 μJ",
"C": "-288 μJ",
"D": "290 μJ"
} | A | 288 μJ | U=½CV². Since C=9 μF, U in μJ is ½×9×(8)²=288 μJ. | {
"A": "Correct. The worked calculation gives 288 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 288 μJ, not 286 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 288 μJ, not -288 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_009633 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_6H_7X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "4",
"C": "2.25",
"D": "1.3"
} | A | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+0−7−1)/2=3. | {
"A": "Correct. The worked calculation gives 3.",
"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 2.25.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003543 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 98 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "665.38464 m",
"B": "831.7308 m",
"C": "415.8654 m",
"D": "830.7308 m"
} | B | 831.7308 m | Range R=u²sin(2θ)/g. Substituting u=98, θ=60° and g=10 gives R=(98)²sin(120°)/10=831.7308 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 831.7308 m, not 665.38464 m.",
"B": "Correct. The worked calculation gives 831.7308 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 831.7308 m, not 415.8654 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_001046 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ -1x² -1x+7. Evaluate f′(5). | {
"A": "441",
"B": "219.5",
"C": "437",
"D": "439"
} | D | 439 | Differentiate: f′(x)=3(6)x²+2(-1)x+(-1). At x=5, f′(5)=3(6)(5)²+2(-1)(5)+(-1)=439. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 439, not 441.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 439, not 219.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 439, not 437.",
"D": "Correct.... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000901 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio 2. What is the sum of its first 8 terms? | {
"A": "281.5",
"B": "4207.5",
"C": "2244",
"D": "2805"
} | D | 2805 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(2^8−1)/(2−1)=2805. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2805, not 281.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2805, not 4207.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2805, not 2244.",
"D": "C... | [
"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_008341 | 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 1.77 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "5.62496 K",
"B": "4.62496 K",
"C": "1.81248 K",
"D": "3.62496 K"
} | D | 3.62496 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.512×1.77=3.62496 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.62496 K, not 5.62496 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.62496 K, not 4.62496 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.62496 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_005208 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +9 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "4.79688 N",
"B": "35.96875 N",
"C": "37.96875 N",
"D": "28.47656 N"
} | C | 37.96875 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(9×10⁻⁶)/(8×10⁻²)²=37.96875 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 37.96875 N, not 4.79688 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 37.96875 N, not 35.96875 N.",
"C": "Correct. The worked calculation gives 37.96875 N.",
"D": "Incorrect. Substituting... | [
"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_003761 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 6 m s⁻¹. A constant net force does 12 N of work over 4 m in the direction of motion. Find its final kinetic energy. | {
"A": "-192 J",
"B": "192 J",
"C": "191 J",
"D": "288 J"
} | B | 192 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(6)²+(12)(4)=192 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 192 J, not -192 J.",
"B": "Correct. The worked calculation gives 192 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 192 J, not 191 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_002514 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, 0], [4, 3]]. | {
"A": "20",
"B": "18",
"C": "-18",
"D": "14.4"
} | B | 18 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(3)−(0)(4)=18. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18, not 20.",
"B": "Correct. The worked calculation gives 18.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18, not -18.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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