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_004796 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 14 Ω and 2 Ω are connected in series; this combination is connected in parallel with a 15 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.775 A",
"B": "0.775 A",
"C": "0.58125 A",
"D": "-0.775 A"
} | B | 0.775 A | Series branch resistance=14+2=16 Ω. Parallel equivalent R_eq=(16×15)/(16+15)=7.74194 Ω. Total current I=V/R_eq=6/7.74194=0.775 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.775 A, not 3.775 A.",
"B": "Correct. The worked calculation gives 0.775 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.775 A, not 0.58125 A.",
"D": "Incorrect. Substituting the stated ... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005874 | 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 0.6 atm at 410 K. What is its pressure at 630 K? | {
"A": "1.0922 atm",
"B": "-0.92195 atm",
"C": "0.92195 atm",
"D": "0.69146 atm"
} | C | 0.92195 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.6)(630)/(410)=0.92195 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.92195 atm, not 1.0922 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.92195 atm, not -0.92195 atm.",
"C": "Correct. The worked calculation gives 0.92195 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_002243 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 12 red, 10 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.33333",
"B": "0.5",
"C": "-0.66667",
"D": "1.03333"
} | A | 0.33333 | Favourable pairs = C(12,2)+C(10,2)+C(6,2)=126. Total pairs=C(28,2)=378. Therefore P=126/378=0.33333. | {
"A": "Correct. The worked calculation gives 0.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not 0.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not -0.66667.",
"D": "Incorrect. Substituting the stated value... | [
"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_004274 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.40. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "5.6 N",
"B": "2.8 N",
"C": "6.6 N",
"D": "4.2 N"
} | A | 5.6 N | Net force=mg(sinθ−μcosθ)=2×10×(0.6−0.40×0.8)=5.6 N. | {
"A": "Correct. The worked calculation gives 5.6 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.6 N, not 2.8 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.6 N, not 6.6 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_000685 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio -3. What is the sum of its first 11 terms? | {
"A": "88575",
"B": "88572",
"C": "88574",
"D": "106288.8"
} | C | 88574 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(-3^11−1)/(-3−1)=88574. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 88574, not 88575.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 88574, not 88572.",
"C": "Correct. The worked calculation gives 88574.",
"D": "Incorrect. Substituting the stated values into ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003578 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 111 m s⁻¹ at 30° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1067.0299 m",
"B": "1600.54485 m",
"C": "1066.0299 m",
"D": "1069.0299 m"
} | A | 1067.0299 m | Range R=u²sin(2θ)/g. Substituting u=111, θ=30° and g=10 gives R=(111)²sin(60°)/10=1067.0299 m. | {
"A": "Correct. The worked calculation gives 1067.0299 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1067.0299 m, not 1600.54485 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1067.0299 m, not 1066.0299 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_004712 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 11 Ω and 9 Ω are connected in series; this combination is connected in parallel with a 3 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.3 A",
"B": "2.3 A",
"C": "3.45 A",
"D": "4.6 A"
} | B | 2.3 A | Series branch resistance=11+9=20 Ω. Parallel equivalent R_eq=(20×3)/(20+3)=2.6087 Ω. Total current I=V/R_eq=6/2.6087=2.3 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.3 A, not 1.3 A.",
"B": "Correct. The worked calculation gives 2.3 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.3 A, not 3.45 A.",
"D": "Incorrect. Substituting the stated values into... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002891 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(7, 6, -6) and v=(-1, 6, 3), calculate u·v. | {
"A": "11",
"B": "13",
"C": "2.1",
"D": "-11"
} | A | 11 | The dot product is the sum of corresponding component products: (7)(-1)+(6)(6)+(-6)(3)=11. | {
"A": "Correct. The worked calculation gives 11.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11, not 13.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11, not 2.1.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002582 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 6], [4, 5]]. | {
"A": "-7",
"B": "-4",
"C": "-6",
"D": "-8"
} | B | -4 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(5)−(6)(4)=-4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4, not -7.",
"B": "Correct. The worked calculation gives -4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -4, not -6.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007783 | 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 97 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "0.37891 mmol L⁻¹",
"B": "0.75781 mmol L⁻¹",
"C": "1.37891 mmol L⁻¹",
"D": "2.37891 mmol L⁻¹"
} | A | 0.37891 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=97/2^8=0.37891 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 0.37891 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.37891 mmol L⁻¹, not 0.75781 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.37891 mmol L⁻¹, not 1.37891 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_008124 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 8 A for 20445 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "53.81378 g",
"B": "-53.81378 g",
"C": "80.72067 g",
"D": "64.57654 g"
} | A | 53.81378 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×8×20445/(2×96500)=53.81378 g. | {
"A": "Correct. The worked calculation gives 53.81378 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 53.81378 g, not -53.81378 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 53.81378 g, not 80.72067 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001289 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ -6x² -6x+7. Evaluate f′(0). | {
"A": "-7",
"B": "-6",
"C": "-5",
"D": "-3"
} | B | -6 | Differentiate: f′(x)=3(6)x²+2(-6)x+(-6). At x=0, f′(0)=3(6)(0)²+2(-6)(0)+(-6)=-6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -6, not -7.",
"B": "Correct. The worked calculation gives -6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -6, not -5.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_001781 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 4 elements can be selected from a set of 49 distinct elements? | {
"A": "-211876",
"B": "211877",
"C": "158907",
"D": "211876"
} | D | 211876 | Order does not matter, so the count is C(49,4)=49!/[4!(45)!]=211876. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 211876, not -211876.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 211876, not 211877.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 211876, not 158907.",... | [
"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_006061 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 39 cm in front of a thin convex lens of focal length 18 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-2.14286",
"B": "0.85714",
"C": "0.42857",
"D": "-0.14286"
} | B | 0.85714 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(39)(18)/(39−18)=33.42857 cm. Thus |m|=v/u=33.42857/39=0.85714. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.85714, not -2.14286.",
"B": "Correct. The worked calculation gives 0.85714.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.85714, not 0.42857.",
"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_006525 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 22 kg is attached to an ideal spring of force constant 381 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.72089 s",
"B": "0.48059 s",
"C": "-0.48059 s",
"D": "1.48059 s"
} | B | 0.48059 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(22/381)=0.48059 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.48059 s, not 0.72089 s.",
"B": "Correct. The worked calculation gives 0.48059 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.48059 s, not -0.48059 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_004056 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 25 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": "127 N",
"B": "128 N",
"C": "126 N",
"D": "13.6 N"
} | C | 126 N | Net force=mg(sinθ−μcosθ)=25×10×(0.6−0.12×0.8)=126 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 126 N, not 127 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 126 N, not 128 N.",
"C": "Correct. The worked calculation gives 126 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_003070 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-10+4i)/(11+5i). What is Re(z), the real part of z? | {
"A": "-0.61644",
"B": "-1.23288",
"C": "-3.61644",
"D": "-0.92466"
} | A | -0.61644 | Multiply numerator and denominator by the conjugate (11-5i). Then Re(z)=(ac+bd)/(c²+d²)=((-10)(11)+(4)(5))/(11²+(5)²)=-0.61644. | {
"A": "Correct. The worked calculation gives -0.61644.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.61644, not -1.23288.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.61644, not -3.61644.",
"D": "Incorrect. Substituting the stat... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008928 | 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 0.11 mol L⁻¹ and initially B is absent. At equilibrium, 12% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.9928",
"B": "0.0072",
"C": "1.0072",
"D": "0.0054"
} | B | 0.0072 | Let α=0.12. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.11)(0.12)²/(1−0.12)=0.0072. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.0072, not -0.9928.",
"B": "Correct. The worked calculation gives 0.0072.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.0072, not 1.0072.",
"D": "Incorrect. Substituting the stated values... | [
"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_005915 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.2 atm at 233 K. What is its pressure at 426 K? | {
"A": "4.02232 atm",
"B": "2.02232 atm",
"C": "2.01116 atm",
"D": "3.01674 atm"
} | A | 4.02232 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.2)(426)/(233)=4.02232 atm. | {
"A": "Correct. The worked calculation gives 4.02232 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.02232 atm, not 2.02232 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.02232 atm, not 2.01116 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_003956 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 15 kg block initially moves at 0 m s⁻¹. A constant net force does 24 N of work over 4 m in the direction of motion. Find its final kinetic energy. | {
"A": "48 J",
"B": "96 J",
"C": "10.6 J",
"D": "76.8 J"
} | B | 96 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(15)(0)²+(24)(4)=96 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 96 J, not 48 J.",
"B": "Correct. The worked calculation gives 96 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 96 J, not 10.6 J.",
"D": "Incorrect. Substituting the stated values into the... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005861 | 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 3.4 atm at 213 K. What is its pressure at 423 K? | {
"A": "10.12817 atm",
"B": "6.75211 atm",
"C": "7.75211 atm",
"D": "-6.75211 atm"
} | B | 6.75211 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.4)(423)/(213)=6.75211 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.75211 atm, not 10.12817 atm.",
"B": "Correct. The worked calculation gives 6.75211 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.75211 atm, not 7.75211 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008076 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 12 A for 28631 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": "12.30405 g",
"B": "84.7804 g",
"C": "113.04053 g",
"D": "114.04053 g"
} | C | 113.04053 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×12×28631/(2×96500)=113.04053 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 113.04053 g, not 12.30405 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 113.04053 g, not 84.7804 g.",
"C": "Correct. The worked calculation gives 113.04053 g.",
"D": "Incorrect. Substitut... | [
"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_004276 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 31 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.29. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "112.08 N",
"B": "114.08 N",
"C": "-114.08 N",
"D": "113.08 N"
} | B | 114.08 N | Net force=mg(sinθ−μcosθ)=31×10×(0.6−0.29×0.8)=114.08 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 114.08 N, not 112.08 N.",
"B": "Correct. The worked calculation gives 114.08 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 114.08 N, not -114.08 N.",
"D": "Incorrect. Substituting the sta... | [
"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_002112 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 6 blue and 5 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.03099",
"B": "0.23246",
"C": "-1.69006",
"D": "0.30994"
} | D | 0.30994 | Favourable pairs = C(8,2)+C(6,2)+C(5,2)=53. Total pairs=C(19,2)=171. Therefore P=53/171=0.30994. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30994, not 1.03099.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30994, not 0.23246.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30994, not -1.69... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004362 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 4 kg and radius 3 m is acted on by a constant torque of 44 N m about its central axis. Find its angular acceleration. | {
"A": "1.22222 rad s⁻²",
"B": "2.44444 rad s⁻²",
"C": "4.88889 rad s⁻²",
"D": "-2.44444 rad s⁻²"
} | B | 2.44444 rad s⁻² | For a solid disc, I=½MR²=½(4)(3)²=18 kg m². Using τ=Iα, α=44/18=2.44444 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.44444 rad s⁻², not 1.22222 rad s⁻².",
"B": "Correct. The worked calculation gives 2.44444 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.44444 rad s⁻², not 4.88889 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_008237 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 2 A for 7829 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": "-5.15173 g",
"B": "7.72759 g",
"C": "3.86379 g",
"D": "5.15173 g"
} | D | 5.15173 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×2×7829/(2×96500)=5.15173 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.15173 g, not -5.15173 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.15173 g, not 7.72759 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.15173 g... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009331 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.88 V, transfers 3 electrons, and has reaction quotient Q=10^-4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.9588 V",
"B": "-1.0412 V",
"C": "0.9588 V",
"D": "0.7191 V"
} | C | 0.9588 V | Apply the Nernst equation: E=0.88−(0.0591/3)(-4)=0.9588 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9588 V, not -0.9588 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9588 V, not -1.0412 V.",
"C": "Correct. The worked calculation gives 0.9588 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_001277 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ +3x² +3x+7. Evaluate f′(4). | {
"A": "267",
"B": "269",
"C": "534",
"D": "320.4"
} | A | 267 | Differentiate: f′(x)=3(5)x²+2(3)x+(3). At x=4, f′(4)=3(5)(4)²+2(3)(4)+(3)=267. | {
"A": "Correct. The worked calculation gives 267.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 267, not 269.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 267, not 534.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004552 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 3 kg and radius 5 m is acted on by a constant torque of 52 N m about its central axis. Find its angular acceleration. | {
"A": "1.38667 rad s⁻²",
"B": "3.38667 rad s⁻²",
"C": "1.13867 rad s⁻²",
"D": "-1.61333 rad s⁻²"
} | A | 1.38667 rad s⁻² | For a solid disc, I=½MR²=½(3)(5)²=37.5 kg m². Using τ=Iα, α=52/37.5=1.38667 rad s⁻². | {
"A": "Correct. The worked calculation gives 1.38667 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.38667 rad s⁻², not 3.38667 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.38667 rad s⁻², not 1.13867 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_007332 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 16 mol of gas at 427 K and 3 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "149.49691 L",
"B": "373.74228 L",
"C": "186.87114 L",
"D": "280.30671 L"
} | C | 186.87114 L | PV=nRT, so V=nRT/P=(16)(0.082057)(427)/(3)=186.87114 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 186.87114 L, not 149.49691 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 186.87114 L, not 373.74228 L.",
"C": "Correct. The worked calculation gives 186.87114 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_004661 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 14 kg and radius 3 m is acted on by a constant torque of 73 N m about its central axis. Find its angular acceleration. | {
"A": "0.15873 rad s⁻²",
"B": "1.7381 rad s⁻²",
"C": "-0.84127 rad s⁻²",
"D": "1.15873 rad s⁻²"
} | D | 1.15873 rad s⁻² | For a solid disc, I=½MR²=½(14)(3)²=63 kg m². Using τ=Iα, α=73/63=1.15873 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.15873 rad s⁻², not 0.15873 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.15873 rad s⁻², not 1.7381 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing re... | [
"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_005990 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.8 atm at 259 K. What is its pressure at 299 K? | {
"A": "2.23243 atm",
"B": "4.23243 atm",
"C": "3.23243 atm",
"D": "2.42432 atm"
} | C | 3.23243 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.8)(299)/(259)=3.23243 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.23243 atm, not 2.23243 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.23243 atm, not 4.23243 atm.",
"C": "Correct. The worked calculation gives 3.23243 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_004973 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 15 Ω are connected in series; this combination is connected in parallel with a 2 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.44565 A",
"B": "4.8913 A",
"C": "3.26087 A",
"D": "1.32609 A"
} | C | 3.26087 A | Series branch resistance=8+15=23 Ω. Parallel equivalent R_eq=(23×2)/(23+2)=1.84 Ω. Total current I=V/R_eq=6/1.84=3.26087 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.26087 A, not 2.44565 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.26087 A, not 4.8913 A.",
"C": "Correct. The worked calculation gives 3.26087 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_002352 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, 8], [1, -6]]. | {
"A": "-100",
"B": "-48",
"C": "-49",
"D": "-50"
} | D | -50 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(-6)−(8)(1)=-50. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -50, not -100.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -50, not -48.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -50, not -49.",
"D": "Correct. ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000307 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 -2x +8=0, let its roots be α and β. What is α²+β²? | {
"A": "-4.04",
"B": "-6.08",
"C": "-3.04",
"D": "-6.04"
} | C | -3.04 | By Vieta's relations, α+β = 2/5 and αβ = 8/5. Then α²+β²=(α+β)²−2αβ = (2/5)²−2(8/5) = -3.04. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -3.04, not -4.04.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -3.04, not -6.08.",
"C": "Correct. The worked calculation gives -3.04.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_002037 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 9 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.64",
"B": "1.36",
"C": "0.18",
"D": "0.36"
} | D | 0.36 | Favourable pairs = C(4,2)+C(9,2)+C(12,2)=108. Total pairs=C(25,2)=300. Therefore P=108/300=0.36. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.36, not -0.64.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36, not 1.36.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.36, not 0.18.",
"D": "Cor... | [
"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_005679 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.7 atm at 388 K. What is its pressure at 666 K? | {
"A": "6.35103 atm",
"B": "8.35103 atm",
"C": "3.35103 atm",
"D": "3.17552 atm"
} | A | 6.35103 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.7)(666)/(388)=6.35103 atm. | {
"A": "Correct. The worked calculation gives 6.35103 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.35103 atm, not 8.35103 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.35103 atm, not 3.35103 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_009433 | 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_19N_1X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "2",
"B": "4",
"C": "-2",
"D": "5"
} | A | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+1−19−2)/2=2. | {
"A": "Correct. The worked calculation gives 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008117 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 14 A for 21284 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": "10.80387 g",
"B": "78.43099 g",
"C": "97.03874 g",
"D": "98.03874 g"
} | D | 98.03874 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×21284/(2×96500)=98.03874 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 98.03874 g, not 10.80387 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 98.03874 g, not 78.43099 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 98.038... | [
"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_000660 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -12 and common difference 8. Find the sum of its first 27 terms. | {
"A": "1242",
"B": "2485",
"C": "-2484",
"D": "2484"
} | D | 2484 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-12, d=8, n=27: Sₙ=27/2[2(-12)+(27−1)(8)]=2484. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2484, not 1242.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2484, not 2485.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2484, not -2484.",
"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_007074 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 8 mol of gas at 196 K and 1.14 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "135.43724 L",
"B": "111.86436 L",
"C": "112.86436 L",
"D": "12.28644 L"
} | C | 112.86436 L | PV=nRT, so V=nRT/P=(8)(0.082057)(196)/(1.14)=112.86436 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 112.86436 L, not 135.43724 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 112.86436 L, not 111.86436 L.",
"C": "Correct. The worked calculation gives 112.86436 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_000565 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -20 and common difference 3. Find the sum of its first 19 terms. | {
"A": "134",
"B": "133",
"C": "131",
"D": "266"
} | B | 133 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-20, d=3, n=19: Sₙ=19/2[2(-20)+(19−1)(3)]=133. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 133, not 134.",
"B": "Correct. The worked calculation gives 133.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 133, not 131.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001926 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 4 elements can be selected from a set of 77 distinct elements? | {
"A": "1353276",
"B": "1353275",
"C": "2706550",
"D": "1623930"
} | B | 1353275 | Order does not matter, so the count is C(77,4)=77!/[4!(73)!]=1353275. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1353275, not 1353276.",
"B": "Correct. The worked calculation gives 1353275.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1353275, not 2706550.",
"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_006523 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 18 kg is attached to an ideal spring of force constant 1165 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.7514 s",
"B": "0.1243 s",
"C": "0.2486 s",
"D": "-0.2486 s"
} | C | 0.2486 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(18/1165)=0.2486 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.2486 s, not -2.7514 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.2486 s, not 0.1243 s.",
"C": "Correct. The worked calculation gives 0.2486 s.",
"D": "Incorrect. Substituting the sta... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009878 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(CN)_5]^-4, each CN ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "1",
"B": "0.75",
"C": "1.1",
"D": "4"
} | A | 1 | Let the formal oxidation state of Cu be x. Charge balance gives x+(5)(−1)=-4; hence x=-4+5=+1. | {
"A": "Correct. The worked calculation gives 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.1.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_003433 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 70 m s⁻¹ at 70° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "472.44889 m",
"B": "315.96593 m",
"C": "314.96593 m",
"D": "236.22445 m"
} | C | 314.96593 m | Range R=u²sin(2θ)/g. Substituting u=70, θ=70° and g=10 gives R=(70)²sin(140°)/10=314.96593 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 314.96593 m, not 472.44889 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 314.96593 m, not 315.96593 m.",
"C": "Correct. The worked calculation gives 314.96593 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005943 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.3 atm at 340 K. What is its pressure at 741 K? | {
"A": "8.01265 atm",
"B": "7.01265 atm",
"C": "5.01265 atm",
"D": "7.51897 atm"
} | C | 5.01265 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.3)(741)/(340)=5.01265 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.01265 atm, not 8.01265 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.01265 atm, not 7.01265 atm.",
"C": "Correct. The worked calculation gives 5.01265 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_007805 | 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 10 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "6 mmol L⁻¹",
"B": "5 mmol L⁻¹",
"C": "2.5 mmol L⁻¹",
"D": "7 mmol L⁻¹"
} | B | 5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=10/2^1=5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5 mmol L⁻¹, not 6 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5 mmol L⁻¹, not 2.5 mmol L⁻¹.",
"D": "Incorrect. Substitut... | [
"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_002367 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, 5], [7, -5]]. | {
"A": "-76",
"B": "-6.5",
"C": "75",
"D": "-75"
} | D | -75 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(-5)−(5)(7)=-75. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -75, not -76.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -75, not -6.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -75, not 75.",
"D": "Correct. T... | [
"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_009720 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(OH)_3]^-1, each OH ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "1.5",
"B": "2",
"C": "4",
"D": "1"
} | B | 2 | Let the formal oxidation state of Cr be x. Charge balance gives x+(3)(−1)=-1; hence x=-1+3=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.5.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 4.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005276 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +4 μC and +1 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "92 N",
"B": "135 N",
"C": "90 N",
"D": "72 N"
} | C | 90 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(4×10⁻⁶)(1×10⁻⁶)/(2×10⁻²)²=90 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 90 N, not 92 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 90 N, not 135 N.",
"C": "Correct. The worked calculation gives 90 N.",
"D": "Incorrect. Substituting the stated values into 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_001517 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (0x² +8x -5) dx. | {
"A": "7",
"B": "5",
"C": "6",
"D": "1.6"
} | C | 6 | An antiderivative is (0/3)x³+(8/2)x²+(-5)x. Evaluating between 0 and 2 gives (0/3)(2)³+(8/2)(2)²+(-5)(2)=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 5.",
"C": "Correct. The worked calculation gives 6.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_009274 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.74 V, transfers 3 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.6415 V",
"B": "1.283 V",
"C": "0.32075 V",
"D": "0.96225 V"
} | A | 0.6415 V | Apply the Nernst equation: E=0.74−(0.0591/3)(5)=0.6415 V. | {
"A": "Correct. The worked calculation gives 0.6415 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6415 V, not 1.283 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.6415 V, not 0.32075 V.",
"D": "Incorrect. Substituting the stat... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002771 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(3, 8, 0) and v=(6, 3, 7), calculate u·v. | {
"A": "50.4",
"B": "5.2",
"C": "-42",
"D": "42"
} | D | 42 | The dot product is the sum of corresponding component products: (3)(6)+(8)(3)+(0)(7)=42. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 42, not 50.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 42, not 5.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 42, not -42.",
"D": "Correct. The... | [
"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_001444 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (-2x² +0x +1) dx. | {
"A": "-140",
"B": "-137",
"C": "-12.8",
"D": "-138"
} | D | -138 | An antiderivative is (-2/3)x³+(0/2)x²+(1)x. Evaluating between 0 and 6 gives (-2/3)(6)³+(0/2)(6)²+(1)(6)=-138. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -138, not -140.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -138, not -137.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -138, not -12.8.",
"D": "Cor... | [
"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_000219 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +16x -10=0, let its roots be α and β. What is α²+β²? | {
"A": "13.24",
"B": "28.48",
"C": "15.24",
"D": "14.24"
} | D | 14.24 | By Vieta's relations, α+β = -16/5 and αβ = -10/5. Then α²+β²=(α+β)²−2αβ = (-16/5)²−2(-10/5) = 14.24. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14.24, not 13.24.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14.24, not 28.48.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14.24, not 15.24.",
"D":... | [
"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_002078 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 4 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.42308",
"B": "0.5641",
"C": "0.28205",
"D": "0.14103"
} | C | 0.28205 | Favourable pairs = C(5,2)+C(4,2)+C(4,2)=22. Total pairs=C(13,2)=78. Therefore P=22/78=0.28205. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.28205, not 0.42308.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.28205, not 0.5641.",
"C": "Correct. The worked calculation gives 0.28205.",
"D": "Incorrect. Substituting the stated val... | [
"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_000364 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -19 and common difference 8. Find the sum of its first 19 terms. | {
"A": "1510.5",
"B": "1007",
"C": "1009",
"D": "-1007"
} | B | 1007 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-19, d=8, n=19: Sₙ=19/2[2(-19)+(19−1)(8)]=1007. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1007, not 1510.5.",
"B": "Correct. The worked calculation gives 1007.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1007, not 1009.",
"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_006003 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.4 atm at 375 K. What is its pressure at 469 K? | {
"A": "1.75093 atm",
"B": "2.6264 atm",
"C": "0.87547 atm",
"D": "-0.24907 atm"
} | A | 1.75093 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.4)(469)/(375)=1.75093 atm. | {
"A": "Correct. The worked calculation gives 1.75093 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.75093 atm, not 2.6264 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.75093 atm, not 0.87547 atm.",
"D": "Incorrect. Substit... | [
"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_007919 | 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 47 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "4.40625 mmol L⁻¹",
"B": "5.875 mmol L⁻¹",
"C": "2.875 mmol L⁻¹",
"D": "2.9375 mmol L⁻¹"
} | B | 5.875 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=47/2^3=5.875 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.875 mmol L⁻¹, not 4.40625 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 5.875 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.875 mmol L⁻¹, not 2.875 mmol L⁻¹.",
"D": "... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005102 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +7 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "11.66667 N",
"B": "17.55556 N",
"C": "15.55556 N",
"D": "31.11111 N"
} | C | 15.55556 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(7×10⁻⁶)/(9×10⁻²)²=15.55556 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15.55556 N, not 11.66667 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15.55556 N, not 17.55556 N.",
"C": "Correct. The worked calculation gives 15.55556 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_003377 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 27 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "7.31333 m",
"B": "50.5066 m",
"C": "63.13325 m",
"D": "61.13325 m"
} | C | 63.13325 m | Range R=u²sin(2θ)/g. Substituting u=27, θ=60° and g=10 gives R=(27)²sin(120°)/10=63.13325 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 63.13325 m, not 7.31333 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 63.13325 m, not 50.5066 m.",
"C": "Correct. The worked calculation gives 63.13325 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_008007 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 3 A for 21062 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": "31.18376 g",
"B": "22.78918 g",
"C": "-20.78918 g",
"D": "20.78918 g"
} | D | 20.78918 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×3×21062/(2×96500)=20.78918 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20.78918 g, not 31.18376 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20.78918 g, not 22.78918 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20.789... | [
"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_003453 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 30 m s⁻¹ at 35° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "42.28617 m",
"B": "84.57234 m",
"C": "101.4868 m",
"D": "83.57234 m"
} | B | 84.57234 m | Range R=u²sin(2θ)/g. Substituting u=30, θ=35° and g=10 gives R=(30)²sin(70°)/10=84.57234 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 84.57234 m, not 42.28617 m.",
"B": "Correct. The worked calculation gives 84.57234 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 84.57234 m, not 101.4868 m.",
"D": "Incorrect. Substitutin... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004455 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 8 kg and radius 3 m is acted on by a constant torque of 77 N m about its central axis. Find its angular acceleration. | {
"A": "2.13889 rad s⁻²",
"B": "1.60417 rad s⁻²",
"C": "4.13889 rad s⁻²",
"D": "0.13889 rad s⁻²"
} | A | 2.13889 rad s⁻² | For a solid disc, I=½MR²=½(8)(3)²=36 kg m². Using τ=Iα, α=77/36=2.13889 rad s⁻². | {
"A": "Correct. The worked calculation gives 2.13889 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.13889 rad s⁻², not 1.60417 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.13889 rad s⁻², not 4.13889 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_005222 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +8 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "1620 N",
"B": "1944 N",
"C": "1619 N",
"D": "1296 N"
} | A | 1620 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(8×10⁻⁶)/(2×10⁻²)²=1620 N. | {
"A": "Correct. The worked calculation gives 1620 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1620 N, not 1944 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1620 N, not 1619 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_008587 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.53 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-2.7244 K",
"B": "-0.7244 K",
"C": "0.2756 K",
"D": "0.5512 K"
} | C | 0.2756 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.52×0.53=0.2756 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.2756 K, not -2.7244 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.2756 K, not -0.7244 K.",
"C": "Correct. The worked calculation gives 0.2756 K.",
"D": "Incorrect. Substituting the st... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008591 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.34 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-2.796 K",
"B": "1.204 K",
"C": "0.204 K",
"D": "2.204 K"
} | C | 0.204 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×0.6×0.34=0.204 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.204 K, not -2.796 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.204 K, not 1.204 K.",
"C": "Correct. The worked calculation gives 0.204 K.",
"D": "Incorrect. Substituting the stated v... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004062 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 34 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.15. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "130.56 N",
"B": "244.8 N",
"C": "17.32 N",
"D": "163.2 N"
} | D | 163.2 N | Net force=mg(sinθ−μcosθ)=34×10×(0.6−0.15×0.8)=163.2 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 163.2 N, not 130.56 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 163.2 N, not 244.8 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 163.2 N, not 17.3... | [
"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_006423 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 9 kg is attached to an ideal spring of force constant 944 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-1.80472 s",
"B": "-2.80472 s",
"C": "2.19528 s",
"D": "0.19528 s"
} | D | 0.19528 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(9/944)=0.19528 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.19528 s, not -1.80472 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.19528 s, not -2.80472 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.19528 ... | [
"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_000694 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio 5. What is the sum of its first 10 terms? | {
"A": "12207032",
"B": "9765624",
"C": "9155272.5",
"D": "12207030"
} | D | 12207030 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(5^10−1)/(5−1)=12207030. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12207030, not 12207032.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12207030, not 9765624.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12207030, not 9... | [
"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_004323 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 22 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.44. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "54.56 N",
"B": "52.56 N",
"C": "109.12 N",
"D": "-54.56 N"
} | A | 54.56 N | Net force=mg(sinθ−μcosθ)=22×10×(0.6−0.44×0.8)=54.56 N. | {
"A": "Correct. The worked calculation gives 54.56 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 54.56 N, not 52.56 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 54.56 N, not 109.12 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_001351 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (0x² -3x +2) dx. | {
"A": "59.5",
"B": "-71.4",
"C": "-59.5",
"D": "-119"
} | C | -59.5 | An antiderivative is (0/3)x³+(-3/2)x²+(2)x. Evaluating between 0 and 7 gives (0/3)(7)³+(-3/2)(7)²+(2)(7)=-59.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -59.5, not 59.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -59.5, not -71.4.",
"C": "Correct. The worked calculation gives -59.5.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_009519 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_10H_6X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "3",
"B": "5",
"C": "12",
"D": "6"
} | D | 6 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×10+2+0−6−4)/2=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"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 12.",
"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_007185 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 15 mol of gas at 433 K and 1.48 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "720.21651 L",
"B": "360.10825 L",
"C": "270.08119 L",
"D": "359.10825 L"
} | B | 360.10825 L | PV=nRT, so V=nRT/P=(15)(0.082057)(433)/(1.48)=360.10825 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 360.10825 L, not 720.21651 L.",
"B": "Correct. The worked calculation gives 360.10825 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 360.10825 L, not 270.08119 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_001973 | 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 34 distinct elements? | {
"A": "-548354040",
"B": "438683232",
"C": "548354040",
"D": "274177020"
} | C | 548354040 | Order does not matter, so the count is C(34,12)=34!/[12!(22)!]=548354040. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 548354040, not -548354040.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 548354040, not 438683232.",
"C": "Correct. The worked calculation gives 548354040.",
"D": "Incorrect. Substituting th... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004976 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 8 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 16 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.45739 A",
"B": "1.94318 A",
"C": "0.97159 A",
"D": "-0.02841 A"
} | C | 0.97159 A | Series branch resistance=8+14=22 Ω. Parallel equivalent R_eq=(22×16)/(22+16)=9.26316 Ω. Total current I=V/R_eq=9/9.26316=0.97159 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.97159 A, not 1.45739 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.97159 A, not 1.94318 A.",
"C": "Correct. The worked calculation gives 0.97159 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_000328 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +3x +11=0, let its roots be α and β. What is α²+β²? | {
"A": "-5.04",
"B": "-3.04",
"C": "-6.04",
"D": "-4.04"
} | D | -4.04 | By Vieta's relations, α+β = -3/5 and αβ = 11/5. Then α²+β²=(α+β)²−2αβ = (-3/5)²−2(11/5) = -4.04. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4.04, not -5.04.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -4.04, not -3.04.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -4.04, not -6.04.",
"D":... | [
"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_000285 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +6x -10=0, let its roots be α and β. What is α²+β²? | {
"A": "8.44",
"B": "3.44",
"C": "5.44",
"D": "2.72"
} | C | 5.44 | By Vieta's relations, α+β = -6/5 and αβ = -10/5. Then α²+β²=(α+β)²−2αβ = (-6/5)²−2(-10/5) = 5.44. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.44, not 8.44.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.44, not 3.44.",
"C": "Correct. The worked calculation gives 5.44.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_006361 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 15 kg is attached to an ideal spring of force constant 764 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-2.71976 s",
"B": "1.28024 s",
"C": "0.42036 s",
"D": "0.28024 s"
} | D | 0.28024 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(15/764)=0.28024 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.28024 s, not -2.71976 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.28024 s, not 1.28024 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.28024 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009927 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(OH)_5]^+3, each OH ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "12",
"B": "7",
"C": "8",
"D": "10"
} | C | 8 | Let the formal oxidation state of Co be x. Charge balance gives x+(5)(−1)=+3; hence x=3+5=+8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 12.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 7.",
"C": "Correct. The worked calculation gives 8.",
"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_001275 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-4x³ +10x² +6x+7. Evaluate f′(3). | {
"A": "-33.6",
"B": "-42",
"C": "-41",
"D": "-63"
} | B | -42 | Differentiate: f′(x)=3(-4)x²+2(10)x+(6). At x=3, f′(3)=3(-4)(3)²+2(10)(3)+(6)=-42. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -42, not -33.6.",
"B": "Correct. The worked calculation gives -42.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -42, not -41.",
"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_002021 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 7 blue and 7 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.0303",
"B": "0.15152",
"C": "0.30303",
"D": "0.22727"
} | C | 0.30303 | Favourable pairs = C(8,2)+C(7,2)+C(7,2)=70. Total pairs=C(22,2)=231. Therefore P=70/231=0.30303. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30303, not 1.0303.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30303, not 0.15152.",
"C": "Correct. The worked calculation gives 0.30303.",
"D": "Incorrect. Substituting the stated val... | [
"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_005033 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +2 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "315 N",
"B": "378 N",
"C": "314 N",
"D": "316 N"
} | A | 315 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(2×10⁻⁶)/(2×10⁻²)²=315 N. | {
"A": "Correct. The worked calculation gives 315 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 315 N, not 378 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 315 N, not 314 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006771 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 33 mol H₂ and 3 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "7 mol",
"B": "3 mol",
"C": "9 mol",
"D": "6 mol"
} | D | 6 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 33 mol H₂O; O₂ can produce 6 mol H₂O. The limiting condition is O₂; product=6 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 7 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 3 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 9 mol.",
"D":... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003025 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(9-6i)/(3+2i). What is Re(z), the real part of z? | {
"A": "1.15385",
"B": "-0.84615",
"C": "-1.84615",
"D": "1.73077"
} | A | 1.15385 | Multiply numerator and denominator by the conjugate (3-2i). Then Re(z)=(ac+bd)/(c²+d²)=((9)(3)+(-6)(2))/(3²+(2)²)=1.15385. | {
"A": "Correct. The worked calculation gives 1.15385.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.15385, not -0.84615.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.15385, not -1.84615.",
"D": "Incorrect. Substituting the stated ... | [
"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_000080 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +13x -7=0, let its roots be α and β. What is α²+β²? | {
"A": "25.44444",
"B": "24.44444",
"C": "11.72222",
"D": "23.44444"
} | D | 23.44444 | By Vieta's relations, α+β = -13/3 and αβ = -7/3. Then α²+β²=(α+β)²−2αβ = (-13/3)²−2(-7/3) = 23.44444. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 23.44444, not 25.44444.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23.44444, not 24.44444.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23.44444, not ... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001752 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 9 elements can be selected from a set of 33 distinct elements? | {
"A": "38567098",
"B": "3856711",
"C": "38567100",
"D": "57850650"
} | C | 38567100 | Order does not matter, so the count is C(33,9)=33!/[9!(24)!]=38567100. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 38567100, not 38567098.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 38567100, not 3856711.",
"C": "Correct. The worked calculation gives 38567100.",
"D": "Incorrect. Substituting the state... | [
"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_007416 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 68 mL of 0.10 M HCl is mixed with 41 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-1.39394",
"B": "2.40909",
"C": "1.60606",
"D": "3.21213"
} | C | 1.60606 | Excess H⁺ moles=0.10×(68−41)/1000=0.002700 mol. Total volume=0.109 L, so [H⁺]=0.024771 M and pH=−log₁₀[H⁺]=1.60606. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.60606, not -1.39394.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.60606, not 2.40909.",
"C": "Correct. The worked calculation gives 1.60606.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008500 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.83 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "4.2948 K",
"B": "3.2948 K",
"C": "2.2948 K",
"D": "1.2948 K"
} | D | 1.2948 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.52×0.83=1.2948 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.2948 K, not 4.2948 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.2948 K, not 3.2948 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2948 K, not ... | [
"colligative properties",
"van't Hoff factor",
"molality"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_boiling_elevation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001698 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 3 elements can be selected from a set of 75 distinct elements? | {
"A": "67525",
"B": "-67525",
"C": "33762.5",
"D": "101287.5"
} | A | 67525 | Order does not matter, so the count is C(75,3)=75!/[3!(72)!]=67525. | {
"A": "Correct. The worked calculation gives 67525.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 67525, not -67525.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 67525, not 33762.5.",
"D": "Incorrect. Substituting the stated values in... | [
"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_008029 | 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 5 A for 17074 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": "28.08806 g",
"B": "29.08806 g",
"C": "33.70567 g",
"D": "56.17611 g"
} | A | 28.08806 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×5×17074/(2×96500)=28.08806 g. | {
"A": "Correct. The worked calculation gives 28.08806 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28.08806 g, not 29.08806 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28.08806 g, not 33.70567 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002944 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-5, 6, 4) and v=(7, -1, 8), calculate u·v. | {
"A": "-7",
"B": "-9",
"C": "-4.5",
"D": "-11"
} | B | -9 | The dot product is the sum of corresponding component products: (-5)(7)+(6)(-1)+(4)(8)=-9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -9, not -7.",
"B": "Correct. The worked calculation gives -9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -9, not -4.5.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003114 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-14-14i)/(12+6i). What is Re(z), the real part of z? | {
"A": "-3.4",
"B": "0.86",
"C": "-2.4",
"D": "-1.4"
} | D | -1.4 | Multiply numerator and denominator by the conjugate (12-6i). Then Re(z)=(ac+bd)/(c²+d²)=((-14)(12)+(-14)(6))/(12²+(6)²)=-1.4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1.4, not -3.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.4, not 0.86.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.4, not -2.4.",
"D": "Corr... | [
"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_005652 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 79 μF capacitor is charged to a potential difference of 17 V. Calculate the energy stored, expressed in μJ. | {
"A": "13698.6 μJ",
"B": "11415.5 μJ",
"C": "9132.4 μJ",
"D": "-11415.5 μJ"
} | B | 11415.5 μJ | U=½CV². Since C=79 μF, U in μJ is ½×79×(17)²=11415.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11415.5 μJ, not 13698.6 μJ.",
"B": "Correct. The worked calculation gives 11415.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11415.5 μJ, not 9132.4 μJ.",
"D": "Incorrect. Substituting... | [
"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_006026 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 45 cm in front of a thin convex lens of focal length 30 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "3",
"B": "1.5",
"C": "0",
"D": "2"
} | D | 2 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(45)(30)/(45−30)=90 cm. Thus |m|=v/u=90/45=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 0.",
"D": "Correct. The worked ... | [
"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_000560 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -4 and common difference 12. Find the sum of its first 29 terms. | {
"A": "2378",
"B": "4755",
"C": "3804.8",
"D": "4756"
} | D | 4756 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-4, d=12, n=29: Sₙ=29/2[2(-4)+(29−1)(12)]=4756. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4756, not 2378.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4756, not 4755.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4756, not 3804.8.",
"D": "Co... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000036 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 -9x -3=0, let its roots be α and β. What is α²+β²? | {
"A": "11",
"B": "22",
"C": "12",
"D": "16.5"
} | A | 11 | By Vieta's relations, α+β = 9/3 and αβ = -3/3. Then α²+β²=(α+β)²−2αβ = (9/3)²−2(-3/3) = 11. | {
"A": "Correct. The worked calculation gives 11.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11, not 22.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11, not 12.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_009286 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.09 V, transfers 1 electrons, and has reaction quotient Q=10^-4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.6736 V",
"B": "0.6632 V",
"C": "1.3264 V",
"D": "0.9948 V"
} | C | 1.3264 V | Apply the Nernst equation: E=1.09−(0.0591/1)(-4)=1.3264 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.3264 V, not -1.6736 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.3264 V, not 0.6632 V.",
"C": "Correct. The worked calculation gives 1.3264 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_006317 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 70 cm in front of a thin convex lens of focal length 22 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.45833",
"B": "1.45833",
"C": "-2.54167",
"D": "0.22917"
} | A | 0.45833 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(70)(22)/(70−22)=32.08333 cm. Thus |m|=v/u=32.08333/70=0.45833. | {
"A": "Correct. The worked calculation gives 0.45833.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.45833, not 1.45833.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.45833, not -2.54167.",
"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 |
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