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_004812 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 11 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 19 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "-1.28421 A",
"B": "0.35789 A",
"C": "1.71579 A",
"D": "0.71579 A"
} | D | 0.71579 A | Series branch resistance=11+4=15 Ω. Parallel equivalent R_eq=(15×19)/(15+19)=8.38235 Ω. Total current I=V/R_eq=6/8.38235=0.71579 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.71579 A, not -1.28421 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.71579 A, not 0.35789 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.71579 A... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008636 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.04 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "4.872 K",
"B": "0.872 K",
"C": "2.872 K",
"D": "1.872 K"
} | D | 1.872 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.6×1.04=1.872 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.872 K, not 4.872 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.872 K, not 0.872 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.872 K, not 2.872... | [
"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_007498 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 27 mL of 0.10 M HCl is mixed with 92 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "15.73737",
"B": "13.73737",
"C": "12.73737",
"D": "19.10605"
} | C | 12.73737 | Excess OH⁻ moles=0.10×(92−27)/1000=0.006500 mol. Total volume=0.119 L, so [OH⁻]=0.054622 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.73737. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.73737, not 15.73737.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.73737, not 13.73737.",
"C": "Correct. The worked calculation gives 12.73737.",
"D": "Incorrect. Substituting the stat... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006430 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 10 kg is attached to an ideal spring of force constant 1133 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.81211 s",
"B": "1.01879 s",
"C": "0.18789 s",
"D": "-1.81211 s"
} | C | 0.18789 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(10/1133)=0.18789 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.18789 s, not -2.81211 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.18789 s, not 1.01879 s.",
"C": "Correct. The worked calculation gives 0.18789 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_004047 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 45 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.22. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "190.8 N",
"B": "228.96 N",
"C": "-190.8 N",
"D": "152.64 N"
} | A | 190.8 N | Net force=mg(sinθ−μcosθ)=45×10×(0.6−0.22×0.8)=190.8 N. | {
"A": "Correct. The worked calculation gives 190.8 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 190.8 N, not 228.96 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 190.8 N, not -190.8 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_000964 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio 5. What is the sum of its first 9 terms? | {
"A": "6591793.5",
"B": "4394527",
"C": "4394528",
"D": "4394529"
} | D | 4394529 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(5^9−1)/(5−1)=4394529. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4394529, not 6591793.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4394529, not 4394527.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4394529, not 439... | [
"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_000675 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio 4. What is the sum of its first 12 terms? | {
"A": "5592405",
"B": "11184810",
"C": "11184811",
"D": "11184812"
} | B | 11184810 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(4^12−1)/(4−1)=11184810. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11184810, not 5592405.",
"B": "Correct. The worked calculation gives 11184810.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11184810, not 11184811.",
"D": "Incorrect. Substituting the state... | [
"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_003045 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-13+15i)/(3+12i). What is Re(z), the real part of z? | {
"A": "-0.92157",
"B": "1.84314",
"C": "1.38235",
"D": "0.92157"
} | D | 0.92157 | Multiply numerator and denominator by the conjugate (3-12i). Then Re(z)=(ac+bd)/(c²+d²)=((-13)(3)+(15)(12))/(3²+(12)²)=0.92157. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.92157, not -0.92157.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.92157, not 1.84314.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.92157, not 1.38... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007754 | 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 13 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "2.8125 mmol L⁻¹",
"B": "3.8125 mmol L⁻¹",
"C": "1.625 mmol L⁻¹",
"D": "0.8125 mmol L⁻¹"
} | D | 0.8125 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=13/2^4=0.8125 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8125 mmol L⁻¹, not 2.8125 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8125 mmol L⁻¹, not 3.8125 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_007875 | 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 85 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "3.125 mmol L⁻¹",
"B": "-21.25 mmol L⁻¹",
"C": "21.25 mmol L⁻¹",
"D": "22.25 mmol L⁻¹"
} | C | 21.25 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=85/2^2=21.25 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21.25 mmol L⁻¹, not 3.125 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21.25 mmol L⁻¹, not -21.25 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 21.25 mmol L⁻¹.",
"D": "I... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002652 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 1], [6, 0]]. | {
"A": "-4.5",
"B": "-6",
"C": "-3",
"D": "-4"
} | B | -6 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(0)−(1)(6)=-6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -6, not -4.5.",
"B": "Correct. The worked calculation gives -6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -6, not -3.",
"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_008534 | 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 0.53 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.08544 K",
"B": "1.62816 K",
"C": "0.54272 K",
"D": "0.08544 K"
} | A | 1.08544 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.512×0.53=1.08544 K. | {
"A": "Correct. The worked calculation gives 1.08544 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.08544 K, not 1.62816 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.08544 K, not 0.54272 K.",
"D": "Incorrect. Substituting the... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009721 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(OH)_4]^-4, each OH ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "0",
"B": "-2",
"C": "3",
"D": "-1"
} | A | 0 | Let the formal oxidation state of Co be x. Charge balance gives x+(4)(−1)=-4; hence x=-4+4=+0. | {
"A": "Correct. The worked calculation gives 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 3.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000609 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -15 and common difference 5. Find the sum of its first 18 terms. | {
"A": "990",
"B": "594",
"C": "495",
"D": "494"
} | C | 495 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-15, d=5, n=18: Sₙ=18/2[2(-15)+(18−1)(5)]=495. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 495, not 990.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 495, not 594.",
"C": "Correct. The worked calculation gives 495.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002007 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 5 blue and 8 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.15686",
"B": "1.31373",
"C": "0.31373",
"D": "-0.68627"
} | C | 0.31373 | Favourable pairs = C(5,2)+C(5,2)+C(8,2)=48. Total pairs=C(18,2)=153. Therefore P=48/153=0.31373. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31373, not 0.15686.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31373, not 1.31373.",
"C": "Correct. The worked calculation gives 0.31373.",
"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_004411 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 15 kg and radius 3 m is acted on by a constant torque of 74 N m about its central axis. Find its angular acceleration. | {
"A": "4.0963 rad s⁻²",
"B": "0.0963 rad s⁻²",
"C": "1.0963 rad s⁻²",
"D": "2.19259 rad s⁻²"
} | C | 1.0963 rad s⁻² | For a solid disc, I=½MR²=½(15)(3)²=67.5 kg m². Using τ=Iα, α=74/67.5=1.0963 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0963 rad s⁻², not 4.0963 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0963 rad s⁻², not 0.0963 rad s⁻².",
"C": "Correct. The worked calculation gives 1.0963 rad s⁻².",
"D": "In... | [
"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_004544 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 11 kg and radius 5 m is acted on by a constant torque of 8 N m about its central axis. Find its angular acceleration. | {
"A": "0.05818 rad s⁻²",
"B": "0.08727 rad s⁻²",
"C": "-0.05818 rad s⁻²",
"D": "-1.94182 rad s⁻²"
} | A | 0.05818 rad s⁻² | For a solid disc, I=½MR²=½(11)(5)²=137.5 kg m². Using τ=Iα, α=8/137.5=0.05818 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.05818 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.05818 rad s⁻², not 0.08727 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.05818 rad s⁻², not -0.05818 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_003140 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-8-14i)/(10+1i). What is Re(z), the real part of z? | {
"A": "0.93069",
"B": "-1.86139",
"C": "-0.93069",
"D": "0.06931"
} | C | -0.93069 | Multiply numerator and denominator by the conjugate (10-1i). Then Re(z)=(ac+bd)/(c²+d²)=((-8)(10)+(-14)(1))/(10²+(1)²)=-0.93069. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.93069, not 0.93069.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.93069, not -1.86139.",
"C": "Correct. The worked calculation gives -0.93069.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008082 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 11 A for 28704 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": "101.88468 g",
"B": "103.88468 g",
"C": "77.91351 g",
"D": "155.82703 g"
} | B | 103.88468 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×28704/(2×96500)=103.88468 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 103.88468 g, not 101.88468 g.",
"B": "Correct. The worked calculation gives 103.88468 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 103.88468 g, not 77.91351 g.",
"D": "Incorrect. Substit... | [
"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_007306 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 15 mol of gas at 476 K and 0.86 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "69.12639 L",
"B": "681.26393 L",
"C": "679.26393 L",
"D": "682.26393 L"
} | B | 681.26393 L | PV=nRT, so V=nRT/P=(15)(0.082057)(476)/(0.86)=681.26393 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 681.26393 L, not 69.12639 L.",
"B": "Correct. The worked calculation gives 681.26393 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 681.26393 L, not 679.26393 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_003886 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 3 m s⁻¹. A constant net force does 24 N of work over 2 m in the direction of motion. Find its final kinetic energy. | {
"A": "52.8 J",
"B": "67 J",
"C": "66 J",
"D": "99 J"
} | C | 66 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(3)²+(24)(2)=66 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 66 J, not 52.8 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 66 J, not 67 J.",
"C": "Correct. The worked calculation gives 66 J.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_004518 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 11 kg and radius 5 m is acted on by a constant torque of 78 N m about its central axis. Find its angular acceleration. | {
"A": "-1.43273 rad s⁻²",
"B": "2.56727 rad s⁻²",
"C": "0.56727 rad s⁻²",
"D": "3.56727 rad s⁻²"
} | C | 0.56727 rad s⁻² | For a solid disc, I=½MR²=½(11)(5)²=137.5 kg m². Using τ=Iα, α=78/137.5=0.56727 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.56727 rad s⁻², not -1.43273 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.56727 rad s⁻², not 2.56727 rad s⁻².",
"C": "Correct. The worked calculation gives 0.56727 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_002462 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, -8], [1, 2]]. | {
"A": "28.8",
"B": "3.4",
"C": "24",
"D": "12"
} | C | 24 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(2)−(-8)(1)=24. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24, not 28.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24, not 3.4.",
"C": "Correct. The worked calculation gives 24.",
"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_000334 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +15x -12=0, let its roots be α and β. What is α²+β²? | {
"A": "24.75",
"B": "49.5",
"C": "39.6",
"D": "33"
} | D | 33 | By Vieta's relations, α+β = -15/3 and αβ = -12/3. Then α²+β²=(α+β)²−2αβ = (-15/3)²−2(-12/3) = 33. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33, not 24.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33, not 49.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 33, not 39.6.",
"D": "Correct. ... | [
"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_005989 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.5 atm at 392 K. What is its pressure at 633 K? | {
"A": "9.26658 atm",
"B": "8.26658 atm",
"C": "10.89987 atm",
"D": "7.26658 atm"
} | D | 7.26658 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.5)(633)/(392)=7.26658 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.26658 atm, not 9.26658 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.26658 atm, not 8.26658 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.... | [
"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_002384 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -5], [4, 8]]. | {
"A": "60",
"B": "7",
"C": "120",
"D": "48"
} | A | 60 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(8)−(-5)(4)=60. | {
"A": "Correct. The worked calculation gives 60.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 60, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 60, not 120.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006569 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 9 kg is attached to an ideal spring of force constant 1039 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.81386 s",
"B": "0.13961 s",
"C": "0.18614 s",
"D": "0.37228 s"
} | C | 0.18614 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(9/1039)=0.18614 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.18614 s, not -0.81386 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.18614 s, not 0.13961 s.",
"C": "Correct. The worked calculation gives 0.18614 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_004915 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 8 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.75 A",
"B": "3.75 A",
"C": "5.75 A",
"D": "6.75 A"
} | B | 3.75 A | Series branch resistance=8+4=12 Ω. Parallel equivalent R_eq=(12×8)/(12+8)=4.8 Ω. Total current I=V/R_eq=18/4.8=3.75 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.75 A, not 4.75 A.",
"B": "Correct. The worked calculation gives 3.75 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.75 A, not 5.75 A.",
"D": "Incorrect. Substituting the stated values ... | [
"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_000899 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio 5. What is the sum of its first 8 terms? | {
"A": "1074218",
"B": "1289059.2",
"C": "537108",
"D": "1074216"
} | D | 1074216 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(5^8−1)/(5−1)=1074216. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1074216, not 1074218.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1074216, not 1289059.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1074216, not 537... | [
"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_008102 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 11 A for 15002 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": "-54.2948 g",
"B": "43.43584 g",
"C": "65.15376 g",
"D": "54.2948 g"
} | D | 54.2948 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×15002/(2×96500)=54.2948 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 54.2948 g, not -54.2948 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 54.2948 g, not 43.43584 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 54.2948 ... | [
"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_001745 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 12 elements can be selected from a set of 50 distinct elements? | {
"A": "121399651100",
"B": "121399651101",
"C": "97119720880",
"D": "242799302200"
} | A | 121399651100 | Order does not matter, so the count is C(50,12)=50!/[12!(38)!]=121399651100. | {
"A": "Correct. The worked calculation gives 121399651100.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 121399651100, not 121399651101.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 121399651100, not 97119720880.",
"D": "Incorrect. Su... | [
"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_007515 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 14 mL of 0.10 M HCl is mixed with 10 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.77815",
"B": "1.77815",
"C": "-0.22185",
"D": "0.77815"
} | B | 1.77815 | Excess H⁺ moles=0.10×(14−10)/1000=0.000400 mol. Total volume=0.024 L, so [H⁺]=0.016667 M and pH=−log₁₀[H⁺]=1.77815. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.77815, not 2.77815.",
"B": "Correct. The worked calculation gives 1.77815.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.77815, not -0.22185.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008089 | 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 4 A for 18074 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": "35.67976 g",
"B": "47.57302 g",
"C": "11.89325 g",
"D": "23.78651 g"
} | D | 23.78651 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×18074/(2×96500)=23.78651 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 23.78651 g, not 35.67976 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23.78651 g, not 47.57302 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23.786... | [
"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_006093 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 39 cm in front of a thin convex lens of focal length 20 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.05263",
"B": "2.10526",
"C": "0.05263",
"D": "0.52632"
} | A | 1.05263 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(39)(20)/(39−20)=41.05263 cm. Thus |m|=v/u=41.05263/39=1.05263. | {
"A": "Correct. The worked calculation gives 1.05263.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.05263, not 2.10526.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.05263, not 0.05263.",
"D": "Incorrect. Substituting the stated va... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005769 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3 atm at 198 K. What is its pressure at 314 K? | {
"A": "3.56818 atm",
"B": "4.75758 atm",
"C": "9.51515 atm",
"D": "7.13636 atm"
} | B | 4.75758 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3)(314)/(198)=4.75758 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.75758 atm, not 3.56818 atm.",
"B": "Correct. The worked calculation gives 4.75758 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.75758 atm, not 9.51515 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006972 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 16 mol H₂ and 6 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "14 mol",
"B": "12 mol",
"C": "10 mol",
"D": "18 mol"
} | B | 12 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 16 mol H₂O; O₂ can produce 12 mol H₂O. The limiting condition is O₂; product=12 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 14 mol.",
"B": "Correct. The worked calculation gives 12 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 10 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_003349 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 47 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "103.78905 m",
"B": "155.68357 m",
"C": "205.5781 m",
"D": "207.5781 m"
} | D | 207.5781 m | Range R=u²sin(2θ)/g. Substituting u=47, θ=55° and g=10 gives R=(47)²sin(110°)/10=207.5781 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 207.5781 m, not 103.78905 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 207.5781 m, not 155.68357 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 207.... | [
"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_009929 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(OH)_4]^-1, each OH ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "3",
"B": "4.5",
"C": "5",
"D": "0"
} | A | 3 | Let the formal oxidation state of Cr be x. Charge balance gives x+(4)(−1)=-1; hence x=-1+4=+3. | {
"A": "Correct. The worked calculation gives 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 5.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004289 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 22 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.30. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "77.2 N",
"B": "158.4 N",
"C": "8.92 N",
"D": "79.2 N"
} | D | 79.2 N | Net force=mg(sinθ−μcosθ)=22×10×(0.6−0.30×0.8)=79.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 79.2 N, not 77.2 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 79.2 N, not 158.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 79.2 N, not 8.92 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_008669 | 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 1.75 mol L⁻¹ and initially B is absent. At equilibrium, 61% of A has dissociated at constant volume. Find K_c. | {
"A": "13.35744",
"B": "7.67872",
"C": "4.67872",
"D": "6.67872"
} | D | 6.67872 | Let α=0.61. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.75)(0.61)²/(1−0.61)=6.67872. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.67872, not 13.35744.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.67872, not 7.67872.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.67872, not 4.67... | [
"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_002794 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(5, 8, -7) and v=(0, -5, -6), calculate u·v. | {
"A": "2",
"B": "4",
"C": "5",
"D": "1"
} | A | 2 | The dot product is the sum of corresponding component products: (5)(0)+(8)(-5)+(-7)(-6)=2. | {
"A": "Correct. The worked calculation gives 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 5.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_003975 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 9 m s⁻¹. A constant net force does 10 N of work over 17 m in the direction of motion. Find its final kinetic energy. | {
"A": "641.4 J",
"B": "535.5 J",
"C": "533.5 J",
"D": "534.5 J"
} | D | 534.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(9)²+(10)(17)=534.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 534.5 J, not 641.4 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 534.5 J, not 535.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 534.5 J, not 533.5... | [
"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_003690 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 3 kg block initially moves at 6 m s⁻¹. A constant net force does 28 N of work over 17 m in the direction of motion. Find its final kinetic energy. | {
"A": "54 J",
"B": "531 J",
"C": "529 J",
"D": "530 J"
} | D | 530 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(3)(6)²+(28)(17)=530 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 530 J, not 54 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 530 J, not 531 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 530 J, not 529 J.",
"D": ... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009826 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(CN)_4]^-2, each CN ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "3",
"B": "-2",
"C": "2",
"D": "1"
} | C | 2 | Let the formal oxidation state of Cu be x. Charge balance gives x+(4)(−1)=-2; hence x=-2+4=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"C": "Correct. The worked calculation gives 2.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003638 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 25 m s⁻¹ at 30° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "40.59494 m",
"B": "43.30127 m",
"C": "-54.12659 m",
"D": "54.12659 m"
} | D | 54.12659 m | Range R=u²sin(2θ)/g. Substituting u=25, θ=30° and g=10 gives R=(25)²sin(60°)/10=54.12659 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 54.12659 m, not 40.59494 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 54.12659 m, not 43.30127 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 54.126... | [
"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_002075 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 6 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.16382",
"B": "1.03276",
"C": "-0.67236",
"D": "0.32764"
} | D | 0.32764 | Favourable pairs = C(10,2)+C(6,2)+C(11,2)=115. Total pairs=C(27,2)=351. Therefore P=115/351=0.32764. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32764, not 0.16382.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32764, not 1.03276.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32764, not -0.67... | [
"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_004830 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 6 Ω and 5 Ω are connected in series; this combination is connected in parallel with a 17 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "-2.1016 A",
"B": "0.4492 A",
"C": "3.8984 A",
"D": "0.8984 A"
} | D | 0.8984 A | Series branch resistance=6+5=11 Ω. Parallel equivalent R_eq=(11×17)/(11+17)=6.67857 Ω. Total current I=V/R_eq=6/6.67857=0.8984 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8984 A, not -2.1016 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8984 A, not 0.4492 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8984 A, not... | [
"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_002815 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(3, 0, -5) and v=(-4, -7, 5), calculate u·v. | {
"A": "-35",
"B": "-74",
"C": "-37",
"D": "-39"
} | C | -37 | The dot product is the sum of corresponding component products: (3)(-4)+(0)(-7)+(-5)(5)=-37. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -37, not -35.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -37, not -74.",
"C": "Correct. The worked calculation gives -37.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009554 | 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_11H_15N_3X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "2",
"C": "4",
"D": "1"
} | C | 4 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+3−15−4)/2=4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"C": "Correct. The worked calculation gives 4.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005387 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 36 μF capacitor is charged to a potential difference of 4 V. Calculate the energy stored, expressed in μJ. | {
"A": "288 μJ",
"B": "289 μJ",
"C": "432 μJ",
"D": "29.8 μJ"
} | A | 288 μJ | U=½CV². Since C=36 μF, U in μJ is ½×36×(4)²=288 μJ. | {
"A": "Correct. The worked calculation gives 288 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 288 μJ, not 289 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 288 μJ, not 432 μJ.",
"D": "Incorrect. Substituting the stated values ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007552 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 17 mL of 0.10 M HCl is mixed with 84 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "15.82175",
"B": "12.82175",
"C": "2.28218",
"D": "25.64351"
} | B | 12.82175 | Excess OH⁻ moles=0.10×(84−17)/1000=0.006700 mol. Total volume=0.101 L, so [OH⁻]=0.066337 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.82175. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.82175, not 15.82175.",
"B": "Correct. The worked calculation gives 12.82175.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.82175, not 2.28218.",
"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_004657 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 12 kg and radius 2 m is acted on by a constant torque of 84 N m about its central axis. Find its angular acceleration. | {
"A": "6.5 rad s⁻²",
"B": "3.5 rad s⁻²",
"C": "4.5 rad s⁻²",
"D": "1.35 rad s⁻²"
} | B | 3.5 rad s⁻² | For a solid disc, I=½MR²=½(12)(2)²=24 kg m². Using τ=Iα, α=84/24=3.5 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.5 rad s⁻², not 6.5 rad s⁻².",
"B": "Correct. The worked calculation gives 3.5 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.5 rad s⁻², not 4.5 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_003559 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 34 m s⁻¹ at 20° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "75.30625 m",
"B": "55.72969 m",
"C": "74.30625 m",
"D": "-74.30625 m"
} | C | 74.30625 m | Range R=u²sin(2θ)/g. Substituting u=34, θ=20° and g=10 gives R=(34)²sin(40°)/10=74.30625 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 74.30625 m, not 75.30625 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 74.30625 m, not 55.72969 m.",
"C": "Correct. The worked calculation gives 74.30625 m.",
"D": "Incorrect. Substitutin... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006848 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 25 mol H₂ and 10 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "15 mol",
"B": "20 mol",
"C": "18 mol",
"D": "10 mol"
} | B | 20 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 25 mol H₂O; O₂ can produce 20 mol H₂O. The limiting condition is O₂; product=20 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20 mol, not 15 mol.",
"B": "Correct. The worked calculation gives 20 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20 mol, not 18 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_004877 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 17 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.01176 A",
"B": "1.50588 A",
"C": "3.01176 A",
"D": "0.01176 A"
} | C | 3.01176 A | Series branch resistance=7+8=15 Ω. Parallel equivalent R_eq=(15×17)/(15+17)=7.96875 Ω. Total current I=V/R_eq=24/7.96875=3.01176 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.01176 A, not 2.01176 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.01176 A, not 1.50588 A.",
"C": "Correct. The worked calculation gives 3.01176 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008210 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 11 A for 2786 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "15.12452 g",
"B": "7.56226 g",
"C": "10.08301 g",
"D": "9.08301 g"
} | C | 10.08301 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×2786/(2×96500)=10.08301 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.08301 g, not 15.12452 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10.08301 g, not 7.56226 g.",
"C": "Correct. The worked calculation gives 10.08301 g.",
"D": "Incorrect. Substituting... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004587 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 4 m is acted on by a constant torque of 62 N m about its central axis. Find its angular acceleration. | {
"A": "0.96875 rad s⁻²",
"B": "1.09688 rad s⁻²",
"C": "-2.03125 rad s⁻²",
"D": "-0.96875 rad s⁻²"
} | A | 0.96875 rad s⁻² | For a solid disc, I=½MR²=½(8)(4)²=64 kg m². Using τ=Iα, α=62/64=0.96875 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.96875 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.96875 rad s⁻², not 1.09688 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.96875 rad s⁻², not -2.03125 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_004447 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 6 kg and radius 4 m is acted on by a constant torque of 64 N m about its central axis. Find its angular acceleration. | {
"A": "-1.66667 rad s⁻²",
"B": "1.33333 rad s⁻²",
"C": "-1.33333 rad s⁻²",
"D": "3.33333 rad s⁻²"
} | B | 1.33333 rad s⁻² | For a solid disc, I=½MR²=½(6)(4)²=48 kg m². Using τ=Iα, α=64/48=1.33333 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.33333 rad s⁻², not -1.66667 rad s⁻².",
"B": "Correct. The worked calculation gives 1.33333 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.33333 rad s⁻², not -1.33333 rad s⁻².",
"... | [
"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_002023 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 7 red, 5 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.17572",
"B": "0.26359",
"C": "2.35145",
"D": "0.35145"
} | D | 0.35145 | Favourable pairs = C(7,2)+C(5,2)+C(12,2)=97. Total pairs=C(24,2)=276. Therefore P=97/276=0.35145. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35145, not 0.17572.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35145, not 0.26359.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35145, not 2.351... | [
"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_001521 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (0x² -4x +3) dx. | {
"A": "-106",
"B": "-103",
"C": "-104",
"D": "-208"
} | C | -104 | An antiderivative is (0/3)x³+(-4/2)x²+(3)x. Evaluating between 0 and 8 gives (0/3)(8)³+(-4/2)(8)²+(3)(8)=-104. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -104, not -106.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -104, not -103.",
"C": "Correct. The worked calculation gives -104.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_005803 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.4 atm at 359 K. What is its pressure at 461 K? | {
"A": "7.65014 atm",
"B": "8.65014 atm",
"C": "8.47521 atm",
"D": "5.65014 atm"
} | D | 5.65014 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.4)(461)/(359)=5.65014 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.65014 atm, not 7.65014 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.65014 atm, not 8.65014 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.... | [
"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_001069 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=1x³ +0x² +11x+7. Evaluate f′(4). | {
"A": "29.5",
"B": "61",
"C": "59",
"D": "58"
} | C | 59 | Differentiate: f′(x)=3(1)x²+2(0)x+(11). At x=4, f′(4)=3(1)(4)²+2(0)(4)+(11)=59. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 59, not 29.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 59, not 61.",
"C": "Correct. The worked calculation gives 59.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005966 | 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 0.7 atm at 434 K. What is its pressure at 784 K? | {
"A": "-0.73548 atm",
"B": "1.26452 atm",
"C": "1.89677 atm",
"D": "2.26452 atm"
} | B | 1.26452 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.7)(784)/(434)=1.26452 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.26452 atm, not -0.73548 atm.",
"B": "Correct. The worked calculation gives 1.26452 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.26452 atm, not 1.89677 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007125 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 4 mol of gas at 528 K and 1.96 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "70.73648 L",
"B": "88.4206 L",
"C": "132.63091 L",
"D": "87.4206 L"
} | B | 88.4206 L | PV=nRT, so V=nRT/P=(4)(0.082057)(528)/(1.96)=88.4206 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 88.4206 L, not 70.73648 L.",
"B": "Correct. The worked calculation gives 88.4206 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 88.4206 L, not 132.63091 L.",
"D": "Incorrect. Substituting ... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004578 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 10 kg and radius 1 m is acted on by a constant torque of 41 N m about its central axis. Find its angular acceleration. | {
"A": "8.2 rad s⁻²",
"B": "1.82 rad s⁻²",
"C": "7.2 rad s⁻²",
"D": "5.2 rad s⁻²"
} | A | 8.2 rad s⁻² | For a solid disc, I=½MR²=½(10)(1)²=5 kg m². Using τ=Iα, α=41/5=8.2 rad s⁻². | {
"A": "Correct. The worked calculation gives 8.2 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.2 rad s⁻², not 1.82 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.2 rad s⁻², not 7.2 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_003954 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block initially moves at 12 m s⁻¹. A constant net force does 26 N of work over 10 m in the direction of motion. Find its final kinetic energy. | {
"A": "1268 J",
"B": "951 J",
"C": "1521.6 J",
"D": "1902 J"
} | A | 1268 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(14)(12)²+(26)(10)=1268 J. | {
"A": "Correct. The worked calculation gives 1268 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1268 J, not 951 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1268 J, not 1521.6 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_008059 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 2 A for 11770 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "15.49005 g",
"B": "7.74503 g",
"C": "5.74503 g",
"D": "1.7745 g"
} | B | 7.74503 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×2×11770/(2×96500)=7.74503 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.74503 g, not 15.49005 g.",
"B": "Correct. The worked calculation gives 7.74503 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.74503 g, not 5.74503 g.",
"D": "Incorrect. Substituting th... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004857 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 6 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 17 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.91765 A",
"B": "2.91765 A",
"C": "5.91765 A",
"D": "-3.91765 A"
} | A | 3.91765 A | Series branch resistance=6+14=20 Ω. Parallel equivalent R_eq=(20×17)/(20+17)=9.18919 Ω. Total current I=V/R_eq=36/9.18919=3.91765 A. | {
"A": "Correct. The worked calculation gives 3.91765 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.91765 A, not 2.91765 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.91765 A, not 5.91765 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009544 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_7H_14N_3X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "1.5",
"B": "1.1",
"C": "1",
"D": "0.75"
} | C | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+3−14−3)/2=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.1.",
"C": "Correct. The worked calculation gives 1.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_009135 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.84 V, transfers 3 electrons, and has reaction quotient Q=10^-4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.9188 V",
"B": "0.4594 V",
"C": "2.9188 V",
"D": "1.9188 V"
} | A | 0.9188 V | Apply the Nernst equation: E=0.84−(0.0591/3)(-4)=0.9188 V. | {
"A": "Correct. The worked calculation gives 0.9188 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9188 V, not 0.4594 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9188 V, not 2.9188 V.",
"D": "Incorrect. Substituting the stat... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003417 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 61 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "699.31925 m",
"B": "-349.65962 m",
"C": "349.65962 m",
"D": "351.65962 m"
} | C | 349.65962 m | Range R=u²sin(2θ)/g. Substituting u=61, θ=55° and g=10 gives R=(61)²sin(110°)/10=349.65962 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 349.65962 m, not 699.31925 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 349.65962 m, not -349.65962 m.",
"C": "Correct. The worked calculation gives 349.65962 m.",
"D": "Incorrect. Subst... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007365 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 12 mL of 0.10 M HCl is mixed with 39 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "9.72379",
"B": "12.72379",
"C": "13.72379",
"D": "9.54285"
} | B | 12.72379 | Excess OH⁻ moles=0.10×(39−12)/1000=0.002700 mol. Total volume=0.051 L, so [OH⁻]=0.052941 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.72379. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.72379, not 9.72379.",
"B": "Correct. The worked calculation gives 12.72379.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.72379, not 13.72379.",
"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_003182 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(4-8i)/(10+5i). What is Re(z), the real part of z? | {
"A": "3",
"B": "1",
"C": "0",
"D": "2"
} | C | 0 | Multiply numerator and denominator by the conjugate (10-5i). Then Re(z)=(ac+bd)/(c²+d²)=((4)(10)+(-8)(5))/(10²+(5)²)=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"C": "Correct. The worked calculation gives 0.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_003917 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 7 m s⁻¹. A constant net force does 14 N of work over 17 m in the direction of motion. Find its final kinetic energy. | {
"A": "436 J",
"B": "44.4 J",
"C": "434 J",
"D": "347.2 J"
} | C | 434 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(7)²+(14)(17)=434 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 434 J, not 436 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 434 J, not 44.4 J.",
"C": "Correct. The worked calculation gives 434 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_006397 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 1 kg is attached to an ideal spring of force constant 494 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.08998 s",
"B": "3.08998 s",
"C": "0.04499 s",
"D": "1.08998 s"
} | A | 0.08998 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(1/494)=0.08998 s. | {
"A": "Correct. The worked calculation gives 0.08998 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.08998 s, not 3.08998 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.08998 s, not 0.04499 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_009589 | 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_9H_18N_1X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "-1",
"B": "1",
"C": "-2",
"D": "0"
} | B | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×9+2+1−18−1)/2=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not -1.",
"B": "Correct. The worked calculation gives 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not -2.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003133 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(4+7i)/(8+1i). What is Re(z), the real part of z? | {
"A": "0.45",
"B": "0.9",
"C": "-1.4",
"D": "0.6"
} | D | 0.6 | Multiply numerator and denominator by the conjugate (8-1i). Then Re(z)=(ac+bd)/(c²+d²)=((4)(8)+(7)(1))/(8²+(1)²)=0.6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6, not 0.45.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6, not 0.9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.6, not -1.4.",
"D": "Correct.... | [
"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_009111 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.22 V, transfers 1 electrons, and has reaction quotient Q=10^0. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "4.22 V",
"B": "-0.78 V",
"C": "0.22 V",
"D": "1.22 V"
} | D | 1.22 V | Apply the Nernst equation: E=1.22−(0.0591/1)(0)=1.22 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.22 V, not 4.22 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.22 V, not -0.78 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.22 V, not 0.22 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_001142 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ +6x² +0x+7. Evaluate f′(2). | {
"A": "-37",
"B": "-36",
"C": "-28.8",
"D": "-18"
} | B | -36 | Differentiate: f′(x)=3(-5)x²+2(6)x+(0). At x=2, f′(2)=3(-5)(2)²+2(6)(2)+(0)=-36. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -36, not -37.",
"B": "Correct. The worked calculation gives -36.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -36, not -28.8.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008674 | 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 1.64 mol L⁻¹ and initially B is absent. At equilibrium, 47% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.26584",
"B": "2.73416",
"C": "1.73416",
"D": "5.46832"
} | B | 2.73416 | Let α=0.47. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.64)(0.47)²/(1−0.47)=2.73416. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.73416, not -0.26584.",
"B": "Correct. The worked calculation gives 2.73416.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.73416, not 1.73416.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004254 | 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 0.20. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "152 N",
"B": "77 N",
"C": "16.4 N",
"D": "154 N"
} | D | 154 N | Net force=mg(sinθ−μcosθ)=35×10×(0.6−0.20×0.8)=154 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 154 N, not 152 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 154 N, not 77 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 154 N, not 16.4 N.",
"D":... | [
"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_002846 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-6, -5, 7) and v=(3, 9, 0), calculate u·v. | {
"A": "-63",
"B": "-50.4",
"C": "-94.5",
"D": "-31.5"
} | A | -63 | The dot product is the sum of corresponding component products: (-6)(3)+(-5)(9)+(7)(0)=-63. | {
"A": "Correct. The worked calculation gives -63.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -63, not -50.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -63, not -94.5.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_003962 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 11 m s⁻¹. A constant net force does 6 N of work over 20 m in the direction of motion. Find its final kinetic energy. | {
"A": "942.6 J",
"B": "785.5 J",
"C": "1178.25 J",
"D": "786.5 J"
} | B | 785.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(11)²+(6)(20)=785.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 785.5 J, not 942.6 J.",
"B": "Correct. The worked calculation gives 785.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 785.5 J, not 1178.25 J.",
"D": "Incorrect. Substituting the stated ... | [
"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_006706 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 6 mol H₂ and 23 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "8 mol",
"B": "5 mol",
"C": "12 mol",
"D": "6 mol"
} | D | 6 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 6 mol H₂O; O₂ can produce 46 mol H₂O. The limiting condition is H₂; product=6 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 8 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 5 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 12 mol.",
"D"... | [
"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_005862 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.8 atm at 227 K. What is its pressure at 371 K? | {
"A": "2.20639 atm",
"B": "5.8837 atm",
"C": "1.29419 atm",
"D": "2.94185 atm"
} | D | 2.94185 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.8)(371)/(227)=2.94185 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.94185 atm, not 2.20639 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.94185 atm, not 5.8837 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.9... | [
"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_009718 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(Cl)_4]^+0, each Cl ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "6",
"B": "7",
"C": "2",
"D": "4"
} | D | 4 | Let the formal oxidation state of Pt be x. Charge balance gives x+(4)(−1)=+0; hence x=0+4=+4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"D": "Correct. The worked ca... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000614 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 26 and common difference 12. Find the sum of its first 24 terms. | {
"A": "3935",
"B": "3936",
"C": "-3936",
"D": "3148.8"
} | B | 3936 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=26, d=12, n=24: Sₙ=24/2[2(26)+(24−1)(12)]=3936. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3936, not 3935.",
"B": "Correct. The worked calculation gives 3936.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3936, not -3936.",
"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_001496 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (-4x² -5x -4) dx. | {
"A": "-11.75",
"B": "-3.91667",
"C": "-7.83333",
"D": "-9.83333"
} | C | -7.83333 | An antiderivative is (-4/3)x³+(-5/2)x²+(-4)x. Evaluating between 0 and 1 gives (-4/3)(1)³+(-5/2)(1)²+(-4)(1)=-7.83333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -7.83333, not -11.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -7.83333, not -3.91667.",
"C": "Correct. The worked calculation gives -7.83333.",
"D": "Incorrect. Substituting the stated... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008251 | 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 4 A for 23805 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": "29.32886 g",
"B": "31.32886 g",
"C": "-31.32886 g",
"D": "15.66443 g"
} | B | 31.32886 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×23805/(2×96500)=31.32886 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 31.32886 g, not 29.32886 g.",
"B": "Correct. The worked calculation gives 31.32886 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 31.32886 g, not -31.32886 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008718 | 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 1.74 mol L⁻¹ and initially B is absent. At equilibrium, 25% of A has dissociated at constant volume. Find K_c. | {
"A": "1.16",
"B": "0.58",
"C": "0.435",
"D": "3.58"
} | B | 0.58 | Let α=0.25. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.74)(0.25)²/(1−0.25)=0.58. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.58, not 1.16.",
"B": "Correct. The worked calculation gives 0.58.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.58, not 0.435.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_004761 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 2 Ω are connected in series; this combination is connected in parallel with a 4 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.09091 A",
"B": "-4.09091 A",
"C": "3.09091 A",
"D": "4.09091 A"
} | D | 4.09091 A | Series branch resistance=9+2=11 Ω. Parallel equivalent R_eq=(11×4)/(11+4)=2.93333 Ω. Total current I=V/R_eq=12/2.93333=4.09091 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.09091 A, not 2.09091 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.09091 A, not -4.09091 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.09091 A... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001263 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ +6x² +4x+7. Evaluate f′(4). | {
"A": "-225.6",
"B": "-188",
"C": "-282",
"D": "-94"
} | B | -188 | Differentiate: f′(x)=3(-5)x²+2(6)x+(4). At x=4, f′(4)=3(-5)(4)²+2(6)(4)+(4)=-188. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -188, not -225.6.",
"B": "Correct. The worked calculation gives -188.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -188, not -282.",
"D": "Incorrect. Substituting the stated values into the... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006557 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 14 kg is attached to an ideal spring of force constant 309 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.42571 s",
"B": "2.42571 s",
"C": "1.04257 s",
"D": "3.42571 s"
} | A | 0.42571 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(14/309)=0.42571 s. | {
"A": "Correct. The worked calculation gives 0.42571 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.42571 s, not 2.42571 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.42571 s, not 1.04257 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_003346 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 51 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "520.2 m",
"B": "130.05 m",
"C": "259.1 m",
"D": "260.1 m"
} | D | 260.1 m | Range R=u²sin(2θ)/g. Substituting u=51, θ=45° and g=10 gives R=(51)²sin(90°)/10=260.1 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 260.1 m, not 520.2 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 260.1 m, not 130.05 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 260.1 m, not 259.... | [
"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_003822 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 7 m s⁻¹. A constant net force does 16 N of work over 18 m in the direction of motion. Find its final kinetic energy. | {
"A": "484 J",
"B": "-484 J",
"C": "968 J",
"D": "483 J"
} | A | 484 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(7)²+(16)(18)=484 J. | {
"A": "Correct. The worked calculation gives 484 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 484 J, not -484 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 484 J, not 968 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_003522 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 78 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "610.4 m",
"B": "608.4 m",
"C": "61.84 m",
"D": "609.4 m"
} | B | 608.4 m | Range R=u²sin(2θ)/g. Substituting u=78, θ=45° and g=10 gives R=(78)²sin(90°)/10=608.4 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 608.4 m, not 610.4 m.",
"B": "Correct. The worked calculation gives 608.4 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 608.4 m, not 61.84 m.",
"D": "Incorrect. Substituting the stated va... | [
"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_001001 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio 4. What is the sum of its first 9 terms? | {
"A": "838857.6",
"B": "699046",
"C": "699050",
"D": "699048"
} | D | 699048 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(4^9−1)/(4−1)=699048. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 699048, not 838857.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 699048, not 699046.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 699048, not 699050."... | [
"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_004301 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.40. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "29.4 N",
"B": "19.6 N",
"C": "23.52 N",
"D": "17.6 N"
} | B | 19.6 N | Net force=mg(sinθ−μcosθ)=7×10×(0.6−0.40×0.8)=19.6 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19.6 N, not 29.4 N.",
"B": "Correct. The worked calculation gives 19.6 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19.6 N, not 23.52 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_003412 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 79 m s⁻¹ at 70° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "-401.16375 m",
"B": "601.74562 m",
"C": "41.11637 m",
"D": "401.16375 m"
} | D | 401.16375 m | Range R=u²sin(2θ)/g. Substituting u=79, θ=70° and g=10 gives R=(79)²sin(140°)/10=401.16375 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 401.16375 m, not -401.16375 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 401.16375 m, not 601.74562 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4... | [
"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_001558 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (2x² +4x -4) dx. | {
"A": "96",
"B": "-192",
"C": "192",
"D": "190"
} | C | 192 | An antiderivative is (2/3)x³+(4/2)x²+(-4)x. Evaluating between 0 and 6 gives (2/3)(6)³+(4/2)(6)²+(-4)(6)=192. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 192, not 96.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 192, not -192.",
"C": "Correct. The worked calculation gives 192.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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