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_004448 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 11 kg and radius 1 m is acted on by a constant torque of 7 N m about its central axis. Find its angular acceleration. | {
"A": "0.27273 rad s⁻²",
"B": "1.90909 rad s⁻²",
"C": "1.27273 rad s⁻²",
"D": "-0.72727 rad s⁻²"
} | C | 1.27273 rad s⁻² | For a solid disc, I=½MR²=½(11)(1)²=5.5 kg m². Using τ=Iα, α=7/5.5=1.27273 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.27273 rad s⁻², not 0.27273 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.27273 rad s⁻², not 1.90909 rad s⁻².",
"C": "Correct. The worked calculation gives 1.27273 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_003682 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 3 m s⁻¹. A constant net force does 25 N of work over 16 m in the direction of motion. Find its final kinetic energy. | {
"A": "448.5 J",
"B": "447.5 J",
"C": "449.5 J",
"D": "224.75 J"
} | C | 449.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(3)²+(25)(16)=449.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 449.5 J, not 448.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 449.5 J, not 447.5 J.",
"C": "Correct. The worked calculation gives 449.5 J.",
"D": "Incorrect. Substituting the stated va... | [
"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_002273 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 5 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-2.69231",
"B": "1.30769",
"C": "-1.69231",
"D": "0.30769"
} | D | 0.30769 | Favourable pairs = C(6,2)+C(5,2)+C(3,2)=28. Total pairs=C(14,2)=91. Therefore P=28/91=0.30769. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not -2.69231.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not 1.30769.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not -1.6... | [
"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_009916 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(Cl)_5]^-4, each Cl ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "1",
"B": "-1",
"C": "3",
"D": "0"
} | A | 1 | Let the formal oxidation state of Cu be x. Charge balance gives x+(5)(−1)=-4; hence x=-4+5=+1. | {
"A": "Correct. The worked calculation gives 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not -1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 3.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001739 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 7 elements can be selected from a set of 15 distinct elements? | {
"A": "7722",
"B": "6435",
"C": "644.5",
"D": "4826.25"
} | B | 6435 | Order does not matter, so the count is C(15,7)=15!/[7!(8)!]=6435. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6435, not 7722.",
"B": "Correct. The worked calculation gives 6435.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6435, not 644.5.",
"D": "Incorrect. Substituting the stated values into the ... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002957 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-4, 1, 4) and v=(-3, -6, 6), calculate u·v. | {
"A": "15",
"B": "30",
"C": "36",
"D": "4"
} | B | 30 | The dot product is the sum of corresponding component products: (-4)(-3)+(1)(-6)+(4)(6)=30. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 30, not 15.",
"B": "Correct. The worked calculation gives 30.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30, not 36.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002339 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[2, -8], [4, 5]]. | {
"A": "44",
"B": "42",
"C": "50.4",
"D": "31.5"
} | B | 42 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (2)(5)−(-8)(4)=42. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 42, not 44.",
"B": "Correct. The worked calculation gives 42.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 42, not 50.4.",
"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_008040 | 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 4 A for 2006 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "5.64002 g",
"B": "1.98002 g",
"C": "1.64002 g",
"D": "2.64002 g"
} | D | 2.64002 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×4×2006/(2×96500)=2.64002 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.64002 g, not 5.64002 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.64002 g, not 1.98002 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.64002 g,... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003332 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-6+6i)/(2+6i). What is Re(z), the real part of z? | {
"A": "2.6",
"B": "1.6",
"C": "0.3",
"D": "0.6"
} | D | 0.6 | Multiply numerator and denominator by the conjugate (2-6i). Then Re(z)=(ac+bd)/(c²+d²)=((-6)(2)+(6)(6))/(2²+(6)²)=0.6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6, not 2.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6, not 1.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.6, not 0.3.",
"D": "Correct. T... | [
"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_008516 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.25 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": "1.95 K",
"B": "1.3 K",
"C": "4.3 K",
"D": "-1.3 K"
} | B | 1.3 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×1.25=1.3 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.3 K, not 1.95 K.",
"B": "Correct. The worked calculation gives 1.3 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.3 K, not 4.3 K.",
"D": "Incorrect. Substituting the stated values into... | [
"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_004967 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 9 Ω are connected in series; this combination is connected in parallel with a 5 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "-4.98462 A",
"B": "4.98462 A",
"C": "1.49846 A",
"D": "2.49231 A"
} | B | 4.98462 A | Series branch resistance=4+9=13 Ω. Parallel equivalent R_eq=(13×5)/(13+5)=3.61111 Ω. Total current I=V/R_eq=18/3.61111=4.98462 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.98462 A, not -4.98462 A.",
"B": "Correct. The worked calculation gives 4.98462 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.98462 A, not 1.49846 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_006116 | 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 10 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.42857",
"B": "0.14286",
"C": "0.28571",
"D": "2.28571"
} | C | 0.28571 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(45)(10)/(45−10)=12.85714 cm. Thus |m|=v/u=12.85714/45=0.28571. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.28571, not 0.42857.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.28571, not 0.14286.",
"C": "Correct. The worked calculation gives 0.28571.",
"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_000557 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -15 and common difference 6. Find the sum of its first 20 terms. | {
"A": "838",
"B": "420",
"C": "841",
"D": "840"
} | D | 840 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-15, d=6, n=20: Sₙ=20/2[2(-15)+(20−1)(6)]=840. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 840, not 838.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 840, not 420.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 840, not 841.",
"D": "Correct. T... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004305 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 39 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.17. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "182.96 N",
"B": "90.48 N",
"C": "180.96 N",
"D": "181.96 N"
} | C | 180.96 N | Net force=mg(sinθ−μcosθ)=39×10×(0.6−0.17×0.8)=180.96 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 180.96 N, not 182.96 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 180.96 N, not 90.48 N.",
"C": "Correct. The worked calculation gives 180.96 N.",
"D": "Incorrect. Substituting the state... | [
"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_003002 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-1, -6, 1) and v=(3, -7, -7), calculate u·v. | {
"A": "48",
"B": "32",
"C": "33",
"D": "64"
} | B | 32 | The dot product is the sum of corresponding component products: (-1)(3)+(-6)(-7)+(1)(-7)=32. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 32, not 48.",
"B": "Correct. The worked calculation gives 32.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 32, not 33.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002664 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, -7], [7, 7]]. | {
"A": "92",
"B": "90",
"C": "109.2",
"D": "91"
} | D | 91 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(7)−(-7)(7)=91. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 91, not 92.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 91, not 90.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 91, not 109.2.",
"D": "Correct. The ... | [
"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_005188 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +7 μC and +6 μC are separated by 3 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "422 N",
"B": "420 N",
"C": "315 N",
"D": "630 N"
} | B | 420 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(7×10⁻⁶)(6×10⁻⁶)/(3×10⁻²)²=420 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 420 N, not 422 N.",
"B": "Correct. The worked calculation gives 420 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 420 N, not 315 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_001541 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (1x² -5x -2) dx. | {
"A": "-6.25",
"B": "-4.16667",
"C": "-3.16667",
"D": "-8.33333"
} | B | -4.16667 | An antiderivative is (1/3)x³+(-5/2)x²+(-2)x. Evaluating between 0 and 1 gives (1/3)(1)³+(-5/2)(1)²+(-2)(1)=-4.16667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4.16667, not -6.25.",
"B": "Correct. The worked calculation gives -4.16667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -4.16667, not -3.16667.",
"D": "Incorrect. Substituting the stated ... | [
"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_009855 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(OH)_4]^-3, each OH ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "0.5",
"B": "1.5",
"C": "1",
"D": "1.1"
} | C | 1 | Let the formal oxidation state of Pt be x. Charge balance gives x+(4)(−1)=-3; hence x=-3+4=+1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 1.5.",
"C": "Correct. The worked calculation gives 1.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003582 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 19 m s⁻¹ at 55° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "40.70748 m",
"B": "33.9229 m",
"C": "4.39229 m",
"D": "16.96145 m"
} | B | 33.9229 m | Range R=u²sin(2θ)/g. Substituting u=19, θ=55° and g=10 gives R=(19)²sin(110°)/10=33.9229 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33.9229 m, not 40.70748 m.",
"B": "Correct. The worked calculation gives 33.9229 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 33.9229 m, not 4.39229 m.",
"D": "Incorrect. Substituting th... | [
"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_003293 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-13-3i)/(12+12i). What is Re(z), the real part of z? | {
"A": "0.66667",
"B": "-0.66667",
"C": "-1.66667",
"D": "0.93333"
} | B | -0.66667 | Multiply numerator and denominator by the conjugate (12-12i). Then Re(z)=(ac+bd)/(c²+d²)=((-13)(12)+(-3)(12))/(12²+(12)²)=-0.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.66667, not 0.66667.",
"B": "Correct. The worked calculation gives -0.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.66667, not -1.66667.",
"D": "Incorrect. Substituting the state... | [
"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_006837 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 2 mol H₂ and 33 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "2 mol",
"B": "-1 mol",
"C": "3 mol",
"D": "1 mol"
} | A | 2 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 2 mol H₂O; O₂ can produce 66 mol H₂O. The limiting condition is H₂; 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 -1 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 3 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_006754 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 23 mol H₂ and 12 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "34.5 mol",
"B": "23 mol",
"C": "3.3 mol",
"D": "11.5 mol"
} | B | 23 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 23 mol H₂O; O₂ can produce 24 mol H₂O. The limiting condition is H₂; product=23 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 23 mol, not 34.5 mol.",
"B": "Correct. The worked calculation gives 23 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 23 mol, not 3.3 mol.",
"D": "Incorrect. Substituting the stated valu... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006066 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 68 cm in front of a thin convex lens of focal length 16 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.15385",
"B": "0.30769",
"C": "0.23077",
"D": "1.03077"
} | B | 0.30769 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(68)(16)/(68−16)=20.92308 cm. Thus |m|=v/u=20.92308/68=0.30769. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not 0.15385.",
"B": "Correct. The worked calculation gives 0.30769.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.30769, not 0.23077.",
"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_001534 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (-1x² -7x +0) dx. | {
"A": "-4.83333",
"B": "-0.83333",
"C": "-3.83333",
"D": "0.61667"
} | C | -3.83333 | An antiderivative is (-1/3)x³+(-7/2)x²+(0)x. Evaluating between 0 and 1 gives (-1/3)(1)³+(-7/2)(1)²+(0)(1)=-3.83333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -3.83333, not -4.83333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -3.83333, not -0.83333.",
"C": "Correct. The worked calculation gives -3.83333.",
"D": "Incorrect. Substituting the stat... | [
"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_005081 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +5 μC and +4 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "452 N",
"B": "450 N",
"C": "449 N",
"D": "540 N"
} | B | 450 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(5×10⁻⁶)(4×10⁻⁶)/(2×10⁻²)²=450 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 450 N, not 452 N.",
"B": "Correct. The worked calculation gives 450 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 450 N, not 449 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_001219 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ -3x² -2x+7. Evaluate f′(-4). | {
"A": "32",
"B": "312",
"C": "308",
"D": "310"
} | D | 310 | Differentiate: f′(x)=3(6)x²+2(-3)x+(-2). At x=-4, f′(-4)=3(6)(-4)²+2(-3)(-4)+(-2)=310. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 310, not 32.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 310, not 312.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 310, not 308.",
"D": "Correct. Th... | [
"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_006148 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 13 cm in front of a thin convex lens of focal length 8 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "2.4",
"B": "1.6",
"C": "3.2",
"D": "0.6"
} | B | 1.6 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(13)(8)/(13−8)=20.8 cm. Thus |m|=v/u=20.8/13=1.6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.6, not 2.4.",
"B": "Correct. The worked calculation gives 1.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.6, not 3.2.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_001732 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 7 elements can be selected from a set of 78 distinct elements? | {
"A": "2641902120",
"B": "1981426590",
"C": "5283804240",
"D": "3962853180"
} | A | 2641902120 | Order does not matter, so the count is C(78,7)=78!/[7!(71)!]=2641902120. | {
"A": "Correct. The worked calculation gives 2641902120.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2641902120, not 1981426590.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2641902120, not 5283804240.",
"D": "Incorrect. Substitutin... | [
"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_001819 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 55 distinct elements? | {
"A": "-29248649430",
"B": "58497298860",
"C": "35098379316",
"D": "29248649430"
} | D | 29248649430 | Order does not matter, so the count is C(55,10)=55!/[10!(45)!]=29248649430. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 29248649430, not -29248649430.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 29248649430, not 58497298860.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2... | [
"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_003445 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 116 m s⁻¹ at 65° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1028.7894 m",
"B": "1032.7894 m",
"C": "1030.7894 m",
"D": "515.3947 m"
} | C | 1030.7894 m | Range R=u²sin(2θ)/g. Substituting u=116, θ=65° and g=10 gives R=(116)²sin(130°)/10=1030.7894 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1030.7894 m, not 1028.7894 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1030.7894 m, not 1032.7894 m.",
"C": "Correct. The worked calculation gives 1030.7894 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000006 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +1x +8=0, let its roots be α and β. What is α²+β²? | {
"A": "-3.16",
"B": "-4.74",
"C": "0.684",
"D": "-6.16"
} | A | -3.16 | By Vieta's relations, α+β = -1/5 and αβ = 8/5. Then α²+β²=(α+β)²−2αβ = (-1/5)²−2(8/5) = -3.16. | {
"A": "Correct. The worked calculation gives -3.16.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -3.16, not -4.74.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -3.16, not 0.684.",
"D": "Incorrect. Substituting the stated values into ... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003321 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(8+12i)/(2+9i). What is Re(z), the real part of z? | {
"A": "0.72941",
"B": "3.45882",
"C": "1.45882",
"D": "2.91765"
} | C | 1.45882 | Multiply numerator and denominator by the conjugate (2-9i). Then Re(z)=(ac+bd)/(c²+d²)=((8)(2)+(12)(9))/(2²+(9)²)=1.45882. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.45882, not 0.72941.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.45882, not 3.45882.",
"C": "Correct. The worked calculation gives 1.45882.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002457 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 2], [5, 5]]. | {
"A": "11",
"B": "15",
"C": "10",
"D": "9"
} | C | 10 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(5)−(2)(5)=10. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10, not 11.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 15.",
"C": "Correct. The worked calculation gives 10.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005798 | 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 3.6 atm at 209 K. What is its pressure at 384 K? | {
"A": "13.22871 atm",
"B": "4.61435 atm",
"C": "7.61435 atm",
"D": "6.61435 atm"
} | D | 6.61435 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.6)(384)/(209)=6.61435 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.61435 atm, not 13.22871 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.61435 atm, not 4.61435 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6... | [
"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_009127 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.58 V, transfers 3 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.29985 V",
"B": "1.5997 V",
"C": "-0.4003 V",
"D": "0.5997 V"
} | D | 0.5997 V | Apply the Nernst equation: E=0.58−(0.0591/3)(-1)=0.5997 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.5997 V, not 0.29985 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.5997 V, not 1.5997 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.5997 V, not... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002294 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 10 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.34387",
"B": "-1.65613",
"C": "0.34387",
"D": "3.34387"
} | C | 0.34387 | Favourable pairs = C(9,2)+C(10,2)+C(4,2)=87. Total pairs=C(23,2)=253. Therefore P=87/253=0.34387. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34387, not 1.34387.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.34387, not -1.65613.",
"C": "Correct. The worked calculation gives 0.34387.",
"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_000273 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 +18x +11=0, let its roots be α and β. What is α²+β²? | {
"A": "14.75",
"B": "13.75",
"C": "15.75",
"D": "29.5"
} | A | 14.75 | By Vieta's relations, α+β = -18/4 and αβ = 11/4. Then α²+β²=(α+β)²−2αβ = (-18/4)²−2(11/4) = 14.75. | {
"A": "Correct. The worked calculation gives 14.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14.75, not 13.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14.75, not 15.75.",
"D": "Incorrect. Substituting the stated values into ... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006161 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 37 cm in front of a thin convex lens of focal length 16 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.7619",
"B": "1.52381",
"C": "1.07619",
"D": "-2.2381"
} | A | 0.7619 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(37)(16)/(37−16)=28.19048 cm. Thus |m|=v/u=28.19048/37=0.7619. | {
"A": "Correct. The worked calculation gives 0.7619.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7619, not 1.52381.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7619, not 1.07619.",
"D": "Incorrect. Substituting the stated value... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006545 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 22 kg is attached to an ideal spring of force constant 496 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.42121 s",
"B": "0.84242 s",
"C": "1.42121 s",
"D": "0.63182 s"
} | A | 0.42121 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(22/496)=0.42121 s. | {
"A": "Correct. The worked calculation gives 0.42121 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.42121 s, not 0.84242 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.42121 s, not 1.42121 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_002088 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 4 red, 7 blue and 8 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.24123",
"B": "0.16082",
"C": "0.32164",
"D": "3.32164"
} | C | 0.32164 | Favourable pairs = C(4,2)+C(7,2)+C(8,2)=55. Total pairs=C(19,2)=171. Therefore P=55/171=0.32164. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32164, not 0.24123.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32164, not 0.16082.",
"C": "Correct. The worked calculation gives 0.32164.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006586 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 22 kg is attached to an ideal spring of force constant 283 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.05576 s",
"B": "-0.44237 s",
"C": "0.83645 s",
"D": "0.55763 s"
} | D | 0.55763 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(22/283)=0.55763 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.55763 s, not 1.05576 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.55763 s, not -0.44237 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.55763 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001315 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-5x³ -1x² -7x+7. Evaluate f′(2). | {
"A": "-106.5",
"B": "71",
"C": "-53.25",
"D": "-71"
} | D | -71 | Differentiate: f′(x)=3(-5)x²+2(-1)x+(-7). At x=2, f′(2)=3(-5)(2)²+2(-1)(2)+(-7)=-71. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -71, not -106.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -71, not 71.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -71, not -53.25.",
"D": "Corre... | [
"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_007558 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 60 mL of 0.10 M HCl is mixed with 12 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-0.82391",
"B": "2.17609",
"C": "2.35218",
"D": "1.17609"
} | D | 1.17609 | Excess H⁺ moles=0.10×(60−12)/1000=0.004800 mol. Total volume=0.072 L, so [H⁺]=0.066667 M and pH=−log₁₀[H⁺]=1.17609. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.17609, not -0.82391.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.17609, not 2.17609.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.17609, not 2.35... | [
"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_009242 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.26 V, transfers 3 electrons, and has reaction quotient Q=10^0. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-1.74 V",
"B": "1.89 V",
"C": "2.52 V",
"D": "1.26 V"
} | D | 1.26 V | Apply the Nernst equation: E=1.26−(0.0591/3)(0)=1.26 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.26 V, not -1.74 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.26 V, not 1.89 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.26 V, not 2.52 V.",... | [
"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_005145 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +7 μC are separated by 2 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "-472.5 N",
"B": "708.75 N",
"C": "472.5 N",
"D": "378 N"
} | C | 472.5 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(7×10⁻⁶)/(2×10⁻²)²=472.5 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 472.5 N, not -472.5 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 472.5 N, not 708.75 N.",
"C": "Correct. The worked calculation gives 472.5 N.",
"D": "Incorrect. Substituting the stated ... | [
"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_004243 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 23 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.13. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "57.04 N",
"B": "113.08 N",
"C": "91.264 N",
"D": "114.08 N"
} | D | 114.08 N | Net force=mg(sinθ−μcosθ)=23×10×(0.6−0.13×0.8)=114.08 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 114.08 N, not 57.04 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 114.08 N, not 113.08 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 114.08 N, not 9... | [
"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_004583 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 6 kg and radius 1 m is acted on by a constant torque of 34 N m about its central axis. Find its angular acceleration. | {
"A": "22.66667 rad s⁻²",
"B": "13.33333 rad s⁻²",
"C": "17 rad s⁻²",
"D": "11.33333 rad s⁻²"
} | D | 11.33333 rad s⁻² | For a solid disc, I=½MR²=½(6)(1)²=3 kg m². Using τ=Iα, α=34/3=11.33333 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.33333 rad s⁻², not 22.66667 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.33333 rad s⁻², not 13.33333 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governi... | [
"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_008912 | 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 0.47 mol L⁻¹ and initially B is absent. At equilibrium, 54% of A has dissociated at constant volume. Find K_c. | {
"A": "0.59588",
"B": "0.19176",
"C": "-1.19176",
"D": "1.19176"
} | D | 1.19176 | Let α=0.54. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.47)(0.54)²/(1−0.54)=1.19176. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.19176, not 0.59588.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.19176, not 0.19176.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.19176, not -1.19... | [
"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_002800 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, 5, -4) and v=(9, -7, -1), calculate u·v. | {
"A": "-22",
"B": "-33",
"C": "-23",
"D": "-21"
} | A | -22 | The dot product is the sum of corresponding component products: (1)(9)+(5)(-7)+(-4)(-1)=-22. | {
"A": "Correct. The worked calculation gives -22.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -22, not -33.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -22, not -23.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007410 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 96 mL of 0.10 M HCl is mixed with 91 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "2.57287",
"B": "0.57287",
"C": "1.92965",
"D": "3.57287"
} | A | 2.57287 | Excess H⁺ moles=0.10×(96−91)/1000=0.000500 mol. Total volume=0.187 L, so [H⁺]=0.002674 M and pH=−log₁₀[H⁺]=2.57287. | {
"A": "Correct. The worked calculation gives 2.57287.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.57287, not 0.57287.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.57287, not 1.92965.",
"D": "Incorrect. Substituting the stated va... | [
"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_008022 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 7 A for 20982 s. Assuming 100% current efficiency, calculate the mass of copper deposited. Use M(Cu)=63.5 g mol⁻¹ and F=96500 C mol⁻¹. | {
"A": "5.83238 g",
"B": "48.32383 g",
"C": "49.32383 g",
"D": "38.65906 g"
} | B | 48.32383 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×7×20982/(2×96500)=48.32383 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 48.32383 g, not 5.83238 g.",
"B": "Correct. The worked calculation gives 48.32383 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 48.32383 g, not 49.32383 g.",
"D": "Incorrect. Substituting... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000592 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 13 and common difference 11. Find the sum of its first 10 terms. | {
"A": "500",
"B": "468.75",
"C": "624",
"D": "625"
} | D | 625 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=13, d=11, n=10: Sₙ=10/2[2(13)+(10−1)(11)]=625. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 625, not 500.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 625, not 468.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 625, not 624.",
"D": "Correct... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007489 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 54 mL of 0.10 M HCl is mixed with 30 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "0.77203",
"B": "-1.45593",
"C": "1.54407",
"D": "1.15441"
} | C | 1.54407 | Excess H⁺ moles=0.10×(54−30)/1000=0.002400 mol. Total volume=0.084 L, so [H⁺]=0.028571 M and pH=−log₁₀[H⁺]=1.54407. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.54407, not 0.77203.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.54407, not -1.45593.",
"C": "Correct. The worked calculation gives 1.54407.",
"D": "Incorrect. Substituting the stated v... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003747 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block initially moves at 3 m s⁻¹. A constant net force does 6 N of work over 16 m in the direction of motion. Find its final kinetic energy. | {
"A": "105 J",
"B": "84 J",
"C": "52.5 J",
"D": "210 J"
} | A | 105 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(2)(3)²+(6)(16)=105 J. | {
"A": "Correct. The worked calculation gives 105 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 105 J, not 84 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 105 J, not 52.5 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_004805 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 5 Ω are connected in series; this combination is connected in parallel with a 6 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "7 A",
"B": "-7 A",
"C": "5.25 A",
"D": "8 A"
} | A | 7 A | Series branch resistance=10+5=15 Ω. Parallel equivalent R_eq=(15×6)/(15+6)=4.28571 Ω. Total current I=V/R_eq=30/4.28571=7 A. | {
"A": "Correct. The worked calculation gives 7 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7 A, not -7 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7 A, not 5.25 A.",
"D": "Incorrect. Substituting the stated values into the go... | [
"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_000886 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio 4. What is the sum of its first 5 terms? | {
"A": "343",
"B": "272.8",
"C": "341",
"D": "-341"
} | C | 341 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(4^5−1)/(4−1)=341. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 341, not 343.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 341, not 272.8.",
"C": "Correct. The worked calculation gives 341.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_005236 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +5 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "36.73469 N",
"B": "22.04082 N",
"C": "18.36735 N",
"D": "20.36735 N"
} | C | 18.36735 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(5×10⁻⁶)/(7×10⁻²)²=18.36735 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18.36735 N, not 36.73469 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18.36735 N, not 22.04082 N.",
"C": "Correct. The worked calculation gives 18.36735 N.",
"D": "Incorrect. Substitutin... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008201 | 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 24761 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": "105.9078 g",
"B": "106.9078 g",
"C": "104.9078 g",
"D": "127.08936 g"
} | A | 105.9078 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×24761/(2×96500)=105.9078 g. | {
"A": "Correct. The worked calculation gives 105.9078 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 105.9078 g, not 106.9078 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 105.9078 g, not 104.9078 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_000624 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 16 and common difference 10. Find the sum of its first 26 terms. | {
"A": "3668",
"B": "2749.5",
"C": "3666",
"D": "3664"
} | C | 3666 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=16, d=10, n=26: Sₙ=26/2[2(16)+(26−1)(10)]=3666. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3666, not 3668.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3666, not 2749.5.",
"C": "Correct. The worked calculation gives 3666.",
"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_009852 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(CN)_5]^-2, each CN ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "1.3",
"B": "3",
"C": "0",
"D": "6"
} | B | 3 | Let the formal oxidation state of Cu be x. Charge balance gives x+(5)(−1)=-2; hence x=-2+5=+3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 1.3.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 0.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006272 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 72 cm in front of a thin convex lens of focal length 22 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "2.44",
"B": "-0.56",
"C": "0.44",
"D": "-2.56"
} | C | 0.44 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(72)(22)/(72−22)=31.68 cm. Thus |m|=v/u=31.68/72=0.44. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.44, not 2.44.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.44, not -0.56.",
"C": "Correct. The worked calculation gives 0.44.",
"D": "Incorrect. Substituting the stated values into the ... | [
"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_005854 | 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 2.9 atm at 324 K. What is its pressure at 624 K? | {
"A": "4.18889 atm",
"B": "7.58519 atm",
"C": "3.58519 atm",
"D": "5.58519 atm"
} | D | 5.58519 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.9)(624)/(324)=5.58519 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.58519 atm, not 4.18889 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.58519 atm, not 7.58519 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_008215 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 14 A for 20792 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": "97.77248 g",
"B": "71.82936 g",
"C": "191.54495 g",
"D": "95.77248 g"
} | D | 95.77248 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×14×20792/(2×96500)=95.77248 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 95.77248 g, not 97.77248 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 95.77248 g, not 71.82936 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 95.772... | [
"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_003395 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 36 m s⁻¹ at 50° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "127.63108 m",
"B": "255.26217 m",
"C": "128.63108 m",
"D": "125.63108 m"
} | A | 127.63108 m | Range R=u²sin(2θ)/g. Substituting u=36, θ=50° and g=10 gives R=(36)²sin(100°)/10=127.63108 m. | {
"A": "Correct. The worked calculation gives 127.63108 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 127.63108 m, not 255.26217 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 127.63108 m, not 128.63108 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002859 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-1, 3, 4) and v=(1, -4, -2), calculate u·v. | {
"A": "-16.8",
"B": "-20",
"C": "-10.5",
"D": "-21"
} | D | -21 | The dot product is the sum of corresponding component products: (-1)(1)+(3)(-4)+(4)(-2)=-21. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -21, not -16.8.",
"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 -10.5.",
"D": "Correc... | [
"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_009665 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_8H_19N_2X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "-1",
"B": "1",
"C": "3",
"D": "0"
} | D | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×8+2+2−19−1)/2=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not -1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 3.",
"D": "Correct. The worked c... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006767 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 19 mol H₂ and 24 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "38 mol",
"B": "22.8 mol",
"C": "14.25 mol",
"D": "19 mol"
} | D | 19 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 19 mol H₂O; O₂ can produce 48 mol H₂O. The limiting condition is H₂; product=19 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 19 mol, not 38 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 19 mol, not 22.8 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 19 mol, not 14.25 mo... | [
"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_005542 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 13 μF capacitor is charged to a potential difference of 10 V. Calculate the energy stored, expressed in μJ. | {
"A": "651 μJ",
"B": "520 μJ",
"C": "650 μJ",
"D": "487.5 μJ"
} | C | 650 μJ | U=½CV². Since C=13 μF, U in μJ is ½×13×(10)²=650 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 650 μJ, not 651 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 650 μJ, not 520 μJ.",
"C": "Correct. The worked calculation gives 650 μJ.",
"D": "Incorrect. Substituting the stated values ... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004070 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.36. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "28.08 N",
"B": "18.72 N",
"C": "14.04 N",
"D": "9.36 N"
} | B | 18.72 N | Net force=mg(sinθ−μcosθ)=6×10×(0.6−0.36×0.8)=18.72 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18.72 N, not 28.08 N.",
"B": "Correct. The worked calculation gives 18.72 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18.72 N, not 14.04 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_003636 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 42 m s⁻¹ at 50° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "260.58013 m",
"B": "208.46411 m",
"C": "173.72009 m",
"D": "86.86004 m"
} | C | 173.72009 m | Range R=u²sin(2θ)/g. Substituting u=42, θ=50° and g=10 gives R=(42)²sin(100°)/10=173.72009 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 173.72009 m, not 260.58013 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 173.72009 m, not 208.46411 m.",
"C": "Correct. The worked calculation gives 173.72009 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006021 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 37 cm in front of a thin convex lens of focal length 27 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "2.7",
"B": "5.7",
"C": "4.05",
"D": "3.7"
} | A | 2.7 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(37)(27)/(37−27)=99.9 cm. Thus |m|=v/u=99.9/37=2.7. | {
"A": "Correct. The worked calculation gives 2.7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.7, not 5.7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.7, not 4.05.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_007570 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 54 mL of 0.10 M HCl is mixed with 95 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "24.8792",
"B": "2.24396",
"C": "14.4396",
"D": "12.4396"
} | D | 12.4396 | Excess OH⁻ moles=0.10×(95−54)/1000=0.004100 mol. Total volume=0.149 L, so [OH⁻]=0.027517 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.4396. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.4396, not 24.8792.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.4396, not 2.24396.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.4396, not 14.43... | [
"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_006647 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 11 kg is attached to an ideal spring of force constant 905 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.2205 s",
"B": "-1.7795 s",
"C": "0.2205 s",
"D": "-2.7795 s"
} | C | 0.2205 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(11/905)=0.2205 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.2205 s, not 1.2205 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.2205 s, not -1.7795 s.",
"C": "Correct. The worked calculation gives 0.2205 s.",
"D": "Incorrect. Substituting the sta... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004407 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 6 m is acted on by a constant torque of 53 N m about its central axis. Find its angular acceleration. | {
"A": "4.47222 rad s⁻²",
"B": "2.47222 rad s⁻²",
"C": "1.47222 rad s⁻²",
"D": "-0.52778 rad s⁻²"
} | C | 1.47222 rad s⁻² | For a solid disc, I=½MR²=½(2)(6)²=36 kg m². Using τ=Iα, α=53/36=1.47222 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.47222 rad s⁻², not 4.47222 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.47222 rad s⁻², not 2.47222 rad s⁻².",
"C": "Correct. The worked calculation gives 1.47222 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_008062 | 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 18434 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": "78.84594 g",
"B": "157.69189 g",
"C": "-78.84594 g",
"D": "118.26891 g"
} | A | 78.84594 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×13×18434/(2×96500)=78.84594 g. | {
"A": "Correct. The worked calculation gives 78.84594 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 78.84594 g, not 157.69189 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 78.84594 g, not -78.84594 g.",
"D": "Incorrect. Substitut... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006682 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 18 mol H₂ and 32 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "27 mol",
"B": "14.4 mol",
"C": "20 mol",
"D": "18 mol"
} | D | 18 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 18 mol H₂O; O₂ can produce 64 mol H₂O. The limiting condition is H₂; product=18 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18 mol, not 27 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18 mol, not 14.4 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18 mol, not 20 mol."... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009416 | 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_13H_28. Treat X as the total number of monovalent halogen atoms. | {
"A": "-2",
"B": "3",
"C": "0",
"D": "2"
} | C | 0 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×13+2+0−28−0)/2=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 3.",
"C": "Correct. The worked calculation gives 0.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"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_008548 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 1.28 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.84 K",
"B": "-3.84 K",
"C": "1.384 K",
"D": "3.84 K"
} | D | 3.84 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×1.0×1.28=3.84 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.84 K, not 0.84 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.84 K, not -3.84 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.84 K, not 1.384 K."... | [
"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_000340 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 21 and common difference 14. Find the sum of its first 12 terms. | {
"A": "2352",
"B": "1175",
"C": "1174",
"D": "1176"
} | D | 1176 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=21, d=14, n=12: Sₙ=12/2[2(21)+(12−1)(14)]=1176. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1176, not 2352.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1176, not 1175.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1176, not 1174.",
"D": "Corr... | [
"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_004035 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 37 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.24. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "16.096 N",
"B": "301.92 N",
"C": "150.96 N",
"D": "113.22 N"
} | C | 150.96 N | Net force=mg(sinθ−μcosθ)=37×10×(0.6−0.24×0.8)=150.96 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 150.96 N, not 16.096 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 150.96 N, not 301.92 N.",
"C": "Correct. The worked calculation gives 150.96 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_005954 | 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 3.6 atm at 287 K. What is its pressure at 392 K? | {
"A": "9.83415 atm",
"B": "2.91707 atm",
"C": "4.91707 atm",
"D": "3.91707 atm"
} | C | 4.91707 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.6)(392)/(287)=4.91707 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.91707 atm, not 9.83415 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.91707 atm, not 2.91707 atm.",
"C": "Correct. The worked calculation gives 4.91707 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006956 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 16 mol H₂ and 9 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "2.6 mol",
"B": "12 mol",
"C": "15 mol",
"D": "16 mol"
} | D | 16 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 16 mol H₂O; O₂ can produce 18 mol H₂O. The limiting condition is H₂; product=16 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 2.6 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 12 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16 mol, not 15 mol.",... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006518 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 24 kg is attached to an ideal spring of force constant 712 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "3.36719 s",
"B": "-0.36719 s",
"C": "0.36719 s",
"D": "-2.63281 s"
} | C | 0.36719 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(24/712)=0.36719 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.36719 s, not 3.36719 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.36719 s, not -0.36719 s.",
"C": "Correct. The worked calculation gives 0.36719 s.",
"D": "Incorrect. Substituting th... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003092 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-3-15i)/(7+2i). What is Re(z), the real part of z? | {
"A": "0.03774",
"B": "-2.96226",
"C": "-3.96226",
"D": "-0.96226"
} | D | -0.96226 | Multiply numerator and denominator by the conjugate (7-2i). Then Re(z)=(ac+bd)/(c²+d²)=((-3)(7)+(-15)(2))/(7²+(2)²)=-0.96226. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.96226, not 0.03774.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.96226, not -2.96226.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.96226, not -... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002177 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 8 red, 12 blue and 3 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.6166",
"B": "0.3834",
"C": "0.5751",
"D": "-2.6166"
} | B | 0.3834 | Favourable pairs = C(8,2)+C(12,2)+C(3,2)=97. Total pairs=C(23,2)=253. Therefore P=97/253=0.3834. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3834, not -0.6166.",
"B": "Correct. The worked calculation gives 0.3834.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3834, not 0.5751.",
"D": "Incorrect. Substituting the stated values... | [
"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_001850 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 6 elements can be selected from a set of 31 distinct elements? | {
"A": "-736281",
"B": "1104421.5",
"C": "736281",
"D": "589024.8"
} | C | 736281 | Order does not matter, so the count is C(31,6)=31!/[6!(25)!]=736281. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 736281, not -736281.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 736281, not 1104421.5.",
"C": "Correct. The worked calculation gives 736281.",
"D": "Incorrect. Substituting the stated val... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002497 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, -1], [5, 5]]. | {
"A": "38",
"B": "40",
"C": "80",
"D": "41"
} | B | 40 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(5)−(-1)(5)=40. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 40, not 38.",
"B": "Correct. The worked calculation gives 40.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 40, not 80.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007627 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 89 mL of 0.10 M HCl is mixed with 65 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "0.80731",
"B": "1.35548",
"C": "1.18073",
"D": "1.80731"
} | D | 1.80731 | Excess H⁺ moles=0.10×(89−65)/1000=0.002400 mol. Total volume=0.154 L, so [H⁺]=0.015584 M and pH=−log₁₀[H⁺]=1.80731. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.80731, not 0.80731.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.80731, not 1.35548.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.80731, not 1.180... | [
"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_002685 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-2, 2, 7) and v=(-6, -2, 5), calculate u·v. | {
"A": "32.25",
"B": "43",
"C": "21.5",
"D": "64.5"
} | B | 43 | The dot product is the sum of corresponding component products: (-2)(-6)+(2)(-2)+(7)(5)=43. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 43, not 32.25.",
"B": "Correct. The worked calculation gives 43.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 43, not 21.5.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001304 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-2x³ +1x² -1x+7. Evaluate f′(0). | {
"A": "-1.5",
"B": "0",
"C": "-1",
"D": "-2"
} | C | -1 | Differentiate: f′(x)=3(-2)x²+2(1)x+(-1). At x=0, f′(0)=3(-2)(0)²+2(1)(0)+(-1)=-1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -1, not -1.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1, not 0.",
"C": "Correct. The worked calculation gives -1.",
"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_001092 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=1x³ +0x² +3x+7. Evaluate f′(3). | {
"A": "36",
"B": "4",
"C": "22.5",
"D": "30"
} | D | 30 | Differentiate: f′(x)=3(1)x²+2(0)x+(3). At x=3, f′(3)=3(1)(3)²+2(0)(3)+(3)=30. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 30, not 36.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 30, not 22.5.",
"D": "Correct. The wo... | [
"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_006292 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 24 cm in front of a thin convex lens of focal length 10 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.42857",
"B": "2.71429",
"C": "0.71429",
"D": "3.71429"
} | C | 0.71429 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(24)(10)/(24−10)=17.14286 cm. Thus |m|=v/u=17.14286/24=0.71429. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.71429, not 1.42857.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.71429, not 2.71429.",
"C": "Correct. The worked calculation gives 0.71429.",
"D": "Incorrect. Substituting the stated va... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007566 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 89 mL of 0.10 M HCl is mixed with 77 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "3.21139",
"B": "4.28185",
"C": "0.14093",
"D": "2.14093"
} | D | 2.14093 | Excess H⁺ moles=0.10×(89−77)/1000=0.001200 mol. Total volume=0.166 L, so [H⁺]=0.007229 M and pH=−log₁₀[H⁺]=2.14093. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.14093, not 3.21139.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.14093, not 4.28185.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.14093, not 0.140... | [
"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_006595 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 19 kg is attached to an ideal spring of force constant 733 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.322 s",
"B": "0.322 s",
"C": "0.483 s",
"D": "3.322 s"
} | B | 0.322 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(19/733)=0.322 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.322 s, not -0.322 s.",
"B": "Correct. The worked calculation gives 0.322 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.322 s, not 0.483 s.",
"D": "Incorrect. Substituting the stated v... | [
"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_009687 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Co(OH)_4]^+1, each OH ligand has charge −1. Determine the formal oxidation state of Co. | {
"A": "3",
"B": "-5",
"C": "8",
"D": "5"
} | D | 5 | Let the formal oxidation state of Co be x. Charge balance gives x+(4)(−1)=+1; hence x=1+4=+5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5, not 3.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5, not -5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5, not 8.",
"D": "Correct. The worked c... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000264 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 +5x -7=0, let its roots be α and β. What is α²+β²? | {
"A": "1.2551",
"B": "2.5102",
"C": "4.5102",
"D": "-0.4898"
} | B | 2.5102 | By Vieta's relations, α+β = -5/7 and αβ = -7/7. Then α²+β²=(α+β)²−2αβ = (-5/7)²−2(-7/7) = 2.5102. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.5102, not 1.2551.",
"B": "Correct. The worked calculation gives 2.5102.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.5102, not 4.5102.",
"D": "Incorrect. Substituting the stated values ... | [
"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_004694 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 5 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": "1.43158 A",
"B": "2.14737 A",
"C": "1.14316 A",
"D": "-1.43158 A"
} | A | 1.43158 A | Series branch resistance=10+5=15 Ω. Parallel equivalent R_eq=(15×19)/(15+19)=8.38235 Ω. Total current I=V/R_eq=12/8.38235=1.43158 A. | {
"A": "Correct. The worked calculation gives 1.43158 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.43158 A, not 2.14737 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.43158 A, not 1.14316 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_006955 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 33 mol H₂ and 35 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "4.3 mol",
"B": "32 mol",
"C": "39.6 mol",
"D": "33 mol"
} | D | 33 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 33 mol H₂O; O₂ can produce 70 mol H₂O. The limiting condition is H₂; product=33 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33 mol, not 4.3 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33 mol, not 32 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 33 mol, not 39.6 mol.... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004778 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 11 Ω are connected in series; this combination is connected in parallel with a 5 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.45714 A",
"B": "4.45714 A",
"C": "5.45714 A",
"D": "1.45714 A"
} | B | 4.45714 A | Series branch resistance=10+11=21 Ω. Parallel equivalent R_eq=(21×5)/(21+5)=4.03846 Ω. Total current I=V/R_eq=18/4.03846=4.45714 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.45714 A, not 3.45714 A.",
"B": "Correct. The worked calculation gives 4.45714 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.45714 A, not 5.45714 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 |
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