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_007206 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 6 mol of gas at 204 K and 3 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "50.21888 L",
"B": "35.47926 L",
"C": "34.47926 L",
"D": "33.47926 L"
} | D | 33.47926 L | PV=nRT, so V=nRT/P=(6)(0.082057)(204)/(3)=33.47926 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33.47926 L, not 50.21888 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33.47926 L, not 35.47926 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 33.479... | [
"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_002499 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 1], [9, 7]]. | {
"A": "13",
"B": "12",
"C": "14",
"D": "9"
} | B | 12 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(7)−(1)(9)=12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12, not 13.",
"B": "Correct. The worked calculation gives 12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12, not 14.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007368 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 32 mL of 0.10 M HCl is mixed with 69 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "9.56388",
"B": "13.56388",
"C": "15.56388",
"D": "12.56388"
} | D | 12.56388 | Excess OH⁻ moles=0.10×(69−32)/1000=0.003700 mol. Total volume=0.101 L, so [OH⁻]=0.036634 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.56388. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.56388, not 9.56388.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.56388, not 13.56388.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.56388, 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_005363 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 36 μF capacitor is charged to a potential difference of 20 V. Calculate the energy stored, expressed in μJ. | {
"A": "7198 μJ",
"B": "7202 μJ",
"C": "7200 μJ",
"D": "3600 μJ"
} | C | 7200 μJ | U=½CV². Since C=36 μF, U in μJ is ½×36×(20)²=7200 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7200 μJ, not 7198 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7200 μJ, not 7202 μJ.",
"C": "Correct. The worked calculation gives 7200 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004985 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 14 Ω and 10 Ω are connected in series; this combination is connected in parallel with a 17 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.80882 A",
"B": "1.35662 A",
"C": "4.80882 A",
"D": "3.61765 A"
} | A | 1.80882 A | Series branch resistance=14+10=24 Ω. Parallel equivalent R_eq=(24×17)/(24+17)=9.95122 Ω. Total current I=V/R_eq=18/9.95122=1.80882 A. | {
"A": "Correct. The worked calculation gives 1.80882 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.80882 A, not 1.35662 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.80882 A, not 4.80882 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_001582 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (3x² +3x -1) dx. | {
"A": "18",
"B": "-12",
"C": "12",
"D": "24"
} | C | 12 | An antiderivative is (3/3)x³+(3/2)x²+(-1)x. Evaluating between 0 and 2 gives (3/3)(2)³+(3/2)(2)²+(-1)(2)=12. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12, not 18.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12, not -12.",
"C": "Correct. The worked calculation gives 12.",
"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_000924 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 4. What is the sum of its first 10 terms? | {
"A": "5242875",
"B": "3495249",
"C": "2796200",
"D": "3495250"
} | D | 3495250 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(4^10−1)/(4−1)=3495250. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3495250, not 5242875.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3495250, not 3495249.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3495250, not 27962... | [
"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_001348 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (0x² -3x -4) dx. | {
"A": "-6.8",
"B": "-62.4",
"C": "-78",
"D": "-58.5"
} | C | -78 | An antiderivative is (0/3)x³+(-3/2)x²+(-4)x. Evaluating between 0 and 6 gives (0/3)(6)³+(-3/2)(6)²+(-4)(6)=-78. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -78, not -6.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -78, not -62.4.",
"C": "Correct. The worked calculation gives -78.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_004802 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 11 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "5.67273 A",
"B": "6.78182 A",
"C": "3.78182 A",
"D": "4.78182 A"
} | C | 3.78182 A | Series branch resistance=8+7=15 Ω. Parallel equivalent R_eq=(15×11)/(15+11)=6.34615 Ω. Total current I=V/R_eq=24/6.34615=3.78182 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.78182 A, not 5.67273 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.78182 A, not 6.78182 A.",
"C": "Correct. The worked calculation gives 3.78182 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_001054 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=3x³ +8x² +0x+7. Evaluate f′(-1). | {
"A": "-7",
"B": "-8",
"C": "-5.25",
"D": "-14"
} | A | -7 | Differentiate: f′(x)=3(3)x²+2(8)x+(0). At x=-1, f′(-1)=3(3)(-1)²+2(8)(-1)+(0)=-7. | {
"A": "Correct. The worked calculation gives -7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -7, not -8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -7, not -5.25.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_000502 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -2 and common difference 4. Find the sum of its first 33 terms. | {
"A": "2045",
"B": "4092",
"C": "1636.8",
"D": "2046"
} | D | 2046 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-2, d=4, n=33: Sₙ=33/2[2(-2)+(33−1)(4)]=2046. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2046, not 2045.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2046, not 4092.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2046, not 1636.8.",
"D": "Co... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008103 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 3 A for 19402 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "19.15068 g",
"B": "17.15068 g",
"C": "18.15068 g",
"D": "28.72602 g"
} | A | 19.15068 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×3×19402/(2×96500)=19.15068 g. | {
"A": "Correct. The worked calculation gives 19.15068 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19.15068 g, not 17.15068 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19.15068 g, not 18.15068 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004929 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 14 Ω and 5 Ω are connected in series; this combination is connected in parallel with a 6 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.97368 A",
"B": "2.31579 A",
"C": "-1.31579 A",
"D": "1.31579 A"
} | D | 1.31579 A | Series branch resistance=14+5=19 Ω. Parallel equivalent R_eq=(19×6)/(19+6)=4.56 Ω. Total current I=V/R_eq=6/4.56=1.31579 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.31579 A, not 1.97368 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.31579 A, not 2.31579 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.31579 A,... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008253 | 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 29606 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": "116.89001 g",
"B": "-116.89001 g",
"C": "58.44501 g",
"D": "175.33502 g"
} | A | 116.89001 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×12×29606/(2×96500)=116.89001 g. | {
"A": "Correct. The worked calculation gives 116.89001 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 116.89001 g, not -116.89001 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 116.89001 g, not 58.44501 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_001951 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 12 elements can be selected from a set of 44 distinct elements? | {
"A": "25308819135.6",
"B": "21090682614",
"C": "21090682611",
"D": "21090682613"
} | D | 21090682613 | Order does not matter, so the count is C(44,12)=44!/[12!(32)!]=21090682613. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21090682613, not 25308819135.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21090682613, not 21090682614.",
"C": "Incorrect. Substituting the stated values into the governing relation gives ... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001459 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (5x² -8x +5) dx. | {
"A": "3.4",
"B": "25",
"C": "19.2",
"D": "24"
} | D | 24 | An antiderivative is (5/3)x³+(-8/2)x²+(5)x. Evaluating between 0 and 3 gives (5/3)(3)³+(-8/2)(3)²+(5)(3)=24. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24, not 3.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24, not 25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24, not 19.2.",
"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_002286 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 7 red, 10 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.32512",
"B": "0.48768",
"C": "0.65025",
"D": "0.32512"
} | D | 0.32512 | Favourable pairs = C(7,2)+C(10,2)+C(12,2)=132. Total pairs=C(29,2)=406. Therefore P=132/406=0.32512. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32512, not 1.32512.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32512, not 0.48768.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32512, not 0.650... | [
"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_006025 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 19 cm in front of a thin convex lens of focal length 7 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.58333",
"B": "3.58333",
"C": "0.29167",
"D": "0.875"
} | A | 0.58333 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(19)(7)/(19−7)=11.08333 cm. Thus |m|=v/u=11.08333/19=0.58333. | {
"A": "Correct. The worked calculation gives 0.58333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.58333, not 3.58333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.58333, not 0.29167.",
"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_003622 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 34 m s⁻¹ at 75° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "28.9 m",
"B": "57.8 m",
"C": "46.24 m",
"D": "115.6 m"
} | B | 57.8 m | Range R=u²sin(2θ)/g. Substituting u=34, θ=75° and g=10 gives R=(34)²sin(150°)/10=57.8 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 57.8 m, not 28.9 m.",
"B": "Correct. The worked calculation gives 57.8 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 57.8 m, not 46.24 m.",
"D": "Incorrect. Substituting the stated values... | [
"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_006719 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 2 mol H₂ and 35 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "1.2 mol",
"B": "4 mol",
"C": "1.5 mol",
"D": "2 mol"
} | D | 2 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 2 mol H₂O; O₂ can produce 70 mol H₂O. The limiting condition is H₂; product=2 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 1.2 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 4 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 1.5 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_009992 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(CN)_5]^+3, each CN ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "12",
"B": "7",
"C": "9",
"D": "8"
} | D | 8 | Let the formal oxidation state of Ni be x. Charge balance gives x+(5)(−1)=+3; hence x=3+5=+8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 12.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 9.",
"D": "Correct. The worked c... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000656 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -16 and common difference 3. Find the sum of its first 27 terms. | {
"A": "931.5",
"B": "621",
"C": "310.5",
"D": "465.75"
} | B | 621 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-16, d=3, n=27: Sₙ=27/2[2(-16)+(27−1)(3)]=621. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 621, not 931.5.",
"B": "Correct. The worked calculation gives 621.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 621, not 310.5.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_004474 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 6 kg and radius 5 m is acted on by a constant torque of 35 N m about its central axis. Find its angular acceleration. | {
"A": "0.23333 rad s⁻²",
"B": "0.93333 rad s⁻²",
"C": "-1.53333 rad s⁻²",
"D": "0.46667 rad s⁻²"
} | D | 0.46667 rad s⁻² | For a solid disc, I=½MR²=½(6)(5)²=75 kg m². Using τ=Iα, α=35/75=0.46667 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.46667 rad s⁻², not 0.23333 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.46667 rad s⁻², not 0.93333 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing r... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004811 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 6 Ω and 6 Ω are connected in series; this combination is connected in parallel with a 14 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "5.64286 A",
"B": "2.64286 A",
"C": "6.96429 A",
"D": "4.64286 A"
} | D | 4.64286 A | Series branch resistance=6+6=12 Ω. Parallel equivalent R_eq=(12×14)/(12+14)=6.46154 Ω. Total current I=V/R_eq=30/6.46154=4.64286 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.64286 A, not 5.64286 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.64286 A, not 2.64286 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.64286 A,... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000872 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio 4. What is the sum of its first 7 terms? | {
"A": "10922",
"B": "10924",
"C": "1093.2",
"D": "10923"
} | A | 10922 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(4^7−1)/(4−1)=10922. | {
"A": "Correct. The worked calculation gives 10922.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10922, not 10924.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10922, not 1093.2.",
"D": "Incorrect. Substituting the stated values into... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008066 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 14 A for 18903 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": "69.65707 g",
"B": "87.07133 g",
"C": "43.53567 g",
"D": "85.07133 g"
} | B | 87.07133 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×18903/(2×96500)=87.07133 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 87.07133 g, not 69.65707 g.",
"B": "Correct. The worked calculation gives 87.07133 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 87.07133 g, not 43.53567 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003535 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 42 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "-135.13024 m",
"B": "135.13024 m",
"C": "202.69536 m",
"D": "134.13024 m"
} | B | 135.13024 m | Range R=u²sin(2θ)/g. Substituting u=42, θ=25° and g=10 gives R=(42)²sin(50°)/10=135.13024 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 135.13024 m, not -135.13024 m.",
"B": "Correct. The worked calculation gives 135.13024 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 135.13024 m, not 202.69536 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_009143 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.52 V, transfers 3 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.28955 V",
"B": "-0.4209 V",
"C": "0.5791 V",
"D": "1.05791 V"
} | C | 0.5791 V | Apply the Nernst equation: E=0.52−(0.0591/3)(-3)=0.5791 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5791 V, not 0.28955 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.5791 V, not -0.4209 V.",
"C": "Correct. The worked calculation gives 0.5791 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_002753 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(6, 6, -7) and v=(-3, 9, -1), calculate u·v. | {
"A": "5.3",
"B": "21.5",
"C": "43",
"D": "41"
} | C | 43 | The dot product is the sum of corresponding component products: (6)(-3)+(6)(9)+(-7)(-1)=43. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 43, not 5.3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 43, not 21.5.",
"C": "Correct. The worked calculation gives 43.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_007583 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 94 mL of 0.10 M HCl is mixed with 58 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "3.62554",
"B": "3.25108",
"C": "1.21916",
"D": "1.62554"
} | D | 1.62554 | Excess H⁺ moles=0.10×(94−58)/1000=0.003600 mol. Total volume=0.152 L, so [H⁺]=0.023684 M and pH=−log₁₀[H⁺]=1.62554. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.62554, not 3.62554.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.62554, not 3.25108.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.62554, not 1.219... | [
"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_002077 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 7 red, 7 blue and 7 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.7",
"B": "0.3",
"C": "2.3",
"D": "-1.7"
} | B | 0.3 | Favourable pairs = C(7,2)+C(7,2)+C(7,2)=63. Total pairs=C(21,2)=210. Therefore P=63/210=0.3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3, not -0.7.",
"B": "Correct. The worked calculation gives 0.3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3, not 2.3.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_004116 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 43 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.28. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "121.26 N",
"B": "161.68 N",
"C": "162.68 N",
"D": "163.68 N"
} | B | 161.68 N | Net force=mg(sinθ−μcosθ)=43×10×(0.6−0.28×0.8)=161.68 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 161.68 N, not 121.26 N.",
"B": "Correct. The worked calculation gives 161.68 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 161.68 N, not 162.68 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_007215 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 10 mol of gas at 400 K and 2.03 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "159.68867 L",
"B": "-161.68867 L",
"C": "161.68867 L",
"D": "129.35094 L"
} | C | 161.68867 L | PV=nRT, so V=nRT/P=(10)(0.082057)(400)/(2.03)=161.68867 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 161.68867 L, not 159.68867 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 161.68867 L, not -161.68867 L.",
"C": "Correct. The worked calculation gives 161.68867 L.",
"D": "Incorrect. Subst... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001786 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 12 elements can be selected from a set of 49 distinct elements? | {
"A": "138395602254",
"B": "73810987868.8",
"C": "184527469672",
"D": "92263734836"
} | D | 92263734836 | Order does not matter, so the count is C(49,12)=49!/[12!(37)!]=92263734836. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 92263734836, not 138395602254.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 92263734836, not 73810987868.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004575 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 4 kg and radius 1 m is acted on by a constant torque of 89 N m about its central axis. Find its angular acceleration. | {
"A": "5.45 rad s⁻²",
"B": "44.5 rad s⁻²",
"C": "45.5 rad s⁻²",
"D": "43.5 rad s⁻²"
} | B | 44.5 rad s⁻² | For a solid disc, I=½MR²=½(4)(1)²=2 kg m². Using τ=Iα, α=89/2=44.5 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 44.5 rad s⁻², not 5.45 rad s⁻².",
"B": "Correct. The worked calculation gives 44.5 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 44.5 rad s⁻², not 45.5 rad s⁻².",
"D": "Incorrect. S... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006809 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 3 mol H₂ and 15 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "2 mol",
"B": "3 mol",
"C": "6 mol",
"D": "1.5 mol"
} | B | 3 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 3 mol H₂O; O₂ can produce 30 mol H₂O. The limiting condition is H₂; product=3 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3 mol, not 2 mol.",
"B": "Correct. The worked calculation gives 3 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3 mol, not 6 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_007367 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 20 mL of 0.10 M HCl is mixed with 19 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "3.8866",
"B": "5.18213",
"C": "2.59106",
"D": "1.25911"
} | C | 2.59106 | Excess H⁺ moles=0.10×(20−19)/1000=0.000100 mol. Total volume=0.039 L, so [H⁺]=0.002564 M and pH=−log₁₀[H⁺]=2.59106. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.59106, not 3.8866.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.59106, not 5.18213.",
"C": "Correct. The worked calculation gives 2.59106.",
"D": "Incorrect. Substituting the stated val... | [
"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_007705 | 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 80 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "38 mmol L⁻¹",
"B": "80 mmol L⁻¹",
"C": "40 mmol L⁻¹",
"D": "32 mmol L⁻¹"
} | C | 40 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=80/2^1=40 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 40 mmol L⁻¹, not 38 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 40 mmol L⁻¹, not 80 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 40 mmol L⁻¹.",
"D": "Incorrect. Substi... | [
"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_000769 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio 2. What is the sum of its first 10 terms? | {
"A": "410.2",
"B": "4092",
"C": "4091",
"D": "-4092"
} | B | 4092 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(2^10−1)/(2−1)=4092. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4092, not 410.2.",
"B": "Correct. The worked calculation gives 4092.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4092, not 4091.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_009619 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_3H_0X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "2.25",
"B": "5",
"C": "3",
"D": "1.3"
} | C | 3 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×3+2+0−0−2)/2=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 5.",
"C": "Correct. The worked calculation gives 3.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007881 | 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 66 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "12.375 mmol L⁻¹",
"B": "8.25 mmol L⁻¹",
"C": "6.25 mmol L⁻¹",
"D": "9.25 mmol L⁻¹"
} | B | 8.25 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=66/2^3=8.25 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.25 mmol L⁻¹, not 12.375 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 8.25 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.25 mmol L⁻¹, not 6.25 mmol L⁻¹.",
"D": "Incor... | [
"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_005171 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +2 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "135 N",
"B": "67.5 N",
"C": "90 N",
"D": "180 N"
} | C | 90 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(2×10⁻⁶)/(2×10⁻²)²=90 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 90 N, not 135 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 90 N, not 67.5 N.",
"C": "Correct. The worked calculation gives 90 N.",
"D": "Incorrect. Substituting the stated values into th... | [
"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_003532 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 34 m s⁻¹ at 30° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "101.11254 m",
"B": "120.13504 m",
"C": "100.11254 m",
"D": "102.11254 m"
} | C | 100.11254 m | Range R=u²sin(2θ)/g. Substituting u=34, θ=30° and g=10 gives R=(34)²sin(60°)/10=100.11254 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 100.11254 m, not 101.11254 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 100.11254 m, not 120.13504 m.",
"C": "Correct. The worked calculation gives 100.11254 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_000702 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio 3. What is the sum of its first 6 terms? | {
"A": "2457",
"B": "3277",
"C": "2620.8",
"D": "3276"
} | D | 3276 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(3^6−1)/(3−1)=3276. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3276, not 2457.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3276, not 3277.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3276, not 2620.8.",
"D": "Co... | [
"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_000999 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio -2. What is the sum of its first 12 terms? | {
"A": "13650",
"B": "-6825",
"C": "-13650",
"D": "-20475"
} | C | -13650 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(-2^12−1)/(-2−1)=-13650. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -13650, not 13650.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -13650, not -6825.",
"C": "Correct. The worked calculation gives -13650.",
"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_008623 | 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 1.41 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.41 K",
"B": "-1.59 K",
"C": "2.115 K",
"D": "1.141 K"
} | A | 1.41 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×1.0×1.41=1.41 K. | {
"A": "Correct. The worked calculation gives 1.41 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.41 K, not -1.59 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.41 K, not 2.115 K.",
"D": "Incorrect. Substituting the stated value... | [
"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_008243 | 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 15 A for 26640 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "129.47461 g",
"B": "130.47461 g",
"C": "131.47461 g",
"D": "105.17969 g"
} | C | 131.47461 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×15×26640/(2×96500)=131.47461 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 131.47461 g, not 129.47461 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 131.47461 g, not 130.47461 g.",
"C": "Correct. The worked calculation gives 131.47461 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_003424 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 113 m s⁻¹ at 30° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "829.37088 m",
"B": "1105.82784 m",
"C": "1103.82784 m",
"D": "884.66227 m"
} | B | 1105.82784 m | Range R=u²sin(2θ)/g. Substituting u=113, θ=30° and g=10 gives R=(113)²sin(60°)/10=1105.82784 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1105.82784 m, not 829.37088 m.",
"B": "Correct. The worked calculation gives 1105.82784 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1105.82784 m, not 1103.82784 m.",
"D": "Incorrect. Su... | [
"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_003253 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(6-6i)/(7+6i). What is Re(z), the real part of z? | {
"A": "1.00706",
"B": "3.07059",
"C": "2.07059",
"D": "0.07059"
} | D | 0.07059 | Multiply numerator and denominator by the conjugate (7-6i). Then Re(z)=(ac+bd)/(c²+d²)=((6)(7)+(-6)(6))/(7²+(6)²)=0.07059. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.07059, not 1.00706.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.07059, not 3.07059.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.07059, not 2.070... | [
"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_004383 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 6 kg and radius 2 m is acted on by a constant torque of 39 N m about its central axis. Find its angular acceleration. | {
"A": "3.25 rad s⁻²",
"B": "1.625 rad s⁻²",
"C": "4.875 rad s⁻²",
"D": "0.25 rad s⁻²"
} | A | 3.25 rad s⁻² | For a solid disc, I=½MR²=½(6)(2)²=12 kg m². Using τ=Iα, α=39/12=3.25 rad s⁻². | {
"A": "Correct. The worked calculation gives 3.25 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.25 rad s⁻², not 1.625 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.25 rad s⁻², not 4.875 rad s⁻².",
"D": "Incorrect.... | [
"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_007316 | 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 194 K and 0.34 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "48.82076 L",
"B": "46.82076 L",
"C": "-46.82076 L",
"D": "70.23114 L"
} | B | 46.82076 L | PV=nRT, so V=nRT/P=(1)(0.082057)(194)/(0.34)=46.82076 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 46.82076 L, not 48.82076 L.",
"B": "Correct. The worked calculation gives 46.82076 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 46.82076 L, not -46.82076 L.",
"D": "Incorrect. Substituti... | [
"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_001767 | 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 23 distinct elements? | {
"A": "196125.6",
"B": "245157",
"C": "122578.5",
"D": "183867.75"
} | B | 245157 | Order does not matter, so the count is C(23,7)=23!/[7!(16)!]=245157. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 245157, not 196125.6.",
"B": "Correct. The worked calculation gives 245157.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 245157, not 122578.5.",
"D": "Incorrect. Substituting the stated val... | [
"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_003033 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-3-2i)/(4+10i). What is Re(z), the real part of z? | {
"A": "-0.27586",
"B": "-2.27586",
"C": "-0.13793",
"D": "0.27586"
} | A | -0.27586 | Multiply numerator and denominator by the conjugate (4-10i). Then Re(z)=(ac+bd)/(c²+d²)=((-3)(4)+(-2)(10))/(4²+(10)²)=-0.27586. | {
"A": "Correct. The worked calculation gives -0.27586.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.27586, not -2.27586.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.27586, not -0.13793.",
"D": "Incorrect. Substituting the stat... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008320 | 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 7 A for 17094 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": "37.36934 g",
"B": "39.36934 g",
"C": "41.36934 g",
"D": "59.05401 g"
} | B | 39.36934 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×7×17094/(2×96500)=39.36934 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 39.36934 g, not 37.36934 g.",
"B": "Correct. The worked calculation gives 39.36934 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39.36934 g, not 41.36934 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009583 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_8H_18N_1X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "1",
"B": "0",
"C": "-2",
"D": "2"
} | B | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×8+2+1−18−1)/2=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"B": "Correct. The worked calculation gives 0.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004532 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 14 kg and radius 1 m is acted on by a constant torque of 43 N m about its central axis. Find its angular acceleration. | {
"A": "1.61429 rad s⁻²",
"B": "4.14286 rad s⁻²",
"C": "12.28571 rad s⁻²",
"D": "6.14286 rad s⁻²"
} | D | 6.14286 rad s⁻² | For a solid disc, I=½MR²=½(14)(1)²=7 kg m². Using τ=Iα, α=43/7=6.14286 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.14286 rad s⁻², not 1.61429 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.14286 rad s⁻², not 4.14286 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing r... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007958 | 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 39 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "3.65625 mmol L⁻¹",
"B": "6.875 mmol L⁻¹",
"C": "4.875 mmol L⁻¹",
"D": "9.75 mmol L⁻¹"
} | C | 4.875 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=39/2^3=4.875 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.875 mmol L⁻¹, not 3.65625 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.875 mmol L⁻¹, not 6.875 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 4.875 mmol L⁻¹.",
"D": "... | [
"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_007197 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 15 mol of gas at 375 K and 1.71 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "215.93947 L",
"B": "269.92434 L",
"C": "-269.92434 L",
"D": "27.99243 L"
} | B | 269.92434 L | PV=nRT, so V=nRT/P=(15)(0.082057)(375)/(1.71)=269.92434 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 269.92434 L, not 215.93947 L.",
"B": "Correct. The worked calculation gives 269.92434 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 269.92434 L, not -269.92434 L.",
"D": "Incorrect. Subst... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002256 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 11 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": "0.47097",
"B": "0.62796",
"C": "0.31398",
"D": "1.0314"
} | C | 0.31398 | Favourable pairs = C(9,2)+C(11,2)+C(11,2)=146. Total pairs=C(31,2)=465. Therefore P=146/465=0.31398. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31398, not 0.47097.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31398, not 0.62796.",
"C": "Correct. The worked calculation gives 0.31398.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004244 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 23 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.26. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "10.016 N",
"B": "135.24 N",
"C": "90.16 N",
"D": "89.16 N"
} | C | 90.16 N | Net force=mg(sinθ−μcosθ)=23×10×(0.6−0.26×0.8)=90.16 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 90.16 N, not 10.016 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 90.16 N, not 135.24 N.",
"C": "Correct. The worked calculation gives 90.16 N.",
"D": "Incorrect. Substituting the stated ... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001725 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 9 elements can be selected from a set of 11 distinct elements? | {
"A": "56",
"B": "55",
"C": "57",
"D": "110"
} | B | 55 | Order does not matter, so the count is C(11,9)=11!/[9!(2)!]=55. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 55, not 56.",
"B": "Correct. The worked calculation gives 55.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 55, not 57.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_004989 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 3 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 14 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.17227 A",
"B": "-1.17227 A",
"C": "1.7584 A",
"D": "2.17227 A"
} | A | 1.17227 A | Series branch resistance=3+14=17 Ω. Parallel equivalent R_eq=(17×14)/(17+14)=7.67742 Ω. Total current I=V/R_eq=9/7.67742=1.17227 A. | {
"A": "Correct. The worked calculation gives 1.17227 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.17227 A, not -1.17227 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.17227 A, not 1.7584 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_005419 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 57 μF capacitor is charged to a potential difference of 2 V. Calculate the energy stored, expressed in μJ. | {
"A": "116 μJ",
"B": "114 μJ",
"C": "228 μJ",
"D": "91.2 μJ"
} | B | 114 μJ | U=½CV². Since C=57 μF, U in μJ is ½×57×(2)²=114 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 114 μJ, not 116 μJ.",
"B": "Correct. The worked calculation gives 114 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 114 μJ, not 228 μJ.",
"D": "Incorrect. Substituting the stated values ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005600 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 8 μF capacitor is charged to a potential difference of 27 V. Calculate the energy stored, expressed in μJ. | {
"A": "2916 μJ",
"B": "2332.8 μJ",
"C": "2187 μJ",
"D": "4374 μJ"
} | A | 2916 μJ | U=½CV². Since C=8 μF, U in μJ is ½×8×(27)²=2916 μJ. | {
"A": "Correct. The worked calculation gives 2916 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2916 μJ, not 2332.8 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2916 μJ, not 2187 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_001991 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 2 elements can be selected from a set of 62 distinct elements? | {
"A": "1891",
"B": "945.5",
"C": "1512.8",
"D": "1418.25"
} | A | 1891 | Order does not matter, so the count is C(62,2)=62!/[2!(60)!]=1891. | {
"A": "Correct. The worked calculation gives 1891.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1891, not 945.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1891, not 1512.8.",
"D": "Incorrect. Substituting the stated values into th... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003712 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 3 kg block initially moves at 5 m s⁻¹. A constant net force does 17 N of work over 13 m in the direction of motion. Find its final kinetic energy. | {
"A": "259.5 J",
"B": "256.5 J",
"C": "257.5 J",
"D": "258.5 J"
} | D | 258.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(3)(5)²+(17)(13)=258.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 258.5 J, not 259.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 258.5 J, not 256.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 258.5 J, not 257.5... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009709 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(Cl)_2]^+3, each Cl ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "7",
"B": "3",
"C": "5",
"D": "2.5"
} | C | 5 | Let the formal oxidation state of Fe be x. Charge balance gives x+(2)(−1)=+3; hence x=3+2=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.",
"C": "Correct. The worked calculation gives 5.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006524 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 3 kg is attached to an ideal spring of force constant 1101 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.0522 s",
"B": "0.1044 s",
"C": "-0.1044 s",
"D": "0.1566 s"
} | B | 0.1044 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(3/1101)=0.1044 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.1044 s, not 0.0522 s.",
"B": "Correct. The worked calculation gives 0.1044 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.1044 s, not -0.1044 s.",
"D": "Incorrect. Substituting the sta... | [
"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_007853 | 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 30 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "0.11719 mmol L⁻¹",
"B": "0.05859 mmol L⁻¹",
"C": "3.11719 mmol L⁻¹",
"D": "0.08789 mmol L⁻¹"
} | A | 0.11719 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=30/2^8=0.11719 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 0.11719 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.11719 mmol L⁻¹, not 0.05859 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.11719 mmol L⁻¹, not 3.11719 mmol L⁻¹.",
... | [
"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_002981 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(6, -4, -2) and v=(1, -3, 3), calculate u·v. | {
"A": "12",
"B": "24",
"C": "2.2",
"D": "14"
} | A | 12 | The dot product is the sum of corresponding component products: (6)(1)+(-4)(-3)+(-2)(3)=12. | {
"A": "Correct. The worked calculation gives 12.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12, not 24.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12, not 2.2.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003995 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 9 m s⁻¹. A constant net force does 10 N of work over 13 m in the direction of motion. Find its final kinetic energy. | {
"A": "350.4 J",
"B": "292 J",
"C": "219 J",
"D": "293 J"
} | B | 292 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(9)²+(10)(13)=292 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 292 J, not 350.4 J.",
"B": "Correct. The worked calculation gives 292 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 292 J, not 219 J.",
"D": "Incorrect. Substituting the stated values int... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001925 | 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 11 distinct elements? | {
"A": "660",
"B": "330",
"C": "34",
"D": "329"
} | B | 330 | Order does not matter, so the count is C(11,7)=11!/[7!(4)!]=330. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 330, not 660.",
"B": "Correct. The worked calculation gives 330.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 330, not 34.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"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_007423 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 76 mL of 0.10 M HCl is mixed with 34 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.12722",
"B": "0.41814",
"C": "-1.41814",
"D": "1.41814"
} | D | 1.41814 | Excess H⁺ moles=0.10×(76−34)/1000=0.004200 mol. Total volume=0.110 L, so [H⁺]=0.038182 M and pH=−log₁₀[H⁺]=1.41814. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.41814, not 2.12722.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.41814, not 0.41814.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.41814, not -1.41... | [
"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_002247 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 12 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": "0.34656",
"B": "0.51984",
"C": "0.17328",
"D": "2.34656"
} | A | 0.34656 | Favourable pairs = C(5,2)+C(12,2)+C(11,2)=131. Total pairs=C(28,2)=378. Therefore P=131/378=0.34656. | {
"A": "Correct. The worked calculation gives 0.34656.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34656, not 0.51984.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34656, not 0.17328.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005766 | 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 3.7 atm at 345 K. What is its pressure at 661 K? | {
"A": "5.31674 atm",
"B": "7.08899 atm",
"C": "5.08899 atm",
"D": "10.63348 atm"
} | B | 7.08899 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.7)(661)/(345)=7.08899 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.08899 atm, not 5.31674 atm.",
"B": "Correct. The worked calculation gives 7.08899 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.08899 atm, not 5.08899 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_000109 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +7x +6=0, let its roots be α and β. What is α²+β²? | {
"A": "2.56",
"B": "-0.33",
"C": "-0.44",
"D": "-0.88"
} | C | -0.44 | By Vieta's relations, α+β = -7/5 and αβ = 6/5. Then α²+β²=(α+β)²−2αβ = (-7/5)²−2(6/5) = -0.44. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.44, not 2.56.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.44, not -0.33.",
"C": "Correct. The worked calculation gives -0.44.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_009455 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_18H_7N_3X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "18",
"B": "15",
"C": "14",
"D": "16"
} | D | 16 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+3−7−2)/2=16. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16, not 18.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16, not 15.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16, not 14.",
"D": "Correct. The wor... | [
"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_007064 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 2 mol of gas at 200 K and 0.22 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "-149.19455 L",
"B": "151.19455 L",
"C": "111.89591 L",
"D": "149.19455 L"
} | D | 149.19455 L | PV=nRT, so V=nRT/P=(2)(0.082057)(200)/(0.22)=149.19455 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 149.19455 L, not -149.19455 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 149.19455 L, not 151.19455 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1... | [
"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_003441 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 81 m s⁻¹ at 75° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "262.44 m",
"B": "328.05 m",
"C": "326.05 m",
"D": "393.66 m"
} | B | 328.05 m | Range R=u²sin(2θ)/g. Substituting u=81, θ=75° and g=10 gives R=(81)²sin(150°)/10=328.05 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 328.05 m, not 262.44 m.",
"B": "Correct. The worked calculation gives 328.05 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 328.05 m, not 326.05 m.",
"D": "Incorrect. Substituting the stat... | [
"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_009890 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(OH)_3]^+2, each OH ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "5",
"B": "2.5",
"C": "7",
"D": "4"
} | A | 5 | Let the formal oxidation state of Mn be x. Charge balance gives x+(3)(−1)=+2; hence x=2+3=+5. | {
"A": "Correct. The worked calculation gives 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 2.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009422 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_14H_24N_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "7",
"B": "1",
"C": "4",
"D": "6"
} | C | 4 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×14+2+2−24−0)/2=4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.",
"C": "Correct. The worked calculation gives 4.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004275 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 17 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.29. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "64.56 N",
"B": "93.84 N",
"C": "62.56 N",
"D": "7.256 N"
} | C | 62.56 N | Net force=mg(sinθ−μcosθ)=17×10×(0.6−0.29×0.8)=62.56 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 62.56 N, not 64.56 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 62.56 N, not 93.84 N.",
"C": "Correct. The worked calculation gives 62.56 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003998 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block initially moves at 11 m s⁻¹. A constant net force does 20 N of work over 18 m in the direction of motion. Find its final kinetic energy. | {
"A": "73.3 J",
"B": "722 J",
"C": "723 J",
"D": "578.4 J"
} | C | 723 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(6)(11)²+(20)(18)=723 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 723 J, not 73.3 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 723 J, not 722 J.",
"C": "Correct. The worked calculation gives 723 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_004475 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 2 m is acted on by a constant torque of 44 N m about its central axis. Find its angular acceleration. | {
"A": "-2.75 rad s⁻²",
"B": "3.75 rad s⁻²",
"C": "2.0625 rad s⁻²",
"D": "2.75 rad s⁻²"
} | D | 2.75 rad s⁻² | For a solid disc, I=½MR²=½(8)(2)²=16 kg m². Using τ=Iα, α=44/16=2.75 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.75 rad s⁻², not -2.75 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.75 rad s⁻², not 3.75 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation giv... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004953 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 10 Ω are connected in series; this combination is connected in parallel with a 18 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.53333 A",
"B": "1.26667 A",
"C": "-0.73333 A",
"D": "1.12667 A"
} | B | 1.26667 A | Series branch resistance=10+10=20 Ω. Parallel equivalent R_eq=(20×18)/(20+18)=9.47368 Ω. Total current I=V/R_eq=12/9.47368=1.26667 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.26667 A, not 2.53333 A.",
"B": "Correct. The worked calculation gives 1.26667 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.26667 A, not -0.73333 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002683 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(2, -7, 9) and v=(0, -3, 0), calculate u·v. | {
"A": "19",
"B": "21",
"C": "3.1",
"D": "42"
} | B | 21 | The dot product is the sum of corresponding component products: (2)(0)+(-7)(-3)+(9)(0)=21. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21, not 19.",
"B": "Correct. The worked calculation gives 21.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21, not 3.1.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008281 | 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 8 A for 16945 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": "53.52162 g",
"B": "45.60135 g",
"C": "-44.60135 g",
"D": "44.60135 g"
} | D | 44.60135 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×8×16945/(2×96500)=44.60135 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 44.60135 g, not 53.52162 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 44.60135 g, not 45.60135 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 44.601... | [
"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_002736 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-1, -2, 5) and v=(-2, 8, -5), calculate u·v. | {
"A": "-41",
"B": "-39",
"C": "-40",
"D": "-38"
} | B | -39 | The dot product is the sum of corresponding component products: (-1)(-2)+(-2)(8)+(5)(-5)=-39. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -39, not -41.",
"B": "Correct. The worked calculation gives -39.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -39, not -40.",
"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_007650 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 20 mL of 0.10 M HCl is mixed with 77 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "10.7691",
"B": "11.7691",
"C": "25.53821",
"D": "12.7691"
} | D | 12.7691 | Excess OH⁻ moles=0.10×(77−20)/1000=0.005700 mol. Total volume=0.097 L, so [OH⁻]=0.058763 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.7691. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.7691, not 10.7691.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.7691, not 11.7691.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.7691, not 25.53... | [
"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_003990 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 12 m s⁻¹. A constant net force does 14 N of work over 2 m in the direction of motion. Find its final kinetic energy. | {
"A": "1352 J",
"B": "677 J",
"C": "338 J",
"D": "676 J"
} | D | 676 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(12)²+(14)(2)=676 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 676 J, not 1352 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 676 J, not 677 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 676 J, not 338 J.",
"D"... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001946 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 9 elements can be selected from a set of 38 distinct elements? | {
"A": "244517460",
"B": "81505820",
"C": "163011640",
"D": "163011641"
} | C | 163011640 | Order does not matter, so the count is C(38,9)=38!/[9!(29)!]=163011640. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 163011640, not 244517460.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 163011640, not 81505820.",
"C": "Correct. The worked calculation gives 163011640.",
"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_001431 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (3x² -1x +7) dx. | {
"A": "5.35",
"B": "34.8",
"C": "44.5",
"D": "43.5"
} | D | 43.5 | An antiderivative is (3/3)x³+(-1/2)x²+(7)x. Evaluating between 0 and 3 gives (3/3)(3)³+(-1/2)(3)²+(7)(3)=43.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 43.5, not 5.35.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 43.5, not 34.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 43.5, not 44.5.",
"D": "Corr... | [
"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_007066 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 14 mol of gas at 388 K and 1.06 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "630.75513 L",
"B": "421.50342 L",
"C": "420.50342 L",
"D": "504.6041 L"
} | C | 420.50342 L | PV=nRT, so V=nRT/P=(14)(0.082057)(388)/(1.06)=420.50342 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 420.50342 L, not 630.75513 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 420.50342 L, not 421.50342 L.",
"C": "Correct. The worked calculation gives 420.50342 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007954 | 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 91 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "1.42188 mmol L⁻¹",
"B": "2.84375 mmol L⁻¹",
"C": "4.84375 mmol L⁻¹",
"D": "1.28438 mmol L⁻¹"
} | B | 2.84375 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=91/2^5=2.84375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.84375 mmol L⁻¹, not 1.42188 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 2.84375 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.84375 mmol L⁻¹, not 4.84375 mmol L⁻¹.",
... | [
"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_002710 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(5, 4, 0) and v=(4, -6, 7), calculate u·v. | {
"A": "-4",
"B": "-2",
"C": "-6",
"D": "-3"
} | A | -4 | The dot product is the sum of corresponding component products: (5)(4)+(4)(-6)+(0)(7)=-4. | {
"A": "Correct. The worked calculation gives -4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -4, not -2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -4, not -6.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004613 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 3 m is acted on by a constant torque of 49 N m about its central axis. Find its angular acceleration. | {
"A": "4.17778 rad s⁻²",
"B": "1.63333 rad s⁻²",
"C": "1.17778 rad s⁻²",
"D": "2.17778 rad s⁻²"
} | D | 2.17778 rad s⁻² | For a solid disc, I=½MR²=½(5)(3)²=22.5 kg m². Using τ=Iα, α=49/22.5=2.17778 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.17778 rad s⁻², not 4.17778 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.17778 rad s⁻², not 1.63333 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing r... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008557 | 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 0.81 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-2.5788 K",
"B": "1.04212 K",
"C": "0.4212 K",
"D": "-0.4212 K"
} | C | 0.4212 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.52×0.81=0.4212 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.4212 K, not -2.5788 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.4212 K, not 1.04212 K.",
"C": "Correct. The worked calculation gives 0.4212 K.",
"D": "Incorrect. Substituting the st... | [
"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_003477 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 26 m s⁻¹ at 75° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "33.8 m",
"B": "31.8 m",
"C": "-33.8 m",
"D": "67.6 m"
} | A | 33.8 m | Range R=u²sin(2θ)/g. Substituting u=26, θ=75° and g=10 gives R=(26)²sin(150°)/10=33.8 m. | {
"A": "Correct. The worked calculation gives 33.8 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33.8 m, not 31.8 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 33.8 m, not -33.8 m.",
"D": "Incorrect. Substituting the stated values... | [
"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_008188 | 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 29717 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": "109.5509 g",
"B": "53.77545 g",
"C": "215.10181 g",
"D": "107.5509 g"
} | D | 107.5509 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×29717/(2×96500)=107.5509 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 107.5509 g, not 109.5509 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 107.5509 g, not 53.77545 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 107.55... | [
"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_003857 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 9 m s⁻¹. A constant net force does 21 N of work over 5 m in the direction of motion. Find its final kinetic energy. | {
"A": "267 J",
"B": "133.5 J",
"C": "268 J",
"D": "-267 J"
} | A | 267 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(9)²+(21)(5)=267 J. | {
"A": "Correct. The worked calculation gives 267 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 267 J, not 133.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 267 J, not 268 J.",
"D": "Incorrect. Substituting the stated values int... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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