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_009035 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.18 V, transfers 3 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.91775 V",
"B": "1.2785 V",
"C": "0.2785 V",
"D": "-1.7215 V"
} | B | 1.2785 V | Apply the Nernst equation: E=1.18−(0.0591/3)(-5)=1.2785 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.2785 V, not 1.91775 V.",
"B": "Correct. The worked calculation gives 1.2785 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.2785 V, not 0.2785 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000622 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -20 and common difference 3. Find the sum of its first 17 terms. | {
"A": "136",
"B": "67",
"C": "68",
"D": "54.4"
} | C | 68 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-20, d=3, n=17: Sₙ=17/2[2(-20)+(17−1)(3)]=68. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 68, not 136.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 68, not 67.",
"C": "Correct. The worked calculation gives 68.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"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_005429 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 21 μF capacitor is charged to a potential difference of 22 V. Calculate the energy stored, expressed in μJ. | {
"A": "509.2 μJ",
"B": "5084 μJ",
"C": "5080 μJ",
"D": "5082 μJ"
} | D | 5082 μJ | U=½CV². Since C=21 μF, U in μJ is ½×21×(22)²=5082 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5082 μJ, not 509.2 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5082 μJ, not 5084 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5082 μJ, not 5080... | [
"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_004399 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 3 kg and radius 2 m is acted on by a constant torque of 18 N m about its central axis. Find its angular acceleration. | {
"A": "1.3 rad s⁻²",
"B": "3 rad s⁻²",
"C": "-3 rad s⁻²",
"D": "4 rad s⁻²"
} | B | 3 rad s⁻² | For a solid disc, I=½MR²=½(3)(2)²=6 kg m². Using τ=Iα, α=18/6=3 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3 rad s⁻², not 1.3 rad s⁻².",
"B": "Correct. The worked calculation gives 3 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3 rad s⁻², not -3 rad s⁻².",
"D": "Incorrect. Substituting ... | [
"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_004137 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.28. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "49.632 N",
"B": "5.136 N",
"C": "42.36 N",
"D": "41.36 N"
} | D | 41.36 N | Net force=mg(sinθ−μcosθ)=11×10×(0.6−0.28×0.8)=41.36 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 41.36 N, not 49.632 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 41.36 N, not 5.136 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 41.36 N, not 42.3... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005808 | 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 4.9 atm at 354 K. What is its pressure at 682 K? | {
"A": "7.08008 atm",
"B": "14.16017 atm",
"C": "7.44011 atm",
"D": "9.44011 atm"
} | D | 9.44011 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.9)(682)/(354)=9.44011 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9.44011 atm, not 7.08008 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.44011 atm, not 14.16017 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9... | [
"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_001635 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (5x² +2x -2) dx. | {
"A": "16.33333",
"B": "13.33333",
"C": "14.33333",
"D": "11.33333"
} | B | 13.33333 | An antiderivative is (5/3)x³+(2/2)x²+(-2)x. Evaluating between 0 and 2 gives (5/3)(2)³+(2/2)(2)²+(-2)(2)=13.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13.33333, not 16.33333.",
"B": "Correct. The worked calculation gives 13.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13.33333, not 14.33333.",
"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_003762 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 10 m s⁻¹. A constant net force does 21 N of work over 17 m in the direction of motion. Find its final kinetic energy. | {
"A": "756 J",
"B": "757 J",
"C": "-757 J",
"D": "567.75 J"
} | B | 757 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(10)²+(21)(17)=757 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 757 J, not 756 J.",
"B": "Correct. The worked calculation gives 757 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 757 J, not -757 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_000207 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 +1x +12=0, let its roots be α and β. What is α²+β²? | {
"A": "-4.76",
"B": "-2.76",
"C": "-3.76",
"D": "-2.38"
} | A | -4.76 | By Vieta's relations, α+β = -1/5 and αβ = 12/5. Then α²+β²=(α+β)²−2αβ = (-1/5)²−2(12/5) = -4.76. | {
"A": "Correct. The worked calculation gives -4.76.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -4.76, not -2.76.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -4.76, not -3.76.",
"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_000021 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 +15x -5=0, let its roots be α and β. What is α²+β²? | {
"A": "235",
"B": "176.25",
"C": "117.5",
"D": "234"
} | A | 235 | By Vieta's relations, α+β = -15/1 and αβ = -5/1. Then α²+β²=(α+β)²−2αβ = (-15/1)²−2(-5/1) = 235. | {
"A": "Correct. The worked calculation gives 235.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 235, not 176.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 235, not 117.5.",
"D": "Incorrect. Substituting the stated values into the g... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002720 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(4, 3, 2) and v=(2, -4, 3), calculate u·v. | {
"A": "4",
"B": "1",
"C": "2",
"D": "1.5"
} | C | 2 | The dot product is the sum of corresponding component products: (4)(2)+(3)(-4)+(2)(3)=2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.",
"C": "Correct. The worked calculation gives 2.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"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_009176 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.73 V, transfers 2 electrons, and has reaction quotient Q=10^-3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.61399 V",
"B": "0.81865 V",
"C": "3.81865 V",
"D": "1.22798 V"
} | B | 0.81865 V | Apply the Nernst equation: E=0.73−(0.0591/2)(-3)=0.81865 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.81865 V, not 0.61399 V.",
"B": "Correct. The worked calculation gives 0.81865 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.81865 V, not 3.81865 V.",
"D": "Incorrect. Substituting the... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000604 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -15 and common difference 7. Find the sum of its first 34 terms. | {
"A": "3416",
"B": "6834",
"C": "3418",
"D": "3417"
} | D | 3417 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-15, d=7, n=34: Sₙ=34/2[2(-15)+(34−1)(7)]=3417. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3417, not 3416.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3417, not 6834.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3417, not 3418.",
"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_000141 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 +11x +3=0, let its roots be α and β. What is α²+β²? | {
"A": "25.25",
"B": "27.25",
"C": "28.25",
"D": "20.4375"
} | B | 27.25 | By Vieta's relations, α+β = -11/2 and αβ = 3/2. Then α²+β²=(α+β)²−2αβ = (-11/2)²−2(3/2) = 27.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 27.25, not 25.25.",
"B": "Correct. The worked calculation gives 27.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 27.25, not 28.25.",
"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_006088 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 80 cm in front of a thin convex lens of focal length 24 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.64286",
"B": "-0.57143",
"C": "-2.57143",
"D": "0.42857"
} | D | 0.42857 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(80)(24)/(80−24)=34.28571 cm. Thus |m|=v/u=34.28571/80=0.42857. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.42857, not 0.64286.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.42857, not -0.57143.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.42857, not -2.5... | [
"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_000876 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 4. What is the sum of its first 7 terms? | {
"A": "54610",
"B": "109220",
"C": "81915",
"D": "-54610"
} | A | 54610 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(4^7−1)/(4−1)=54610. | {
"A": "Correct. The worked calculation gives 54610.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 54610, not 109220.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 54610, not 81915.",
"D": "Incorrect. Substituting the stated values into... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009571 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_18H_32X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "1",
"B": "0",
"C": "2",
"D": "0.5"
} | A | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×18+2+0−32−4)/2=1. | {
"A": "Correct. The worked calculation gives 1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 2.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000654 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 6 and common difference 15. Find the sum of its first 12 terms. | {
"A": "849.6",
"B": "796.5",
"C": "1062",
"D": "1060"
} | C | 1062 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=6, d=15, n=12: Sₙ=12/2[2(6)+(12−1)(15)]=1062. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1062, not 849.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1062, not 796.5.",
"C": "Correct. The worked calculation gives 1062.",
"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_000389 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 23 and common difference 2. Find the sum of its first 15 terms. | {
"A": "832.5",
"B": "554",
"C": "555",
"D": "666"
} | C | 555 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=23, d=2, n=15: Sₙ=15/2[2(23)+(15−1)(2)]=555. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 555, not 832.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 555, not 554.",
"C": "Correct. The worked calculation gives 555.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001408 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^5 (4x² +6x -5) dx. | {
"A": "216.66667",
"B": "-216.66667",
"C": "260",
"D": "162.5"
} | A | 216.66667 | An antiderivative is (4/3)x³+(6/2)x²+(-5)x. Evaluating between 0 and 5 gives (4/3)(5)³+(6/2)(5)²+(-5)(5)=216.66667. | {
"A": "Correct. The worked calculation gives 216.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 216.66667, not -216.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 216.66667, not 260.",
"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_001976 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 48 distinct elements? | {
"A": "452818792.8",
"B": "566023491",
"C": "377348994",
"D": "754697988"
} | C | 377348994 | Order does not matter, so the count is C(48,8)=48!/[8!(40)!]=377348994. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 377348994, not 452818792.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 377348994, not 566023491.",
"C": "Correct. The worked calculation gives 377348994.",
"D": "Incorrect. Substituting t... | [
"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_004022 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 16 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.34. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "41.984 N",
"B": "6.248 N",
"C": "52.48 N",
"D": "51.48 N"
} | C | 52.48 N | Net force=mg(sinθ−μcosθ)=16×10×(0.6−0.34×0.8)=52.48 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 52.48 N, not 41.984 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 52.48 N, not 6.248 N.",
"C": "Correct. The worked calculation gives 52.48 N.",
"D": "Incorrect. Substituting the stated v... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004013 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 34 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.23. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "142.44 N",
"B": "143.44 N",
"C": "212.16 N",
"D": "141.44 N"
} | D | 141.44 N | Net force=mg(sinθ−μcosθ)=34×10×(0.6−0.23×0.8)=141.44 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 141.44 N, not 142.44 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 141.44 N, not 143.44 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 141.44 N, not ... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007033 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 18 mol of gas at 475 K and 0.94 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "1492.73904 L",
"B": "746.36952 L",
"C": "748.36952 L",
"D": "559.77714 L"
} | B | 746.36952 L | PV=nRT, so V=nRT/P=(18)(0.082057)(475)/(0.94)=746.36952 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 746.36952 L, not 1492.73904 L.",
"B": "Correct. The worked calculation gives 746.36952 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 746.36952 L, not 748.36952 L.",
"D": "Incorrect. Subst... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004061 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 44 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.23. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "-183.04 N",
"B": "183.04 N",
"C": "184.04 N",
"D": "182.04 N"
} | B | 183.04 N | Net force=mg(sinθ−μcosθ)=44×10×(0.6−0.23×0.8)=183.04 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 183.04 N, not -183.04 N.",
"B": "Correct. The worked calculation gives 183.04 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 183.04 N, not 184.04 N.",
"D": "Incorrect. Substituting the sta... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008146 | 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 19520 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": "-44.95668 g",
"B": "45.95668 g",
"C": "43.95668 g",
"D": "44.95668 g"
} | D | 44.95668 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×7×19520/(2×96500)=44.95668 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 44.95668 g, not -44.95668 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 44.95668 g, not 45.95668 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 44.95... | [
"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_001977 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 2 elements can be selected from a set of 26 distinct elements? | {
"A": "326",
"B": "325",
"C": "-325",
"D": "327"
} | B | 325 | Order does not matter, so the count is C(26,2)=26!/[2!(24)!]=325. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 325, not 326.",
"B": "Correct. The worked calculation gives 325.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 325, not -325.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_001821 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 4 elements can be selected from a set of 73 distinct elements? | {
"A": "1088432",
"B": "-1088430",
"C": "870744",
"D": "1088430"
} | D | 1088430 | Order does not matter, so the count is C(73,4)=73!/[4!(69)!]=1088430. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1088430, not 1088432.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1088430, not -1088430.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1088430, not 8707... | [
"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_008018 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 15 A for 15095 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": "89.39681 g",
"B": "-74.49734 g",
"C": "37.24867 g",
"D": "74.49734 g"
} | D | 74.49734 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×15×15095/(2×96500)=74.49734 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 74.49734 g, not 89.39681 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 74.49734 g, not -74.49734 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 74.49... | [
"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_007825 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 63 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "-15.75 mmol L⁻¹",
"B": "17.75 mmol L⁻¹",
"C": "16.75 mmol L⁻¹",
"D": "15.75 mmol L⁻¹"
} | D | 15.75 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=63/2^2=15.75 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15.75 mmol L⁻¹, not -15.75 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 15.75 mmol L⁻¹, not 17.75 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing rela... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008096 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 12 A for 22547 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": "-89.01976 g",
"B": "88.01976 g",
"C": "66.76482 g",
"D": "89.01976 g"
} | D | 89.01976 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×12×22547/(2×96500)=89.01976 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 89.01976 g, not -89.01976 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 89.01976 g, not 88.01976 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 89.01... | [
"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_004687 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 15 Ω are connected in series; this combination is connected in parallel with a 19 Ω resistor across a 6 V ideal battery. Find the total current supplied by the battery. | {
"A": "-2.43421 A",
"B": "1.13158 A",
"C": "0.42434 A",
"D": "0.56579 A"
} | D | 0.56579 A | Series branch resistance=9+15=24 Ω. Parallel equivalent R_eq=(24×19)/(24+19)=10.60465 Ω. Total current I=V/R_eq=6/10.60465=0.56579 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.56579 A, not -2.43421 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.56579 A, not 1.13158 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.56579 A... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000288 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 -8x -3=0, let its roots be α and β. What is α²+β²? | {
"A": "4.16667",
"B": "-2.77778",
"C": "2.77778",
"D": "3.77778"
} | C | 2.77778 | By Vieta's relations, α+β = 8/6 and αβ = -3/6. Then α²+β²=(α+β)²−2αβ = (8/6)²−2(-3/6) = 2.77778. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.77778, not 4.16667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.77778, not -2.77778.",
"C": "Correct. The worked calculation gives 2.77778.",
"D": "Incorrect. Substituting the stated v... | [
"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_007639 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 25 mL of 0.10 M HCl is mixed with 52 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "13.54487",
"B": "12.54487",
"C": "18.81731",
"D": "15.54487"
} | B | 12.54487 | Excess OH⁻ moles=0.10×(52−25)/1000=0.002700 mol. Total volume=0.077 L, so [OH⁻]=0.035065 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.54487. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.54487, not 13.54487.",
"B": "Correct. The worked calculation gives 12.54487.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.54487, not 18.81731.",
"D": "Incorrect. Substituting the stat... | [
"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_004760 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 12 Ω are connected in series; this combination is connected in parallel with a 4 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.14286 A",
"B": "5.35714 A",
"C": "5.14286 A",
"D": "7.14286 A"
} | D | 7.14286 A | Series branch resistance=9+12=21 Ω. Parallel equivalent R_eq=(21×4)/(21+4)=3.36 Ω. Total current I=V/R_eq=24/3.36=7.14286 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.14286 A, not 4.14286 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.14286 A, not 5.35714 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.14286 A,... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000576 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 7 and common difference 10. Find the sum of its first 33 terms. | {
"A": "2755.5",
"B": "5509",
"C": "5511",
"D": "-5511"
} | C | 5511 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=7, d=10, n=33: Sₙ=33/2[2(7)+(33−1)(10)]=5511. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5511, not 2755.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5511, not 5509.",
"C": "Correct. The worked calculation gives 5511.",
"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_008731 | 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 0.34 mol L⁻¹ and initially B is absent. At equilibrium, 43% of A has dissociated at constant volume. Find K_c. | {
"A": "1.04412",
"B": "0.44116",
"C": "-2.55884",
"D": "2.44116"
} | B | 0.44116 | Let α=0.43. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.34)(0.43)²/(1−0.43)=0.44116. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.44116, not 1.04412.",
"B": "Correct. The worked calculation gives 0.44116.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.44116, not -2.55884.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007707 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 32 mmol L⁻¹, what concentration remains after 140 minutes? | {
"A": "-1.75 mmol L⁻¹",
"B": "0.125 mmol L⁻¹",
"C": "3.25 mmol L⁻¹",
"D": "0.25 mmol L⁻¹"
} | D | 0.25 mmol L⁻¹ | 140 minutes corresponds to 7 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=32/2^7=0.25 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25 mmol L⁻¹, not -1.75 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25 mmol L⁻¹, not 0.125 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relatio... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000915 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio 5. What is the sum of its first 12 terms? | {
"A": "244140624",
"B": "12207032.2",
"C": "122070312",
"D": "61035156"
} | C | 122070312 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(5^12−1)/(5−1)=122070312. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 122070312, not 244140624.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 122070312, not 12207032.2.",
"C": "Correct. The worked calculation gives 122070312.",
"D": "Incorrect. Substituting th... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006095 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 52 cm in front of a thin convex lens of focal length 23 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "2.7931",
"B": "0.7931",
"C": "1.7931",
"D": "-0.7931"
} | B | 0.7931 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(52)(23)/(52−23)=41.24138 cm. Thus |m|=v/u=41.24138/52=0.7931. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.7931, not 2.7931.",
"B": "Correct. The worked calculation gives 0.7931.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7931, not 1.7931.",
"D": "Incorrect. Substituting the stated values ... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002847 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-4, -4, 1) and v=(0, 8, 3), calculate u·v. | {
"A": "-28",
"B": "-34.8",
"C": "-1.9",
"D": "-29"
} | D | -29 | The dot product is the sum of corresponding component products: (-4)(0)+(-4)(8)+(1)(3)=-29. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -29, not -28.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -29, not -34.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -29, not -1.9.",
"D": "Correct... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006440 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 13 kg is attached to an ideal spring of force constant 848 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "-0.75237 s",
"B": "1.02476 s",
"C": "0.24763 s",
"D": "0.18572 s"
} | C | 0.24763 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(13/848)=0.24763 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.24763 s, not -0.75237 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.24763 s, not 1.02476 s.",
"C": "Correct. The worked calculation gives 0.24763 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_005551 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 12 μF capacitor is charged to a potential difference of 8 V. Calculate the energy stored, expressed in μJ. | {
"A": "383 μJ",
"B": "576 μJ",
"C": "768 μJ",
"D": "384 μJ"
} | D | 384 μJ | U=½CV². Since C=12 μF, U in μJ is ½×12×(8)²=384 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 384 μJ, not 383 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 384 μJ, not 576 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 384 μJ, not 768 μJ.",
... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007989 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 58 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "0.33984 mmol L⁻¹",
"B": "-0.22656 mmol L⁻¹",
"C": "0.22656 mmol L⁻¹",
"D": "-0.77344 mmol L⁻¹"
} | C | 0.22656 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=58/2^8=0.22656 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.22656 mmol L⁻¹, not 0.33984 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.22656 mmol L⁻¹, not -0.22656 mmol L⁻¹.",
"C": "Correct. The worked calculation gives 0.22656 mmol L⁻¹.",... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002697 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(0, -3, 7) and v=(0, 0, -6), calculate u·v. | {
"A": "-41",
"B": "-42",
"C": "-50.4",
"D": "42"
} | B | -42 | The dot product is the sum of corresponding component products: (0)(0)+(-3)(0)+(7)(-6)=-42. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -42, not -41.",
"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 gove... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002852 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(7, -3, 8) and v=(6, -6, 5), calculate u·v. | {
"A": "11",
"B": "100",
"C": "50",
"D": "102"
} | B | 100 | The dot product is the sum of corresponding component products: (7)(6)+(-3)(-6)+(8)(5)=100. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 100, not 11.",
"B": "Correct. The worked calculation gives 100.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 100, not 50.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007187 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 4 mol of gas at 621 K and 0.21 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "970.61709 L",
"B": "485.30854 L",
"C": "-970.61709 L",
"D": "1455.92563 L"
} | A | 970.61709 L | PV=nRT, so V=nRT/P=(4)(0.082057)(621)/(0.21)=970.61709 L. | {
"A": "Correct. The worked calculation gives 970.61709 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 970.61709 L, not 485.30854 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 970.61709 L, not -970.61709 L.",
"D": "Incorrect. Subst... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006852 | 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 11 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "1.2 mol",
"B": "1.5 mol",
"C": "-1 mol",
"D": "2 mol"
} | D | 2 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 2 mol H₂O; O₂ can produce 22 mol H₂O. The limiting condition is H₂; product=2 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 1.2 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not 1.5 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2 mol, not -1 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_007300 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 15 mol of gas at 330 K and 2.3 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "264.9014 L",
"B": "132.4507 L",
"C": "174.60093 L",
"D": "176.60093 L"
} | D | 176.60093 L | PV=nRT, so V=nRT/P=(15)(0.082057)(330)/(2.3)=176.60093 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 176.60093 L, not 264.9014 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 176.60093 L, not 132.4507 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 176.... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006346 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 25 kg is attached to an ideal spring of force constant 223 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.66965 s",
"B": "-2.33035 s",
"C": "0.33482 s",
"D": "1.3393 s"
} | A | 0.66965 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(25/223)=0.66965 s. | {
"A": "Correct. The worked calculation gives 0.66965 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.66965 s, not -2.33035 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.66965 s, not 0.33482 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_002394 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, -8], [7, 1]]. | {
"A": "65",
"B": "67",
"C": "-65",
"D": "130"
} | A | 65 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(1)−(-8)(7)=65. | {
"A": "Correct. The worked calculation gives 65.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 65, not 67.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 65, not -65.",
"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_008697 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.56 mol L⁻¹ and initially B is absent. At equilibrium, 47% of A has dissociated at constant volume. Find K_c. | {
"A": "5.20157",
"B": "2.60078",
"C": "-2.60078",
"D": "1.60078"
} | B | 2.60078 | Let α=0.47. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.56)(0.47)²/(1−0.47)=2.60078. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.60078, not 5.20157.",
"B": "Correct. The worked calculation gives 2.60078.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.60078, not -2.60078.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008878 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.88 mol L⁻¹ and initially B is absent. At equilibrium, 58% of A has dissociated at constant volume. Find K_c. | {
"A": "6.02316",
"B": "3.01158",
"C": "-6.02316",
"D": "9.03474"
} | A | 6.02316 | Let α=0.58. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.88)(0.58)²/(1−0.58)=6.02316. | {
"A": "Correct. The worked calculation gives 6.02316.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.02316, not 3.01158.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.02316, not -6.02316.",
"D": "Incorrect. Substituting the stated v... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000918 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 5 and common ratio 4. What is the sum of its first 7 terms? | {
"A": "40957.5",
"B": "32766",
"C": "27303",
"D": "27305"
} | D | 27305 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=5(4^7−1)/(4−1)=27305. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 27305, not 40957.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 27305, not 32766.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 27305, not 27303.",
"D... | [
"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_000852 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 1 and common ratio 2. What is the sum of its first 6 terms? | {
"A": "126",
"B": "75.6",
"C": "65",
"D": "63"
} | D | 63 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=1(2^6−1)/(2−1)=63. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 63, not 126.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 63, not 75.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 63, not 65.",
"D": "Correct. The ... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002386 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 8], [4, -5]]. | {
"A": "-23.5",
"B": "-3.7",
"C": "-47",
"D": "-94"
} | C | -47 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(-5)−(8)(4)=-47. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -47, not -23.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -47, not -3.7.",
"C": "Correct. The worked calculation gives -47.",
"D": "Incorrect. Substituting the stated values into the gov... | [
"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_001101 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=0x³ -7x² +7x+7. Evaluate f′(-4). | {
"A": "63",
"B": "64",
"C": "62",
"D": "-63"
} | A | 63 | Differentiate: f′(x)=3(0)x²+2(-7)x+(7). At x=-4, f′(-4)=3(0)(-4)²+2(-7)(-4)+(7)=63. | {
"A": "Correct. The worked calculation gives 63.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 63, not 64.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 63, not 62.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003324 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-11+3i)/(7+12i). What is Re(z), the real part of z? | {
"A": "-0.31865",
"B": "0.21244",
"C": "2.78756",
"D": "-0.21244"
} | D | -0.21244 | Multiply numerator and denominator by the conjugate (7-12i). Then Re(z)=(ac+bd)/(c²+d²)=((-11)(7)+(3)(12))/(7²+(12)²)=-0.21244. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.21244, not -0.31865.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.21244, not 0.21244.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.21244, not 2... | [
"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_004938 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 2 Ω and 3 Ω are connected in series; this combination is connected in parallel with a 13 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "3.64615 A",
"B": "6.64615 A",
"C": "-6.64615 A",
"D": "13.29231 A"
} | B | 6.64615 A | Series branch resistance=2+3=5 Ω. Parallel equivalent R_eq=(5×13)/(5+13)=3.61111 Ω. Total current I=V/R_eq=24/3.61111=6.64615 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.64615 A, not 3.64615 A.",
"B": "Correct. The worked calculation gives 6.64615 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.64615 A, not -6.64615 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_006650 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 7 kg is attached to an ideal spring of force constant 938 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.17277 s",
"B": "1.01728 s",
"C": "3.17277 s",
"D": "0.25916 s"
} | A | 0.17277 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(7/938)=0.17277 s. | {
"A": "Correct. The worked calculation gives 0.17277 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.17277 s, not 1.01728 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.17277 s, not 3.17277 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_003362 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 97 m s⁻¹ at 20° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "603.79886 m",
"B": "604.79886 m",
"C": "483.83909 m",
"D": "1209.59772 m"
} | B | 604.79886 m | Range R=u²sin(2θ)/g. Substituting u=97, θ=20° and g=10 gives R=(97)²sin(40°)/10=604.79886 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 604.79886 m, not 603.79886 m.",
"B": "Correct. The worked calculation gives 604.79886 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 604.79886 m, not 483.83909 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_005596 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 39 μF capacitor is charged to a potential difference of 28 V. Calculate the energy stored, expressed in μJ. | {
"A": "1529.8 μJ",
"B": "15288 μJ",
"C": "22932 μJ",
"D": "15286 μJ"
} | B | 15288 μJ | U=½CV². Since C=39 μF, U in μJ is ½×39×(28)²=15288 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 15288 μJ, not 1529.8 μJ.",
"B": "Correct. The worked calculation gives 15288 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 15288 μJ, not 22932 μJ.",
"D": "Incorrect. Substituting the sta... | [
"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_003562 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 29 m s⁻¹ at 60° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "-72.83274 m",
"B": "8.28327 m",
"C": "74.83274 m",
"D": "72.83274 m"
} | D | 72.83274 m | Range R=u²sin(2θ)/g. Substituting u=29, θ=60° and g=10 gives R=(29)²sin(120°)/10=72.83274 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 72.83274 m, not -72.83274 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 72.83274 m, not 8.28327 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 72.832... | [
"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_009224 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.43 V, transfers 3 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.4497 V",
"B": "0.72485 V",
"C": "-1.4497 V",
"D": "-1.5503 V"
} | A | 1.4497 V | Apply the Nernst equation: E=1.43−(0.0591/3)(-1)=1.4497 V. | {
"A": "Correct. The worked calculation gives 1.4497 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.4497 V, not 0.72485 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.4497 V, not -1.4497 V.",
"D": "Incorrect. Substituting the st... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009723 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cr(CN)_3]^+3, each CN ligand has charge −1. Determine the formal oxidation state of Cr. | {
"A": "9",
"B": "12",
"C": "1.6",
"D": "6"
} | D | 6 | Let the formal oxidation state of Cr be x. Charge balance gives x+(3)(−1)=+3; hence x=3+3=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 1.6.",
"D": "Correct. The worked... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001870 | 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 89 distinct elements? | {
"A": "290553494",
"B": "581106989",
"C": "581106988",
"D": "58110699.8"
} | C | 581106988 | Order does not matter, so the count is C(89,6)=89!/[6!(83)!]=581106988. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 581106988, not 290553494.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 581106988, not 581106989.",
"C": "Correct. The worked calculation gives 581106988.",
"D": "Incorrect. Substituting the... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001418 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (4x² -2x +1) dx. | {
"A": "110",
"B": "-73.33333",
"C": "73.33333",
"D": "36.66667"
} | C | 73.33333 | An antiderivative is (4/3)x³+(-2/2)x²+(1)x. Evaluating between 0 and 4 gives (4/3)(4)³+(-2/2)(4)²+(1)(4)=73.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 73.33333, not 110.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 73.33333, not -73.33333.",
"C": "Correct. The worked calculation gives 73.33333.",
"D": "Incorrect. Substituting the stated v... | [
"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_007632 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 11 mL of 0.10 M HCl is mixed with 42 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.76709",
"B": "14.76709",
"C": "9.76709",
"D": "9.57531"
} | A | 12.76709 | Excess OH⁻ moles=0.10×(42−11)/1000=0.003100 mol. Total volume=0.053 L, so [OH⁻]=0.058491 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.76709. | {
"A": "Correct. The worked calculation gives 12.76709.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.76709, not 14.76709.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.76709, not 9.76709.",
"D": "Incorrect. Substituting the state... | [
"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_008639 | 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 1.7 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": "1.768 K",
"B": "3.536 K",
"C": "2.652 K",
"D": "1.1768 K"
} | A | 1.768 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.52×1.7=1.768 K. | {
"A": "Correct. The worked calculation gives 1.768 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.768 K, not 3.536 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.768 K, not 2.652 K.",
"D": "Incorrect. Substituting the stated va... | [
"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_007274 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 15 mol of gas at 260 K and 1.77 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "-180.80356 L",
"B": "19.08036 L",
"C": "180.80356 L",
"D": "361.60712 L"
} | C | 180.80356 L | PV=nRT, so V=nRT/P=(15)(0.082057)(260)/(1.77)=180.80356 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 180.80356 L, not -180.80356 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 180.80356 L, not 19.08036 L.",
"C": "Correct. The worked calculation gives 180.80356 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008808 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.71 mol L⁻¹ and initially B is absent. At equilibrium, 72% of A has dissociated at constant volume. Find K_c. | {
"A": "15.66377",
"B": "12.66377",
"C": "-12.66377",
"D": "10.66377"
} | B | 12.66377 | Let α=0.72. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.71)(0.72)²/(1−0.72)=12.66377. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.66377, not 15.66377.",
"B": "Correct. The worked calculation gives 12.66377.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.66377, not -12.66377.",
"D": "Incorrect. Substituting the sta... | [
"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_007683 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 93 mmol L⁻¹, what concentration remains after 60 minutes? | {
"A": "8.71875 mmol L⁻¹",
"B": "11.625 mmol L⁻¹",
"C": "17.4375 mmol L⁻¹",
"D": "8.625 mmol L⁻¹"
} | B | 11.625 mmol L⁻¹ | 60 minutes corresponds to 3 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=93/2^3=11.625 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.625 mmol L⁻¹, not 8.71875 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 11.625 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.625 mmol L⁻¹, not 17.4375 mmol L⁻¹.",
"... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008458 | 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 1.92 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.05088 K",
"B": "1.94912 K",
"C": "4.94912 K",
"D": "2.94912 K"
} | D | 2.94912 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.512×1.92=2.94912 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.94912 K, not -0.05088 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.94912 K, not 1.94912 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.94912 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_001317 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-1x³ -10x² -2x+7. Evaluate f′(2). | {
"A": "-108",
"B": "54",
"C": "-43.2",
"D": "-54"
} | D | -54 | Differentiate: f′(x)=3(-1)x²+2(-10)x+(-2). At x=2, f′(2)=3(-1)(2)²+2(-10)(2)+(-2)=-54. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -54, not -108.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -54, not 54.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -54, not -43.2.",
"D": "Correct.... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003492 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 29 m s⁻¹ at 75° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "44.05 m",
"B": "42.05 m",
"C": "-42.05 m",
"D": "63.075 m"
} | B | 42.05 m | Range R=u²sin(2θ)/g. Substituting u=29, θ=75° and g=10 gives R=(29)²sin(150°)/10=42.05 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 42.05 m, not 44.05 m.",
"B": "Correct. The worked calculation gives 42.05 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 42.05 m, not -42.05 m.",
"D": "Incorrect. Substituting the stated v... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000135 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 +7x -11=0, let its roots be α and β. What is α²+β²? | {
"A": "3.14286",
"B": "4.14286",
"C": "6.14286",
"D": "2.07143"
} | B | 4.14286 | By Vieta's relations, α+β = -7/7 and αβ = -11/7. Then α²+β²=(α+β)²−2αβ = (-7/7)²−2(-11/7) = 4.14286. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.14286, not 3.14286.",
"B": "Correct. The worked calculation gives 4.14286.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.14286, not 6.14286.",
"D": "Incorrect. Substituting the stated va... | [
"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_002109 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 8 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": "-1.64762",
"B": "0.35238",
"C": "0.70476",
"D": "0.52857"
} | B | 0.35238 | Favourable pairs = C(3,2)+C(8,2)+C(4,2)=37. Total pairs=C(15,2)=105. Therefore P=37/105=0.35238. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35238, not -1.64762.",
"B": "Correct. The worked calculation gives 0.35238.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35238, not 0.70476.",
"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_001095 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=6x³ -5x² +10x+7. Evaluate f′(0). | {
"A": "10",
"B": "7.5",
"C": "12",
"D": "15"
} | A | 10 | Differentiate: f′(x)=3(6)x²+2(-5)x+(10). At x=0, f′(0)=3(6)(0)²+2(-5)(0)+(10)=10. | {
"A": "Correct. The worked calculation gives 10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10, not 7.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10, not 12.",
"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_003581 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 51 m s⁻¹ at 30° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "225.25321 m",
"B": "180.20257 m",
"C": "270.30385 m",
"D": "227.25321 m"
} | A | 225.25321 m | Range R=u²sin(2θ)/g. Substituting u=51, θ=30° and g=10 gives R=(51)²sin(60°)/10=225.25321 m. | {
"A": "Correct. The worked calculation gives 225.25321 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 225.25321 m, not 180.20257 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 225.25321 m, not 270.30385 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_004859 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 9 Ω are connected in series; this combination is connected in parallel with a 4 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.375 A",
"B": "0.75 A",
"C": "2.75 A",
"D": "-0.25 A"
} | C | 2.75 A | Series branch resistance=9+9=18 Ω. Parallel equivalent R_eq=(18×4)/(18+4)=3.27273 Ω. Total current I=V/R_eq=9/3.27273=2.75 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.75 A, not 1.375 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.75 A, not 0.75 A.",
"C": "Correct. The worked calculation gives 2.75 A.",
"D": "Incorrect. Substituting the stated values... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003692 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 8 kg block initially moves at 4 m s⁻¹. A constant net force does 19 N of work over 14 m in the direction of motion. Find its final kinetic energy. | {
"A": "330 J",
"B": "264 J",
"C": "328 J",
"D": "495 J"
} | A | 330 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(8)(4)²+(19)(14)=330 J. | {
"A": "Correct. The worked calculation gives 330 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 330 J, not 264 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 330 J, not 328 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_000919 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 12 and common ratio 4. What is the sum of its first 5 terms? | {
"A": "8184",
"B": "4092",
"C": "4091",
"D": "4093"
} | B | 4092 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=12(4^5−1)/(4−1)=4092. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4092, not 8184.",
"B": "Correct. The worked calculation gives 4092.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4092, not 4091.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_000589 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 5 and common difference 12. Find the sum of its first 33 terms. | {
"A": "651.1",
"B": "9751.5",
"C": "5200.8",
"D": "6501"
} | D | 6501 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=5, d=12, n=33: Sₙ=33/2[2(5)+(33−1)(12)]=6501. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6501, not 651.1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6501, not 9751.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6501, not 5200.8.",
"D": ... | [
"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_002789 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(9, 6, 9) and v=(-7, -2, 9), calculate u·v. | {
"A": "1.6",
"B": "6",
"C": "3",
"D": "7"
} | B | 6 | The dot product is the sum of corresponding component products: (9)(-7)+(6)(-2)+(9)(9)=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 1.6.",
"B": "Correct. The worked calculation gives 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009087 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.98 V, transfers 3 electrons, and has reaction quotient Q=10^-1. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-2.0003 V",
"B": "0.9997 V",
"C": "2.9997 V",
"D": "1.9997 V"
} | B | 0.9997 V | Apply the Nernst equation: E=0.98−(0.0591/3)(-1)=0.9997 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.9997 V, not -2.0003 V.",
"B": "Correct. The worked calculation gives 0.9997 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9997 V, not 2.9997 V.",
"D": "Incorrect. Substituting the sta... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002032 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 12 blue and 9 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.31724",
"B": "0.23793",
"C": "2.31724",
"D": "0.31724"
} | D | 0.31724 | Favourable pairs = C(9,2)+C(12,2)+C(9,2)=138. Total pairs=C(30,2)=435. Therefore P=138/435=0.31724. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31724, not 1.31724.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31724, not 0.23793.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31724, not 2.317... | [
"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_001538 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^8 (2x² +5x +3) dx. | {
"A": "525.33333",
"B": "788",
"C": "394",
"D": "-525.33333"
} | A | 525.33333 | An antiderivative is (2/3)x³+(5/2)x²+(3)x. Evaluating between 0 and 8 gives (2/3)(8)³+(5/2)(8)²+(3)(8)=525.33333. | {
"A": "Correct. The worked calculation gives 525.33333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 525.33333, not 788.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 525.33333, not 394.",
"D": "Incorrect. Substituting the stated valu... | [
"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_004377 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 5 m is acted on by a constant torque of 47 N m about its central axis. Find its angular acceleration. | {
"A": "3.752 rad s⁻²",
"B": "2.752 rad s⁻²",
"C": "0.752 rad s⁻²",
"D": "1.128 rad s⁻²"
} | C | 0.752 rad s⁻² | For a solid disc, I=½MR²=½(5)(5)²=62.5 kg m². Using τ=Iα, α=47/62.5=0.752 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.752 rad s⁻², not 3.752 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.752 rad s⁻², not 2.752 rad s⁻².",
"C": "Correct. The worked calculation gives 0.752 rad s⁻².",
"D": "Incorre... | [
"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_006405 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 23 kg is attached to an ideal spring of force constant 1167 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.14039 s",
"B": "0.28078 s",
"C": "0.42116 s",
"D": "1.02808 s"
} | B | 0.28078 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(23/1167)=0.28078 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.28078 s, not 0.14039 s.",
"B": "Correct. The worked calculation gives 0.28078 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.28078 s, not 0.42116 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_000253 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 -14x -7=0, let its roots be α and β. What is α²+β²? | {
"A": "-26.44444",
"B": "26.44444",
"C": "31.73333",
"D": "19.83333"
} | B | 26.44444 | By Vieta's relations, α+β = 14/3 and αβ = -7/3. Then α²+β²=(α+β)²−2αβ = (14/3)²−2(-7/3) = 26.44444. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26.44444, not -26.44444.",
"B": "Correct. The worked calculation gives 26.44444.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26.44444, not 31.73333.",
"D": "Incorrect. Substituting the sta... | [
"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_001511 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (5x² -5x +4) dx. | {
"A": "292",
"B": "294",
"C": "588",
"D": "220.5"
} | B | 294 | An antiderivative is (5/3)x³+(-5/2)x²+(4)x. Evaluating between 0 and 6 gives (5/3)(6)³+(-5/2)(6)²+(4)(6)=294. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 294, not 292.",
"B": "Correct. The worked calculation gives 294.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 294, not 588.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_004001 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 3 kg block initially moves at 7 m s⁻¹. A constant net force does 8 N of work over 11 m in the direction of motion. Find its final kinetic energy. | {
"A": "193.8 J",
"B": "161.5 J",
"C": "163.5 J",
"D": "-161.5 J"
} | B | 161.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(3)(7)²+(8)(11)=161.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 161.5 J, not 193.8 J.",
"B": "Correct. The worked calculation gives 161.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 161.5 J, not 163.5 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_009786 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Ni(Cl)_5]^+3, each Cl ligand has charge −1. Determine the formal oxidation state of Ni. | {
"A": "6",
"B": "5",
"C": "8",
"D": "12"
} | C | 8 | Let the formal oxidation state of Ni be x. Charge balance gives x+(5)(−1)=+3; hence x=3+5=+8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 5.",
"C": "Correct. The worked calculation gives 8.",
"D": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003663 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 113 m s⁻¹ at 25° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "733.62161 m",
"B": "98.81621 m",
"C": "782.52972 m",
"D": "978.16215 m"
} | D | 978.16215 m | Range R=u²sin(2θ)/g. Substituting u=113, θ=25° and g=10 gives R=(113)²sin(50°)/10=978.16215 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 978.16215 m, not 733.62161 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 978.16215 m, not 98.81621 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 978... | [
"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_006730 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 31 mol H₂ and 13 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "27 mol",
"B": "26 mol",
"C": "13 mol",
"D": "24 mol"
} | B | 26 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 31 mol H₂O; O₂ can produce 26 mol H₂O. The limiting condition is O₂; product=26 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 27 mol.",
"B": "Correct. The worked calculation gives 26 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 26 mol, not 13 mol.",
"D": "Incorrect. Substituting the stated values ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008833 | chemistry | physical_chemistry | equilibrium_degree_dissociation | very_hard | provisional_template_level_label | single_correct_mcq | For A(g) ⇌ 2B(g), the initial concentration of A is 1.23 mol L⁻¹ and initially B is absent. At equilibrium, 62% of A has dissociated at constant volume. Find K_c. | {
"A": "1.4977",
"B": "2.48848",
"C": "7.97697",
"D": "4.97697"
} | D | 4.97697 | Let α=0.62. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.23)(0.62)²/(1−0.62)=4.97697. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.97697, not 1.4977.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.97697, not 2.48848.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.97697, not 7.9769... | [
"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_002299 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 9 red, 12 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": "0.3202",
"B": "-1.6798",
"C": "0.1601",
"D": "3.3202"
} | A | 0.3202 | Favourable pairs = C(9,2)+C(12,2)+C(8,2)=130. Total pairs=C(29,2)=406. Therefore P=130/406=0.3202. | {
"A": "Correct. The worked calculation gives 0.3202.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3202, not -1.6798.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3202, not 0.1601.",
"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_007037 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 12 mol of gas at 473 K and 0.55 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "635.12118 L",
"B": "848.82824 L",
"C": "846.82824 L",
"D": "845.82824 L"
} | C | 846.82824 L | PV=nRT, so V=nRT/P=(12)(0.082057)(473)/(0.55)=846.82824 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 846.82824 L, not 635.12118 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 846.82824 L, not 848.82824 L.",
"C": "Correct. The worked calculation gives 846.82824 L.",
"D": "Incorrect. Substi... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006738 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 29 mol H₂ and 7 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "11 mol",
"B": "2.4 mol",
"C": "7 mol",
"D": "14 mol"
} | D | 14 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 29 mol H₂O; O₂ can produce 14 mol H₂O. The limiting condition is O₂; product=14 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 14 mol, not 11 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 14 mol, not 2.4 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 14 mol, not 7 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_009027 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.83 V, transfers 3 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.9482 V",
"B": "-0.0518 V",
"C": "-2.0518 V",
"D": "1.09482 V"
} | A | 0.9482 V | Apply the Nernst equation: E=0.83−(0.0591/3)(-6)=0.9482 V. | {
"A": "Correct. The worked calculation gives 0.9482 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9482 V, not -0.0518 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9482 V, not -2.0518 V.",
"D": "Incorrect. Substituting the st... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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