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_006258 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 92 cm in front of a thin convex lens of focal length 22 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.31429",
"B": "0.31429",
"C": "-0.68571",
"D": "0.15714"
} | B | 0.31429 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(92)(22)/(92−22)=28.91429 cm. Thus |m|=v/u=28.91429/92=0.31429. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31429, not 1.31429.",
"B": "Correct. The worked calculation gives 0.31429.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31429, not -0.68571.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001349 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (-3x² -5x +7) dx. | {
"A": "-28.5",
"B": "-14.25",
"C": "-27.5",
"D": "-34.2"
} | A | -28.5 | An antiderivative is (-3/3)x³+(-5/2)x²+(7)x. Evaluating between 0 and 3 gives (-3/3)(3)³+(-5/2)(3)²+(7)(3)=-28.5. | {
"A": "Correct. The worked calculation gives -28.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -28.5, not -14.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -28.5, not -27.5.",
"D": "Incorrect. Substituting the stated values into... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003513 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 76 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "442.46727 m",
"B": "331.85045 m",
"C": "-442.46727 m",
"D": "444.46727 m"
} | A | 442.46727 m | Range R=u²sin(2θ)/g. Substituting u=76, θ=25° and g=10 gives R=(76)²sin(50°)/10=442.46727 m. | {
"A": "Correct. The worked calculation gives 442.46727 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 442.46727 m, not 331.85045 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 442.46727 m, not -442.46727 m.",
"D": "Incorrect. Subst... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005919 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.5 atm at 204 K. What is its pressure at 397 K? | {
"A": "5.8652 atm",
"B": "4.8652 atm",
"C": "2.8652 atm",
"D": "9.73039 atm"
} | B | 4.8652 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.5)(397)/(204)=4.8652 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.8652 atm, not 5.8652 atm.",
"B": "Correct. The worked calculation gives 4.8652 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.8652 atm, not 2.8652 atm.",
"D": "Incorrect. Substitutin... | [
"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_009960 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(CN)_2]^-1, each CN ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "0.5",
"B": "1.1",
"C": "-1",
"D": "1"
} | D | 1 | Let the formal oxidation state of Cr be x. Charge balance gives x+(2)(−1)=-1; hence x=-1+2=+1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not -1.",
"D": "Correct. The work... | [
"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_003034 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(14-2i)/(5+8i). What is Re(z), the real part of z? | {
"A": "1.21348",
"B": "0.60674",
"C": "0.30337",
"D": "2.60674"
} | B | 0.60674 | Multiply numerator and denominator by the conjugate (5-8i). Then Re(z)=(ac+bd)/(c²+d²)=((14)(5)+(-2)(8))/(5²+(8)²)=0.60674. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.60674, not 1.21348.",
"B": "Correct. The worked calculation gives 0.60674.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.60674, not 0.30337.",
"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_000590 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 15 and common difference 6. Find the sum of its first 13 terms. | {
"A": "662",
"B": "663",
"C": "994.5",
"D": "-663"
} | B | 663 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=15, d=6, n=13: Sₙ=13/2[2(15)+(13−1)(6)]=663. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 663, not 662.",
"B": "Correct. The worked calculation gives 663.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 663, not 994.5.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005655 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 71 μF capacitor is charged to a potential difference of 8 V. Calculate the energy stored, expressed in μJ. | {
"A": "2271 μJ",
"B": "2272 μJ",
"C": "2726.4 μJ",
"D": "-2272 μJ"
} | B | 2272 μJ | U=½CV². Since C=71 μF, U in μJ is ½×71×(8)²=2272 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2272 μJ, not 2271 μJ.",
"B": "Correct. The worked calculation gives 2272 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2272 μJ, not 2726.4 μJ.",
"D": "Incorrect. Substituting the stated ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003199 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-3+8i)/(7+9i). What is Re(z), the real part of z? | {
"A": "1.39231",
"B": "0.58846",
"C": "0.19615",
"D": "0.39231"
} | D | 0.39231 | Multiply numerator and denominator by the conjugate (7-9i). Then Re(z)=(ac+bd)/(c²+d²)=((-3)(7)+(8)(9))/(7²+(9)²)=0.39231. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.39231, not 1.39231.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.39231, not 0.58846.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.39231, not 0.196... | [
"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_005692 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.9 atm at 439 K. What is its pressure at 459 K? | {
"A": "4.07768 atm",
"B": "2.03884 atm",
"C": "7.07768 atm",
"D": "1.40777 atm"
} | A | 4.07768 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.9)(459)/(439)=4.07768 atm. | {
"A": "Correct. The worked calculation gives 4.07768 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.07768 atm, not 2.03884 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.07768 atm, not 7.07768 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002549 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, 4], [4, -3]]. | {
"A": "-40.8",
"B": "-25.5",
"C": "34",
"D": "-34"
} | D | -34 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(-3)−(4)(4)=-34. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -34, not -40.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -34, not -25.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -34, not 34.",
"D": "Correct... | [
"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_008474 | 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 1.6 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-3.328 K",
"B": "3.328 K",
"C": "4.992 K",
"D": "0.328 K"
} | B | 3.328 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.52×1.6=3.328 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.328 K, not -3.328 K.",
"B": "Correct. The worked calculation gives 3.328 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.328 K, not 4.992 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_008108 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 11 A for 1577 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "4.70743 g",
"B": "2.85372 g",
"C": "1.57074 g",
"D": "5.70743 g"
} | D | 5.70743 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×1577/(2×96500)=5.70743 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.70743 g, not 4.70743 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.70743 g, not 2.85372 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.70743 g,... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002409 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, -5], [8, 4]]. | {
"A": "76",
"B": "77",
"C": "152",
"D": "75"
} | A | 76 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(4)−(-5)(8)=76. | {
"A": "Correct. The worked calculation gives 76.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 76, not 77.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 76, not 152.",
"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_007866 | 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 51 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "4.375 mmol L⁻¹",
"B": "4.78125 mmol L⁻¹",
"C": "9.375 mmol L⁻¹",
"D": "6.375 mmol L⁻¹"
} | D | 6.375 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=51/2^3=6.375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.375 mmol L⁻¹, not 4.375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.375 mmol L⁻¹, not 4.78125 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing rel... | [
"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_004891 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 11 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 8 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "0.8125 A",
"B": "4.625 A",
"C": "3.25 A",
"D": "1.625 A"
} | D | 1.625 A | Series branch resistance=11+7=18 Ω. Parallel equivalent R_eq=(18×8)/(18+8)=5.53846 Ω. Total current I=V/R_eq=9/5.53846=1.625 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.625 A, not 0.8125 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.625 A, not 4.625 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.625 A, not 3.25... | [
"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_008620 | 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 0.6 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.06144 K",
"B": "3.6144 K",
"C": "0.6144 K",
"D": "0.4608 K"
} | C | 0.6144 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×0.6=0.6144 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6144 K, not 1.06144 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6144 K, not 3.6144 K.",
"C": "Correct. The worked calculation gives 0.6144 K.",
"D": "Incorrect. Substituting the sta... | [
"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_001318 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=3x³ -5x² +9x+7. Evaluate f′(-3). | {
"A": "120",
"B": "118",
"C": "122",
"D": "144"
} | A | 120 | Differentiate: f′(x)=3(3)x²+2(-5)x+(9). At x=-3, f′(-3)=3(3)(-3)²+2(-5)(-3)+(9)=120. | {
"A": "Correct. The worked calculation gives 120.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 120, not 118.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 120, not 122.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005993 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.6 atm at 394 K. What is its pressure at 684 K? | {
"A": "3.51371 atm",
"B": "4.51371 atm",
"C": "3.38528 atm",
"D": "6.51371 atm"
} | B | 4.51371 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.6)(684)/(394)=4.51371 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.51371 atm, not 3.51371 atm.",
"B": "Correct. The worked calculation gives 4.51371 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.51371 atm, not 3.38528 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001077 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ +3x² +3x+7. Evaluate f′(0). | {
"A": "4",
"B": "2.25",
"C": "0",
"D": "3"
} | D | 3 | Differentiate: f′(x)=3(6)x²+2(3)x+(3). At x=0, f′(0)=3(6)(0)²+2(3)(0)+(3)=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 0.",
"D": "Correct. The worked... | [
"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_003382 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 103 m s⁻¹ at 65° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1625.3931 m",
"B": "814.69655 m",
"C": "406.34827 m",
"D": "812.69655 m"
} | D | 812.69655 m | Range R=u²sin(2θ)/g. Substituting u=103, θ=65° and g=10 gives R=(103)²sin(130°)/10=812.69655 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 812.69655 m, not 1625.3931 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 812.69655 m, not 814.69655 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 81... | [
"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_004825 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 15 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 16 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.07237 A",
"B": "2.07237 A",
"C": "3.07237 A",
"D": "1.03618 A"
} | B | 2.07237 A | Series branch resistance=15+4=19 Ω. Parallel equivalent R_eq=(19×16)/(19+16)=8.68571 Ω. Total current I=V/R_eq=18/8.68571=2.07237 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.07237 A, not 1.07237 A.",
"B": "Correct. The worked calculation gives 2.07237 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.07237 A, not 3.07237 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_006990 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 26 mol H₂ and 18 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "3.6 mol",
"B": "-26 mol",
"C": "26 mol",
"D": "52 mol"
} | C | 26 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 26 mol H₂O; O₂ can produce 36 mol H₂O. The limiting condition is H₂; product=26 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 3.6 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not -26 mol.",
"C": "Correct. The worked calculation gives 26 mol.",
"D": "Incorrect. Substituting the stated value... | [
"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_007796 | 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 20 minutes? | {
"A": "-38.5 mmol L⁻¹",
"B": "46.2 mmol L⁻¹",
"C": "19.25 mmol L⁻¹",
"D": "38.5 mmol L⁻¹"
} | D | 38.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=77/2^1=38.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 38.5 mmol L⁻¹, not -38.5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 38.5 mmol L⁻¹, not 46.2 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation... | [
"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_006114 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 47 cm in front of a thin convex lens of focal length 16 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.51613",
"B": "-0.48387",
"C": "-0.51613",
"D": "0.51613"
} | D | 0.51613 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(47)(16)/(47−16)=24.25806 cm. Thus |m|=v/u=24.25806/47=0.51613. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.51613, not 1.51613.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.51613, not -0.48387.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.51613, not -0.5... | [
"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_008292 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 12 A for 28470 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "112.40487 g",
"B": "224.80974 g",
"C": "114.40487 g",
"D": "-112.40487 g"
} | A | 112.40487 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×12×28470/(2×96500)=112.40487 g. | {
"A": "Correct. The worked calculation gives 112.40487 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 112.40487 g, not 224.80974 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 112.40487 g, not 114.40487 g.",
"D": "Incorrect. Substi... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006169 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 30 cm in front of a thin convex lens of focal length 17 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-1.30769",
"B": "4.30769",
"C": "0.65385",
"D": "1.30769"
} | D | 1.30769 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(30)(17)/(30−17)=39.23077 cm. Thus |m|=v/u=39.23077/30=1.30769. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.30769, not -1.30769.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.30769, not 4.30769.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.30769, not 0.65... | [
"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_006410 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 11 kg is attached to an ideal spring of force constant 285 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.60708 s",
"B": "3.39292 s",
"C": "0.39292 s",
"D": "-0.39292 s"
} | C | 0.39292 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(11/285)=0.39292 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.39292 s, not -2.60708 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.39292 s, not 3.39292 s.",
"C": "Correct. The worked calculation gives 0.39292 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007227 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 1 mol of gas at 271 K and 0.66 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "16.84655 L",
"B": "4.36931 L",
"C": "33.6931 L",
"D": "32.6931 L"
} | C | 33.6931 L | PV=nRT, so V=nRT/P=(1)(0.082057)(271)/(0.66)=33.6931 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33.6931 L, not 16.84655 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33.6931 L, not 4.36931 L.",
"C": "Correct. The worked calculation gives 33.6931 L.",
"D": "Incorrect. Substituting th... | [
"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_003733 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block initially moves at 9 m s⁻¹. A constant net force does 19 N of work over 15 m in the direction of motion. Find its final kinetic energy. | {
"A": "792 J",
"B": "1056 J",
"C": "633.6 J",
"D": "528 J"
} | D | 528 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(6)(9)²+(19)(15)=528 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 528 J, not 792 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 528 J, not 1056 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 528 J, not 633.6 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_001804 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 7 elements can be selected from a set of 43 distinct elements? | {
"A": "24168085.5",
"B": "32224114",
"C": "25779291.2",
"D": "48336171"
} | B | 32224114 | Order does not matter, so the count is C(43,7)=43!/[7!(36)!]=32224114. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 32224114, not 24168085.5.",
"B": "Correct. The worked calculation gives 32224114.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 32224114, not 25779291.2.",
"D": "Incorrect. Substituting the ... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006800 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 21 mol H₂ and 26 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "16.8 mol",
"B": "3.1 mol",
"C": "-21 mol",
"D": "21 mol"
} | D | 21 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 21 mol H₂O; O₂ can produce 52 mol H₂O. The limiting condition is H₂; product=21 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21 mol, not 16.8 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21 mol, not 3.1 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21 mol, not -21 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_007938 | 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 32 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "5 mmol L⁻¹",
"B": "0 mmol L⁻¹",
"C": "4 mmol L⁻¹",
"D": "2 mmol L⁻¹"
} | D | 2 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=32/2^4=2 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2 mmol L⁻¹, not 5 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2 mmol L⁻¹, not 0 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2 mmol... | [
"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_000399 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 12 and common difference 14. Find the sum of its first 8 terms. | {
"A": "487",
"B": "585.6",
"C": "732",
"D": "488"
} | D | 488 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=12, d=14, n=8: Sₙ=8/2[2(12)+(8−1)(14)]=488. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 488, not 487.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 488, not 585.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 488, not 732.",
"D": "Correct.... | [
"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_004685 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 9 Ω are connected in series; this combination is connected in parallel with a 20 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "-2.325 A",
"B": "0.675 A",
"C": "-0.325 A",
"D": "1.0125 A"
} | B | 0.675 A | Series branch resistance=7+9=16 Ω. Parallel equivalent R_eq=(16×20)/(16+20)=8.88889 Ω. Total current I=V/R_eq=6/8.88889=0.675 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.675 A, not -2.325 A.",
"B": "Correct. The worked calculation gives 0.675 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.675 A, not -0.325 A.",
"D": "Incorrect. Substituting the stated ... | [
"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_004321 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 36 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.18. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "164.16 N",
"B": "246.24 N",
"C": "166.16 N",
"D": "163.16 N"
} | A | 164.16 N | Net force=mg(sinθ−μcosθ)=36×10×(0.6−0.18×0.8)=164.16 N. | {
"A": "Correct. The worked calculation gives 164.16 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 164.16 N, not 246.24 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 164.16 N, not 166.16 N.",
"D": "Incorrect. Substituting the stat... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005159 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +6 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "58.0625 N",
"B": "59.0625 N",
"C": "61.0625 N",
"D": "118.125 N"
} | B | 59.0625 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(6×10⁻⁶)/(8×10⁻²)²=59.0625 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 59.0625 N, not 58.0625 N.",
"B": "Correct. The worked calculation gives 59.0625 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 59.0625 N, not 61.0625 N.",
"D": "Incorrect. Substituting the... | [
"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_005765 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3 atm at 181 K. What is its pressure at 522 K? | {
"A": "8.65193 atm",
"B": "-8.65193 atm",
"C": "9.65193 atm",
"D": "6.48895 atm"
} | A | 8.65193 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3)(522)/(181)=8.65193 atm. | {
"A": "Correct. The worked calculation gives 8.65193 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.65193 atm, not -8.65193 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.65193 atm, not 9.65193 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_008239 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 9 A for 7912 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "3.34285 g",
"B": "23.42854 g",
"C": "22.42854 g",
"D": "-23.42854 g"
} | B | 23.42854 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×9×7912/(2×96500)=23.42854 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 23.42854 g, not 3.34285 g.",
"B": "Correct. The worked calculation gives 23.42854 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23.42854 g, not 22.42854 g.",
"D": "Incorrect. Substituting... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001644 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (1x² +6x -5) dx. | {
"A": "3.1",
"B": "21",
"C": "20",
"D": "31.5"
} | B | 21 | An antiderivative is (1/3)x³+(6/2)x²+(-5)x. Evaluating between 0 and 3 gives (1/3)(3)³+(6/2)(3)²+(-5)(3)=21. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21, not 3.1.",
"B": "Correct. The worked calculation gives 21.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21, not 20.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001064 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-2x³ +6x² -10x+7. Evaluate f′(-2). | {
"A": "-116",
"B": "58",
"C": "-58",
"D": "-87"
} | C | -58 | Differentiate: f′(x)=3(-2)x²+2(6)x+(-10). At x=-2, f′(-2)=3(-2)(-2)²+2(6)(-2)+(-10)=-58. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -58, not -116.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -58, not 58.",
"C": "Correct. The worked calculation gives -58.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004702 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 15 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 17 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.34365 A",
"B": "1.34365 A",
"C": "2.50774 A",
"D": "4.34365 A"
} | A | 3.34365 A | Series branch resistance=15+4=19 Ω. Parallel equivalent R_eq=(19×17)/(19+17)=8.97222 Ω. Total current I=V/R_eq=30/8.97222=3.34365 A. | {
"A": "Correct. The worked calculation gives 3.34365 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.34365 A, not 1.34365 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.34365 A, not 2.50774 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_005641 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 27 μF capacitor is charged to a potential difference of 33 V. Calculate the energy stored, expressed in μJ. | {
"A": "14702.5 μJ",
"B": "-14701.5 μJ",
"C": "14699.5 μJ",
"D": "14701.5 μJ"
} | D | 14701.5 μJ | U=½CV². Since C=27 μF, U in μJ is ½×27×(33)²=14701.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14701.5 μJ, not 14702.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14701.5 μJ, not -14701.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14701... | [
"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_007698 | 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 73 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "73 mmol L⁻¹",
"B": "-36.5 mmol L⁻¹",
"C": "36.5 mmol L⁻¹",
"D": "35.5 mmol L⁻¹"
} | C | 36.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=73/2^1=36.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 36.5 mmol L⁻¹, not 73 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 36.5 mmol L⁻¹, not -36.5 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 36.5 mmol L⁻¹.",
"D": "Incorrec... | [
"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_003374 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 39 m s⁻¹ at 50° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "151.78926 m",
"B": "179.74711 m",
"C": "149.78926 m",
"D": "15.97893 m"
} | C | 149.78926 m | Range R=u²sin(2θ)/g. Substituting u=39, θ=50° and g=10 gives R=(39)²sin(100°)/10=149.78926 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 149.78926 m, not 151.78926 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 149.78926 m, not 179.74711 m.",
"C": "Correct. The worked calculation gives 149.78926 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002435 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, 3], [9, 8]]. | {
"A": "11",
"B": "19.5",
"C": "26",
"D": "13"
} | D | 13 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(8)−(3)(9)=13. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13, not 11.",
"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 26.",
"D": "Correct. The w... | [
"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_008395 | 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 1.5 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "3.51 K",
"B": "0.34 K",
"C": "2.34 K",
"D": "4.68 K"
} | C | 2.34 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.52×1.5=2.34 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.34 K, not 3.51 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.34 K, not 0.34 K.",
"C": "Correct. The worked calculation gives 2.34 K.",
"D": "Incorrect. Substituting the stated values ... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005942 | 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 1.3 atm at 182 K. What is its pressure at 430 K? | {
"A": "-3.07143 atm",
"B": "3.07143 atm",
"C": "6.07143 atm",
"D": "4.60714 atm"
} | B | 3.07143 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.3)(430)/(182)=3.07143 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.07143 atm, not -3.07143 atm.",
"B": "Correct. The worked calculation gives 3.07143 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.07143 atm, not 6.07143 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_002378 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, -1], [3, 5]]. | {
"A": "10",
"B": "1.8",
"C": "8",
"D": "11"
} | C | 8 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(5)−(-1)(3)=8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 1.8.",
"C": "Correct. The worked calculation gives 8.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"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_002092 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 5 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.37368",
"B": "-0.37368",
"C": "-2.62632",
"D": "0.28026"
} | A | 0.37368 | Favourable pairs = C(4,2)+C(5,2)+C(11,2)=71. Total pairs=C(20,2)=190. Therefore P=71/190=0.37368. | {
"A": "Correct. The worked calculation gives 0.37368.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.37368, not -0.37368.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.37368, not -2.62632.",
"D": "Incorrect. Substituting the stated ... | [
"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_007460 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 46 mL of 0.10 M HCl is mixed with 61 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "11.14671",
"B": "14.14671",
"C": "12.14671",
"D": "2.21467"
} | C | 12.14671 | Excess OH⁻ moles=0.10×(61−46)/1000=0.001500 mol. Total volume=0.107 L, so [OH⁻]=0.014019 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.14671. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.14671, not 11.14671.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.14671, not 14.14671.",
"C": "Correct. The worked calculation gives 12.14671.",
"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_008586 | 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 0.12 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.18432 K",
"B": "0.13824 K",
"C": "0.18432 K",
"D": "1.18432 K"
} | C | 0.18432 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.512×0.12=0.18432 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.18432 K, not -0.18432 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.18432 K, not 0.13824 K.",
"C": "Correct. The worked calculation gives 0.18432 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_009048 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.48 V, transfers 3 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.5003 V",
"B": "1.4997 V",
"C": "-1.5003 V",
"D": "3.4997 V"
} | B | 1.4997 V | Apply the Nernst equation: E=1.48−(0.0591/3)(-1)=1.4997 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.4997 V, not -0.5003 V.",
"B": "Correct. The worked calculation gives 1.4997 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.4997 V, not -1.5003 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_004930 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 11 Ω and 5 Ω are connected in series; this combination is connected in parallel with a 4 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.75 A",
"B": "4.75 A",
"C": "5.625 A",
"D": "1.75 A"
} | A | 3.75 A | Series branch resistance=11+5=16 Ω. Parallel equivalent R_eq=(16×4)/(16+4)=3.2 Ω. Total current I=V/R_eq=12/3.2=3.75 A. | {
"A": "Correct. The worked calculation gives 3.75 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.75 A, not 4.75 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.75 A, not 5.625 A.",
"D": "Incorrect. Substituting the stated values... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005573 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 51 μF capacitor is charged to a potential difference of 31 V. Calculate the energy stored, expressed in μJ. | {
"A": "2451.55 μJ",
"B": "24506.5 μJ",
"C": "24505.5 μJ",
"D": "36758.25 μJ"
} | C | 24505.5 μJ | U=½CV². Since C=51 μF, U in μJ is ½×51×(31)²=24505.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24505.5 μJ, not 2451.55 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24505.5 μJ, not 24506.5 μJ.",
"C": "Correct. The worked calculation gives 24505.5 μJ.",
"D": "Incorrect. Substitutin... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000454 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -12 and common difference 14. Find the sum of its first 16 terms. | {
"A": "1116",
"B": "1490",
"C": "1488",
"D": "1487"
} | C | 1488 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-12, d=14, n=16: Sₙ=16/2[2(-12)+(16−1)(14)]=1488. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1488, not 1116.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1488, not 1490.",
"C": "Correct. The worked calculation gives 1488.",
"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_001776 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 66 distinct elements? | {
"A": "8936928",
"B": "8936926",
"C": "8936929",
"D": "7149542.4"
} | A | 8936928 | Order does not matter, so the count is C(66,5)=66!/[5!(61)!]=8936928. | {
"A": "Correct. The worked calculation gives 8936928.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8936928, not 8936926.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8936928, not 8936929.",
"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_008479 | 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 1.69 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.845 K",
"B": "1.69 K",
"C": "0.69 K",
"D": "4.69 K"
} | B | 1.69 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×1.0×1.69=1.69 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.69 K, not 0.845 K.",
"B": "Correct. The worked calculation gives 1.69 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.69 K, not 0.69 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003769 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 6 m s⁻¹. A constant net force does 10 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "234 J",
"B": "236 J",
"C": "-236 J",
"D": "24.6 J"
} | B | 236 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(6)²+(10)(11)=236 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 236 J, not 234 J.",
"B": "Correct. The worked calculation gives 236 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 236 J, not -236 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_001743 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 11 elements can be selected from a set of 51 distinct elements? | {
"A": "47626016970",
"B": "35719512727.5",
"C": "-47626016970",
"D": "47626016971"
} | A | 47626016970 | Order does not matter, so the count is C(51,11)=51!/[11!(40)!]=47626016970. | {
"A": "Correct. The worked calculation gives 47626016970.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 47626016970, not 35719512727.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 47626016970, not -47626016970.",
"D": "Incorrect. Sub... | [
"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_004219 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 19 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.11. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "-97.28 N",
"B": "77.824 N",
"C": "10.728 N",
"D": "97.28 N"
} | D | 97.28 N | Net force=mg(sinθ−μcosθ)=19×10×(0.6−0.11×0.8)=97.28 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 97.28 N, not -97.28 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 97.28 N, not 77.824 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 97.28 N, not 10.... | [
"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_004091 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.37. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "-21.28 N",
"B": "42.56 N",
"C": "21.28 N",
"D": "3.128 N"
} | C | 21.28 N | Net force=mg(sinθ−μcosθ)=7×10×(0.6−0.37×0.8)=21.28 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21.28 N, not -21.28 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21.28 N, not 42.56 N.",
"C": "Correct. The worked calculation gives 21.28 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_001141 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ -1x² +6x+7. Evaluate f′(2). | {
"A": "-87",
"B": "-58",
"C": "58",
"D": "-4.8"
} | B | -58 | Differentiate: f′(x)=3(-5)x²+2(-1)x+(6). At x=2, f′(2)=3(-5)(2)²+2(-1)(2)+(6)=-58. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -58, not -87.",
"B": "Correct. The worked calculation gives -58.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -58, not 58.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_008608 | 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 0.92 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.84 K",
"B": "3.84 K",
"C": "1.184 K",
"D": "0.84 K"
} | A | 1.84 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×1.0×0.92=1.84 K. | {
"A": "Correct. The worked calculation gives 1.84 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.84 K, not 3.84 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.84 K, not 1.184 K.",
"D": "Incorrect. Substituting the stated values... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006441 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 1 kg is attached to an ideal spring of force constant 103 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.09853 s",
"B": "0.19707 s",
"C": "-0.19707 s",
"D": "-0.80293 s"
} | B | 0.19707 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(1/103)=0.19707 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.19707 s, not 0.09853 s.",
"B": "Correct. The worked calculation gives 0.19707 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.19707 s, not -0.19707 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000478 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 18 and common difference 9. Find the sum of its first 30 terms. | {
"A": "6682.5",
"B": "4455",
"C": "446.5",
"D": "8910"
} | B | 4455 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=18, d=9, n=30: Sₙ=30/2[2(18)+(30−1)(9)]=4455. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4455, not 6682.5.",
"B": "Correct. The worked calculation gives 4455.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4455, not 446.5.",
"D": "Incorrect. Substituting the stated values into th... | [
"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_009410 | 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_5H_8N_3X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "1.5",
"B": "-2",
"C": "1",
"D": "2"
} | D | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×5+2+3−8−3)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"D": "Correct. The worked... | [
"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_006103 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 114 cm in front of a thin convex lens of focal length 25 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.02809",
"B": "0.2809",
"C": "-0.7191",
"D": "0.21067"
} | B | 0.2809 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(114)(25)/(114−25)=32.02247 cm. Thus |m|=v/u=32.02247/114=0.2809. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.2809, not 1.02809.",
"B": "Correct. The worked calculation gives 0.2809.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.2809, not -0.7191.",
"D": "Incorrect. Substituting the stated value... | [
"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_006973 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 28 mol H₂ and 3 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "12 mol",
"B": "6 mol",
"C": "8 mol",
"D": "5 mol"
} | B | 6 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 28 mol H₂O; O₂ can produce 6 mol H₂O. The limiting condition is O₂; product=6 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 12 mol.",
"B": "Correct. The worked calculation gives 6 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 8 mol.",
"D": "Incorrect. Substituting the stated values into... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001362 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (0x² -2x -4) dx. | {
"A": "-3.75",
"B": "-7",
"C": "-4",
"D": "-5"
} | D | -5 | An antiderivative is (0/3)x³+(-2/2)x²+(-4)x. Evaluating between 0 and 1 gives (0/3)(1)³+(-2/2)(1)²+(-4)(1)=-5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -5, not -3.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -5, not -7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -5, not -4.",
"D": "Correct. The ... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000807 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio 5. What is the sum of its first 7 terms? | {
"A": "39062",
"B": "46874.4",
"C": "-39062",
"D": "3907.2"
} | A | 39062 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(5^7−1)/(5−1)=39062. | {
"A": "Correct. The worked calculation gives 39062.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39062, not 46874.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39062, not -39062.",
"D": "Incorrect. Substituting the stated values in... | [
"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_000663 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -7 and common difference 14. Find the sum of its first 28 terms. | {
"A": "5096",
"B": "10192",
"C": "2548",
"D": "5098"
} | A | 5096 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-7, d=14, n=28: Sₙ=28/2[2(-7)+(28−1)(14)]=5096. | {
"A": "Correct. The worked calculation gives 5096.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5096, not 10192.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5096, not 2548.",
"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_006197 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 12 cm in front of a thin convex lens of focal length 5 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "2.71429",
"B": "0.71429",
"C": "1.71429",
"D": "1.07143"
} | B | 0.71429 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(12)(5)/(12−5)=8.57143 cm. Thus |m|=v/u=8.57143/12=0.71429. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.71429, not 2.71429.",
"B": "Correct. The worked calculation gives 0.71429.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.71429, not 1.71429.",
"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_006269 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 114 cm in front of a thin convex lens of focal length 24 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "3.26667",
"B": "0.53333",
"C": "1.02667",
"D": "0.26667"
} | D | 0.26667 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(114)(24)/(114−24)=30.4 cm. Thus |m|=v/u=30.4/114=0.26667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.26667, not 3.26667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.26667, not 0.53333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.26667, not 1.026... | [
"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_007727 | 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 90 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "18 mmol L⁻¹",
"B": "22.5 mmol L⁻¹",
"C": "11.25 mmol L⁻¹",
"D": "3.25 mmol L⁻¹"
} | B | 22.5 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=90/2^2=22.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 22.5 mmol L⁻¹, not 18 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 22.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 22.5 mmol L⁻¹, not 11.25 mmol L⁻¹.",
"D": "Incorrec... | [
"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_000225 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 +3x +5=0, let its roots be α and β. What is α²+β²? | {
"A": "-1.75",
"B": "-2.0625",
"C": "-2.75",
"D": "-5.75"
} | C | -2.75 | By Vieta's relations, α+β = -3/2 and αβ = 5/2. Then α²+β²=(α+β)²−2αβ = (-3/2)²−2(5/2) = -2.75. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2.75, not -1.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -2.75, not -2.0625.",
"C": "Correct. The worked calculation gives -2.75.",
"D": "Incorrect. Substituting the stated values int... | [
"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_006878 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 26 mol H₂ and 14 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "26 mol",
"B": "-26 mol",
"C": "13 mol",
"D": "27 mol"
} | A | 26 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 26 mol H₂O; O₂ can produce 28 mol H₂O. The limiting condition is H₂; product=26 mol. | {
"A": "Correct. The worked calculation gives 26 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not -26 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 13 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_003378 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 31 m s⁻¹ at 70° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "-61.77189 m",
"B": "123.54378 m",
"C": "46.32892 m",
"D": "61.77189 m"
} | D | 61.77189 m | Range R=u²sin(2θ)/g. Substituting u=31, θ=70° and g=10 gives R=(31)²sin(140°)/10=61.77189 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 61.77189 m, not -61.77189 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 61.77189 m, not 123.54378 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 61.7... | [
"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_004492 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 15 kg and radius 3 m is acted on by a constant torque of 90 N m about its central axis. Find its angular acceleration. | {
"A": "-1.33333 rad s⁻²",
"B": "-0.66667 rad s⁻²",
"C": "1.33333 rad s⁻²",
"D": "0.66667 rad s⁻²"
} | C | 1.33333 rad s⁻² | For a solid disc, I=½MR²=½(15)(3)²=67.5 kg m². Using τ=Iα, α=90/67.5=1.33333 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.33333 rad s⁻², not -1.33333 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.33333 rad s⁻², not -0.66667 rad s⁻².",
"C": "Correct. The worked calculation gives 1.33333 rad s⁻².",
"... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005192 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +3 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "5 N",
"B": "8 N",
"C": "12 N",
"D": "10 N"
} | D | 10 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(3×10⁻⁶)/(9×10⁻²)²=10 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10 N, not 5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10 N, not 8 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10 N, not 12 N.",
"D": "Correc... | [
"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_005512 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 77 μF capacitor is charged to a potential difference of 39 V. Calculate the energy stored, expressed in μJ. | {
"A": "58558.5 μJ",
"B": "87837.75 μJ",
"C": "70270.2 μJ",
"D": "58556.5 μJ"
} | A | 58558.5 μJ | U=½CV². Since C=77 μF, U in μJ is ½×77×(39)²=58558.5 μJ. | {
"A": "Correct. The worked calculation gives 58558.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 58558.5 μJ, not 87837.75 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 58558.5 μJ, not 70270.2 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_003784 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block initially moves at 8 m s⁻¹. A constant net force does 15 N of work over 4 m in the direction of motion. Find its final kinetic energy. | {
"A": "506 J",
"B": "508 J",
"C": "1016 J",
"D": "254 J"
} | B | 508 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(14)(8)²+(15)(4)=508 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 508 J, not 506 J.",
"B": "Correct. The worked calculation gives 508 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 508 J, not 1016 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_003239 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-5-2i)/(10+9i). What is Re(z), the real part of z? | {
"A": "1.62431",
"B": "-0.56354",
"C": "-1.37569",
"D": "-0.37569"
} | D | -0.37569 | Multiply numerator and denominator by the conjugate (10-9i). Then Re(z)=(ac+bd)/(c²+d²)=((-5)(10)+(-2)(9))/(10²+(9)²)=-0.37569. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.37569, not 1.62431.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.37569, not -0.56354.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.37569, not -... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001969 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 4 elements can be selected from a set of 65 distinct elements? | {
"A": "677038",
"B": "677040",
"C": "338520",
"D": "677039"
} | B | 677040 | Order does not matter, so the count is C(65,4)=65!/[4!(61)!]=677040. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 677040, not 677038.",
"B": "Correct. The worked calculation gives 677040.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 677040, not 338520.",
"D": "Incorrect. Substituting the stated values ... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003042 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(3-5i)/(1+2i). What is Re(z), the real part of z? | {
"A": "-3.4",
"B": "1.4",
"C": "-1.4",
"D": "-2.1"
} | C | -1.4 | Multiply numerator and denominator by the conjugate (1-2i). Then Re(z)=(ac+bd)/(c²+d²)=((3)(1)+(-5)(2))/(1²+(2)²)=-1.4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.4, not -3.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.4, not 1.4.",
"C": "Correct. The worked calculation gives -1.4.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_003791 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block initially moves at 12 m s⁻¹. A constant net force does 6 N of work over 15 m in the direction of motion. Find its final kinetic energy. | {
"A": "522 J",
"B": "53.2 J",
"C": "523 J",
"D": "417.6 J"
} | A | 522 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(6)(12)²+(6)(15)=522 J. | {
"A": "Correct. The worked calculation gives 522 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 522 J, not 53.2 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 522 J, not 523 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_007388 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 55 mL of 0.10 M HCl is mixed with 75 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.21871",
"B": "13.18709",
"C": "14.18709",
"D": "12.18709"
} | D | 12.18709 | Excess OH⁻ moles=0.10×(75−55)/1000=0.002000 mol. Total volume=0.130 L, so [OH⁻]=0.015385 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.18709. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.18709, not 2.21871.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.18709, not 13.18709.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.18709, not 1... | [
"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_000029 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 -11x -5=0, let its roots be α and β. What is α²+β²? | {
"A": "1.94898",
"B": "4.89796",
"C": "1.89796",
"D": "3.89796"
} | D | 3.89796 | By Vieta's relations, α+β = 11/7 and αβ = -5/7. Then α²+β²=(α+β)²−2αβ = (11/7)²−2(-5/7) = 3.89796. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.89796, not 1.94898.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.89796, not 4.89796.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.89796, not 1.897... | [
"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_000134 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 -18x -1=0, let its roots be α and β. What is α²+β²? | {
"A": "38.66667",
"B": "36.66667",
"C": "35.66667",
"D": "27.5"
} | B | 36.66667 | By Vieta's relations, α+β = 18/3 and αβ = -1/3. Then α²+β²=(α+β)²−2αβ = (18/3)²−2(-1/3) = 36.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 36.66667, not 38.66667.",
"B": "Correct. The worked calculation gives 36.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 36.66667, not 35.66667.",
"D": "Incorrect. Substituting the stat... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009292 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.01 V, transfers 1 electrons, and has reaction quotient Q=10^-4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.2464 V",
"B": "1.2464 V",
"C": "0.6232 V",
"D": "2.2464 V"
} | B | 1.2464 V | Apply the Nernst equation: E=1.01−(0.0591/1)(-4)=1.2464 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.2464 V, not -1.2464 V.",
"B": "Correct. The worked calculation gives 1.2464 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2464 V, not 0.6232 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_009559 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_6H_8N_1X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "4",
"B": "2",
"C": "0",
"D": "1"
} | B | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×6+2+1−8−3)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 4.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 0.",
"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_009717 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(OH)_3]^-3, each OH ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "-3",
"B": "3",
"C": "0",
"D": "-2"
} | C | 0 | Let the formal oxidation state of Pt be x. Charge balance gives x+(3)(−1)=-3; hence x=-3+3=+0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 3.",
"C": "Correct. The worked calculation gives 0.",
"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_002702 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-2, 9, 0) and v=(3, -6, -3), calculate u·v. | {
"A": "-59",
"B": "-60",
"C": "-48",
"D": "-30"
} | B | -60 | The dot product is the sum of corresponding component products: (-2)(3)+(9)(-6)+(0)(-3)=-60. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -60, not -59.",
"B": "Correct. The worked calculation gives -60.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -60, not -48.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008179 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 1 A for 25428 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "7.36621 g",
"B": "9.36621 g",
"C": "6.36621 g",
"D": "8.36621 g"
} | D | 8.36621 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×1×25428/(2×96500)=8.36621 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.36621 g, not 7.36621 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.36621 g, not 9.36621 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.36621 g,... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005031 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +5 μC are separated by 5 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "162 N",
"B": "86.4 N",
"C": "107 N",
"D": "108 N"
} | D | 108 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(5×10⁻⁶)/(5×10⁻²)²=108 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 108 N, not 162 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 108 N, not 86.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 108 N, not 107 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_005913 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.5 atm at 230 K. What is its pressure at 703 K? | {
"A": "2.29239 atm",
"B": "2.52826 atm",
"C": "1.52826 atm",
"D": "3.52826 atm"
} | C | 1.52826 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.5)(703)/(230)=1.52826 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.52826 atm, not 2.29239 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.52826 atm, not 2.52826 atm.",
"C": "Correct. The worked calculation gives 1.52826 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002315 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 11 red, 11 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-2.64308",
"B": "0.35692",
"C": "0.17846",
"D": "0.53538"
} | B | 0.35692 | Favourable pairs = C(11,2)+C(11,2)+C(4,2)=116. Total pairs=C(26,2)=325. Therefore P=116/325=0.35692. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35692, not -2.64308.",
"B": "Correct. The worked calculation gives 0.35692.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35692, not 0.17846.",
"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_000475 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 20 and common difference 7. Find the sum of its first 35 terms. | {
"A": "4865",
"B": "4866",
"C": "4867",
"D": "2432.5"
} | A | 4865 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=20, d=7, n=35: Sₙ=35/2[2(20)+(35−1)(7)]=4865. | {
"A": "Correct. The worked calculation gives 4865.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4865, not 4866.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4865, not 4867.",
"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_003776 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block initially moves at 8 m s⁻¹. A constant net force does 15 N of work over 20 m in the direction of motion. Find its final kinetic energy. | {
"A": "492 J",
"B": "491 J",
"C": "369 J",
"D": "393.6 J"
} | A | 492 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(6)(8)²+(15)(20)=492 J. | {
"A": "Correct. The worked calculation gives 492 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 492 J, not 491 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 492 J, not 369 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_009306 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.96 V, transfers 3 electrons, and has reaction quotient Q=10^2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.0794 V",
"B": "0.69045 V",
"C": "0.9206 V",
"D": "-0.9206 V"
} | C | 0.9206 V | Apply the Nernst equation: E=0.96−(0.0591/3)(2)=0.9206 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9206 V, not -1.0794 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9206 V, not 0.69045 V.",
"C": "Correct. The worked calculation gives 0.9206 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 |
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