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_002945 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-4, 3, 7) and v=(4, 3, 5), calculate u·v. | {
"A": "29",
"B": "42",
"C": "26",
"D": "28"
} | D | 28 | The dot product is the sum of corresponding component products: (-4)(4)+(3)(3)+(7)(5)=28. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28, not 29.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28, not 42.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28, not 26.",
"D": "Correct. The wor... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006896 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 4 mol H₂ and 19 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "3 mol",
"B": "-4 mol",
"C": "4 mol",
"D": "8 mol"
} | C | 4 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 4 mol H₂O; O₂ can produce 38 mol H₂O. The limiting condition is H₂; product=4 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4 mol, not 3 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4 mol, not -4 mol.",
"C": "Correct. The worked calculation gives 4 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_006549 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 24 kg is attached to an ideal spring of force constant 849 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.66373 s",
"B": "-0.33627 s",
"C": "0.2522 s",
"D": "0.33627 s"
} | D | 0.33627 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(24/849)=0.33627 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33627 s, not -0.66373 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33627 s, not -0.33627 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33627 ... | [
"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_007272 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 17 mol of gas at 596 K and 2.83 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "294.78146 L",
"B": "293.78146 L",
"C": "30.37815 L",
"D": "295.78146 L"
} | B | 293.78146 L | PV=nRT, so V=nRT/P=(17)(0.082057)(596)/(2.83)=293.78146 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 293.78146 L, not 294.78146 L.",
"B": "Correct. The worked calculation gives 293.78146 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 293.78146 L, not 30.37815 L.",
"D": "Incorrect. Substit... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004341 | 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 52 N m about its central axis. Find its angular acceleration. | {
"A": "0.71429 rad s⁻²",
"B": "2.78571 rad s⁻²",
"C": "2.71429 rad s⁻²",
"D": "3.71429 rad s⁻²"
} | D | 3.71429 rad s⁻² | For a solid disc, I=½MR²=½(7)(2)²=14 kg m². Using τ=Iα, α=52/14=3.71429 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.71429 rad s⁻², not 0.71429 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.71429 rad s⁻², not 2.78571 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing r... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003639 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 53 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "278.9 m",
"B": "280.9 m",
"C": "210.675 m",
"D": "561.8 m"
} | B | 280.9 m | Range R=u²sin(2θ)/g. Substituting u=53, θ=45° and g=10 gives R=(53)²sin(90°)/10=280.9 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 280.9 m, not 278.9 m.",
"B": "Correct. The worked calculation gives 280.9 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 280.9 m, not 210.675 m.",
"D": "Incorrect. Substituting the stated ... | [
"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_009273 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.74 V, transfers 3 electrons, and has reaction quotient Q=10^2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.0509 V",
"B": "-2.2994 V",
"C": "0.52545 V",
"D": "0.7006 V"
} | D | 0.7006 V | Apply the Nernst equation: E=0.74−(0.0591/3)(2)=0.7006 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7006 V, not 1.0509 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7006 V, not -2.2994 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7006 V, not... | [
"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_003235 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-6-9i)/(12+3i). What is Re(z), the real part of z? | {
"A": "1.35294",
"B": "2.35294",
"C": "-3.64706",
"D": "-0.64706"
} | D | -0.64706 | Multiply numerator and denominator by the conjugate (12-3i). Then Re(z)=(ac+bd)/(c²+d²)=((-6)(12)+(-9)(3))/(12²+(3)²)=-0.64706. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.64706, not 1.35294.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.64706, not 2.35294.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.64706, not -3... | [
"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_004032 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.45. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "-19.2 N",
"B": "20.2 N",
"C": "15.36 N",
"D": "19.2 N"
} | D | 19.2 N | Net force=mg(sinθ−μcosθ)=8×10×(0.6−0.45×0.8)=19.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19.2 N, not -19.2 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19.2 N, not 20.2 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19.2 N, not 15.36 N."... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000569 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 27 and common difference 15. Find the sum of its first 29 terms. | {
"A": "6875",
"B": "8247.6",
"C": "3436.5",
"D": "6873"
} | D | 6873 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=27, d=15, n=29: Sₙ=29/2[2(27)+(29−1)(15)]=6873. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6873, not 6875.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6873, not 8247.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6873, not 3436.5.",
"D": "... | [
"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_000229 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 -7x +2=0, let its roots be α and β. What is α²+β²? | {
"A": "0.42857",
"B": "1.04286",
"C": "-2.57143",
"D": "1.42857"
} | A | 0.42857 | By Vieta's relations, α+β = 7/7 and αβ = 2/7. Then α²+β²=(α+β)²−2αβ = (7/7)²−2(2/7) = 0.42857. | {
"A": "Correct. The worked calculation gives 0.42857.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.42857, not 1.04286.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.42857, not -2.57143.",
"D": "Incorrect. Substituting the stated v... | [
"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_009487 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_18H_27N_2X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "6",
"B": "9",
"C": "12",
"D": "-6"
} | A | 6 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+2−27−1)/2=6. | {
"A": "Correct. The worked calculation gives 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 12.",
"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_002060 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 10 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.16",
"B": "0.32",
"C": "-1.68",
"D": "1.32"
} | B | 0.32 | Favourable pairs = C(9,2)+C(10,2)+C(6,2)=96. Total pairs=C(25,2)=300. Therefore P=96/300=0.32. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32, not 0.16.",
"B": "Correct. The worked calculation gives 0.32.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32, not -1.68.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_006741 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 7 mol H₂ and 7 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "5.25 mol",
"B": "7 mol",
"C": "5 mol",
"D": "3.5 mol"
} | B | 7 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 7 mol H₂O; O₂ can produce 14 mol H₂O. The limiting condition is H₂; product=7 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7 mol, not 5.25 mol.",
"B": "Correct. The worked calculation gives 7 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7 mol, not 5 mol.",
"D": "Incorrect. Substituting the stated values in... | [
"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_003789 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block initially moves at 12 m s⁻¹. A constant net force does 8 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "358.4 J",
"B": "224 J",
"C": "448 J",
"D": "537.6 J"
} | C | 448 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(5)(12)²+(8)(11)=448 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 448 J, not 358.4 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 448 J, not 224 J.",
"C": "Correct. The worked calculation gives 448 J.",
"D": "Incorrect. Substituting the stated values int... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000504 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 11 and common difference 10. Find the sum of its first 22 terms. | {
"A": "2041.6",
"B": "2551",
"C": "2554",
"D": "2552"
} | D | 2552 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=11, d=10, n=22: Sₙ=22/2[2(11)+(22−1)(10)]=2552. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2552, not 2041.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2552, not 2551.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2552, not 2554.",
"D": "Co... | [
"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_004401 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 4 kg and radius 2 m is acted on by a constant torque of 22 N m about its central axis. Find its angular acceleration. | {
"A": "1.275 rad s⁻²",
"B": "-0.25 rad s⁻²",
"C": "0.75 rad s⁻²",
"D": "2.75 rad s⁻²"
} | D | 2.75 rad s⁻² | For a solid disc, I=½MR²=½(4)(2)²=8 kg m². Using τ=Iα, α=22/8=2.75 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.75 rad s⁻², not 1.275 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.75 rad s⁻², not -0.25 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gi... | [
"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_000541 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 22 and common difference 3. Find the sum of its first 20 terms. | {
"A": "1011",
"B": "1010",
"C": "-1010",
"D": "505"
} | B | 1010 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=22, d=3, n=20: Sₙ=20/2[2(22)+(20−1)(3)]=1010. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1010, not 1011.",
"B": "Correct. The worked calculation gives 1010.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1010, not -1010.",
"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_000419 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -8 and common difference 3. Find the sum of its first 11 terms. | {
"A": "-77",
"B": "57.75",
"C": "77",
"D": "115.5"
} | C | 77 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-8, d=3, n=11: Sₙ=11/2[2(-8)+(11−1)(3)]=77. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 77, not -77.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 77, not 57.75.",
"C": "Correct. The worked calculation gives 77.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_009711 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(CN)_6]^-2, each CN ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "-4",
"B": "2",
"C": "8",
"D": "4"
} | D | 4 | Let the formal oxidation state of Cr be x. Charge balance gives x+(6)(−1)=-2; hence x=-2+6=+4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not -4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 8.",
"D": "Correct. The worked c... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001854 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 9 elements can be selected from a set of 32 distinct elements? | {
"A": "42073200",
"B": "28048800",
"C": "56097600",
"D": "2804881"
} | B | 28048800 | Order does not matter, so the count is C(32,9)=32!/[9!(23)!]=28048800. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28048800, not 42073200.",
"B": "Correct. The worked calculation gives 28048800.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28048800, not 56097600.",
"D": "Incorrect. Substituting the stat... | [
"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_003827 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 3 kg block initially moves at 1 m s⁻¹. A constant net force does 21 N of work over 5 m in the direction of motion. Find its final kinetic energy. | {
"A": "107.5 J",
"B": "106.5 J",
"C": "53.25 J",
"D": "79.875 J"
} | B | 106.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(3)(1)²+(21)(5)=106.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 106.5 J, not 107.5 J.",
"B": "Correct. The worked calculation gives 106.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 106.5 J, not 53.25 J.",
"D": "Incorrect. Substituting the stated va... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004046 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 28 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.34. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "73.472 N",
"B": "-91.84 N",
"C": "91.84 N",
"D": "45.92 N"
} | C | 91.84 N | Net force=mg(sinθ−μcosθ)=28×10×(0.6−0.34×0.8)=91.84 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 91.84 N, not 73.472 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 91.84 N, not -91.84 N.",
"C": "Correct. The worked calculation gives 91.84 N.",
"D": "Incorrect. Substituting the stated ... | [
"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_005189 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +1 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "8.3 N",
"B": "3.15 N",
"C": "6.3 N",
"D": "9.45 N"
} | C | 6.3 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(1×10⁻⁶)/(10×10⁻²)²=6.3 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.3 N, not 8.3 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.3 N, not 3.15 N.",
"C": "Correct. The worked calculation gives 6.3 N.",
"D": "Incorrect. Substituting the stated values into... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006855 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 42 mol H₂ and 1 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "4 mol",
"B": "2 mol",
"C": "-2 mol",
"D": "3 mol"
} | B | 2 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 42 mol H₂O; O₂ can produce 2 mol H₂O. The limiting condition is O₂; product=2 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 4 mol.",
"B": "Correct. The worked calculation gives 2 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not -2 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_003745 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 12 m s⁻¹. A constant net force does 21 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "1095 J",
"B": "110.5 J",
"C": "1094 J",
"D": "1097 J"
} | A | 1095 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(12)²+(21)(11)=1095 J. | {
"A": "Correct. The worked calculation gives 1095 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1095 J, not 110.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1095 J, not 1094 J.",
"D": "Incorrect. Substituting the stated values... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000082 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +0x +1=0, let its roots be α and β. What is α²+β²? | {
"A": "-0.66667",
"B": "-2.66667",
"C": "1.33333",
"D": "-1"
} | A | -0.66667 | By Vieta's relations, α+β = 0/3 and αβ = 1/3. Then α²+β²=(α+β)²−2αβ = (0/3)²−2(1/3) = -0.66667. | {
"A": "Correct. The worked calculation gives -0.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.66667, not -2.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.66667, not 1.33333.",
"D": "Incorrect. Substituting the state... | [
"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_005828 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.1 atm at 442 K. What is its pressure at 581 K? | {
"A": "0.06572 atm",
"B": "0.19717 atm",
"C": "3.13145 atm",
"D": "0.13145 atm"
} | D | 0.13145 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.1)(581)/(442)=0.13145 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.13145 atm, not 0.06572 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.13145 atm, not 0.19717 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.... | [
"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_001100 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=2x³ -7x² -10x+7. Evaluate f′(-1). | {
"A": "12",
"B": "5",
"C": "7",
"D": "10"
} | D | 10 | Differentiate: f′(x)=3(2)x²+2(-7)x+(-10). At x=-1, f′(-1)=3(2)(-1)²+2(-7)(-1)+(-10)=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 12.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 7.",
"D": "Correct. The worke... | [
"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_005220 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +8 μC and +9 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "41.5 N",
"B": "403 N",
"C": "405 N",
"D": "486 N"
} | C | 405 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(8×10⁻⁶)(9×10⁻⁶)/(4×10⁻²)²=405 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 405 N, not 41.5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 405 N, not 403 N.",
"C": "Correct. The worked calculation gives 405 N.",
"D": "Incorrect. Substituting the stated values into... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005492 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 72 μF capacitor is charged to a potential difference of 16 V. Calculate the energy stored, expressed in μJ. | {
"A": "9216 μJ",
"B": "6912 μJ",
"C": "9215 μJ",
"D": "922.6 μJ"
} | A | 9216 μJ | U=½CV². Since C=72 μF, U in μJ is ½×72×(16)²=9216 μJ. | {
"A": "Correct. The worked calculation gives 9216 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9216 μJ, not 6912 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9216 μJ, not 9215 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004025 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.45. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "24 N",
"B": "23 N",
"C": "18 N",
"D": "-24 N"
} | A | 24 N | Net force=mg(sinθ−μcosθ)=10×10×(0.6−0.45×0.8)=24 N. | {
"A": "Correct. The worked calculation gives 24 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24 N, not 23 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24 N, not 18 N.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_003797 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block initially moves at 3 m s⁻¹. A constant net force does 30 N of work over 8 m in the direction of motion. Find its final kinetic energy. | {
"A": "267 J",
"B": "266 J",
"C": "265 J",
"D": "200.25 J"
} | A | 267 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(6)(3)²+(30)(8)=267 J. | {
"A": "Correct. The worked calculation gives 267 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 267 J, not 266 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 267 J, not 265 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_003431 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 14 m s⁻¹ at 65° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "22.52171 m",
"B": "7.50724 m",
"C": "15.01447 m",
"D": "-15.01447 m"
} | C | 15.01447 m | Range R=u²sin(2θ)/g. Substituting u=14, θ=65° and g=10 gives R=(14)²sin(130°)/10=15.01447 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15.01447 m, not 22.52171 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15.01447 m, not 7.50724 m.",
"C": "Correct. The worked calculation gives 15.01447 m.",
"D": "Incorrect. Substituting... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007808 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 86 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "1.34375 mmol L⁻¹",
"B": "5.375 mmol L⁻¹",
"C": "3.6875 mmol L⁻¹",
"D": "2.6875 mmol L⁻¹"
} | D | 2.6875 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=86/2^5=2.6875 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.6875 mmol L⁻¹, not 1.34375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.6875 mmol L⁻¹, not 5.375 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing r... | [
"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_006129 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 40 cm in front of a thin convex lens of focal length 8 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.25",
"B": "-1.75",
"C": "1.25",
"D": "-0.25"
} | A | 0.25 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(40)(8)/(40−8)=10 cm. Thus |m|=v/u=10/40=0.25. | {
"A": "Correct. The worked calculation gives 0.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25, not -1.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25, not 1.25.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_006368 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 4 kg is attached to an ideal spring of force constant 413 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.14762 s",
"B": "0.19683 s",
"C": "1.19683 s",
"D": "1.01968 s"
} | B | 0.19683 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(4/413)=0.19683 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.19683 s, not 0.14762 s.",
"B": "Correct. The worked calculation gives 0.19683 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.19683 s, not 1.19683 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007224 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 6 mol of gas at 525 K and 1.14 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "227.73645 L",
"B": "113.36822 L",
"C": "226.73645 L",
"D": "453.47289 L"
} | C | 226.73645 L | PV=nRT, so V=nRT/P=(6)(0.082057)(525)/(1.14)=226.73645 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 226.73645 L, not 227.73645 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 226.73645 L, not 113.36822 L.",
"C": "Correct. The worked calculation gives 226.73645 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_004608 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 15 kg and radius 2 m is acted on by a constant torque of 66 N m about its central axis. Find its angular acceleration. | {
"A": "1.65 rad s⁻²",
"B": "2.2 rad s⁻²",
"C": "3.3 rad s⁻²",
"D": "1.2 rad s⁻²"
} | B | 2.2 rad s⁻² | For a solid disc, I=½MR²=½(15)(2)²=30 kg m². Using τ=Iα, α=66/30=2.2 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.2 rad s⁻², not 1.65 rad s⁻².",
"B": "Correct. The worked calculation gives 2.2 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.2 rad s⁻², not 3.3 rad s⁻².",
"D": "Incorrect. Subst... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000216 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 -1x -11=0, let its roots be α and β. What is α²+β²? | {
"A": "11.5",
"B": "-23",
"C": "23",
"D": "3.3"
} | C | 23 | By Vieta's relations, α+β = 1/1 and αβ = -11/1. Then α²+β²=(α+β)²−2αβ = (1/1)²−2(-11/1) = 23. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 23, not 11.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23, not -23.",
"C": "Correct. The worked calculation gives 23.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_007411 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 38 mL of 0.10 M HCl is mixed with 71 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "9.36082",
"B": "18.72163",
"C": "12.48109",
"D": "6.24054"
} | C | 12.48109 | Excess OH⁻ moles=0.10×(71−38)/1000=0.003300 mol. Total volume=0.109 L, so [OH⁻]=0.030275 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.48109. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.48109, not 9.36082.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.48109, not 18.72163.",
"C": "Correct. The worked calculation gives 12.48109.",
"D": "Incorrect. Substituting the state... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004500 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 4 m is acted on by a constant torque of 51 N m about its central axis. Find its angular acceleration. | {
"A": "1.09107 rad s⁻²",
"B": "0.45536 rad s⁻²",
"C": "0.91071 rad s⁻²",
"D": "-1.08929 rad s⁻²"
} | C | 0.91071 rad s⁻² | For a solid disc, I=½MR²=½(7)(4)²=56 kg m². Using τ=Iα, α=51/56=0.91071 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.91071 rad s⁻², not 1.09107 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.91071 rad s⁻², not 0.45536 rad s⁻².",
"C": "Correct. The worked calculation gives 0.91071 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_001766 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 12 distinct elements? | {
"A": "792",
"B": "594",
"C": "1584",
"D": "950.4"
} | A | 792 | Order does not matter, so the count is C(12,5)=12!/[5!(7)!]=792. | {
"A": "Correct. The worked calculation gives 792.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 792, not 594.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 792, not 1584.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006898 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 41 mol H₂ and 18 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "27 mol",
"B": "36 mol",
"C": "34 mol",
"D": "35 mol"
} | B | 36 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 41 mol H₂O; O₂ can produce 36 mol H₂O. The limiting condition is O₂; product=36 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 36 mol, not 27 mol.",
"B": "Correct. The worked calculation gives 36 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 36 mol, not 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_005144 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +8 μC and +5 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "720 N",
"B": "675 N",
"C": "898 N",
"D": "900 N"
} | D | 900 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(8×10⁻⁶)(5×10⁻⁶)/(2×10⁻²)²=900 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 900 N, not 720 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 900 N, not 675 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 900 N, not 898 N.",
"D":... | [
"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_007102 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 18 mol of gas at 371 K and 0.85 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "-644.67841 L",
"B": "1289.35681 L",
"C": "322.3392 L",
"D": "644.67841 L"
} | D | 644.67841 L | PV=nRT, so V=nRT/P=(18)(0.082057)(371)/(0.85)=644.67841 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 644.67841 L, not -644.67841 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 644.67841 L, not 1289.35681 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives ... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009411 | 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_14H_12N_1X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "7",
"B": "4",
"C": "16",
"D": "8"
} | D | 8 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×14+2+1−12−3)/2=8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 16.",
"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_006564 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 11 kg is attached to an ideal spring of force constant 877 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.22399 s",
"B": "-0.22399 s",
"C": "0.11199 s",
"D": "0.44798 s"
} | A | 0.22399 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(11/877)=0.22399 s. | {
"A": "Correct. The worked calculation gives 0.22399 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.22399 s, not -0.22399 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.22399 s, not 0.11199 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_006305 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 59 cm in front of a thin convex lens of focal length 24 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-2.31429",
"B": "1.37143",
"C": "0.68571",
"D": "1.68571"
} | C | 0.68571 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(59)(24)/(59−24)=40.45714 cm. Thus |m|=v/u=40.45714/59=0.68571. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.68571, not -2.31429.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.68571, not 1.37143.",
"C": "Correct. The worked calculation gives 0.68571.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008156 | 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 5 A for 9908 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": "19.55932 g",
"B": "14.29943 g",
"C": "24.44915 g",
"D": "16.29943 g"
} | D | 16.29943 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×5×9908/(2×96500)=16.29943 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16.29943 g, not 19.55932 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16.29943 g, not 14.29943 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16.299... | [
"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_009011 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.41 V, transfers 2 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.49865 V",
"B": "1.49865 V",
"C": "0.49865 V",
"D": "3.49865 V"
} | B | 1.49865 V | Apply the Nernst equation: E=1.41−(0.0591/2)(-3)=1.49865 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.49865 V, not 2.49865 V.",
"B": "Correct. The worked calculation gives 1.49865 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.49865 V, not 0.49865 V.",
"D": "Incorrect. Substituting the... | [
"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_008733 | 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 1.96 mol L⁻¹ and initially B is absent. At equilibrium, 32% of A has dissociated at constant volume. Find K_c. | {
"A": "2.36122",
"B": "3.18061",
"C": "1.18061",
"D": "-0.81939"
} | C | 1.18061 | Let α=0.32. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.96)(0.32)²/(1−0.32)=1.18061. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.18061, not 2.36122.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.18061, not 3.18061.",
"C": "Correct. The worked calculation gives 1.18061.",
"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_007247 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 13 mol of gas at 233 K and 0.85 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "294.41253 L",
"B": "30.24125 L",
"C": "292.41253 L",
"D": "438.6188 L"
} | C | 292.41253 L | PV=nRT, so V=nRT/P=(13)(0.082057)(233)/(0.85)=292.41253 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 292.41253 L, not 294.41253 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 292.41253 L, not 30.24125 L.",
"C": "Correct. The worked calculation gives 292.41253 L.",
"D": "Incorrect. Substit... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004278 | 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 0.13. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "248 N",
"B": "247 N",
"C": "198.4 N",
"D": "186 N"
} | A | 248 N | Net force=mg(sinθ−μcosθ)=50×10×(0.6−0.13×0.8)=248 N. | {
"A": "Correct. The worked calculation gives 248 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 248 N, not 247 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 248 N, not 198.4 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_003974 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block initially moves at 4 m s⁻¹. A constant net force does 29 N of work over 13 m in the direction of motion. Find its final kinetic energy. | {
"A": "586.8 J",
"B": "978 J",
"C": "489 J",
"D": "-489 J"
} | C | 489 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(14)(4)²+(29)(13)=489 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 489 J, not 586.8 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 489 J, not 978 J.",
"C": "Correct. The worked calculation gives 489 J.",
"D": "Incorrect. Substituting the stated values int... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002558 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, 8], [4, -3]]. | {
"A": "-88.5",
"B": "-29.5",
"C": "-118",
"D": "-59"
} | D | -59 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(-3)−(8)(4)=-59. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -59, not -88.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -59, not -29.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -59, not -118.",
"D": "Corre... | [
"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_000607 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 28 and common difference 14. Find the sum of its first 24 terms. | {
"A": "-4536",
"B": "9072",
"C": "454.6",
"D": "4536"
} | D | 4536 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=28, d=14, n=24: Sₙ=24/2[2(28)+(24−1)(14)]=4536. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4536, not -4536.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4536, not 9072.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4536, not 454.6.",
"D": "Co... | [
"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_009245 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.10 V, transfers 2 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "4.24775 V",
"B": "-1.75225 V",
"C": "0.62388 V",
"D": "1.24775 V"
} | D | 1.24775 V | Apply the Nernst equation: E=1.10−(0.0591/2)(-5)=1.24775 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.24775 V, not 4.24775 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.24775 V, not -1.75225 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.24775 V... | [
"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_006614 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 20 kg is attached to an ideal spring of force constant 759 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.24349 s",
"B": "1.03247 s",
"C": "-0.67534 s",
"D": "0.32466 s"
} | D | 0.32466 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(20/759)=0.32466 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32466 s, not 0.24349 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32466 s, not 1.03247 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32466 s,... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008453 | 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 0.95 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.95 K",
"B": "0.95 K",
"C": "-0.05 K",
"D": "1.095 K"
} | B | 0.95 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×1.0×0.95=0.95 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.95 K, not 1.95 K.",
"B": "Correct. The worked calculation gives 0.95 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.95 K, not -0.05 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001733 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 9 elements can be selected from a set of 46 distinct elements? | {
"A": "2203432660",
"B": "110171634",
"C": "1101716331",
"D": "1101716330"
} | D | 1101716330 | Order does not matter, so the count is C(46,9)=46!/[9!(37)!]=1101716330. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1101716330, not 2203432660.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1101716330, not 110171634.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1101716... | [
"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_002437 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, -8], [2, 2]]. | {
"A": "32",
"B": "-32",
"C": "64",
"D": "30"
} | A | 32 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(2)−(-8)(2)=32. | {
"A": "Correct. The worked calculation gives 32.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 32, not -32.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 32, not 64.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008184 | 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 3 A for 1913 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "1.18882 g",
"B": "0.94411 g",
"C": "1.41617 g",
"D": "1.88822 g"
} | D | 1.88822 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×3×1913/(2×96500)=1.88822 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.88822 g, not 1.18882 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.88822 g, not 0.94411 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.88822 g,... | [
"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_006343 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 21 kg is attached to an ideal spring of force constant 330 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.49548 s",
"B": "-0.50452 s",
"C": "0.50452 s",
"D": "1.05045 s"
} | C | 0.50452 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(21/330)=0.50452 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.50452 s, not -1.49548 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.50452 s, not -0.50452 s.",
"C": "Correct. The worked calculation gives 0.50452 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_002374 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, 3], [9, 1]]. | {
"A": "-40",
"B": "-15",
"C": "-20",
"D": "-24"
} | C | -20 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(1)−(3)(9)=-20. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -20, not -40.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -20, not -15.",
"C": "Correct. The worked calculation gives -20.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009820 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(CN)_4]^-3, each CN ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "2",
"B": "1",
"C": "3",
"D": "-2"
} | B | 1 | Let the formal oxidation state of Pd be x. Charge balance gives x+(4)(−1)=-3; hence x=-3+4=+1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"B": "Correct. The worked calculation gives 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 3.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002751 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, 5, 3) and v=(-3, 9, 8), calculate u·v. | {
"A": "56",
"B": "114",
"C": "57",
"D": "6.7"
} | C | 57 | The dot product is the sum of corresponding component products: (4)(-3)+(5)(9)+(3)(8)=57. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 57, not 56.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 57, not 114.",
"C": "Correct. The worked calculation gives 57.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008750 | 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 1.11 mol L⁻¹ and initially B is absent. At equilibrium, 55% of A has dissociated at constant volume. Find K_c. | {
"A": "2.98467",
"B": "1.98467",
"C": "4.98467",
"D": "2.2385"
} | A | 2.98467 | Let α=0.55. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.11)(0.55)²/(1−0.55)=2.98467. | {
"A": "Correct. The worked calculation gives 2.98467.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.98467, not 1.98467.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.98467, not 4.98467.",
"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_004127 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 35 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.32. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "120.4 N",
"B": "119.4 N",
"C": "96.32 N",
"D": "180.6 N"
} | A | 120.4 N | Net force=mg(sinθ−μcosθ)=35×10×(0.6−0.32×0.8)=120.4 N. | {
"A": "Correct. The worked calculation gives 120.4 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 120.4 N, not 119.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 120.4 N, not 96.32 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002185 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 8 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "2.33538",
"B": "0.33538",
"C": "1.33538",
"D": "1.03354"
} | B | 0.33538 | Favourable pairs = C(6,2)+C(8,2)+C(12,2)=109. Total pairs=C(26,2)=325. Therefore P=109/325=0.33538. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33538, not 2.33538.",
"B": "Correct. The worked calculation gives 0.33538.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33538, not 1.33538.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003528 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 84 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "706.6 m",
"B": "705.6 m",
"C": "846.72 m",
"D": "703.6 m"
} | B | 705.6 m | Range R=u²sin(2θ)/g. Substituting u=84, θ=45° and g=10 gives R=(84)²sin(90°)/10=705.6 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 705.6 m, not 706.6 m.",
"B": "Correct. The worked calculation gives 705.6 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 705.6 m, not 846.72 m.",
"D": "Incorrect. Substituting the stated v... | [
"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_006607 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 16 kg is attached to an ideal spring of force constant 1080 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.24343 s",
"B": "-2.75657 s",
"C": "0.48686 s",
"D": "0.36515 s"
} | A | 0.24343 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(16/1080)=0.24343 s. | {
"A": "Correct. The worked calculation gives 0.24343 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.24343 s, not -2.75657 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.24343 s, not 0.48686 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_001923 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 9 elements can be selected from a set of 90 distinct elements? | {
"A": "353126264315",
"B": "847503034356",
"C": "565002022904",
"D": "706252528630"
} | D | 706252528630 | Order does not matter, so the count is C(90,9)=90!/[9!(81)!]=706252528630. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 706252528630, not 353126264315.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 706252528630, not 847503034356.",
"C": "Incorrect. Substituting the stated values into the governing relation give... | [
"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_001986 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 9 elements can be selected from a set of 73 distinct elements? | {
"A": "9708202147.5",
"B": "-97082021465",
"C": "48541010732.5",
"D": "97082021465"
} | D | 97082021465 | Order does not matter, so the count is C(73,9)=73!/[9!(64)!]=97082021465. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 97082021465, not 9708202147.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 97082021465, not -97082021465.",
"C": "Incorrect. Substituting the stated values into the governing relation gives ... | [
"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_009184 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.85 V, transfers 1 electrons, and has reaction quotient Q=10^1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.07909 V",
"B": "0.7909 V",
"C": "3.7909 V",
"D": "2.7909 V"
} | B | 0.7909 V | Apply the Nernst equation: E=0.85−(0.0591/1)(1)=0.7909 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7909 V, not 1.07909 V.",
"B": "Correct. The worked calculation gives 0.7909 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7909 V, not 3.7909 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007784 | 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 94 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "10.75 mmol L⁻¹",
"B": "14.75 mmol L⁻¹",
"C": "8.8125 mmol L⁻¹",
"D": "11.75 mmol L⁻¹"
} | D | 11.75 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=94/2^3=11.75 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.75 mmol L⁻¹, not 10.75 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.75 mmol L⁻¹, not 14.75 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relat... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002996 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-1, -1, 5) and v=(0, -1, 5), calculate u·v. | {
"A": "31.2",
"B": "25",
"C": "26",
"D": "24"
} | C | 26 | The dot product is the sum of corresponding component products: (-1)(0)+(-1)(-1)+(5)(5)=26. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26, not 31.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26, not 25.",
"C": "Correct. The worked calculation gives 26.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004706 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 10 Ω are connected in series; this combination is connected in parallel with a 13 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.52308 A",
"B": "-0.47692 A",
"C": "2.52308 A",
"D": "-1.52308 A"
} | A | 1.52308 A | Series branch resistance=10+10=20 Ω. Parallel equivalent R_eq=(20×13)/(20+13)=7.87879 Ω. Total current I=V/R_eq=12/7.87879=1.52308 A. | {
"A": "Correct. The worked calculation gives 1.52308 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.52308 A, not -0.47692 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.52308 A, not 2.52308 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006656 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 5 kg is attached to an ideal spring of force constant 574 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.37333 s",
"B": "-1.81334 s",
"C": "0.18666 s",
"D": "1.01867 s"
} | C | 0.18666 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(5/574)=0.18666 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.18666 s, not 0.37333 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.18666 s, not -1.81334 s.",
"C": "Correct. The worked calculation gives 0.18666 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_001449 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (4x² -7x +4) dx. | {
"A": "-186",
"B": "184",
"C": "279",
"D": "186"
} | D | 186 | An antiderivative is (4/3)x³+(-7/2)x²+(4)x. Evaluating between 0 and 6 gives (4/3)(6)³+(-7/2)(6)²+(4)(6)=186. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 186, not -186.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 186, not 184.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 186, not 279.",
"D": "Correct. ... | [
"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_005628 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 10 μF capacitor is charged to a potential difference of 19 V. Calculate the energy stored, expressed in μJ. | {
"A": "1805 μJ",
"B": "1803 μJ",
"C": "2166 μJ",
"D": "-1805 μJ"
} | A | 1805 μJ | U=½CV². Since C=10 μF, U in μJ is ½×10×(19)²=1805 μJ. | {
"A": "Correct. The worked calculation gives 1805 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1805 μJ, not 1803 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1805 μJ, not 2166 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002475 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, 2], [8, -7]]. | {
"A": "-48.75",
"B": "-65",
"C": "65",
"D": "-130"
} | B | -65 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(-7)−(2)(8)=-65. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -65, not -48.75.",
"B": "Correct. The worked calculation gives -65.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -65, not 65.",
"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_004557 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 6 m is acted on by a constant torque of 18 N m about its central axis. Find its angular acceleration. | {
"A": "2.5 rad s⁻²",
"B": "0.5 rad s⁻²",
"C": "1.5 rad s⁻²",
"D": "-0.5 rad s⁻²"
} | B | 0.5 rad s⁻² | For a solid disc, I=½MR²=½(2)(6)²=36 kg m². Using τ=Iα, α=18/36=0.5 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5 rad s⁻², not 2.5 rad s⁻².",
"B": "Correct. The worked calculation gives 0.5 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5 rad s⁻², not 1.5 rad s⁻².",
"D": "Incorrect. Substi... | [
"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_005455 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 77 μF capacitor is charged to a potential difference of 27 V. Calculate the energy stored, expressed in μJ. | {
"A": "2807.65 μJ",
"B": "28067.5 μJ",
"C": "28066.5 μJ",
"D": "56133 μJ"
} | C | 28066.5 μJ | U=½CV². Since C=77 μF, U in μJ is ½×77×(27)²=28066.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28066.5 μJ, not 2807.65 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28066.5 μJ, not 28067.5 μJ.",
"C": "Correct. The worked calculation gives 28066.5 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_001952 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 6 elements can be selected from a set of 74 distinct elements? | {
"A": "185250785",
"B": "185250786",
"C": "-185250786",
"D": "277876179"
} | B | 185250786 | Order does not matter, so the count is C(74,6)=74!/[6!(68)!]=185250786. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 185250786, not 185250785.",
"B": "Correct. The worked calculation gives 185250786.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 185250786, not -185250786.",
"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_007811 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 23 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "2.71875 mmol L⁻¹",
"B": "1.07187 mmol L⁻¹",
"C": "0.53906 mmol L⁻¹",
"D": "0.71875 mmol L⁻¹"
} | D | 0.71875 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=23/2^5=0.71875 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.71875 mmol L⁻¹, not 2.71875 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.71875 mmol L⁻¹, not 1.07187 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governi... | [
"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_003650 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 18 m s⁻¹ at 30° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "28.05922 m",
"B": "14.02961 m",
"C": "-28.05922 m",
"D": "26.05922 m"
} | A | 28.05922 m | Range R=u²sin(2θ)/g. Substituting u=18, θ=30° and g=10 gives R=(18)²sin(60°)/10=28.05922 m. | {
"A": "Correct. The worked calculation gives 28.05922 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28.05922 m, not 14.02961 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28.05922 m, not -28.05922 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_009265 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.28 V, transfers 1 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.5755 V",
"B": "1.18162 V",
"C": "0.78775 V",
"D": "0.5755 V"
} | A | 1.5755 V | Apply the Nernst equation: E=1.28−(0.0591/1)(-5)=1.5755 V. | {
"A": "Correct. The worked calculation gives 1.5755 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.5755 V, not 1.18162 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.5755 V, not 0.78775 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_007127 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 11 mol of gas at 526 K and 2.81 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "170.9615 L",
"B": "167.9615 L",
"C": "135.1692 L",
"D": "168.9615 L"
} | D | 168.9615 L | PV=nRT, so V=nRT/P=(11)(0.082057)(526)/(2.81)=168.9615 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 168.9615 L, not 170.9615 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 168.9615 L, not 167.9615 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 168.96... | [
"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_004277 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 3 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.33. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "11.08 N",
"B": "7.08 N",
"C": "-10.08 N",
"D": "10.08 N"
} | D | 10.08 N | Net force=mg(sinθ−μcosθ)=3×10×(0.6−0.33×0.8)=10.08 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.08 N, not 11.08 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.08 N, not 7.08 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10.08 N, not -10.08... | [
"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_005513 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 77 μF capacitor is charged to a potential difference of 10 V. Calculate the energy stored, expressed in μJ. | {
"A": "4620 μJ",
"B": "-3850 μJ",
"C": "3849 μJ",
"D": "3850 μJ"
} | D | 3850 μJ | U=½CV². Since C=77 μF, U in μJ is ½×77×(10)²=3850 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3850 μJ, not 4620 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3850 μJ, not -3850 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3850 μJ, not 3849... | [
"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_007337 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 55 mL of 0.10 M HCl is mixed with 24 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-0.59373",
"B": "2.1094",
"C": "0.40627",
"D": "1.40627"
} | D | 1.40627 | Excess H⁺ moles=0.10×(55−24)/1000=0.003100 mol. Total volume=0.079 L, so [H⁺]=0.039241 M and pH=−log₁₀[H⁺]=1.40627. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.40627, not -0.59373.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.40627, not 2.1094.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.40627, not 0.406... | [
"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_004068 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.10. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "72.8 N",
"B": "-72.8 N",
"C": "70.8 N",
"D": "58.24 N"
} | A | 72.8 N | Net force=mg(sinθ−μcosθ)=14×10×(0.6−0.10×0.8)=72.8 N. | {
"A": "Correct. The worked calculation gives 72.8 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 72.8 N, not -72.8 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 72.8 N, not 70.8 N.",
"D": "Incorrect. Substituting the stated values... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004836 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 2 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 15 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "6 A",
"B": "4 A",
"C": "8 A",
"D": "9 A"
} | A | 6 A | Series branch resistance=2+8=10 Ω. Parallel equivalent R_eq=(10×15)/(10+15)=6 Ω. Total current I=V/R_eq=36/6=6 A. | {
"A": "Correct. The worked calculation gives 6 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6 A, not 4 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6 A, not 8 A.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_002595 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, 0], [4, -6]]. | {
"A": "12",
"B": "-12",
"C": "-6",
"D": "-18"
} | B | -12 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(-6)−(0)(4)=-12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -12, not 12.",
"B": "Correct. The worked calculation gives -12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -12, not -6.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_000673 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio -3. What is the sum of its first 9 terms? | {
"A": "24607",
"B": "24604",
"C": "36907.5",
"D": "24605"
} | D | 24605 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(-3^9−1)/(-3−1)=24605. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24605, not 24607.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24605, not 24604.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24605, not 36907.5.",
"D... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005327 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +1 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "8.26531 N",
"B": "12.02041 N",
"C": "5.5102 N",
"D": "11.02041 N"
} | D | 11.02041 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(1×10⁻⁶)/(7×10⁻²)²=11.02041 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.02041 N, not 8.26531 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.02041 N, not 12.02041 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.0204... | [
"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_008211 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 14 A for 16898 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": "78.83587 g",
"B": "77.83587 g",
"C": "116.7538 g",
"D": "58.3769 g"
} | B | 77.83587 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×16898/(2×96500)=77.83587 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 77.83587 g, not 78.83587 g.",
"B": "Correct. The worked calculation gives 77.83587 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 77.83587 g, not 116.7538 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002655 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, 2], [5, -5]]. | {
"A": "-16",
"B": "-20",
"C": "-24",
"D": "-30"
} | B | -20 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(-5)−(2)(5)=-20. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -20, not -16.",
"B": "Correct. The worked calculation gives -20.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -20, not -24.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004441 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 5 m is acted on by a constant torque of 5 N m about its central axis. Find its angular acceleration. | {
"A": "0.05714 rad s⁻²",
"B": "-0.05714 rad s⁻²",
"C": "1.00571 rad s⁻²",
"D": "1.05714 rad s⁻²"
} | A | 0.05714 rad s⁻² | For a solid disc, I=½MR²=½(7)(5)²=87.5 kg m². Using τ=Iα, α=5/87.5=0.05714 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.05714 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.05714 rad s⁻², not -0.05714 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.05714 rad s⁻², not 1.00571 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 |
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