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_001174 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=0x³ +8x² +1x+7. Evaluate f′(-2). | {
"A": "-29",
"B": "-37.2",
"C": "-31",
"D": "-15.5"
} | C | -31 | Differentiate: f′(x)=3(0)x²+2(8)x+(1). At x=-2, f′(-2)=3(0)(-2)²+2(8)(-2)+(1)=-31. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -31, not -29.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -31, not -37.2.",
"C": "Correct. The worked calculation gives -31.",
"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_002767 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(0, 9, -1) and v=(-3, 1, 6), calculate u·v. | {
"A": "6",
"B": "3",
"C": "1",
"D": "4.5"
} | B | 3 | The dot product is the sum of corresponding component products: (0)(-3)+(9)(1)+(-1)(6)=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.",
"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_007405 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 63 mL of 0.10 M HCl is mixed with 17 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "0.93025",
"B": "1.12403",
"C": "4.24033",
"D": "1.24033"
} | D | 1.24033 | Excess H⁺ moles=0.10×(63−17)/1000=0.004600 mol. Total volume=0.080 L, so [H⁺]=0.057500 M and pH=−log₁₀[H⁺]=1.24033. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.24033, not 0.93025.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.24033, not 1.12403.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.24033, not 4.240... | [
"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_000883 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 12 and common ratio 2. What is the sum of its first 11 terms? | {
"A": "24562",
"B": "12282",
"C": "24563",
"D": "24564"
} | D | 24564 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=12(2^11−1)/(2−1)=24564. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24564, not 24562.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24564, not 12282.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24564, not 24563.",
"D":... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005106 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +1 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "3.6 N",
"B": "2.7 N",
"C": "7.2 N",
"D": "1.8 N"
} | A | 3.6 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(1×10⁻⁶)/(10×10⁻²)²=3.6 N. | {
"A": "Correct. The worked calculation gives 3.6 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.6 N, not 2.7 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.6 N, not 7.2 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000540 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -18 and common difference 12. Find the sum of its first 21 terms. | {
"A": "2142",
"B": "3213",
"C": "1071",
"D": "2140"
} | A | 2142 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-18, d=12, n=21: Sₙ=21/2[2(-18)+(21−1)(12)]=2142. | {
"A": "Correct. The worked calculation gives 2142.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2142, not 3213.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2142, not 1071.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002129 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 8 blue and 7 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.45714",
"B": "1.03048",
"C": "-2.69524",
"D": "0.30476"
} | D | 0.30476 | Favourable pairs = C(6,2)+C(8,2)+C(7,2)=64. Total pairs=C(21,2)=210. Therefore P=64/210=0.30476. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30476, not 0.45714.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30476, not 1.03048.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30476, not -2.69... | [
"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_009739 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(Cl)_4]^+0, each Cl ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "4",
"B": "3",
"C": "1.4",
"D": "-4"
} | A | 4 | Let the formal oxidation state of Ni be x. Charge balance gives x+(4)(−1)=+0; hence x=0+4=+4. | {
"A": "Correct. The worked calculation gives 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.4.",
"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_002543 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, -2], [1, -3]]. | {
"A": "-13",
"B": "-19.5",
"C": "13",
"D": "-0.3"
} | A | -13 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(-3)−(-2)(1)=-13. | {
"A": "Correct. The worked calculation gives -13.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -13, not -19.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -13, not 13.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_008435 | 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 0.66 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.208 K",
"B": "0.792 K",
"C": "3.792 K",
"D": "1.0792 K"
} | B | 0.792 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.6×0.66=0.792 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.792 K, not -0.208 K.",
"B": "Correct. The worked calculation gives 0.792 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.792 K, not 3.792 K.",
"D": "Incorrect. Substituting the stated v... | [
"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_000205 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 -18x -8=0, let its roots be α and β. What is α²+β²? | {
"A": "11.66667",
"B": "5.83333",
"C": "8.75",
"D": "8.66667"
} | A | 11.66667 | By Vieta's relations, α+β = 18/6 and αβ = -8/6. Then α²+β²=(α+β)²−2αβ = (18/6)²−2(-8/6) = 11.66667. | {
"A": "Correct. The worked calculation gives 11.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.66667, not 5.83333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.66667, not 8.75.",
"D": "Incorrect. Substituting the stated va... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003929 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 5 m s⁻¹. A constant net force does 5 N of work over 15 m in the direction of motion. Find its final kinetic energy. | {
"A": "375 J",
"B": "150 J",
"C": "225 J",
"D": "187.5 J"
} | D | 187.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(5)²+(5)(15)=187.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 187.5 J, not 375 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 187.5 J, not 150 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 187.5 J, not 225 J.",
... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004212 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.45. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "31.6 N",
"B": "33.6 N",
"C": "67.2 N",
"D": "-33.6 N"
} | B | 33.6 N | Net force=mg(sinθ−μcosθ)=14×10×(0.6−0.45×0.8)=33.6 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33.6 N, not 31.6 N.",
"B": "Correct. The worked calculation gives 33.6 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 33.6 N, not 67.2 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_008678 | 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 1.23 mol L⁻¹ and initially B is absent. At equilibrium, 44% of A has dissociated at constant volume. Find K_c. | {
"A": "0.70091",
"B": "1.70091",
"C": "-1.29909",
"D": "-0.29909"
} | B | 1.70091 | Let α=0.44. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.23)(0.44)²/(1−0.44)=1.70091. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.70091, not 0.70091.",
"B": "Correct. The worked calculation gives 1.70091.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.70091, not -1.29909.",
"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_003486 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 106 m s⁻¹ at 15° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "561.8 m",
"B": "674.16 m",
"C": "-561.8 m",
"D": "449.44 m"
} | A | 561.8 m | Range R=u²sin(2θ)/g. Substituting u=106, θ=15° and g=10 gives R=(106)²sin(30°)/10=561.8 m. | {
"A": "Correct. The worked calculation gives 561.8 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 561.8 m, not 674.16 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 561.8 m, not -561.8 m.",
"D": "Incorrect. Substituting the stated ... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004729 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 2 Ω and 10 Ω are connected in series; this combination is connected in parallel with a 2 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.05 A",
"B": "10.5 A",
"C": "9.5 A",
"D": "5.25 A"
} | B | 10.5 A | Series branch resistance=2+10=12 Ω. Parallel equivalent R_eq=(12×2)/(12+2)=1.71429 Ω. Total current I=V/R_eq=18/1.71429=10.5 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.5 A, not 2.05 A.",
"B": "Correct. The worked calculation gives 10.5 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10.5 A, not 9.5 A.",
"D": "Incorrect. Substituting the stated values i... | [
"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_005646 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 17 μF capacitor is charged to a potential difference of 23 V. Calculate the energy stored, expressed in μJ. | {
"A": "450.65 μJ",
"B": "5395.8 μJ",
"C": "4496.5 μJ",
"D": "2248.25 μJ"
} | C | 4496.5 μJ | U=½CV². Since C=17 μF, U in μJ is ½×17×(23)²=4496.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4496.5 μJ, not 450.65 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4496.5 μJ, not 5395.8 μJ.",
"C": "Correct. The worked calculation gives 4496.5 μJ.",
"D": "Incorrect. Substituting the... | [
"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_002379 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, -4], [6, -2]]. | {
"A": "10",
"B": "12",
"C": "-10",
"D": "9"
} | A | 10 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(-2)−(-4)(6)=10. | {
"A": "Correct. The worked calculation gives 10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not -10.",
"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_003268 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(8+4i)/(4+3i). What is Re(z), the real part of z? | {
"A": "0.76",
"B": "-1.76",
"C": "1.176",
"D": "1.76"
} | D | 1.76 | Multiply numerator and denominator by the conjugate (4-3i). Then Re(z)=(ac+bd)/(c²+d²)=((8)(4)+(4)(3))/(4²+(3)²)=1.76. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.76, not 0.76.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.76, not -1.76.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.76, not 1.176.",
"D": "Co... | [
"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_008511 | 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 0.34 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-2.82592 K",
"B": "1.01741 K",
"C": "0.17408 K",
"D": "-1.82592 K"
} | C | 0.17408 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.512×0.34=0.17408 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.17408 K, not -2.82592 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.17408 K, not 1.01741 K.",
"C": "Correct. The worked calculation gives 0.17408 K.",
"D": "Incorrect. Substituting th... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005981 | 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 1.4 atm at 351 K. What is its pressure at 692 K? | {
"A": "2.76011 atm",
"B": "1.76011 atm",
"C": "-0.23989 atm",
"D": "3.76011 atm"
} | A | 2.76011 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.4)(692)/(351)=2.76011 atm. | {
"A": "Correct. The worked calculation gives 2.76011 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.76011 atm, not 1.76011 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.76011 atm, not -0.23989 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_000034 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +10x +12=0, let its roots be α and β. What is α²+β²? | {
"A": "0.8",
"B": "-0.4",
"C": "-0.8",
"D": "1.2"
} | C | -0.8 | By Vieta's relations, α+β = -10/5 and αβ = 12/5. Then α²+β²=(α+β)²−2αβ = (-10/5)²−2(12/5) = -0.8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.8, not 0.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.8, not -0.4.",
"C": "Correct. The worked calculation gives -0.8.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_004361 | 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 51 N m about its central axis. Find its angular acceleration. | {
"A": "3.125 rad s⁻²",
"B": "2.125 rad s⁻²",
"C": "0.125 rad s⁻²",
"D": "4.25 rad s⁻²"
} | B | 2.125 rad s⁻² | For a solid disc, I=½MR²=½(12)(2)²=24 kg m². Using τ=Iα, α=51/24=2.125 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.125 rad s⁻², not 3.125 rad s⁻².",
"B": "Correct. The worked calculation gives 2.125 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.125 rad s⁻², not 0.125 rad s⁻².",
"D": "Incorre... | [
"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_007080 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 12 mol of gas at 471 K and 2.54 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "136.94473 L",
"B": "180.59298 L",
"C": "184.59298 L",
"D": "182.59298 L"
} | D | 182.59298 L | PV=nRT, so V=nRT/P=(12)(0.082057)(471)/(2.54)=182.59298 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 182.59298 L, not 136.94473 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 182.59298 L, not 180.59298 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18... | [
"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_004477 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 4 kg and radius 1 m is acted on by a constant torque of 21 N m about its central axis. Find its angular acceleration. | {
"A": "7.5 rad s⁻²",
"B": "10.5 rad s⁻²",
"C": "12.5 rad s⁻²",
"D": "2.05 rad s⁻²"
} | B | 10.5 rad s⁻² | For a solid disc, I=½MR²=½(4)(1)²=2 kg m². Using τ=Iα, α=21/2=10.5 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10.5 rad s⁻², not 7.5 rad s⁻².",
"B": "Correct. The worked calculation gives 10.5 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10.5 rad s⁻², not 12.5 rad s⁻².",
"D": "Incorrect. Su... | [
"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_004496 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 13 kg and radius 6 m is acted on by a constant torque of 95 N m about its central axis. Find its angular acceleration. | {
"A": "-2.59402 rad s⁻²",
"B": "0.40598 rad s⁻²",
"C": "1.40598 rad s⁻²",
"D": "0.60897 rad s⁻²"
} | B | 0.40598 rad s⁻² | For a solid disc, I=½MR²=½(13)(6)²=234 kg m². Using τ=Iα, α=95/234=0.40598 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.40598 rad s⁻², not -2.59402 rad s⁻².",
"B": "Correct. The worked calculation gives 0.40598 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.40598 rad s⁻², not 1.40598 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_002254 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 8 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": "-0.34503",
"B": "0.34503",
"C": "0.17251",
"D": "0.51754"
} | B | 0.34503 | Favourable pairs = C(3,2)+C(8,2)+C(8,2)=59. Total pairs=C(19,2)=171. Therefore P=59/171=0.34503. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34503, not -0.34503.",
"B": "Correct. The worked calculation gives 0.34503.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34503, not 0.17251.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004597 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 6 m is acted on by a constant torque of 24 N m about its central axis. Find its angular acceleration. | {
"A": "2.16667 rad s⁻²",
"B": "0.16667 rad s⁻²",
"C": "0.33333 rad s⁻²",
"D": "0.25 rad s⁻²"
} | B | 0.16667 rad s⁻² | For a solid disc, I=½MR²=½(8)(6)²=144 kg m². Using τ=Iα, α=24/144=0.16667 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.16667 rad s⁻², not 2.16667 rad s⁻².",
"B": "Correct. The worked calculation gives 0.16667 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.16667 rad s⁻², not 0.33333 rad s⁻².",
"D"... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005167 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +6 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "28 N",
"B": "-270 N",
"C": "216 N",
"D": "270 N"
} | D | 270 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(6×10⁻⁶)/(2×10⁻²)²=270 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 270 N, not 28 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 270 N, not -270 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 270 N, not 216 N.",
"D":... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003648 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 95 m s⁻¹ at 65° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "689.35511 m",
"B": "518.51633 m",
"C": "692.35511 m",
"D": "691.35511 m"
} | D | 691.35511 m | Range R=u²sin(2θ)/g. Substituting u=95, θ=65° and g=10 gives R=(95)²sin(130°)/10=691.35511 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 691.35511 m, not 689.35511 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 691.35511 m, not 518.51633 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 69... | [
"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_005427 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 69 μF capacitor is charged to a potential difference of 37 V. Calculate the energy stored, expressed in μJ. | {
"A": "70845.75 μJ",
"B": "47232.5 μJ",
"C": "47230.5 μJ",
"D": "47231.5 μJ"
} | C | 47230.5 μJ | U=½CV². Since C=69 μF, U in μJ is ½×69×(37)²=47230.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 47230.5 μJ, not 70845.75 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 47230.5 μJ, not 47232.5 μJ.",
"C": "Correct. The worked calculation gives 47230.5 μJ.",
"D": "Incorrect. Substituti... | [
"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_000031 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 -15x -3=0, let its roots be α and β. What is α²+β²? | {
"A": "7.25",
"B": "1.725",
"C": "5.4375",
"D": "10.875"
} | A | 7.25 | By Vieta's relations, α+β = 15/6 and αβ = -3/6. Then α²+β²=(α+β)²−2αβ = (15/6)²−2(-3/6) = 7.25. | {
"A": "Correct. The worked calculation gives 7.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.25, not 1.725.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.25, not 5.4375.",
"D": "Incorrect. Substituting the stated values into th... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003275 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-10-15i)/(10+9i). What is Re(z), the real part of z? | {
"A": "-1.94751",
"B": "0.87017",
"C": "-1.29834",
"D": "-0.29834"
} | C | -1.29834 | Multiply numerator and denominator by the conjugate (10-9i). Then Re(z)=(ac+bd)/(c²+d²)=((-10)(10)+(-15)(9))/(10²+(9)²)=-1.29834. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.29834, not -1.94751.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.29834, not 0.87017.",
"C": "Correct. The worked calculation gives -1.29834.",
"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_007921 | 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 34 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "17 mmol L⁻¹",
"B": "12.75 mmol L⁻¹",
"C": "5.5 mmol L⁻¹",
"D": "8.5 mmol L⁻¹"
} | D | 8.5 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=34/2^2=8.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.5 mmol L⁻¹, not 17 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.5 mmol L⁻¹, not 12.75 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation giv... | [
"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_004335 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 17 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.36. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "42.432 N",
"B": "55.04 N",
"C": "53.04 N",
"D": "79.56 N"
} | C | 53.04 N | Net force=mg(sinθ−μcosθ)=17×10×(0.6−0.36×0.8)=53.04 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 53.04 N, not 42.432 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 53.04 N, not 55.04 N.",
"C": "Correct. The worked calculation gives 53.04 N.",
"D": "Incorrect. Substituting the stated v... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009868 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(CN)_4]^+3, each CN ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "7",
"B": "8",
"C": "-7",
"D": "1.7"
} | A | 7 | Let the formal oxidation state of Fe be x. Charge balance gives x+(4)(−1)=+3; hence x=3+4=+7. | {
"A": "Correct. The worked calculation gives 7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not -7.",
"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_005411 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 59 μF capacitor is charged to a potential difference of 32 V. Calculate the energy stored, expressed in μJ. | {
"A": "3021.8 μJ",
"B": "30208 μJ",
"C": "15104 μJ",
"D": "30210 μJ"
} | B | 30208 μJ | U=½CV². Since C=59 μF, U in μJ is ½×59×(32)²=30208 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 30208 μJ, not 3021.8 μJ.",
"B": "Correct. The worked calculation gives 30208 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30208 μJ, not 15104 μJ.",
"D": "Incorrect. Substituting the sta... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007912 | 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 77 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "17.25 mmol L⁻¹",
"B": "19.25 mmol L⁻¹",
"C": "15.4 mmol L⁻¹",
"D": "23.1 mmol L⁻¹"
} | B | 19.25 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=77/2^2=19.25 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19.25 mmol L⁻¹, not 17.25 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 19.25 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19.25 mmol L⁻¹, not 15.4 mmol L⁻¹.",
"D": "Inc... | [
"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_000332 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +16x +1=0, let its roots be α and β. What is α²+β²? | {
"A": "33.33333",
"B": "55.55556",
"C": "29.77778",
"D": "27.77778"
} | D | 27.77778 | By Vieta's relations, α+β = -16/3 and αβ = 1/3. Then α²+β²=(α+β)²−2αβ = (-16/3)²−2(1/3) = 27.77778. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 27.77778, not 33.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 27.77778, not 55.55556.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 27.77778, not ... | [
"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_009133 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.21 V, transfers 2 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "3.2691 V",
"B": "2.5382 V",
"C": "1.2691 V",
"D": "0.95182 V"
} | C | 1.2691 V | Apply the Nernst equation: E=1.21−(0.0591/2)(-2)=1.2691 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.2691 V, not 3.2691 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.2691 V, not 2.5382 V.",
"C": "Correct. The worked calculation gives 1.2691 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_000906 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 11 and common ratio 4. What is the sum of its first 8 terms? | {
"A": "480590",
"B": "240293",
"C": "180221.25",
"D": "240295"
} | D | 240295 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=11(4^8−1)/(4−1)=240295. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 240295, not 480590.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 240295, not 240293.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 240295, not 180221.25.... | [
"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_004606 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 4 kg and radius 5 m is acted on by a constant torque of 18 N m about its central axis. Find its angular acceleration. | {
"A": "0.36 rad s⁻²",
"B": "0.27 rad s⁻²",
"C": "2.36 rad s⁻²",
"D": "1.36 rad s⁻²"
} | A | 0.36 rad s⁻² | For a solid disc, I=½MR²=½(4)(5)²=50 kg m². Using τ=Iα, α=18/50=0.36 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.36 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36 rad s⁻², not 0.27 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.36 rad s⁻², not 2.36 rad s⁻².",
"D": "Incorrect. S... | [
"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_000944 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio 5. What is the sum of its first 11 terms? | {
"A": "42724608.5",
"B": "85449219",
"C": "85449215",
"D": "85449217"
} | D | 85449217 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(5^11−1)/(5−1)=85449217. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 85449217, not 42724608.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 85449217, not 85449219.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 85449217, no... | [
"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_006963 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 48 mol H₂ and 26 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "49 mol",
"B": "24 mol",
"C": "48 mol",
"D": "47 mol"
} | C | 48 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 48 mol H₂O; O₂ can produce 52 mol H₂O. The limiting condition is H₂; product=48 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 48 mol, not 49 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 48 mol, not 24 mol.",
"C": "Correct. The worked calculation gives 48 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_003460 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 64 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "-409.6 m",
"B": "409.6 m",
"C": "327.68 m",
"D": "408.6 m"
} | B | 409.6 m | Range R=u²sin(2θ)/g. Substituting u=64, θ=45° and g=10 gives R=(64)²sin(90°)/10=409.6 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 409.6 m, not -409.6 m.",
"B": "Correct. The worked calculation gives 409.6 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 409.6 m, not 327.68 m.",
"D": "Incorrect. Substituting the stated ... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007017 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 8 mol of gas at 362 K and 2.86 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "83.08989 L",
"B": "-83.08989 L",
"C": "166.17977 L",
"D": "41.54494 L"
} | A | 83.08989 L | PV=nRT, so V=nRT/P=(8)(0.082057)(362)/(2.86)=83.08989 L. | {
"A": "Correct. The worked calculation gives 83.08989 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 83.08989 L, not -83.08989 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 83.08989 L, not 166.17977 L.",
"D": "Incorrect. Substitut... | [
"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_006119 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 119 cm in front of a thin convex lens of focal length 26 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "3.27957",
"B": "0.13978",
"C": "0.20968",
"D": "0.27957"
} | D | 0.27957 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(119)(26)/(119−26)=33.26882 cm. Thus |m|=v/u=33.26882/119=0.27957. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.27957, not 3.27957.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.27957, not 0.13978.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.27957, not 0.209... | [
"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_003265 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(8+8i)/(2+1i). What is Re(z), the real part of z? | {
"A": "1.48",
"B": "4.8",
"C": "9.6",
"D": "5.8"
} | B | 4.8 | Multiply numerator and denominator by the conjugate (2-1i). Then Re(z)=(ac+bd)/(c²+d²)=((8)(2)+(8)(1))/(2²+(1)²)=4.8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.8, not 1.48.",
"B": "Correct. The worked calculation gives 4.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.8, not 9.6.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_004890 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 15 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 10 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "-0.12727 A",
"B": "3.87273 A",
"C": "1.87273 A",
"D": "0.87273 A"
} | D | 0.87273 A | Series branch resistance=15+7=22 Ω. Parallel equivalent R_eq=(22×10)/(22+10)=6.875 Ω. Total current I=V/R_eq=6/6.875=0.87273 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.87273 A, not -0.12727 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.87273 A, not 3.87273 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.87273 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_000843 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio -3. What is the sum of its first 8 terms? | {
"A": "-1640",
"B": "-1968",
"C": "-1642",
"D": "-820"
} | A | -1640 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(-3^8−1)/(-3−1)=-1640. | {
"A": "Correct. The worked calculation gives -1640.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1640, not -1968.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1640, not -1642.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_009675 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(Cl)_6]^+0, each Cl ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "12",
"B": "6",
"C": "4",
"D": "9"
} | B | 6 | Let the formal oxidation state of Pd be x. Charge balance gives x+(6)(−1)=+0; hence x=0+6=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 12.",
"B": "Correct. The worked calculation gives 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.",
"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_008386 | 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 1.05 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.819 K",
"B": "-1.092 K",
"C": "1.092 K",
"D": "0.546 K"
} | C | 1.092 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×1.05=1.092 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.092 K, not 0.819 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.092 K, not -1.092 K.",
"C": "Correct. The worked calculation gives 1.092 K.",
"D": "Incorrect. Substituting the stated v... | [
"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_005648 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 21 μF capacitor is charged to a potential difference of 39 V. Calculate the energy stored, expressed in μJ. | {
"A": "15970.5 μJ",
"B": "7985.25 μJ",
"C": "19164.6 μJ",
"D": "1598.05 μJ"
} | A | 15970.5 μJ | U=½CV². Since C=21 μF, U in μJ is ½×21×(39)²=15970.5 μJ. | {
"A": "Correct. The worked calculation gives 15970.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15970.5 μJ, not 7985.25 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15970.5 μJ, not 19164.6 μJ.",
"D": "Incorrect. Substitutin... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007007 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 12 mol of gas at 496 K and 2.99 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "163.34557 L",
"B": "-163.34557 L",
"C": "122.50918 L",
"D": "326.69115 L"
} | A | 163.34557 L | PV=nRT, so V=nRT/P=(12)(0.082057)(496)/(2.99)=163.34557 L. | {
"A": "Correct. The worked calculation gives 163.34557 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 163.34557 L, not -163.34557 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 163.34557 L, not 122.50918 L.",
"D": "Incorrect. Subst... | [
"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_006188 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 45 cm in front of a thin convex lens of focal length 11 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.32353",
"B": "3.32353",
"C": "0.32353",
"D": "-2.67647"
} | C | 0.32353 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(45)(11)/(45−11)=14.55882 cm. Thus |m|=v/u=14.55882/45=0.32353. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32353, not 1.32353.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32353, not 3.32353.",
"C": "Correct. The worked calculation gives 0.32353.",
"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_003925 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 6 m s⁻¹. A constant net force does 11 N of work over 8 m in the direction of motion. Find its final kinetic energy. | {
"A": "80 J",
"B": "160 J",
"C": "320 J",
"D": "192 J"
} | B | 160 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(6)²+(11)(8)=160 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 160 J, not 80 J.",
"B": "Correct. The worked calculation gives 160 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 160 J, not 320 J.",
"D": "Incorrect. Substituting the stated values into t... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004764 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 2 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 20 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.4 A",
"B": "5.4 A",
"C": "4.05 A",
"D": "10.8 A"
} | B | 5.4 A | Series branch resistance=2+8=10 Ω. Parallel equivalent R_eq=(10×20)/(10+20)=6.66667 Ω. Total current I=V/R_eq=36/6.66667=5.4 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.4 A, not 4.4 A.",
"B": "Correct. The worked calculation gives 5.4 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.4 A, not 4.05 A.",
"D": "Incorrect. Substituting the stated values into... | [
"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_003272 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(12+12i)/(10+8i). What is Re(z), the real part of z? | {
"A": "0.65854",
"B": "3.31707",
"C": "1.31707",
"D": "2.31707"
} | C | 1.31707 | Multiply numerator and denominator by the conjugate (10-8i). Then Re(z)=(ac+bd)/(c²+d²)=((12)(10)+(12)(8))/(10²+(8)²)=1.31707. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.31707, not 0.65854.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.31707, not 3.31707.",
"C": "Correct. The worked calculation gives 1.31707.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008457 | 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 1.62 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": "2.916 K",
"B": "3.916 K",
"C": "4.916 K",
"D": "-0.084 K"
} | A | 2.916 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.6×1.62=2.916 K. | {
"A": "Correct. The worked calculation gives 2.916 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.916 K, not 3.916 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.916 K, not 4.916 K.",
"D": "Incorrect. Substituting the stated va... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004342 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 14 kg and radius 1 m is acted on by a constant torque of 51 N m about its central axis. Find its angular acceleration. | {
"A": "7.28571 rad s⁻²",
"B": "8.28571 rad s⁻²",
"C": "10.92857 rad s⁻²",
"D": "4.28571 rad s⁻²"
} | A | 7.28571 rad s⁻² | For a solid disc, I=½MR²=½(14)(1)²=7 kg m². Using τ=Iα, α=51/7=7.28571 rad s⁻². | {
"A": "Correct. The worked calculation gives 7.28571 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.28571 rad s⁻², not 8.28571 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.28571 rad s⁻², not 10.92857 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_001780 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 29 distinct elements? | {
"A": "4292147",
"B": "4292145",
"C": "4292144",
"D": "3433716"
} | B | 4292145 | Order does not matter, so the count is C(29,8)=29!/[8!(21)!]=4292145. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4292145, not 4292147.",
"B": "Correct. The worked calculation gives 4292145.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4292145, not 4292144.",
"D": "Incorrect. Substituting the stated va... | [
"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_007194 | 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 339 K and 0.75 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "557.34646 L",
"B": "417.25984 L",
"C": "1112.69292 L",
"D": "556.34646 L"
} | D | 556.34646 L | PV=nRT, so V=nRT/P=(15)(0.082057)(339)/(0.75)=556.34646 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 556.34646 L, not 557.34646 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 556.34646 L, not 417.25984 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 55... | [
"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_005454 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 27 μF capacitor is charged to a potential difference of 16 V. Calculate the energy stored, expressed in μJ. | {
"A": "2592 μJ",
"B": "3456 μJ",
"C": "5184 μJ",
"D": "6912 μJ"
} | B | 3456 μJ | U=½CV². Since C=27 μF, U in μJ is ½×27×(16)²=3456 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3456 μJ, not 2592 μJ.",
"B": "Correct. The worked calculation gives 3456 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3456 μJ, not 5184 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008962 | 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 1.24 mol L⁻¹ and initially B is absent. At equilibrium, 67% of A has dissociated at constant volume. Find K_c. | {
"A": "9.7471",
"B": "3.7471",
"C": "10.12065",
"D": "6.7471"
} | D | 6.7471 | Let α=0.67. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.24)(0.67)²/(1−0.67)=6.7471. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.7471, not 9.7471.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.7471, not 3.7471.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.7471, not 10.12065."... | [
"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_005414 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 4 μF capacitor is charged to a potential difference of 28 V. Calculate the energy stored, expressed in μJ. | {
"A": "2352 μJ",
"B": "1570 μJ",
"C": "1568 μJ",
"D": "1566 μJ"
} | C | 1568 μJ | U=½CV². Since C=4 μF, U in μJ is ½×4×(28)²=1568 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1568 μJ, not 2352 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1568 μJ, not 1570 μJ.",
"C": "Correct. The worked calculation gives 1568 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008407 | 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 0.96 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": "0.728 K",
"B": "1.296 K",
"C": "1.728 K",
"D": "-1.272 K"
} | C | 1.728 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.6×0.96=1.728 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.728 K, not 0.728 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.728 K, not 1.296 K.",
"C": "Correct. The worked calculation gives 1.728 K.",
"D": "Incorrect. Substituting the stated va... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007611 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 89 mL of 0.10 M HCl is mixed with 73 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "4.0054",
"B": "1.0027",
"C": "2.0054",
"D": "1.20054"
} | C | 2.0054 | Excess H⁺ moles=0.10×(89−73)/1000=0.001600 mol. Total volume=0.162 L, so [H⁺]=0.009877 M and pH=−log₁₀[H⁺]=2.0054. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.0054, not 4.0054.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.0054, not 1.0027.",
"C": "Correct. The worked calculation gives 2.0054.",
"D": "Incorrect. Substituting the stated values ... | [
"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_007486 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 59 mL of 0.10 M HCl is mixed with 90 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "14.31818",
"B": "12.31818",
"C": "10.31818",
"D": "24.63635"
} | B | 12.31818 | Excess OH⁻ moles=0.10×(90−59)/1000=0.003100 mol. Total volume=0.149 L, so [OH⁻]=0.020805 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.31818. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.31818, not 14.31818.",
"B": "Correct. The worked calculation gives 12.31818.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.31818, not 10.31818.",
"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_003804 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 1 m s⁻¹. A constant net force does 15 N of work over 18 m in the direction of motion. Find its final kinetic energy. | {
"A": "28.6 J",
"B": "276 J",
"C": "274 J",
"D": "277 J"
} | B | 276 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(1)²+(15)(18)=276 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 276 J, not 28.6 J.",
"B": "Correct. The worked calculation gives 276 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 276 J, not 274 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_006900 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 42 mol H₂ and 34 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "31.5 mol",
"B": "43 mol",
"C": "-42 mol",
"D": "42 mol"
} | D | 42 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 42 mol H₂O; O₂ can produce 68 mol H₂O. The limiting condition is H₂; product=42 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 42 mol, not 31.5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 42 mol, not 43 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 42 mol, not -42 mol.... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009128 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.45 V, transfers 3 electrons, and has reaction quotient Q=10^3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.3909 V",
"B": "-1.6091 V",
"C": "-1.3909 V",
"D": "4.3909 V"
} | A | 1.3909 V | Apply the Nernst equation: E=1.45−(0.0591/3)(3)=1.3909 V. | {
"A": "Correct. The worked calculation gives 1.3909 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.3909 V, not -1.6091 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.3909 V, not -1.3909 V.",
"D": "Incorrect. Substituting the st... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002818 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-2, -4, 5) and v=(2, 6, -7), calculate u·v. | {
"A": "-126",
"B": "-64",
"C": "-63",
"D": "-5.3"
} | C | -63 | The dot product is the sum of corresponding component products: (-2)(2)+(-4)(6)+(5)(-7)=-63. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -63, not -126.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -63, not -64.",
"C": "Correct. The worked calculation gives -63.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_002792 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(2, 4, 5) and v=(5, 7, 4), calculate u·v. | {
"A": "46.4",
"B": "58",
"C": "43.5",
"D": "60"
} | B | 58 | The dot product is the sum of corresponding component products: (2)(5)+(4)(7)+(5)(4)=58. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 58, not 46.4.",
"B": "Correct. The worked calculation gives 58.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 58, not 43.5.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_004682 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 2 Ω and 5 Ω are connected in series; this combination is connected in parallel with a 15 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.77143 A",
"B": "2.51429 A",
"C": "3.51429 A",
"D": "4.51429 A"
} | B | 2.51429 A | Series branch resistance=2+5=7 Ω. Parallel equivalent R_eq=(7×15)/(7+15)=4.77273 Ω. Total current I=V/R_eq=12/4.77273=2.51429 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.51429 A, not 3.77143 A.",
"B": "Correct. The worked calculation gives 2.51429 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.51429 A, not 3.51429 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_008790 | 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 1.51 mol L⁻¹ and initially B is absent. At equilibrium, 78% of A has dissociated at constant volume. Find K_c. | {
"A": "-16.70335",
"B": "25.05502",
"C": "16.70335",
"D": "12.52751"
} | C | 16.70335 | Let α=0.78. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.51)(0.78)²/(1−0.78)=16.70335. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16.70335, not -16.70335.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16.70335, not 25.05502.",
"C": "Correct. The worked calculation gives 16.70335.",
"D": "Incorrect. Substituting the sta... | [
"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_004692 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 3 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 4 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "13.11765 A",
"B": "-11.11765 A",
"C": "16.67647 A",
"D": "11.11765 A"
} | D | 11.11765 A | Series branch resistance=3+14=17 Ω. Parallel equivalent R_eq=(17×4)/(17+4)=3.2381 Ω. Total current I=V/R_eq=36/3.2381=11.11765 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.11765 A, not 13.11765 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.11765 A, not -11.11765 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.11... | [
"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_004391 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 1 m is acted on by a constant torque of 9 N m about its central axis. Find its angular acceleration. | {
"A": "3.375 rad s⁻²",
"B": "3.25 rad s⁻²",
"C": "-2.25 rad s⁻²",
"D": "2.25 rad s⁻²"
} | D | 2.25 rad s⁻² | For a solid disc, I=½MR²=½(8)(1)²=4 kg m². Using τ=Iα, α=9/4=2.25 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.25 rad s⁻², not 3.375 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.25 rad s⁻², not 3.25 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation giv... | [
"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_006623 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 25 kg is attached to an ideal spring of force constant 370 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.05199 s",
"B": "1.51988 s",
"C": "1.03975 s",
"D": "0.51988 s"
} | D | 0.51988 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(25/370)=0.51988 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.51988 s, not 1.05199 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.51988 s, not 1.51988 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.51988 s,... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004674 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 13 Ω and 15 Ω are connected in series; this combination is connected in parallel with a 13 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.53434 A",
"B": "5.06868 A",
"C": "3.37912 A",
"D": "1.68956 A"
} | C | 3.37912 A | Series branch resistance=13+15=28 Ω. Parallel equivalent R_eq=(28×13)/(28+13)=8.87805 Ω. Total current I=V/R_eq=30/8.87805=3.37912 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.37912 A, not 2.53434 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.37912 A, not 5.06868 A.",
"C": "Correct. The worked calculation gives 3.37912 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_004239 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 27 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.36. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "42.12 N",
"B": "126.36 N",
"C": "84.24 N",
"D": "9.424 N"
} | C | 84.24 N | Net force=mg(sinθ−μcosθ)=27×10×(0.6−0.36×0.8)=84.24 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 84.24 N, not 42.12 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 84.24 N, not 126.36 N.",
"C": "Correct. The worked calculation gives 84.24 N.",
"D": "Incorrect. Substituting the stated v... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006982 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 33 mol H₂ and 6 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "11 mol",
"B": "2.2 mol",
"C": "12 mol",
"D": "9 mol"
} | C | 12 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 33 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 11 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12 mol, not 2.2 mol.",
"C": "Correct. The worked calculation gives 12 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_006680 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 48 mol H₂ and 5 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "7.5 mol",
"B": "7 mol",
"C": "10 mol",
"D": "-10 mol"
} | C | 10 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 48 mol H₂O; O₂ can produce 10 mol H₂O. The limiting condition is O₂; product=10 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 7.5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10 mol, not 7 mol.",
"C": "Correct. The worked calculation gives 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_009353 | 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_15H_31N_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "1",
"C": "2",
"D": "1.5"
} | B | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×15+2+1−31−0)/2=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 3.",
"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 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_009732 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(OH)_5]^+2, each OH ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "7",
"B": "3.5",
"C": "9",
"D": "10"
} | A | 7 | Let the formal oxidation state of Cu be x. Charge balance gives x+(5)(−1)=+2; hence x=2+5=+7. | {
"A": "Correct. The worked calculation gives 7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 3.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 9.",
"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_006012 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 26 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": "3.33333",
"B": "4.33333",
"C": "2.33333",
"D": "1.33333"
} | A | 3.33333 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(26)(20)/(26−20)=86.66667 cm. Thus |m|=v/u=86.66667/26=3.33333. | {
"A": "Correct. The worked calculation gives 3.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.33333, not 4.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.33333, not 2.33333.",
"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_005558 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 60 μF capacitor is charged to a potential difference of 11 V. Calculate the energy stored, expressed in μJ. | {
"A": "364 μJ",
"B": "3630 μJ",
"C": "3628 μJ",
"D": "4356 μJ"
} | B | 3630 μJ | U=½CV². Since C=60 μF, U in μJ is ½×60×(11)²=3630 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3630 μJ, not 364 μJ.",
"B": "Correct. The worked calculation gives 3630 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3630 μJ, not 3628 μJ.",
"D": "Incorrect. Substituting the stated val... | [
"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_009606 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_10H_22. Treat X as the total number of monovalent halogen atoms. | {
"A": "0",
"B": "1",
"C": "-2",
"D": "-3"
} | A | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×10+2+0−22−0)/2=0. | {
"A": "Correct. The worked calculation gives 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006903 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 35 mol H₂ and 23 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "28 mol",
"B": "70 mol",
"C": "35 mol",
"D": "36 mol"
} | C | 35 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 35 mol H₂O; O₂ can produce 46 mol H₂O. The limiting condition is H₂; product=35 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 35 mol, not 28 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 35 mol, not 70 mol.",
"C": "Correct. The worked calculation gives 35 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_007418 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 67 mL of 0.10 M HCl is mixed with 30 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-1.58143",
"B": "-1.41857",
"C": "0.41857",
"D": "1.41857"
} | D | 1.41857 | Excess H⁺ moles=0.10×(67−30)/1000=0.003700 mol. Total volume=0.097 L, so [H⁺]=0.038144 M and pH=−log₁₀[H⁺]=1.41857. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.41857, not -1.58143.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.41857, not -1.41857.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.41857, not 0.4... | [
"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_000363 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -16 and common difference 11. Find the sum of its first 11 terms. | {
"A": "431",
"B": "429",
"C": "427",
"D": "643.5"
} | B | 429 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-16, d=11, n=11: Sₙ=11/2[2(-16)+(11−1)(11)]=429. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 429, not 431.",
"B": "Correct. The worked calculation gives 429.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 429, not 427.",
"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_000223 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 +12x +9=0, let its roots be α and β. What is α²+β²? | {
"A": "-1",
"B": "3",
"C": "0",
"D": "1"
} | D | 1 | By Vieta's relations, α+β = -12/6 and αβ = 9/6. Then α²+β²=(α+β)²−2αβ = (-12/6)²−2(9/6) = 1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not -1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.",
"D": "Correct. The worked c... | [
"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_009318 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.00 V, transfers 2 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.6454 V",
"B": "1.08227 V",
"C": "3.8227 V",
"D": "0.8227 V"
} | D | 0.8227 V | Apply the Nernst equation: E=1.00−(0.0591/2)(6)=0.8227 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8227 V, not 1.6454 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8227 V, not 1.08227 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8227 V, not... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000577 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 3 and common difference 8. Find the sum of its first 21 terms. | {
"A": "1741",
"B": "1743",
"C": "2614.5",
"D": "1307.25"
} | B | 1743 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=3, d=8, n=21: Sₙ=21/2[2(3)+(21−1)(8)]=1743. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1743, not 1741.",
"B": "Correct. The worked calculation gives 1743.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1743, not 2614.5.",
"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_003124 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-7-13i)/(9+4i). What is Re(z), the real part of z? | {
"A": "-1.18557",
"B": "-3.18557",
"C": "-2.18557",
"D": "-4.18557"
} | A | -1.18557 | Multiply numerator and denominator by the conjugate (9-4i). Then Re(z)=(ac+bd)/(c²+d²)=((-7)(9)+(-13)(4))/(9²+(4)²)=-1.18557. | {
"A": "Correct. The worked calculation gives -1.18557.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.18557, not -3.18557.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.18557, not -2.18557.",
"D": "Incorrect. Substituting the stat... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004526 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 3 kg and radius 5 m is acted on by a constant torque of 97 N m about its central axis. Find its angular acceleration. | {
"A": "3.58667 rad s⁻²",
"B": "2.58667 rad s⁻²",
"C": "4.58667 rad s⁻²",
"D": "1.94 rad s⁻²"
} | B | 2.58667 rad s⁻² | For a solid disc, I=½MR²=½(3)(5)²=37.5 kg m². Using τ=Iα, α=97/37.5=2.58667 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.58667 rad s⁻², not 3.58667 rad s⁻².",
"B": "Correct. The worked calculation gives 2.58667 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.58667 rad s⁻², not 4.58667 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_005079 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +9 μC are separated by 4 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "303.75 N",
"B": "301.75 N",
"C": "455.625 N",
"D": "364.5 N"
} | A | 303.75 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(9×10⁻⁶)/(4×10⁻²)²=303.75 N. | {
"A": "Correct. The worked calculation gives 303.75 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 303.75 N, not 301.75 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 303.75 N, not 455.625 N.",
"D": "Incorrect. Substituting the sta... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009282 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.92 V, transfers 1 electrons, and has reaction quotient Q=10^4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.0254 V",
"B": "-0.6836 V",
"C": "0.6836 V",
"D": "2.6836 V"
} | C | 0.6836 V | Apply the Nernst equation: E=0.92−(0.0591/1)(4)=0.6836 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6836 V, not 1.0254 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6836 V, not -0.6836 V.",
"C": "Correct. The worked calculation gives 0.6836 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003764 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block initially moves at 4 m s⁻¹. A constant net force does 16 N of work over 4 m in the direction of motion. Find its final kinetic energy. | {
"A": "184 J",
"B": "147.2 J",
"C": "368 J",
"D": "186 J"
} | A | 184 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(15)(4)²+(16)(4)=184 J. | {
"A": "Correct. The worked calculation gives 184 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 184 J, not 147.2 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 184 J, not 368 J.",
"D": "Incorrect. Substituting the stated values int... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003385 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 21 m s⁻¹ at 75° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "33.075 m",
"B": "21.05 m",
"C": "44.1 m",
"D": "22.05 m"
} | D | 22.05 m | Range R=u²sin(2θ)/g. Substituting u=21, θ=75° and g=10 gives R=(21)²sin(150°)/10=22.05 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22.05 m, not 33.075 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 22.05 m, not 21.05 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22.05 m, not 44.1... | [
"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_007062 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 12 mol of gas at 187 K and 0.95 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "96.91364 L",
"B": "193.82727 L",
"C": "145.37045 L",
"D": "387.65454 L"
} | B | 193.82727 L | PV=nRT, so V=nRT/P=(12)(0.082057)(187)/(0.95)=193.82727 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 193.82727 L, not 96.91364 L.",
"B": "Correct. The worked calculation gives 193.82727 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 193.82727 L, not 145.37045 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 |
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