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_000250 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 +14x -1=0, let its roots be α and β. What is α²+β²? | {
"A": "50",
"B": "40",
"C": "100",
"D": "25"
} | A | 50 | By Vieta's relations, α+β = -14/2 and αβ = -1/2. Then α²+β²=(α+β)²−2αβ = (-14/2)²−2(-1/2) = 50. | {
"A": "Correct. The worked calculation gives 50.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 50, not 40.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 50, not 100.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"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_000199 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 +10x +4=0, let its roots be α and β. What is α²+β²? | {
"A": "21",
"B": "20",
"C": "31.5",
"D": "19"
} | A | 21 | By Vieta's relations, α+β = -10/2 and αβ = 4/2. Then α²+β²=(α+β)²−2αβ = (-10/2)²−2(4/2) = 21. | {
"A": "Correct. The worked calculation gives 21.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21, not 20.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 21, not 31.5.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"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_004208 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 27 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.35. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "69.12 N",
"B": "86.4 N",
"C": "9.64 N",
"D": "64.8 N"
} | B | 86.4 N | Net force=mg(sinθ−μcosθ)=27×10×(0.6−0.35×0.8)=86.4 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 86.4 N, not 69.12 N.",
"B": "Correct. The worked calculation gives 86.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 86.4 N, not 9.64 N.",
"D": "Incorrect. Substituting the stated values... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006406 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 16 kg is attached to an ideal spring of force constant 344 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.56867 s",
"B": "-1.56867 s",
"C": "0.43133 s",
"D": "2.43133 s"
} | C | 0.43133 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(16/344)=0.43133 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.43133 s, not -0.56867 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.43133 s, not -1.56867 s.",
"C": "Correct. The worked calculation gives 0.43133 s.",
"D": "Incorrect. Substituting t... | [
"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_003175 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-7-7i)/(11+2i). What is Re(z), the real part of z? | {
"A": "-0.364",
"B": "0.9272",
"C": "-0.728",
"D": "1.272"
} | C | -0.728 | Multiply numerator and denominator by the conjugate (11-2i). Then Re(z)=(ac+bd)/(c²+d²)=((-7)(11)+(-7)(2))/(11²+(2)²)=-0.728. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.728, not -0.364.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.728, not 0.9272.",
"C": "Correct. The worked calculation gives -0.728.",
"D": "Incorrect. Substituting the stated values ... | [
"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_008518 | 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 3 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.08268 K",
"B": "-1.1732 K",
"C": "0.8268 K",
"D": "1.8268 K"
} | C | 0.8268 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.52×0.53=0.8268 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8268 K, not 1.08268 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8268 K, not -1.1732 K.",
"C": "Correct. The worked calculation gives 0.8268 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_004751 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 12 Ω and 4 Ω are connected in series; this combination is connected in parallel with a 16 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.75 A",
"B": "3.75 A",
"C": "0.75 A",
"D": "-1.25 A"
} | C | 0.75 A | Series branch resistance=12+4=16 Ω. Parallel equivalent R_eq=(16×16)/(16+16)=8 Ω. Total current I=V/R_eq=6/8=0.75 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.75 A, not 1.75 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.75 A, not 3.75 A.",
"C": "Correct. The worked calculation gives 0.75 A.",
"D": "Incorrect. Substituting the stated values ... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008811 | 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, 80% of A has dissociated at constant volume. Find K_c. | {
"A": "1.408",
"B": "2.112",
"C": "4.408",
"D": "-1.592"
} | A | 1.408 | Let α=0.8. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.11)(0.8)²/(1−0.8)=1.408. | {
"A": "Correct. The worked calculation gives 1.408.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.408, not 2.112.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.408, not 4.408.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_007507 | 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 14 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "0.59071",
"B": "2.18142",
"C": "3.18142",
"D": "1.18142"
} | D | 1.18142 | Excess H⁺ moles=0.10×(68−14)/1000=0.005400 mol. Total volume=0.082 L, so [H⁺]=0.065854 M and pH=−log₁₀[H⁺]=1.18142. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.18142, not 0.59071.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.18142, not 2.18142.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.18142, not 3.181... | [
"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_003168 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(15-9i)/(8+11i). What is Re(z), the real part of z? | {
"A": "0.05676",
"B": "0.22703",
"C": "3.11351",
"D": "0.11351"
} | D | 0.11351 | Multiply numerator and denominator by the conjugate (8-11i). Then Re(z)=(ac+bd)/(c²+d²)=((15)(8)+(-9)(11))/(8²+(11)²)=0.11351. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.11351, not 0.05676.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.11351, not 0.22703.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.11351, not 3.113... | [
"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_006302 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 46 cm in front of a thin convex lens of focal length 14 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "3.4375",
"B": "0.875",
"C": "0.4375",
"D": "0.65625"
} | C | 0.4375 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(46)(14)/(46−14)=20.125 cm. Thus |m|=v/u=20.125/46=0.4375. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.4375, not 3.4375.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.4375, not 0.875.",
"C": "Correct. The worked calculation gives 0.4375.",
"D": "Incorrect. Substituting the stated values i... | [
"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_009047 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.14 V, transfers 1 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.3173 V",
"B": "1.3173 V",
"C": "2.3173 V",
"D": "2.6346 V"
} | B | 1.3173 V | Apply the Nernst equation: E=1.14−(0.0591/1)(-3)=1.3173 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.3173 V, not 0.3173 V.",
"B": "Correct. The worked calculation gives 1.3173 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.3173 V, not 2.3173 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_003300 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-14+6i)/(10+11i). What is Re(z), the real part of z? | {
"A": "0.96652",
"B": "-0.33484",
"C": "2.66516",
"D": "-0.50226"
} | B | -0.33484 | Multiply numerator and denominator by the conjugate (10-11i). Then Re(z)=(ac+bd)/(c²+d²)=((-14)(10)+(6)(11))/(10²+(11)²)=-0.33484. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.33484, not 0.96652.",
"B": "Correct. The worked calculation gives -0.33484.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.33484, not 2.66516.",
"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_003099 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(2+0i)/(11+2i). What is Re(z), the real part of z? | {
"A": "0.176",
"B": "2.176",
"C": "0.352",
"D": "3.176"
} | A | 0.176 | Multiply numerator and denominator by the conjugate (11-2i). Then Re(z)=(ac+bd)/(c²+d²)=((2)(11)+(0)(2))/(11²+(2)²)=0.176. | {
"A": "Correct. The worked calculation gives 0.176.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.176, not 2.176.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.176, not 0.352.",
"D": "Incorrect. Substituting the stated values into ... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004558 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 14 kg and radius 6 m is acted on by a constant torque of 91 N m about its central axis. Find its angular acceleration. | {
"A": "0.27083 rad s⁻²",
"B": "0.54167 rad s⁻²",
"C": "0.36111 rad s⁻²",
"D": "-0.36111 rad s⁻²"
} | C | 0.36111 rad s⁻² | For a solid disc, I=½MR²=½(14)(6)²=252 kg m². Using τ=Iα, α=91/252=0.36111 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.36111 rad s⁻², not 0.27083 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36111 rad s⁻², not 0.54167 rad s⁻².",
"C": "Correct. The worked calculation gives 0.36111 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_006054 | 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 23 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.04545",
"B": "0.78409",
"C": "4.04545",
"D": "3.04545"
} | A | 1.04545 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(45)(23)/(45−23)=47.04545 cm. Thus |m|=v/u=47.04545/45=1.04545. | {
"A": "Correct. The worked calculation gives 1.04545.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.04545, not 0.78409.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.04545, not 4.04545.",
"D": "Incorrect. Substituting the stated va... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001159 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=4x³ +5x² -10x+7. Evaluate f′(-3). | {
"A": "-68",
"B": "68",
"C": "102",
"D": "54.4"
} | B | 68 | Differentiate: f′(x)=3(4)x²+2(5)x+(-10). At x=-3, f′(-3)=3(4)(-3)²+2(5)(-3)+(-10)=68. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 68, not -68.",
"B": "Correct. The worked calculation gives 68.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 68, not 102.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"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_009848 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Fe(Cl)_6]^-3, each Cl ligand has charge −1. Determine the formal oxidation state of Fe. | {
"A": "2.25",
"B": "5",
"C": "2",
"D": "3"
} | D | 3 | Let the formal oxidation state of Fe be x. Charge balance gives x+(6)(−1)=-3; hence x=-3+6=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not 5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 2.",
"D": "Correct. The worked... | [
"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_002866 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(0, 1, 2) and v=(9, 1, 8), calculate u·v. | {
"A": "34",
"B": "19",
"C": "-17",
"D": "17"
} | D | 17 | The dot product is the sum of corresponding component products: (0)(9)+(1)(1)+(2)(8)=17. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 17, not 34.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17, not 19.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17, not -17.",
"D": "Correct. The wo... | [
"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_000603 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 5 and common difference 12. Find the sum of its first 26 terms. | {
"A": "4030",
"B": "8060",
"C": "4032",
"D": "3224"
} | A | 4030 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=5, d=12, n=26: Sₙ=26/2[2(5)+(26−1)(12)]=4030. | {
"A": "Correct. The worked calculation gives 4030.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4030, not 8060.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4030, not 4032.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009034 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.97 V, transfers 3 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.0094 V",
"B": "-1.0094 V",
"C": "-0.9906 V",
"D": "0.75705 V"
} | A | 1.0094 V | Apply the Nernst equation: E=0.97−(0.0591/3)(-2)=1.0094 V. | {
"A": "Correct. The worked calculation gives 1.0094 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0094 V, not -1.0094 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.0094 V, not -0.9906 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_005832 | 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 atm at 202 K. What is its pressure at 340 K? | {
"A": "3.36634 atm",
"B": "5.36634 atm",
"C": "5.0495 atm",
"D": "6.73267 atm"
} | A | 3.36634 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2)(340)/(202)=3.36634 atm. | {
"A": "Correct. The worked calculation gives 3.36634 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.36634 atm, not 5.36634 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.36634 atm, not 5.0495 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_003824 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block initially moves at 12 m s⁻¹. A constant net force does 24 N of work over 2 m in the direction of motion. Find its final kinetic energy. | {
"A": "408 J",
"B": "612 J",
"C": "41.8 J",
"D": "489.6 J"
} | A | 408 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(5)(12)²+(24)(2)=408 J. | {
"A": "Correct. The worked calculation gives 408 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 408 J, not 612 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 408 J, not 41.8 J.",
"D": "Incorrect. Substituting the stated values into... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000714 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 8 and common ratio 5. What is the sum of its first 10 terms? | {
"A": "14648436",
"B": "19531248",
"C": "19531246",
"D": "29296872"
} | B | 19531248 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=8(5^10−1)/(5−1)=19531248. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19531248, not 14648436.",
"B": "Correct. The worked calculation gives 19531248.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19531248, not 19531246.",
"D": "Incorrect. Substituting the stat... | [
"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_004263 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 20 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.30. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "-72 N",
"B": "72 N",
"C": "144 N",
"D": "8.2 N"
} | B | 72 N | Net force=mg(sinθ−μcosθ)=20×10×(0.6−0.30×0.8)=72 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 72 N, not -72 N.",
"B": "Correct. The worked calculation gives 72 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 72 N, not 144 N.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_002554 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, 7], [4, -8]]. | {
"A": "-57",
"B": "-6.6",
"C": "-74",
"D": "-76"
} | D | -76 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(-8)−(7)(4)=-76. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -76, not -57.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -76, not -6.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -76, not -74.",
"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_004030 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 32 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.27. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "92.16 N",
"B": "61.44 N",
"C": "122.88 N",
"D": "124.88 N"
} | C | 122.88 N | Net force=mg(sinθ−μcosθ)=32×10×(0.6−0.27×0.8)=122.88 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 122.88 N, not 92.16 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 122.88 N, not 61.44 N.",
"C": "Correct. The worked calculation gives 122.88 N.",
"D": "Incorrect. Substituting the stated... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005670 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 4 μF capacitor is charged to a potential difference of 21 V. Calculate the energy stored, expressed in μJ. | {
"A": "882 μJ",
"B": "89.2 μJ",
"C": "1323 μJ",
"D": "1058.4 μJ"
} | A | 882 μJ | U=½CV². Since C=4 μF, U in μJ is ½×4×(21)²=882 μJ. | {
"A": "Correct. The worked calculation gives 882 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 882 μJ, not 89.2 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 882 μJ, not 1323 μJ.",
"D": "Incorrect. Substituting the stated value... | [
"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_002355 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, 1], [8, 2]]. | {
"A": "8",
"B": "6",
"C": "12",
"D": "-8"
} | A | 8 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(2)−(1)(8)=8. | {
"A": "Correct. The worked calculation gives 8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 12.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_002421 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, -1], [8, 8]]. | {
"A": "8",
"B": "16",
"C": "32",
"D": "12"
} | B | 16 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(8)−(-1)(8)=16. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16, not 8.",
"B": "Correct. The worked calculation gives 16.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16, not 32.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_008684 | 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 0.3 mol L⁻¹ and initially B is absent. At equilibrium, 40% of A has dissociated at constant volume. Find K_c. | {
"A": "-1.68",
"B": "3.32",
"C": "1.32",
"D": "0.32"
} | D | 0.32 | Let α=0.4. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.3)(0.4)²/(1−0.4)=0.32. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32, not -1.68.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32, not 3.32.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32, not 1.32.",
"D": "Cor... | [
"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_001563 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (-1x² -6x -5) dx. | {
"A": "-294.33333",
"B": "-296.33333",
"C": "296.33333",
"D": "-444.5"
} | B | -296.33333 | An antiderivative is (-1/3)x³+(-6/2)x²+(-5)x. Evaluating between 0 and 7 gives (-1/3)(7)³+(-6/2)(7)²+(-5)(7)=-296.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -296.33333, not -294.33333.",
"B": "Correct. The worked calculation gives -296.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -296.33333, not 296.33333.",
"D": "Incorrect. Substituting... | [
"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_009661 | 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_3N_2X_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "13",
"B": "10",
"C": "12",
"D": "7"
} | B | 10 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×11+2+2−3−3)/2=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 13.",
"B": "Correct. The worked calculation gives 10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 12.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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_005651 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 58 μF capacitor is charged to a potential difference of 24 V. Calculate the energy stored, expressed in μJ. | {
"A": "16704 μJ",
"B": "13363.2 μJ",
"C": "1671.4 μJ",
"D": "8352 μJ"
} | A | 16704 μJ | U=½CV². Since C=58 μF, U in μJ is ½×58×(24)²=16704 μJ. | {
"A": "Correct. The worked calculation gives 16704 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16704 μJ, not 13363.2 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16704 μJ, not 1671.4 μJ.",
"D": "Incorrect. Substituting the s... | [
"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_009998 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(CN)_3]^-4, each CN ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "-4",
"B": "-2",
"C": "0",
"D": "-1"
} | D | -1 | Let the formal oxidation state of Cu be x. Charge balance gives x+(3)(−1)=-4; hence x=-4+3=-1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1, not -4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1, not -2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1, not 0.",
"D": "Correct. The work... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001372 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (-4x² +7x +6) dx. | {
"A": "-94.5",
"B": "-128",
"C": "-126",
"D": "-11.6"
} | C | -126 | An antiderivative is (-4/3)x³+(7/2)x²+(6)x. Evaluating between 0 and 6 gives (-4/3)(6)³+(7/2)(6)²+(6)(6)=-126. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -126, not -94.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -126, not -128.",
"C": "Correct. The worked calculation gives -126.",
"D": "Incorrect. Substituting the stated values into the ... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005408 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 41 μF capacitor is charged to a potential difference of 2 V. Calculate the energy stored, expressed in μJ. | {
"A": "82 μJ",
"B": "81 μJ",
"C": "80 μJ",
"D": "9.2 μJ"
} | A | 82 μJ | U=½CV². Since C=41 μF, U in μJ is ½×41×(2)²=82 μJ. | {
"A": "Correct. The worked calculation gives 82 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 82 μJ, not 81 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 82 μJ, not 80 μJ.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_004893 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 15 Ω are connected in series; this combination is connected in parallel with a 19 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.11116 A",
"B": "1.11158 A",
"C": "-1.88842 A",
"D": "1.66737 A"
} | B | 1.11158 A | Series branch resistance=10+15=25 Ω. Parallel equivalent R_eq=(25×19)/(25+19)=10.79545 Ω. Total current I=V/R_eq=12/10.79545=1.11158 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.11158 A, not 1.11116 A.",
"B": "Correct. The worked calculation gives 1.11158 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.11158 A, not -1.88842 A.",
"D": "Incorrect. Substituting th... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007692 | 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 59 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "14.75 mmol L⁻¹",
"B": "44.25 mmol L⁻¹",
"C": "29.5 mmol L⁻¹",
"D": "23.6 mmol L⁻¹"
} | C | 29.5 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=59/2^1=29.5 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 29.5 mmol L⁻¹, not 14.75 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 29.5 mmol L⁻¹, not 44.25 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 29.5 mmol L⁻¹.",
"D": "Incor... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005514 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 8 μF capacitor is charged to a potential difference of 30 V. Calculate the energy stored, expressed in μJ. | {
"A": "3600 μJ",
"B": "3601 μJ",
"C": "5400 μJ",
"D": "2700 μJ"
} | A | 3600 μJ | U=½CV². Since C=8 μF, U in μJ is ½×8×(30)²=3600 μJ. | {
"A": "Correct. The worked calculation gives 3600 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3600 μJ, not 3601 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3600 μJ, not 5400 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005813 | 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 1.9 atm at 279 K. What is its pressure at 339 K? | {
"A": "1.73145 atm",
"B": "1.3086 atm",
"C": "5.3086 atm",
"D": "2.3086 atm"
} | D | 2.3086 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.9)(339)/(279)=2.3086 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.3086 atm, not 1.73145 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.3086 atm, not 1.3086 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.308... | [
"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_003979 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 0 m s⁻¹. A constant net force does 18 N of work over 20 m in the direction of motion. Find its final kinetic energy. | {
"A": "360 J",
"B": "361 J",
"C": "362 J",
"D": "180 J"
} | A | 360 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(0)²+(18)(20)=360 J. | {
"A": "Correct. The worked calculation gives 360 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 360 J, not 361 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 360 J, not 362 J.",
"D": "Incorrect. Substituting the stated values into ... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006538 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 7 kg is attached to an ideal spring of force constant 121 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.36078 s",
"B": "0.48105 s",
"C": "3.48105 s",
"D": "-0.51895 s"
} | B | 0.48105 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(7/121)=0.48105 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.48105 s, not 0.36078 s.",
"B": "Correct. The worked calculation gives 0.48105 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.48105 s, not 3.48105 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001354 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (4x² +8x +6) dx. | {
"A": "260",
"B": "346.66667",
"C": "130",
"D": "173.33333"
} | D | 173.33333 | An antiderivative is (4/3)x³+(8/2)x²+(6)x. Evaluating between 0 and 4 gives (4/3)(4)³+(8/2)(4)²+(6)(4)=173.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 173.33333, not 260.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 173.33333, not 346.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 173.33333, not 1... | [
"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_004337 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 33 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.31. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "92.928 N",
"B": "115.16 N",
"C": "12.616 N",
"D": "116.16 N"
} | D | 116.16 N | Net force=mg(sinθ−μcosθ)=33×10×(0.6−0.31×0.8)=116.16 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 116.16 N, not 92.928 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 116.16 N, not 115.16 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 116.16 N, not ... | [
"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_004948 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 11 Ω are connected in series; this combination is connected in parallel with a 19 Ω resistor across a 12 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.23158 A",
"B": "1.23158 A",
"C": "0.23158 A",
"D": "0.92368 A"
} | B | 1.23158 A | Series branch resistance=9+11=20 Ω. Parallel equivalent R_eq=(20×19)/(20+19)=9.74359 Ω. Total current I=V/R_eq=12/9.74359=1.23158 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.23158 A, not 3.23158 A.",
"B": "Correct. The worked calculation gives 1.23158 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.23158 A, not 0.23158 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_000013 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 -2x -2=0, let its roots be α and β. What is α²+β²? | {
"A": "0.625",
"B": "0.25",
"C": "1.25",
"D": "2.25"
} | C | 1.25 | By Vieta's relations, α+β = 2/4 and αβ = -2/4. Then α²+β²=(α+β)²−2αβ = (2/4)²−2(-2/4) = 1.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.25, not 0.625.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.25, not 0.25.",
"C": "Correct. The worked calculation gives 1.25.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_005774 | 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 0.8 atm at 274 K. What is its pressure at 668 K? | {
"A": "-1.95036 atm",
"B": "0.95036 atm",
"C": "1.95036 atm",
"D": "0.97518 atm"
} | C | 1.95036 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.8)(668)/(274)=1.95036 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.95036 atm, not -1.95036 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.95036 atm, not 0.95036 atm.",
"C": "Correct. The worked calculation gives 1.95036 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_002547 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, -1], [8, 3]]. | {
"A": "17",
"B": "34",
"C": "2.7",
"D": "13.6"
} | A | 17 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(3)−(-1)(8)=17. | {
"A": "Correct. The worked calculation gives 17.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17, not 34.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17, not 2.7.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005490 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 41 μF capacitor is charged to a potential difference of 35 V. Calculate the energy stored, expressed in μJ. | {
"A": "-25112.5 μJ",
"B": "25113.5 μJ",
"C": "25112.5 μJ",
"D": "50225 μJ"
} | C | 25112.5 μJ | U=½CV². Since C=41 μF, U in μJ is ½×41×(35)²=25112.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 25112.5 μJ, not -25112.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 25112.5 μJ, not 25113.5 μJ.",
"C": "Correct. The worked calculation gives 25112.5 μJ.",
"D": "Incorrect. Substituti... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009414 | 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_4H_3N_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "-4",
"B": "2",
"C": "1",
"D": "4"
} | D | 4 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×4+2+1−3−0)/2=4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not -4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.",
"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_004621 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 9 kg and radius 5 m is acted on by a constant torque of 42 N m about its central axis. Find its angular acceleration. | {
"A": "1.37333 rad s⁻²",
"B": "1.03733 rad s⁻²",
"C": "0.37333 rad s⁻²",
"D": "-0.62667 rad s⁻²"
} | C | 0.37333 rad s⁻² | For a solid disc, I=½MR²=½(9)(5)²=112.5 kg m². Using τ=Iα, α=42/112.5=0.37333 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.37333 rad s⁻², not 1.37333 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.37333 rad s⁻², not 1.03733 rad s⁻².",
"C": "Correct. The worked calculation gives 0.37333 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_005322 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +4 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "15.85124 N",
"B": "14.28099 N",
"C": "35.70248 N",
"D": "17.85124 N"
} | D | 17.85124 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(4×10⁻⁶)/(11×10⁻²)²=17.85124 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 17.85124 N, not 15.85124 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 17.85124 N, not 14.28099 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 17.851... | [
"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_000521 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 1 and common difference 9. Find the sum of its first 23 terms. | {
"A": "2302",
"B": "1725",
"C": "2300",
"D": "4600"
} | C | 2300 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=1, d=9, n=23: Sₙ=23/2[2(1)+(23−1)(9)]=2300. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2300, not 2302.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2300, not 1725.",
"C": "Correct. The worked calculation gives 2300.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001452 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (0x² -7x -4) dx. | {
"A": "-44.5",
"B": "-52.2",
"C": "-43.5",
"D": "-41.5"
} | C | -43.5 | An antiderivative is (0/3)x³+(-7/2)x²+(-4)x. Evaluating between 0 and 3 gives (0/3)(3)³+(-7/2)(3)²+(-4)(3)=-43.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -43.5, not -44.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -43.5, not -52.2.",
"C": "Correct. The worked calculation gives -43.5.",
"D": "Incorrect. Substituting the stated values into ... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005131 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +8 μC and +7 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "51.4 N",
"B": "50.4 N",
"C": "40.32 N",
"D": "75.6 N"
} | B | 50.4 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(8×10⁻⁶)(7×10⁻⁶)/(10×10⁻²)²=50.4 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 50.4 N, not 51.4 N.",
"B": "Correct. The worked calculation gives 50.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 50.4 N, not 40.32 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_003556 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 54 m s⁻¹ at 45° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "291.6 m",
"B": "218.7 m",
"C": "-291.6 m",
"D": "437.4 m"
} | A | 291.6 m | Range R=u²sin(2θ)/g. Substituting u=54, θ=45° and g=10 gives R=(54)²sin(90°)/10=291.6 m. | {
"A": "Correct. The worked calculation gives 291.6 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 291.6 m, not 218.7 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 291.6 m, not -291.6 m.",
"D": "Incorrect. Substituting the stated v... | [
"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_005124 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +1 μC and +6 μC are separated by 10 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "5.4 N",
"B": "6.4 N",
"C": "3.4 N",
"D": "7.4 N"
} | A | 5.4 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(1×10⁻⁶)(6×10⁻⁶)/(10×10⁻²)²=5.4 N. | {
"A": "Correct. The worked calculation gives 5.4 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.4 N, not 6.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.4 N, not 3.4 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_009055 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.73 V, transfers 2 electrons, and has reaction quotient Q=10^1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.70045 V",
"B": "0.35023 V",
"C": "2.70045 V",
"D": "-0.29955 V"
} | A | 0.70045 V | Apply the Nernst equation: E=0.73−(0.0591/2)(1)=0.70045 V. | {
"A": "Correct. The worked calculation gives 0.70045 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.70045 V, not 0.35023 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.70045 V, not 2.70045 V.",
"D": "Incorrect. Substituting the... | [
"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_002396 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, -8], [8, 0]]. | {
"A": "32",
"B": "-64",
"C": "64",
"D": "51.2"
} | C | 64 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(0)−(-8)(8)=64. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 64, not 32.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 64, not -64.",
"C": "Correct. The worked calculation gives 64.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008008 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 10 A for 14207 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": "70.11486 g",
"B": "47.74324 g",
"C": "35.05743 g",
"D": "46.74324 g"
} | D | 46.74324 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×10×14207/(2×96500)=46.74324 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 46.74324 g, not 70.11486 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 46.74324 g, not 47.74324 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 46.743... | [
"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_006019 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 106 cm in front of a thin convex lens of focal length 24 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.70732",
"B": "-2.70732",
"C": "0.43902",
"D": "0.29268"
} | D | 0.29268 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(106)(24)/(106−24)=31.02439 cm. Thus |m|=v/u=31.02439/106=0.29268. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.29268, not -0.70732.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.29268, not -2.70732.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.29268, not 0.4... | [
"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_006487 | 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 209 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.05869 s",
"B": "0.58694 s",
"C": "1.17388 s",
"D": "-1.41306 s"
} | B | 0.58694 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(18/209)=0.58694 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.58694 s, not 1.05869 s.",
"B": "Correct. The worked calculation gives 0.58694 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.58694 s, not 1.17388 s.",
"D": "Incorrect. Substituting the... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001956 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 15 distinct elements? | {
"A": "2252.25",
"B": "3003",
"C": "3002",
"D": "3004"
} | B | 3003 | Order does not matter, so the count is C(15,5)=15!/[5!(10)!]=3003. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3003, not 2252.25.",
"B": "Correct. The worked calculation gives 3003.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3003, not 3002.",
"D": "Incorrect. Substituting the stated values into th... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009636 | 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_7H_13N_2X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "1.5",
"B": "3",
"C": "2",
"D": "1"
} | C | 2 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+2−13−1)/2=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"C": "Correct. The worked calculation gives 2.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000430 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -10 and common difference 11. Find the sum of its first 32 terms. | {
"A": "-5136",
"B": "5136",
"C": "5138",
"D": "7704"
} | B | 5136 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-10, d=11, n=32: Sₙ=32/2[2(-10)+(32−1)(11)]=5136. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5136, not -5136.",
"B": "Correct. The worked calculation gives 5136.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5136, not 5138.",
"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_003058 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-7-3i)/(9+6i). What is Re(z), the real part of z? | {
"A": "1.30769",
"B": "-0.69231",
"C": "0.93077",
"D": "-2.69231"
} | B | -0.69231 | Multiply numerator and denominator by the conjugate (9-6i). Then Re(z)=(ac+bd)/(c²+d²)=((-7)(9)+(-3)(6))/(9²+(6)²)=-0.69231. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.69231, not 1.30769.",
"B": "Correct. The worked calculation gives -0.69231.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.69231, not 0.93077.",
"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_000459 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 13 and common difference 15. Find the sum of its first 24 terms. | {
"A": "4451",
"B": "4452",
"C": "6678",
"D": "446.2"
} | B | 4452 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=13, d=15, n=24: Sₙ=24/2[2(13)+(24−1)(15)]=4452. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4452, not 4451.",
"B": "Correct. The worked calculation gives 4452.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4452, not 6678.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008469 | 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 0.33 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.1716 K",
"B": "0.3432 K",
"C": "0.2574 K",
"D": "-1.6568 K"
} | B | 0.3432 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×0.33=0.3432 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3432 K, not 0.1716 K.",
"B": "Correct. The worked calculation gives 0.3432 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3432 K, not 0.2574 K.",
"D": "Incorrect. Substituting the stat... | [
"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_001643 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (5x² +6x -5) dx. | {
"A": "-438",
"B": "657",
"C": "438",
"D": "525.6"
} | C | 438 | An antiderivative is (5/3)x³+(6/2)x²+(-5)x. Evaluating between 0 and 6 gives (5/3)(6)³+(6/2)(6)²+(-5)(6)=438. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 438, not -438.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 438, not 657.",
"C": "Correct. The worked calculation gives 438.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_008939 | 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 0.95 mol L⁻¹ and initially B is absent. At equilibrium, 48% of A has dissociated at constant volume. Find K_c. | {
"A": "2.68369",
"B": "1.16837",
"C": "1.68369",
"D": "3.36738"
} | C | 1.68369 | Let α=0.48. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.95)(0.48)²/(1−0.48)=1.68369. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.68369, not 2.68369.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.68369, not 1.16837.",
"C": "Correct. The worked calculation gives 1.68369.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006995 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 26 mol H₂ and 1 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "2 mol",
"B": "5 mol",
"C": "1 mol",
"D": "0 mol"
} | A | 2 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 26 mol H₂O; O₂ can produce 2 mol H₂O. The limiting condition is O₂; product=2 mol. | {
"A": "Correct. The worked calculation gives 2 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 5 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 1 mol.",
"D": "Incorrect. Substituting the stated values into ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000815 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 4 and common ratio -2. What is the sum of its first 7 terms? | {
"A": "172",
"B": "129",
"C": "170",
"D": "18.2"
} | A | 172 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=4(-2^7−1)/(-2−1)=172. | {
"A": "Correct. The worked calculation gives 172.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 172, not 129.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 172, not 170.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_002288 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 8 blue and 9 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.30667",
"B": "0.61333",
"C": "-1.69333",
"D": "-2.69333"
} | A | 0.30667 | Favourable pairs = C(8,2)+C(8,2)+C(9,2)=92. Total pairs=C(25,2)=300. Therefore P=92/300=0.30667. | {
"A": "Correct. The worked calculation gives 0.30667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30667, not 0.61333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30667, not -1.69333.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003633 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 77 m s⁻¹ at 35° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "555.14375 m",
"B": "556.14375 m",
"C": "445.715 m",
"D": "557.14375 m"
} | D | 557.14375 m | Range R=u²sin(2θ)/g. Substituting u=77, θ=35° and g=10 gives R=(77)²sin(70°)/10=557.14375 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 557.14375 m, not 555.14375 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 557.14375 m, not 556.14375 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 55... | [
"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_000532 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -3 and common difference 10. Find the sum of its first 8 terms. | {
"A": "256",
"B": "258",
"C": "512",
"D": "257"
} | A | 256 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-3, d=10, n=8: Sₙ=8/2[2(-3)+(8−1)(10)]=256. | {
"A": "Correct. The worked calculation gives 256.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 256, not 258.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 256, not 512.",
"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_009075 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.94 V, transfers 1 electrons, and has reaction quotient Q=10^-4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.1764 V",
"B": "3.1764 V",
"C": "-1.1764 V",
"D": "4.1764 V"
} | A | 1.1764 V | Apply the Nernst equation: E=0.94−(0.0591/1)(-4)=1.1764 V. | {
"A": "Correct. The worked calculation gives 1.1764 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1764 V, not 3.1764 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1764 V, not -1.1764 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_008903 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 0.54 mol L⁻¹ and initially B is absent. At equilibrium, 33% of A has dissociated at constant volume. Find K_c. | {
"A": "1.35108",
"B": "1.03511",
"C": "0.70216",
"D": "0.35108"
} | D | 0.35108 | Let α=0.33. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.54)(0.33)²/(1−0.33)=0.35108. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35108, not 1.35108.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35108, not 1.03511.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35108, not 0.702... | [
"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_008025 | 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 13 A for 6944 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": "29.70089 g",
"B": "28.70089 g",
"C": "31.70089 g",
"D": "35.64107 g"
} | A | 29.70089 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×6944/(2×96500)=29.70089 g. | {
"A": "Correct. The worked calculation gives 29.70089 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 29.70089 g, not 28.70089 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29.70089 g, not 31.70089 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_001691 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 53 distinct elements? | {
"A": "886322709",
"B": "886322710",
"C": "1063587252",
"D": "1772645420"
} | B | 886322710 | Order does not matter, so the count is C(53,8)=53!/[8!(45)!]=886322710. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 886322710, not 886322709.",
"B": "Correct. The worked calculation gives 886322710.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 886322710, not 1063587252.",
"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_007112 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 20 mol of gas at 573 K and 0.13 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "7233.64015 L",
"B": "7232.64015 L",
"C": "10850.46023 L",
"D": "8680.36818 L"
} | A | 7233.64015 L | PV=nRT, so V=nRT/P=(20)(0.082057)(573)/(0.13)=7233.64015 L. | {
"A": "Correct. The worked calculation gives 7233.64015 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7233.64015 L, not 7232.64015 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7233.64015 L, not 10850.46023 L.",
"D": "Incorrect. ... | [
"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_003394 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 20 m s⁻¹ at 50° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "39.39231 m",
"B": "40.39231 m",
"C": "37.39231 m",
"D": "29.54423 m"
} | A | 39.39231 m | Range R=u²sin(2θ)/g. Substituting u=20, θ=50° and g=10 gives R=(20)²sin(100°)/10=39.39231 m. | {
"A": "Correct. The worked calculation gives 39.39231 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 39.39231 m, not 40.39231 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 39.39231 m, not 37.39231 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_009991 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(CN)_4]^+3, each CN ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "8",
"B": "7",
"C": "5.25",
"D": "6"
} | B | 7 | Let the formal oxidation state of Pt be x. Charge balance gives x+(4)(−1)=+3; hence x=3+4=+7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 8.",
"B": "Correct. The worked calculation gives 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 5.25.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004183 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 49 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.16. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "173.46 N",
"B": "231.28 N",
"C": "230.28 N",
"D": "232.28 N"
} | B | 231.28 N | Net force=mg(sinθ−μcosθ)=49×10×(0.6−0.16×0.8)=231.28 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 231.28 N, not 173.46 N.",
"B": "Correct. The worked calculation gives 231.28 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 231.28 N, not 230.28 N.",
"D": "Incorrect. Substituting the stat... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000635 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 13 and common difference 7. Find the sum of its first 11 terms. | {
"A": "422.4",
"B": "528",
"C": "264",
"D": "633.6"
} | B | 528 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=13, d=7, n=11: Sₙ=11/2[2(13)+(11−1)(7)]=528. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 528, not 422.4.",
"B": "Correct. The worked calculation gives 528.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 528, not 264.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002519 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 8], [2, 4]]. | {
"A": "-3",
"B": "0",
"C": "1",
"D": "3"
} | B | 0 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(4)−(8)(2)=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not -3.",
"B": "Correct. The worked calculation gives 0.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_009252 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.24 V, transfers 1 electrons, and has reaction quotient Q=10^-4. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.2146 V",
"B": "-1.5236 V",
"C": "1.4764 V",
"D": "0.7382 V"
} | C | 1.4764 V | Apply the Nernst equation: E=1.24−(0.0591/1)(-4)=1.4764 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.4764 V, not 2.2146 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4764 V, not -1.5236 V.",
"C": "Correct. The worked calculation gives 1.4764 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_005759 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3 atm at 214 K. What is its pressure at 381 K? | {
"A": "8.01168 atm",
"B": "10.68224 atm",
"C": "4.00584 atm",
"D": "5.34112 atm"
} | D | 5.34112 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3)(381)/(214)=5.34112 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.34112 atm, not 8.01168 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.34112 atm, not 10.68224 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5... | [
"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_006941 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 46 mol H₂ and 28 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "46 mol",
"B": "92 mol",
"C": "-46 mol",
"D": "34.5 mol"
} | A | 46 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 46 mol H₂O; O₂ can produce 56 mol H₂O. The limiting condition is H₂; product=46 mol. | {
"A": "Correct. The worked calculation gives 46 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 46 mol, not 92 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 46 mol, not -46 mol.",
"D": "Incorrect. Substituting the stated values... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005597 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 19 μF capacitor is charged to a potential difference of 15 V. Calculate the energy stored, expressed in μJ. | {
"A": "3206.25 μJ",
"B": "2136.5 μJ",
"C": "2138.5 μJ",
"D": "2137.5 μJ"
} | D | 2137.5 μJ | U=½CV². Since C=19 μF, U in μJ is ½×19×(15)²=2137.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2137.5 μJ, not 3206.25 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2137.5 μJ, not 2136.5 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2137.5 μJ... | [
"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_003383 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 110 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "926.91378 m",
"B": "924.91378 m",
"C": "93.69138 m",
"D": "-926.91378 m"
} | A | 926.91378 m | Range R=u²sin(2θ)/g. Substituting u=110, θ=25° and g=10 gives R=(110)²sin(50°)/10=926.91378 m. | {
"A": "Correct. The worked calculation gives 926.91378 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 926.91378 m, not 924.91378 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 926.91378 m, not 93.69138 m.",
"D": "Incorrect. Substit... | [
"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_008848 | 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 0.62 mol L⁻¹ and initially B is absent. At equilibrium, 33% of A has dissociated at constant volume. Find K_c. | {
"A": "0.40309",
"B": "-0.59691",
"C": "0.80619",
"D": "-1.59691"
} | A | 0.40309 | Let α=0.33. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.62)(0.33)²/(1−0.33)=0.40309. | {
"A": "Correct. The worked calculation gives 0.40309.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.40309, not -0.59691.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.40309, not 0.80619.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001694 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 40 distinct elements? | {
"A": "-658008",
"B": "658008",
"C": "65801.8",
"D": "1316016"
} | B | 658008 | Order does not matter, so the count is C(40,5)=40!/[5!(35)!]=658008. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 658008, not -658008.",
"B": "Correct. The worked calculation gives 658008.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 658008, not 65801.8.",
"D": "Incorrect. Substituting the stated value... | [
"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_002684 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(3, -2, -5) and v=(-3, -5, -5), calculate u·v. | {
"A": "26",
"B": "3.6",
"C": "27",
"D": "24"
} | A | 26 | The dot product is the sum of corresponding component products: (3)(-3)+(-2)(-5)+(-5)(-5)=26. | {
"A": "Correct. The worked calculation gives 26.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 26, not 3.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26, not 27.",
"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_002467 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[5, 5], [4, -1]]. | {
"A": "-25",
"B": "-23",
"C": "-27",
"D": "-24"
} | A | -25 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (5)(-1)−(5)(4)=-25. | {
"A": "Correct. The worked calculation gives -25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -25, not -23.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -25, not -27.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_004467 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 6 kg and radius 4 m is acted on by a constant torque of 32 N m about its central axis. Find its angular acceleration. | {
"A": "0.66667 rad s⁻²",
"B": "1.66667 rad s⁻²",
"C": "0.5 rad s⁻²",
"D": "-1.33333 rad s⁻²"
} | A | 0.66667 rad s⁻² | For a solid disc, I=½MR²=½(6)(4)²=48 kg m². Using τ=Iα, α=32/48=0.66667 rad s⁻². | {
"A": "Correct. The worked calculation gives 0.66667 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.66667 rad s⁻², not 1.66667 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.66667 rad s⁻², not 0.5 rad s⁻².",
"D": "I... | [
"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_004270 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 21 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.42. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "55.44 N",
"B": "53.44 N",
"C": "41.58 N",
"D": "66.528 N"
} | A | 55.44 N | Net force=mg(sinθ−μcosθ)=21×10×(0.6−0.42×0.8)=55.44 N. | {
"A": "Correct. The worked calculation gives 55.44 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 55.44 N, not 53.44 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 55.44 N, not 41.58 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003744 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 7 m s⁻¹. A constant net force does 17 N of work over 18 m in the direction of motion. Find its final kinetic energy. | {
"A": "500 J",
"B": "502 J",
"C": "503 J",
"D": "1004 J"
} | B | 502 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(7)²+(17)(18)=502 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 502 J, not 500 J.",
"B": "Correct. The worked calculation gives 502 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 502 J, not 503 J.",
"D": "Incorrect. Substituting the stated values into ... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001903 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 84 distinct elements? | {
"A": "30872016",
"B": "3087202.6",
"C": "30872018",
"D": "-30872016"
} | A | 30872016 | Order does not matter, so the count is C(84,5)=84!/[5!(79)!]=30872016. | {
"A": "Correct. The worked calculation gives 30872016.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30872016, not 3087202.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30872016, not 30872018.",
"D": "Incorrect. Substituting the sta... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009343 | 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_16H_11N_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "13",
"B": "15",
"C": "16",
"D": "11"
} | A | 13 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×16+2+3−11−0)/2=13. | {
"A": "Correct. The worked calculation gives 13.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13, not 15.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13, not 16.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"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 |
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