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_000536 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 16 and common difference 8. Find the sum of its first 27 terms. | {
"A": "-3240",
"B": "1620",
"C": "2430",
"D": "3240"
} | D | 3240 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=16, d=8, n=27: Sₙ=27/2[2(16)+(27−1)(8)]=3240. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3240, not -3240.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3240, not 1620.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3240, not 2430.",
"D": "Cor... | [
"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_003749 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 10 kg block initially moves at 7 m s⁻¹. A constant net force does 16 N of work over 9 m in the direction of motion. Find its final kinetic energy. | {
"A": "391 J",
"B": "389 J",
"C": "-389 J",
"D": "291.75 J"
} | B | 389 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(10)(7)²+(16)(9)=389 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 389 J, not 391 J.",
"B": "Correct. The worked calculation gives 389 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 389 J, not -389 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_009509 | 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_0N_3X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "4",
"B": "2",
"C": "5",
"D": "6"
} | A | 4 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×3+2+3−0−3)/2=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 5.",
"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_001982 | 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 71 distinct elements? | {
"A": "9602052688410",
"B": "1280273691789",
"C": "12802736917880",
"D": "19204105376820"
} | C | 12802736917880 | Order does not matter, so the count is C(71,12)=71!/[12!(59)!]=12802736917880. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12802736917880, not 9602052688410.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12802736917880, not 1280273691789.",
"C": "Correct. The worked calculation gives 12802736917880.",
"D": "Inco... | [
"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_009578 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_11H_5N_3X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "11",
"B": "18",
"C": "9",
"D": "10"
} | C | 9 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+3−5−4)/2=9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9, not 11.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9, not 18.",
"C": "Correct. The worked calculation gives 9.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000531 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -5 and common difference 5. Find the sum of its first 33 terms. | {
"A": "3712.5",
"B": "2475",
"C": "2477",
"D": "2474"
} | B | 2475 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-5, d=5, n=33: Sₙ=33/2[2(-5)+(33−1)(5)]=2475. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2475, not 3712.5.",
"B": "Correct. The worked calculation gives 2475.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2475, not 2477.",
"D": "Incorrect. Substituting the stated values into the... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001857 | 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 86 distinct elements? | {
"A": "3657",
"B": "3654",
"C": "3655",
"D": "2741.25"
} | C | 3655 | Order does not matter, so the count is C(86,2)=86!/[2!(84)!]=3655. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3655, not 3657.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3655, not 3654.",
"C": "Correct. The worked calculation gives 3655.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_003558 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 44 m s⁻¹ at 35° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "136.44337 m",
"B": "19.19245 m",
"C": "363.84898 m",
"D": "181.92449 m"
} | D | 181.92449 m | Range R=u²sin(2θ)/g. Substituting u=44, θ=35° and g=10 gives R=(44)²sin(70°)/10=181.92449 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 181.92449 m, not 136.44337 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 181.92449 m, not 19.19245 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 181... | [
"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_004087 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 40 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.12. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "-201.6 N",
"B": "201.6 N",
"C": "200.6 N",
"D": "199.6 N"
} | B | 201.6 N | Net force=mg(sinθ−μcosθ)=40×10×(0.6−0.12×0.8)=201.6 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 201.6 N, not -201.6 N.",
"B": "Correct. The worked calculation gives 201.6 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 201.6 N, not 200.6 N.",
"D": "Incorrect. Substituting the stated v... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006319 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 73 cm in front of a thin convex lens of focal length 23 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "3.46",
"B": "0.69",
"C": "0.92",
"D": "0.46"
} | D | 0.46 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(73)(23)/(73−23)=33.58 cm. Thus |m|=v/u=33.58/73=0.46. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.46, not 3.46.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.46, not 0.69.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.46, not 0.92.",
"D": "Corr... | [
"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_001260 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-2x³ +3x² -3x+7. Evaluate f′(-2). | {
"A": "-40",
"B": "-39",
"C": "-31.2",
"D": "-37"
} | B | -39 | Differentiate: f′(x)=3(-2)x²+2(3)x+(-3). At x=-2, f′(-2)=3(-2)(-2)²+2(3)(-2)+(-3)=-39. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -39, not -40.",
"B": "Correct. The worked calculation gives -39.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -39, not -31.2.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005001 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 13 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.25481 A",
"B": "2.25481 A",
"C": "1.12548 A",
"D": "-1.25481 A"
} | A | 1.25481 A | Series branch resistance=9+7=16 Ω. Parallel equivalent R_eq=(16×13)/(16+13)=7.17241 Ω. Total current I=V/R_eq=9/7.17241=1.25481 A. | {
"A": "Correct. The worked calculation gives 1.25481 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.25481 A, not 2.25481 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.25481 A, not 1.12548 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_005886 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3 atm at 347 K. What is its pressure at 673 K? | {
"A": "2.90922 atm",
"B": "2.81844 atm",
"C": "5.81844 atm",
"D": "7.81844 atm"
} | C | 5.81844 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3)(673)/(347)=5.81844 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.81844 atm, not 2.90922 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.81844 atm, not 2.81844 atm.",
"C": "Correct. The worked calculation gives 5.81844 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_003866 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block initially moves at 11 m s⁻¹. A constant net force does 20 N of work over 15 m in the direction of motion. Find its final kinetic energy. | {
"A": "604.5 J",
"B": "301.25 J",
"C": "602.5 J",
"D": "601.5 J"
} | C | 602.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(5)(11)²+(20)(15)=602.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 602.5 J, not 604.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 602.5 J, not 301.25 J.",
"C": "Correct. The worked calculation gives 602.5 J.",
"D": "Incorrect. Substituting the stated v... | [
"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_001760 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 83 distinct elements? | {
"A": "2432332329572",
"B": "243233232958",
"C": "2432332329570",
"D": "2432332329571"
} | C | 2432332329570 | Order does not matter, so the count is C(83,10)=83!/[10!(73)!]=2432332329570. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2432332329570, not 2432332329572.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2432332329570, not 243233232958.",
"C": "Correct. The worked calculation gives 2432332329570.",
"D": "Incorrec... | [
"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_005376 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 38 μF capacitor is charged to a potential difference of 24 V. Calculate the energy stored, expressed in μJ. | {
"A": "10943 μJ",
"B": "10944 μJ",
"C": "13132.8 μJ",
"D": "5472 μJ"
} | B | 10944 μJ | U=½CV². Since C=38 μF, U in μJ is ½×38×(24)²=10944 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10944 μJ, not 10943 μJ.",
"B": "Correct. The worked calculation gives 10944 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10944 μJ, not 13132.8 μJ.",
"D": "Incorrect. Substituting the st... | [
"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_003478 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 54 m s⁻¹ at 65° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "223.37856 m",
"B": "-223.37856 m",
"C": "446.75712 m",
"D": "335.06784 m"
} | A | 223.37856 m | Range R=u²sin(2θ)/g. Substituting u=54, θ=65° and g=10 gives R=(54)²sin(130°)/10=223.37856 m. | {
"A": "Correct. The worked calculation gives 223.37856 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 223.37856 m, not -223.37856 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 223.37856 m, not 446.75712 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_004855 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 15 Ω are connected in series; this combination is connected in parallel with a 8 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.98 A",
"B": "-1.02 A",
"C": "1.198 A",
"D": "0.98 A"
} | A | 1.98 A | Series branch resistance=10+15=25 Ω. Parallel equivalent R_eq=(25×8)/(25+8)=6.06061 Ω. Total current I=V/R_eq=12/6.06061=1.98 A. | {
"A": "Correct. The worked calculation gives 1.98 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.98 A, not -1.02 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.98 A, not 1.198 A.",
"D": "Incorrect. Substituting the stated value... | [
"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_000573 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 23 and common difference 2. Find the sum of its first 12 terms. | {
"A": "306",
"B": "407",
"C": "816",
"D": "408"
} | D | 408 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=23, d=2, n=12: Sₙ=12/2[2(23)+(12−1)(2)]=408. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 408, not 306.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 408, not 407.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 408, not 816.",
"D": "Correct. T... | [
"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_008329 | 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 10 A for 18843 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": "59.9964 g",
"B": "61.9964 g",
"C": "60.9964 g",
"D": "49.59712 g"
} | B | 61.9964 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×10×18843/(2×96500)=61.9964 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 61.9964 g, not 59.9964 g.",
"B": "Correct. The worked calculation gives 61.9964 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 61.9964 g, not 60.9964 g.",
"D": "Incorrect. Substituting the... | [
"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_002765 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-3, -3, 5) and v=(9, -7, -4), calculate u·v. | {
"A": "-20.8",
"B": "-52",
"C": "-24",
"D": "-26"
} | D | -26 | The dot product is the sum of corresponding component products: (-3)(9)+(-3)(-7)+(5)(-4)=-26. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -26, not -20.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -26, not -52.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -26, not -24.",
"D": "Correct.... | [
"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_001769 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 66 distinct elements? | {
"A": "-210980549208",
"B": "210980549208",
"C": "210980549209",
"D": "210980549206"
} | B | 210980549208 | Order does not matter, so the count is C(66,10)=66!/[10!(56)!]=210980549208. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 210980549208, not -210980549208.",
"B": "Correct. The worked calculation gives 210980549208.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 210980549208, not 210980549209.",
"D": "Incorrect. ... | [
"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_007833 | 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 98 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "0.76562 mmol L⁻¹",
"B": "1.07656 mmol L⁻¹",
"C": "0.57422 mmol L⁻¹",
"D": "-0.76562 mmol L⁻¹"
} | A | 0.76562 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=98/2^7=0.76562 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 0.76562 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.76562 mmol L⁻¹, not 1.07656 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.76562 mmol L⁻¹, not 0.57422 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_003310 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(2+13i)/(11+2i). What is Re(z), the real part of z? | {
"A": "0.576",
"B": "0.384",
"C": "0.288",
"D": "0.192"
} | B | 0.384 | Multiply numerator and denominator by the conjugate (11-2i). Then Re(z)=(ac+bd)/(c²+d²)=((2)(11)+(13)(2))/(11²+(2)²)=0.384. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.384, not 0.576.",
"B": "Correct. The worked calculation gives 0.384.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.384, not 0.288.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_001150 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ -6x² +9x+7. Evaluate f′(4). | {
"A": "-229",
"B": "231",
"C": "-346.5",
"D": "-231"
} | D | -231 | Differentiate: f′(x)=3(-4)x²+2(-6)x+(9). At x=4, f′(4)=3(-4)(4)²+2(-6)(4)+(9)=-231. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -231, not -229.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -231, not 231.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -231, not -346.5.",
"D": "Cor... | [
"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_008753 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.54 mol L⁻¹ and initially B is absent. At equilibrium, 62% of A has dissociated at constant volume. Find K_c. | {
"A": "5.18501",
"B": "2.18501",
"C": "4.18501",
"D": "3.18501"
} | B | 2.18501 | Let α=0.62. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.54)(0.62)²/(1−0.62)=2.18501. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.18501, not 5.18501.",
"B": "Correct. The worked calculation gives 2.18501.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.18501, not 4.18501.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002575 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, 5], [4, 7]]. | {
"A": "42",
"B": "32.25",
"C": "43",
"D": "45"
} | C | 43 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(7)−(5)(4)=43. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 43, not 42.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 43, not 32.25.",
"C": "Correct. The worked calculation gives 43.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009185 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.08 V, transfers 3 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.8806 V",
"B": "0.1194 V",
"C": "-1.8806 V",
"D": "1.1194 V"
} | D | 1.1194 V | Apply the Nernst equation: E=1.08−(0.0591/3)(-2)=1.1194 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.1194 V, not -0.8806 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1194 V, not 0.1194 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1194 V, not... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006227 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 47 cm in front of a thin convex lens of focal length 26 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.2381",
"B": "0.61905",
"C": "-0.7619",
"D": "1.85714"
} | A | 1.2381 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(47)(26)/(47−26)=58.19048 cm. Thus |m|=v/u=58.19048/47=1.2381. | {
"A": "Correct. The worked calculation gives 1.2381.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.2381, not 0.61905.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2381, not -0.7619.",
"D": "Incorrect. Substituting the stated value... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006040 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 43 cm in front of a thin convex lens of focal length 12 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "3.3871",
"B": "0.19355",
"C": "1.03871",
"D": "0.3871"
} | D | 0.3871 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(43)(12)/(43−12)=16.64516 cm. Thus |m|=v/u=16.64516/43=0.3871. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3871, not 3.3871.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3871, not 0.19355.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3871, not 1.03871."... | [
"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_008726 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.97 mol L⁻¹ and initially B is absent. At equilibrium, 20% of A has dissociated at constant volume. Find K_c. | {
"A": "0.2955",
"B": "-2.606",
"C": "0.394",
"D": "-0.394"
} | C | 0.394 | Let α=0.2. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.97)(0.2)²/(1−0.2)=0.394. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.394, not 0.2955.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.394, not -2.606.",
"C": "Correct. The worked calculation gives 0.394.",
"D": "Incorrect. Substituting the stated values int... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005047 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +8 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "26.8 N",
"B": "28.8 N",
"C": "3.88 N",
"D": "30.8 N"
} | B | 28.8 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(8×10⁻⁶)/(10×10⁻²)²=28.8 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 28.8 N, not 26.8 N.",
"B": "Correct. The worked calculation gives 28.8 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28.8 N, not 3.88 N.",
"D": "Incorrect. Substituting the stated values ... | [
"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_004395 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 12 kg and radius 5 m is acted on by a constant torque of 45 N m about its central axis. Find its angular acceleration. | {
"A": "0.45 rad s⁻²",
"B": "0.15 rad s⁻²",
"C": "0.225 rad s⁻²",
"D": "0.3 rad s⁻²"
} | D | 0.3 rad s⁻² | For a solid disc, I=½MR²=½(12)(5)²=150 kg m². Using τ=Iα, α=45/150=0.3 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3 rad s⁻², not 0.45 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3 rad s⁻², not 0.15 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives ... | [
"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_009168 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.80 V, transfers 3 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.62955 V",
"B": "0.8394 V",
"C": "1.08394 V",
"D": "-0.8394 V"
} | B | 0.8394 V | Apply the Nernst equation: E=0.80−(0.0591/3)(-2)=0.8394 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8394 V, not 0.62955 V.",
"B": "Correct. The worked calculation gives 0.8394 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.8394 V, not 1.08394 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_001500 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (4x² +4x +7) dx. | {
"A": "403",
"B": "41.2",
"C": "404",
"D": "402"
} | D | 402 | An antiderivative is (4/3)x³+(4/2)x²+(7)x. Evaluating between 0 and 6 gives (4/3)(6)³+(4/2)(6)²+(7)(6)=402. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 402, not 403.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 402, not 41.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 402, not 404.",
"D": "Correct. ... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009468 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_11H_15N_1X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "2",
"B": "-4",
"C": "3",
"D": "4"
} | D | 4 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+1−15−2)/2=4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not -4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 3.",
"D": "Correct. The worked c... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001866 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 64 distinct elements? | {
"A": "7624512",
"B": "762452.2",
"C": "7624511",
"D": "9149414.4"
} | A | 7624512 | Order does not matter, so the count is C(64,5)=64!/[5!(59)!]=7624512. | {
"A": "Correct. The worked calculation gives 7624512.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7624512, not 762452.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7624512, not 7624511.",
"D": "Incorrect. Substituting the stated v... | [
"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_001701 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 56 distinct elements? | {
"A": "5729724",
"B": "3819816",
"C": "2864862",
"D": "3819818"
} | B | 3819816 | Order does not matter, so the count is C(56,5)=56!/[5!(51)!]=3819816. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3819816, not 5729724.",
"B": "Correct. The worked calculation gives 3819816.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3819816, not 2864862.",
"D": "Incorrect. Substituting the stated va... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006443 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 8 kg is attached to an ideal spring of force constant 251 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.35706 s",
"B": "0.35706 s",
"C": "1.03571 s",
"D": "3.35706 s"
} | B | 0.35706 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(8/251)=0.35706 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35706 s, not -0.35706 s.",
"B": "Correct. The worked calculation gives 0.35706 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35706 s, not 1.03571 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003081 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-14-3i)/(6+9i). What is Re(z), the real part of z? | {
"A": "-1.42308",
"B": "-1.89744",
"C": "2.05128",
"D": "-0.94872"
} | D | -0.94872 | Multiply numerator and denominator by the conjugate (6-9i). Then Re(z)=(ac+bd)/(c²+d²)=((-14)(6)+(-3)(9))/(6²+(9)²)=-0.94872. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.94872, not -1.42308.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.94872, not -1.89744.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.94872, not ... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000904 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio -2. What is the sum of its first 8 terms? | {
"A": "-318.75",
"B": "-427",
"C": "-425",
"D": "425"
} | C | -425 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(-2^8−1)/(-2−1)=-425. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -425, not -318.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -425, not -427.",
"C": "Correct. The worked calculation gives -425.",
"D": "Incorrect. Substituting the stated values into th... | [
"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_009524 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_5H_1N_3X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "7.5",
"B": "4",
"C": "5",
"D": "6"
} | C | 5 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×5+2+3−1−4)/2=5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 7.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not 4.",
"C": "Correct. The worked calculation gives 5.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007679 | 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 67 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "2.1875 mmol L⁻¹",
"B": "3.1875 mmol L⁻¹",
"C": "4.1875 mmol L⁻¹",
"D": "6.28125 mmol L⁻¹"
} | C | 4.1875 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=67/2^4=4.1875 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.1875 mmol L⁻¹, not 2.1875 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.1875 mmol L⁻¹, not 3.1875 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 4.1875 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_000543 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 20 and common difference 5. Find the sum of its first 33 terms. | {
"A": "4950",
"B": "3300",
"C": "6600",
"D": "2475"
} | B | 3300 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=20, d=5, n=33: Sₙ=33/2[2(20)+(33−1)(5)]=3300. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3300, not 4950.",
"B": "Correct. The worked calculation gives 3300.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3300, not 6600.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009963 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(Cl)_3]^-1, each Cl ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "2",
"B": "1.5",
"C": "-1",
"D": "4"
} | A | 2 | Let the formal oxidation state of Cu be x. Charge balance gives x+(3)(−1)=-1; hence x=-1+3=+2. | {
"A": "Correct. The worked calculation gives 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not -1.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"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_001302 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-2x³ -8x² -5x+7. Evaluate f′(2). | {
"A": "-48.8",
"B": "61",
"C": "-60",
"D": "-61"
} | D | -61 | Differentiate: f′(x)=3(-2)x²+2(-8)x+(-5). At x=2, f′(2)=3(-2)(2)²+2(-8)(2)+(-5)=-61. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -61, not -48.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -61, not 61.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -61, not -60.",
"D": "Correct. ... | [
"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_000365 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -6 and common difference 6. Find the sum of its first 21 terms. | {
"A": "907.2",
"B": "-1134",
"C": "1134",
"D": "114.4"
} | C | 1134 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-6, d=6, n=21: Sₙ=21/2[2(-6)+(21−1)(6)]=1134. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1134, not 907.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1134, not -1134.",
"C": "Correct. The worked calculation gives 1134.",
"D": "Incorrect. Substituting the stated values into the... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004093 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.26. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "-31.36 N",
"B": "15.68 N",
"C": "30.36 N",
"D": "31.36 N"
} | D | 31.36 N | Net force=mg(sinθ−μcosθ)=8×10×(0.6−0.26×0.8)=31.36 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 31.36 N, not -31.36 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 31.36 N, not 15.68 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 31.36 N, not 30.3... | [
"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_001333 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ +2x² +5x+7. Evaluate f′(-1). | {
"A": "-16.5",
"B": "11",
"C": "-14",
"D": "-11"
} | D | -11 | Differentiate: f′(x)=3(-4)x²+2(2)x+(5). At x=-1, f′(-1)=3(-4)(-1)²+2(2)(-1)+(5)=-11. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -11, not -16.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -11, not 11.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -11, not -14.",
"D": "Correct. ... | [
"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_006996 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 8 mol H₂ and 2 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "4 mol",
"B": "3 mol",
"C": "5 mol",
"D": "2 mol"
} | A | 4 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 8 mol H₂O; O₂ can produce 4 mol H₂O. The limiting condition is O₂; product=4 mol. | {
"A": "Correct. The worked calculation gives 4 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4 mol, not 3 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4 mol, not 5 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_006578 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 24 kg is attached to an ideal spring of force constant 347 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.52598 s",
"B": "0.26299 s",
"C": "3.52598 s",
"D": "1.05196 s"
} | A | 0.52598 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(24/347)=0.52598 s. | {
"A": "Correct. The worked calculation gives 0.52598 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.52598 s, not 0.26299 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.52598 s, not 3.52598 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002872 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-6, -7, -7) and v=(7, 7, -2), calculate u·v. | {
"A": "-38.5",
"B": "-78",
"C": "-77",
"D": "-57.75"
} | C | -77 | The dot product is the sum of corresponding component products: (-6)(7)+(-7)(7)+(-7)(-2)=-77. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -77, not -38.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -77, not -78.",
"C": "Correct. The worked calculation gives -77.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_009946 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(CN)_2]^+1, each CN ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "2.25",
"B": "3",
"C": "-3",
"D": "2"
} | B | 3 | Let the formal oxidation state of Fe be x. Charge balance gives x+(2)(−1)=+1; hence x=1+2=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not -3.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_000690 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio 4. What is the sum of its first 6 terms? | {
"A": "9555",
"B": "9553",
"C": "19110",
"D": "11466"
} | A | 9555 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(4^6−1)/(4−1)=9555. | {
"A": "Correct. The worked calculation gives 9555.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9555, not 9553.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9555, not 19110.",
"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_005704 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.1 atm at 386 K. What is its pressure at 476 K? | {
"A": "-2.87668 atm",
"B": "1.01233 atm",
"C": "-0.87668 atm",
"D": "0.12332 atm"
} | D | 0.12332 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.1)(476)/(386)=0.12332 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.12332 atm, not -2.87668 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.12332 atm, not 1.01233 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001026 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ -3x² -5x+7. Evaluate f′(-1). | {
"A": "-8.25",
"B": "-10",
"C": "-11",
"D": "-12"
} | C | -11 | Differentiate: f′(x)=3(-4)x²+2(-3)x+(-5). At x=-1, f′(-1)=3(-4)(-1)²+2(-3)(-1)+(-5)=-11. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -11, not -8.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -11, not -10.",
"C": "Correct. The worked calculation gives -11.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005021 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +4 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "2.97521 N",
"B": "5.95041 N",
"C": "7.95041 N",
"D": "11.90083 N"
} | B | 5.95041 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(4×10⁻⁶)/(11×10⁻²)²=5.95041 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.95041 N, not 2.97521 N.",
"B": "Correct. The worked calculation gives 5.95041 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.95041 N, not 7.95041 N.",
"D": "Incorrect. Substituting the... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004845 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 18 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "5.27273 A",
"B": "1.26364 A",
"C": "2.63636 A",
"D": "0.63636 A"
} | C | 2.63636 A | Series branch resistance=7+4=11 Ω. Parallel equivalent R_eq=(11×18)/(11+18)=6.82759 Ω. Total current I=V/R_eq=18/6.82759=2.63636 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.63636 A, not 5.27273 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.63636 A, not 1.26364 A.",
"C": "Correct. The worked calculation gives 2.63636 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_006829 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 49 mol H₂ and 21 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "42 mol",
"B": "-42 mol",
"C": "33.6 mol",
"D": "5.2 mol"
} | A | 42 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 49 mol H₂O; O₂ can produce 42 mol H₂O. The limiting condition is O₂; product=42 mol. | {
"A": "Correct. The worked calculation gives 42 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 42 mol, not -42 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 42 mol, not 33.6 mol.",
"D": "Incorrect. Substituting the stated valu... | [
"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_004561 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 11 kg and radius 2 m is acted on by a constant torque of 68 N m about its central axis. Find its angular acceleration. | {
"A": "2.31818 rad s⁻²",
"B": "6.09091 rad s⁻²",
"C": "3.09091 rad s⁻²",
"D": "4.63636 rad s⁻²"
} | C | 3.09091 rad s⁻² | For a solid disc, I=½MR²=½(11)(2)²=22 kg m². Using τ=Iα, α=68/22=3.09091 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.09091 rad s⁻², not 2.31818 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.09091 rad s⁻², not 6.09091 rad s⁻².",
"C": "Correct. The worked calculation gives 3.09091 rad s⁻².",
"D"... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002970 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-5, 8, -5) and v=(-5, 7, 8), calculate u·v. | {
"A": "30.75",
"B": "41",
"C": "20.5",
"D": "61.5"
} | B | 41 | The dot product is the sum of corresponding component products: (-5)(-5)+(8)(7)+(-5)(8)=41. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 41, not 30.75.",
"B": "Correct. The worked calculation gives 41.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 41, not 20.5.",
"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_007298 | 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 297 K and 0.26 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "561.40605 L",
"B": "674.88726 L",
"C": "562.40605 L",
"D": "1124.81211 L"
} | C | 562.40605 L | PV=nRT, so V=nRT/P=(6)(0.082057)(297)/(0.26)=562.40605 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 562.40605 L, not 561.40605 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 562.40605 L, not 674.88726 L.",
"C": "Correct. The worked calculation gives 562.40605 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_006013 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 46 cm in front of a thin convex lens of focal length 16 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.26667",
"B": "0.53333",
"C": "-0.46667",
"D": "-2.46667"
} | B | 0.53333 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(46)(16)/(46−16)=24.53333 cm. Thus |m|=v/u=24.53333/46=0.53333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.53333, not 0.26667.",
"B": "Correct. The worked calculation gives 0.53333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.53333, not -0.46667.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007259 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 12 mol of gas at 306 K and 2.7 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "133.91702 L",
"B": "111.59752 L",
"C": "112.59752 L",
"D": "83.69814 L"
} | B | 111.59752 L | PV=nRT, so V=nRT/P=(12)(0.082057)(306)/(2.7)=111.59752 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 111.59752 L, not 133.91702 L.",
"B": "Correct. The worked calculation gives 111.59752 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 111.59752 L, not 112.59752 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_001864 | 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 37 distinct elements? | {
"A": "10295472",
"B": "1029548.2",
"C": "20590944",
"D": "10295471"
} | A | 10295472 | Order does not matter, so the count is C(37,7)=37!/[7!(30)!]=10295472. | {
"A": "Correct. The worked calculation gives 10295472.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10295472, not 1029548.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10295472, not 20590944.",
"D": "Incorrect. Substituting the sta... | [
"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_005564 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 28 μF capacitor is charged to a potential difference of 26 V. Calculate the energy stored, expressed in μJ. | {
"A": "7571.2 μJ",
"B": "14196 μJ",
"C": "9466 μJ",
"D": "9464 μJ"
} | D | 9464 μJ | U=½CV². Since C=28 μF, U in μJ is ½×28×(26)²=9464 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9464 μJ, not 7571.2 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9464 μJ, not 14196 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9464 μJ, not 94... | [
"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_006296 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 120 cm in front of a thin convex lens of focal length 26 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.2766",
"B": "3.2766",
"C": "0.2766",
"D": "0.1383"
} | C | 0.2766 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(120)(26)/(120−26)=33.19149 cm. Thus |m|=v/u=33.19149/120=0.2766. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.2766, not -0.2766.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.2766, not 3.2766.",
"C": "Correct. The worked calculation gives 0.2766.",
"D": "Incorrect. Substituting the stated values... | [
"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_001896 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 35 distinct elements? | {
"A": "35303730",
"B": "23535821",
"C": "23535820",
"D": "17651865"
} | C | 23535820 | Order does not matter, so the count is C(35,8)=35!/[8!(27)!]=23535820. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 23535820, not 35303730.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23535820, not 23535821.",
"C": "Correct. The worked calculation gives 23535820.",
"D": "Incorrect. Substituting the stat... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005524 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 80 μF capacitor is charged to a potential difference of 34 V. Calculate the energy stored, expressed in μJ. | {
"A": "4625 μJ",
"B": "46239 μJ",
"C": "46240 μJ",
"D": "55488 μJ"
} | C | 46240 μJ | U=½CV². Since C=80 μF, U in μJ is ½×80×(34)²=46240 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 46240 μJ, not 4625 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 46240 μJ, not 46239 μJ.",
"C": "Correct. The worked calculation gives 46240 μJ.",
"D": "Incorrect. Substituting the state... | [
"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_003873 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block initially moves at 5 m s⁻¹. A constant net force does 11 N of work over 13 m in the direction of motion. Find its final kinetic energy. | {
"A": "330.5 J",
"B": "328.5 J",
"C": "247.875 J",
"D": "34.05 J"
} | A | 330.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(15)(5)²+(11)(13)=330.5 J. | {
"A": "Correct. The worked calculation gives 330.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 330.5 J, not 328.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 330.5 J, not 247.875 J.",
"D": "Incorrect. Substituting the stated ... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000303 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 +18x +3=0, let its roots be α and β. What is α²+β²? | {
"A": "6",
"B": "4",
"C": "8",
"D": "9"
} | C | 8 | By Vieta's relations, α+β = -18/6 and αβ = 3/6. Then α²+β²=(α+β)²−2αβ = (-18/6)²−2(3/6) = 8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 4.",
"C": "Correct. The worked calculation gives 8.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_002899 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-2, 8, 9) and v=(-1, -4, 0), calculate u·v. | {
"A": "-36",
"B": "-30",
"C": "30",
"D": "-45"
} | B | -30 | The dot product is the sum of corresponding component products: (-2)(-1)+(8)(-4)+(9)(0)=-30. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -30, not -36.",
"B": "Correct. The worked calculation gives -30.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -30, not 30.",
"D": "Incorrect. Substituting the stated values into the governi... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005006 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +5 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "73.46939 N",
"B": "36.73469 N",
"C": "37.73469 N",
"D": "27.55102 N"
} | B | 36.73469 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(5×10⁻⁶)/(7×10⁻²)²=36.73469 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 36.73469 N, not 73.46939 N.",
"B": "Correct. The worked calculation gives 36.73469 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 36.73469 N, not 37.73469 N.",
"D": "Incorrect. Substitutin... | [
"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_007986 | 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 69 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "6.46875 mmol L⁻¹",
"B": "17.25 mmol L⁻¹",
"C": "8.625 mmol L⁻¹",
"D": "11.625 mmol L⁻¹"
} | C | 8.625 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=69/2^3=8.625 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.625 mmol L⁻¹, not 6.46875 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.625 mmol L⁻¹, not 17.25 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 8.625 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_007004 | 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 269 K and 1.98 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "154.07407 L",
"B": "312.14814 L",
"C": "156.07407 L",
"D": "117.05555 L"
} | C | 156.07407 L | PV=nRT, so V=nRT/P=(14)(0.082057)(269)/(1.98)=156.07407 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 156.07407 L, not 154.07407 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 156.07407 L, not 312.14814 L.",
"C": "Correct. The worked calculation gives 156.07407 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_006803 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 35 mol H₂ and 35 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "-35 mol",
"B": "34 mol",
"C": "4.5 mol",
"D": "35 mol"
} | D | 35 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 35 mol H₂O; O₂ can produce 70 mol H₂O. The limiting condition is H₂; product=35 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 35 mol, not -35 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 35 mol, not 34 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 35 mol, not 4.5 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_009970 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(Cl)_5]^+3, each Cl ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "8",
"B": "11",
"C": "7",
"D": "-8"
} | A | 8 | Let the formal oxidation state of Pd be x. Charge balance gives x+(5)(−1)=+3; hence x=3+5=+8. | {
"A": "Correct. The worked calculation gives 8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 11.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 7.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_010000 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(OH)_3]^+3, each OH ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "6",
"B": "5",
"C": "9",
"D": "-6"
} | A | 6 | Let the formal oxidation state of Fe be x. Charge balance gives x+(3)(−1)=+3; hence x=3+3=+6. | {
"A": "Correct. The worked calculation gives 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"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_003440 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 25 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "54.12659 m",
"B": "55.12659 m",
"C": "-54.12659 m",
"D": "6.41266 m"
} | A | 54.12659 m | Range R=u²sin(2θ)/g. Substituting u=25, θ=60° and g=10 gives R=(25)²sin(120°)/10=54.12659 m. | {
"A": "Correct. The worked calculation gives 54.12659 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 54.12659 m, not 55.12659 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 54.12659 m, not -54.12659 m.",
"D": "Incorrect. Substituti... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006250 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 89 cm in front of a thin convex lens of focal length 27 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.43548",
"B": "-0.43548",
"C": "1.04355",
"D": "2.43548"
} | A | 0.43548 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(89)(27)/(89−27)=38.75806 cm. Thus |m|=v/u=38.75806/89=0.43548. | {
"A": "Correct. The worked calculation gives 0.43548.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.43548, not -0.43548.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.43548, not 1.04355.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002044 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 8 blue and 8 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-2.68923",
"B": "1.03108",
"C": "3.31077",
"D": "0.31077"
} | D | 0.31077 | Favourable pairs = C(10,2)+C(8,2)+C(8,2)=101. Total pairs=C(26,2)=325. Therefore P=101/325=0.31077. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31077, not -2.68923.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31077, not 1.03108.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31077, not 3.31... | [
"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_000959 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio 5. What is the sum of its first 10 terms? | {
"A": "21972652",
"B": "21972656",
"C": "21972653",
"D": "21972654"
} | D | 21972654 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(5^10−1)/(5−1)=21972654. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21972654, not 21972652.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21972654, not 21972656.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21972654, not ... | [
"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_006810 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 49 mol H₂ and 10 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "20 mol",
"B": "18 mol",
"C": "30 mol",
"D": "19 mol"
} | A | 20 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 49 mol H₂O; O₂ can produce 20 mol H₂O. The limiting condition is O₂; product=20 mol. | {
"A": "Correct. The worked calculation gives 20 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20 mol, not 18 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20 mol, not 30 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004134 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 19 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.28. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "35.72 N",
"B": "142.88 N",
"C": "71.44 N",
"D": "-71.44 N"
} | C | 71.44 N | Net force=mg(sinθ−μcosθ)=19×10×(0.6−0.28×0.8)=71.44 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 71.44 N, not 35.72 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 71.44 N, not 142.88 N.",
"C": "Correct. The worked calculation gives 71.44 N.",
"D": "Incorrect. Substituting the stated v... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008906 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.04 mol L⁻¹ and initially B is absent. At equilibrium, 72% of A has dissociated at constant volume. Find K_c. | {
"A": "0.29623",
"B": "2.29623",
"C": "0.14811",
"D": "1.29623"
} | A | 0.29623 | Let α=0.72. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.04)(0.72)²/(1−0.72)=0.29623. | {
"A": "Correct. The worked calculation gives 0.29623.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29623, not 2.29623.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29623, not 0.14811.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006666 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 12 kg is attached to an ideal spring of force constant 566 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.21841 s",
"B": "0.29121 s",
"C": "0.58243 s",
"D": "-1.70879 s"
} | B | 0.29121 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(12/566)=0.29121 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29121 s, not 0.21841 s.",
"B": "Correct. The worked calculation gives 0.29121 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29121 s, not 0.58243 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004160 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 20 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.39. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "6.76 N",
"B": "57.6 N",
"C": "86.4 N",
"D": "43.2 N"
} | B | 57.6 N | Net force=mg(sinθ−μcosθ)=20×10×(0.6−0.39×0.8)=57.6 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 57.6 N, not 6.76 N.",
"B": "Correct. The worked calculation gives 57.6 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 57.6 N, not 86.4 N.",
"D": "Incorrect. Substituting the stated values ... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009278 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.94 V, transfers 3 electrons, and has reaction quotient Q=10^1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.69022 V",
"B": "0.9203 V",
"C": "2.9203 V",
"D": "1.9203 V"
} | B | 0.9203 V | Apply the Nernst equation: E=0.94−(0.0591/3)(1)=0.9203 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9203 V, not 0.69022 V.",
"B": "Correct. The worked calculation gives 0.9203 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9203 V, not 2.9203 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007588 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 31 mL of 0.10 M HCl is mixed with 100 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.27216",
"B": "9.54118",
"C": "10.72158",
"D": "12.72158"
} | D | 12.72158 | Excess OH⁻ moles=0.10×(100−31)/1000=0.006900 mol. Total volume=0.131 L, so [OH⁻]=0.052672 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.72158. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.72158, not 2.27216.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.72158, not 9.54118.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.72158, not 10... | [
"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_004198 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 3 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.26. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "11.76 N",
"B": "12.76 N",
"C": "23.52 N",
"D": "13.76 N"
} | A | 11.76 N | Net force=mg(sinθ−μcosθ)=3×10×(0.6−0.26×0.8)=11.76 N. | {
"A": "Correct. The worked calculation gives 11.76 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.76 N, not 12.76 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.76 N, not 23.52 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_001537 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (1x² -6x -3) dx. | {
"A": "-37.66667",
"B": "-38.66667",
"C": "-39.66667",
"D": "-46.4"
} | B | -38.66667 | An antiderivative is (1/3)x³+(-6/2)x²+(-3)x. Evaluating between 0 and 4 gives (1/3)(4)³+(-6/2)(4)²+(-3)(4)=-38.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -38.66667, not -37.66667.",
"B": "Correct. The worked calculation gives -38.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -38.66667, not -39.66667.",
"D": "Incorrect. Substituting 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_003203 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(13-13i)/(7+12i). What is Re(z), the real part of z? | {
"A": "-0.16839",
"B": "0.66321",
"C": "-0.25259",
"D": "-0.33679"
} | D | -0.33679 | Multiply numerator and denominator by the conjugate (7-12i). Then Re(z)=(ac+bd)/(c²+d²)=((13)(7)+(-13)(12))/(7²+(12)²)=-0.33679. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.33679, not -0.16839.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.33679, not 0.66321.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.33679, not -... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004110 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 28 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.33. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "93.08 N",
"B": "47.04 N",
"C": "94.08 N",
"D": "-94.08 N"
} | C | 94.08 N | Net force=mg(sinθ−μcosθ)=28×10×(0.6−0.33×0.8)=94.08 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 94.08 N, not 93.08 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 94.08 N, not 47.04 N.",
"C": "Correct. The worked calculation gives 94.08 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_003410 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 12 m s⁻¹ at 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "2.41812 m",
"B": "12.18123 m",
"C": "14.18123 m",
"D": "21.27185 m"
} | C | 14.18123 m | Range R=u²sin(2θ)/g. Substituting u=12, θ=40° and g=10 gives R=(12)²sin(80°)/10=14.18123 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14.18123 m, not 2.41812 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14.18123 m, not 12.18123 m.",
"C": "Correct. The worked calculation gives 14.18123 m.",
"D": "Incorrect. Substituting... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002733 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, -3, 1) and v=(2, 2, -1), calculate u·v. | {
"A": "2",
"B": "1.1",
"C": "1",
"D": "1.5"
} | C | 1 | The dot product is the sum of corresponding component products: (4)(2)+(-3)(2)+(1)(-1)=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.1.",
"C": "Correct. The worked calculation gives 1.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"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_002986 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-6, -2, 2) and v=(3, 3, -6), calculate u·v. | {
"A": "-43.2",
"B": "-34",
"C": "-36",
"D": "-72"
} | C | -36 | The dot product is the sum of corresponding component products: (-6)(3)+(-2)(3)+(2)(-6)=-36. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -36, not -43.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -36, not -34.",
"C": "Correct. The worked calculation gives -36.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_009770 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(Cl)_2]^-1, each Cl ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "1",
"B": "2",
"C": "1.5",
"D": "-1"
} | A | 1 | Let the formal oxidation state of Pt be x. Charge balance gives x+(2)(−1)=-1; hence x=-1+2=+1. | {
"A": "Correct. The worked calculation gives 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.5.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005827 | 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 3.8 atm at 238 K. What is its pressure at 598 K? | {
"A": "19.0958 atm",
"B": "9.5479 atm",
"C": "-9.5479 atm",
"D": "7.5479 atm"
} | B | 9.5479 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.8)(598)/(238)=9.5479 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.5479 atm, not 19.0958 atm.",
"B": "Correct. The worked calculation gives 9.5479 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.5479 atm, not -9.5479 atm.",
"D": "Incorrect. Substitut... | [
"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_005150 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +7 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "17.61983 N",
"B": "16.61983 N",
"C": "18.7438 N",
"D": "15.61983 N"
} | D | 15.61983 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(7×10⁻⁶)/(11×10⁻²)²=15.61983 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15.61983 N, not 17.61983 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15.61983 N, not 16.61983 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15.619... | [
"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_006395 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 20 kg is attached to an ideal spring of force constant 148 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.10282 s",
"B": "-0.26479 s",
"C": "0.73521 s",
"D": "-2.26479 s"
} | C | 0.73521 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(20/148)=0.73521 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.73521 s, not 1.10282 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.73521 s, not -0.26479 s.",
"C": "Correct. The worked calculation gives 0.73521 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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