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_001619 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^4 (-4x² +5x -5) dx. | {
"A": "-98",
"B": "-65.33333",
"C": "65.33333",
"D": "-63.33333"
} | B | -65.33333 | An antiderivative is (-4/3)x³+(5/2)x²+(-5)x. Evaluating between 0 and 4 gives (-4/3)(4)³+(5/2)(4)²+(-5)(4)=-65.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -65.33333, not -98.",
"B": "Correct. The worked calculation gives -65.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -65.33333, not 65.33333.",
"D": "Incorrect. Substituting the stated... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009182 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.41 V, transfers 2 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "4.55775 V",
"B": "1.55775 V",
"C": "0.77887 V",
"D": "1.15577 V"
} | B | 1.55775 V | Apply the Nernst equation: E=1.41−(0.0591/2)(-5)=1.55775 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.55775 V, not 4.55775 V.",
"B": "Correct. The worked calculation gives 1.55775 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.55775 V, not 0.77887 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_000040 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 1x^2 -13x -8=0, let its roots be α and β. What is α²+β²? | {
"A": "92.5",
"B": "148",
"C": "277.5",
"D": "185"
} | D | 185 | By Vieta's relations, α+β = 13/1 and αβ = -8/1. Then α²+β²=(α+β)²−2αβ = (13/1)²−2(-8/1) = 185. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 185, not 92.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 185, not 148.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 185, not 277.5.",
"D": "Correct... | [
"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_001032 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-2x³ -7x² +8x+7. Evaluate f′(1). | {
"A": "-12",
"B": "-6",
"C": "-0.2",
"D": "12"
} | A | -12 | Differentiate: f′(x)=3(-2)x²+2(-7)x+(8). At x=1, f′(1)=3(-2)(1)²+2(-7)(1)+(8)=-12. | {
"A": "Correct. The worked calculation gives -12.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -12, not -6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -12, not -0.2.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005381 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 21 μF capacitor is charged to a potential difference of 3 V. Calculate the energy stored, expressed in μJ. | {
"A": "113.4 μJ",
"B": "93.5 μJ",
"C": "94.5 μJ",
"D": "70.875 μJ"
} | C | 94.5 μJ | U=½CV². Since C=21 μF, U in μJ is ½×21×(3)²=94.5 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 94.5 μJ, not 113.4 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 94.5 μJ, not 93.5 μJ.",
"C": "Correct. The worked calculation gives 94.5 μJ.",
"D": "Incorrect. Substituting the stated v... | [
"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_009945 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(CN)_5]^-1, each CN ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "-4",
"B": "4",
"C": "1.4",
"D": "7"
} | B | 4 | Let the formal oxidation state of Mn be x. Charge balance gives x+(5)(−1)=-1; hence x=-1+5=+4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not -4.",
"B": "Correct. The worked calculation gives 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 1.4.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003608 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 39 m s⁻¹ at 18° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "90.40214 m",
"B": "134.10321 m",
"C": "178.80427 m",
"D": "89.40214 m"
} | D | 89.40214 m | Range R=u²sin(2θ)/g. Substituting u=39, θ=18° and g=10 gives R=(39)²sin(36°)/10=89.40214 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 89.40214 m, not 90.40214 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 89.40214 m, not 134.10321 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 89.40... | [
"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_009751 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(CN)_6]^+2, each CN ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "10",
"B": "4",
"C": "7",
"D": "8"
} | D | 8 | Let the formal oxidation state of Pt be x. Charge balance gives x+(6)(−1)=+2; hence x=2+6=+8. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8, not 10.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8, not 4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8, not 7.",
"D": "Correct. The worked c... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006336 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 49 cm in front of a thin convex lens of focal length 19 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-0.63333",
"B": "0.63333",
"C": "-0.36667",
"D": "0.95"
} | B | 0.63333 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(49)(19)/(49−19)=31.03333 cm. Thus |m|=v/u=31.03333/49=0.63333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.63333, not -0.63333.",
"B": "Correct. The worked calculation gives 0.63333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.63333, not -0.36667.",
"D": "Incorrect. Substituting the stated ... | [
"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_003845 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 6 kg block initially moves at 1 m s⁻¹. A constant net force does 17 N of work over 7 m in the direction of motion. Find its final kinetic energy. | {
"A": "123 J",
"B": "183 J",
"C": "121 J",
"D": "122 J"
} | D | 122 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(6)(1)²+(17)(7)=122 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 122 J, not 123 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 122 J, not 183 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 122 J, not 121 J.",
"D":... | [
"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_000907 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 3 and common ratio 4. What is the sum of its first 11 terms? | {
"A": "6291454.5",
"B": "4194302",
"C": "5033163.6",
"D": "4194303"
} | D | 4194303 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=3(4^11−1)/(4−1)=4194303. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4194303, not 6291454.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4194303, not 4194302.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4194303, not 503... | [
"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_003065 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(14+10i)/(11+12i). What is Re(z), the real part of z? | {
"A": "-1.03396",
"B": "1.03396",
"C": "2.03396",
"D": "4.03396"
} | B | 1.03396 | Multiply numerator and denominator by the conjugate (11-12i). Then Re(z)=(ac+bd)/(c²+d²)=((14)(11)+(10)(12))/(11²+(12)²)=1.03396. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.03396, not -1.03396.",
"B": "Correct. The worked calculation gives 1.03396.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.03396, not 2.03396.",
"D": "Incorrect. Substituting the stated v... | [
"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_005567 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 14 μF capacitor is charged to a potential difference of 25 V. Calculate the energy stored, expressed in μJ. | {
"A": "2187.5 μJ",
"B": "4373 μJ",
"C": "4375 μJ",
"D": "4377 μJ"
} | C | 4375 μJ | U=½CV². Since C=14 μF, U in μJ is ½×14×(25)²=4375 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4375 μJ, not 2187.5 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4375 μJ, not 4373 μJ.",
"C": "Correct. The worked calculation gives 4375 μJ.",
"D": "Incorrect. Substituting the stated ... | [
"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_000280 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 +12x -12=0, let its roots be α and β. What is α²+β²? | {
"A": "19.2",
"B": "26",
"C": "24",
"D": "25"
} | C | 24 | By Vieta's relations, α+β = -12/3 and αβ = -12/3. Then α²+β²=(α+β)²−2αβ = (-12/3)²−2(-12/3) = 24. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24, not 19.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 24, not 26.",
"C": "Correct. The worked calculation gives 24.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"Vieta's formulas",
"symmetric polynomial expressions"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_quadratic_vieta | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005697 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 0.9 atm at 296 K. What is its pressure at 729 K? | {
"A": "4.21655 atm",
"B": "1.22166 atm",
"C": "-2.21655 atm",
"D": "2.21655 atm"
} | D | 2.21655 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.9)(729)/(296)=2.21655 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.21655 atm, not 4.21655 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.21655 atm, not 1.22166 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.... | [
"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_008054 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 8 A for 9166 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": "25.12605 g",
"B": "24.12605 g",
"C": "18.09454 g",
"D": "3.41261 g"
} | B | 24.12605 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×8×9166/(2×96500)=24.12605 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 24.12605 g, not 25.12605 g.",
"B": "Correct. The worked calculation gives 24.12605 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24.12605 g, not 18.09454 g.",
"D": "Incorrect. Substitutin... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001384 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (-2x² +1x -5) dx. | {
"A": "-156",
"B": "-14.6",
"C": "-155",
"D": "-234"
} | A | -156 | An antiderivative is (-2/3)x³+(1/2)x²+(-5)x. Evaluating between 0 and 6 gives (-2/3)(6)³+(1/2)(6)²+(-5)(6)=-156. | {
"A": "Correct. The worked calculation gives -156.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -156, not -14.6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -156, not -155.",
"D": "Incorrect. Substituting the stated values into the ... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004538 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 4 kg and radius 1 m is acted on by a constant torque of 71 N m about its central axis. Find its angular acceleration. | {
"A": "36.5 rad s⁻²",
"B": "53.25 rad s⁻²",
"C": "35.5 rad s⁻²",
"D": "17.75 rad s⁻²"
} | C | 35.5 rad s⁻² | For a solid disc, I=½MR²=½(4)(1)²=2 kg m². Using τ=Iα, α=71/2=35.5 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 35.5 rad s⁻², not 36.5 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 35.5 rad s⁻², not 53.25 rad s⁻².",
"C": "Correct. The worked calculation gives 35.5 rad s⁻².",
"D": "Incorrect. ... | [
"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_009084 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.92 V, transfers 1 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.5191 V",
"B": "2.0764 V",
"C": "1.0382 V",
"D": "0.77865 V"
} | C | 1.0382 V | Apply the Nernst equation: E=0.92−(0.0591/1)(-2)=1.0382 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0382 V, not 0.5191 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0382 V, not 2.0764 V.",
"C": "Correct. The worked calculation gives 1.0382 V.",
"D": "Incorrect. Substituting the stat... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001674 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 12 elements can be selected from a set of 52 distinct elements? | {
"A": "206379406870",
"B": "412758813740",
"C": "309569110305",
"D": "103189703435"
} | A | 206379406870 | Order does not matter, so the count is C(52,12)=52!/[12!(40)!]=206379406870. | {
"A": "Correct. The worked calculation gives 206379406870.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 206379406870, not 412758813740.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 206379406870, not 309569110305.",
"D": "Incorrect. S... | [
"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_008869 | 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 0.56 mol L⁻¹ and initially B is absent. At equilibrium, 41% of A has dissociated at constant volume. Find K_c. | {
"A": "1.63821",
"B": "0.63821",
"C": "-2.36179",
"D": "-0.63821"
} | B | 0.63821 | Let α=0.41. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.56)(0.41)²/(1−0.41)=0.63821. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.63821, not 1.63821.",
"B": "Correct. The worked calculation gives 0.63821.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.63821, not -2.36179.",
"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_005533 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 30 μF capacitor is charged to a potential difference of 17 V. Calculate the energy stored, expressed in μJ. | {
"A": "4337 μJ",
"B": "4336 μJ",
"C": "4333 μJ",
"D": "4335 μJ"
} | D | 4335 μJ | U=½CV². Since C=30 μF, U in μJ is ½×30×(17)²=4335 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4335 μJ, not 4337 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4335 μJ, not 4336 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4335 μJ, not 4333 ... | [
"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_000790 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 3. What is the sum of its first 10 terms? | {
"A": "442860",
"B": "295240",
"C": "354288",
"D": "-295240"
} | B | 295240 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(3^10−1)/(3−1)=295240. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 295240, not 442860.",
"B": "Correct. The worked calculation gives 295240.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 295240, not 354288.",
"D": "Incorrect. Substituting the stated values ... | [
"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_009412 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_8H_9N_3. Treat X as the total number of monovalent halogen atoms. | {
"A": "6",
"B": "9",
"C": "4.5",
"D": "3"
} | A | 6 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×8+2+3−9−0)/2=6. | {
"A": "Correct. The worked calculation gives 6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.5.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008936 | 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 0.18 mol L⁻¹ and initially B is absent. At equilibrium, 65% of A has dissociated at constant volume. Find K_c. | {
"A": "0.86914",
"B": "1.08691",
"C": "3.86914",
"D": "-1.13086"
} | A | 0.86914 | Let α=0.65. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.18)(0.65)²/(1−0.65)=0.86914. | {
"A": "Correct. The worked calculation gives 0.86914.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.86914, not 1.08691.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.86914, not 3.86914.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009617 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_10H_8. Treat X as the total number of monovalent halogen atoms. | {
"A": "1.7",
"B": "3.5",
"C": "7",
"D": "8"
} | C | 7 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×10+2+0−8−0)/2=7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 1.7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 3.5.",
"C": "Correct. The worked calculation gives 7.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_006073 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 34 cm in front of a thin convex lens of focal length 11 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.3587",
"B": "0.47826",
"C": "0.95652",
"D": "3.47826"
} | B | 0.47826 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(34)(11)/(34−11)=16.26087 cm. Thus |m|=v/u=16.26087/34=0.47826. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.47826, not 0.3587.",
"B": "Correct. The worked calculation gives 0.47826.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.47826, not 0.95652.",
"D": "Incorrect. Substituting the stated val... | [
"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_005835 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.8 atm at 341 K. What is its pressure at 634 K? | {
"A": "2.60293 atm",
"B": "3.9044 atm",
"C": "8.20587 atm",
"D": "5.20587 atm"
} | D | 5.20587 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.8)(634)/(341)=5.20587 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.20587 atm, not 2.60293 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.20587 atm, not 3.9044 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.2... | [
"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_000492 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 10 and common difference 13. Find the sum of its first 10 terms. | {
"A": "685",
"B": "822",
"C": "548",
"D": "-685"
} | A | 685 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=10, d=13, n=10: Sₙ=10/2[2(10)+(10−1)(13)]=685. | {
"A": "Correct. The worked calculation gives 685.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 685, not 822.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 685, not 548.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000182 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 -13x -11=0, let its roots be α and β. What is α²+β²? | {
"A": "16.72222",
"B": "7.36111",
"C": "8.36111",
"D": "4.18056"
} | C | 8.36111 | By Vieta's relations, α+β = 13/6 and αβ = -11/6. Then α²+β²=(α+β)²−2αβ = (13/6)²−2(-11/6) = 8.36111. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.36111, not 16.72222.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.36111, not 7.36111.",
"C": "Correct. The worked calculation gives 8.36111.",
"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_002444 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, -7], [3, 6]]. | {
"A": "29",
"B": "27",
"C": "20.25",
"D": "13.5"
} | B | 27 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(6)−(-7)(3)=27. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 27, not 29.",
"B": "Correct. The worked calculation gives 27.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 27, not 20.25.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000885 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 2. What is the sum of its first 10 terms? | {
"A": "12276",
"B": "-10230",
"C": "20460",
"D": "10230"
} | D | 10230 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(2^10−1)/(2−1)=10230. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10230, not 12276.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 10230, not -10230.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10230, not 20460.",
"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_002423 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, 3], [5, -7]]. | {
"A": "-22",
"B": "-11",
"C": "-44",
"D": "-24"
} | A | -22 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(-7)−(3)(5)=-22. | {
"A": "Correct. The worked calculation gives -22.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -22, not -11.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -22, not -44.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002216 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 9 blue and 6 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.31429",
"B": "0.47143",
"C": "1.03143",
"D": "-1.68571"
} | A | 0.31429 | Favourable pairs = C(6,2)+C(9,2)+C(6,2)=66. Total pairs=C(21,2)=210. Therefore P=66/210=0.31429. | {
"A": "Correct. The worked calculation gives 0.31429.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31429, not 0.47143.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31429, not 1.03143.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006485 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 19 kg is attached to an ideal spring of force constant 770 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.31417 s",
"B": "2.31417 s",
"C": "-0.31417 s",
"D": "-1.68583 s"
} | A | 0.31417 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(19/770)=0.31417 s. | {
"A": "Correct. The worked calculation gives 0.31417 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31417 s, not 2.31417 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31417 s, not -0.31417 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_006822 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 44 mol H₂ and 17 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "36 mol",
"B": "34 mol",
"C": "27.2 mol",
"D": "17 mol"
} | B | 34 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 44 mol H₂O; O₂ can produce 34 mol H₂O. The limiting condition is O₂; product=34 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 34 mol, not 36 mol.",
"B": "Correct. The worked calculation gives 34 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 34 mol, not 27.2 mol.",
"D": "Incorrect. Substituting the stated value... | [
"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_004084 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 35 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.19. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "156.8 N",
"B": "125.44 N",
"C": "155.8 N",
"D": "154.8 N"
} | A | 156.8 N | Net force=mg(sinθ−μcosθ)=35×10×(0.6−0.19×0.8)=156.8 N. | {
"A": "Correct. The worked calculation gives 156.8 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 156.8 N, not 125.44 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 156.8 N, not 155.8 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_008654 | 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 1.51 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "6.04 K",
"B": "1.604 K",
"C": "-6.04 K",
"D": "4.53 K"
} | A | 6.04 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×1.0×1.51=6.04 K. | {
"A": "Correct. The worked calculation gives 6.04 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.04 K, not 1.604 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.04 K, not -6.04 K.",
"D": "Incorrect. Substituting the stated value... | [
"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_003187 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(3-3i)/(10+10i). What is Re(z), the real part of z? | {
"A": "-2",
"B": "2",
"C": "1",
"D": "0"
} | D | 0 | Multiply numerator and denominator by the conjugate (10-10i). Then Re(z)=(ac+bd)/(c²+d²)=((3)(10)+(-3)(10))/(10²+(10)²)=0. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0, not -2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0, not 1.",
"D": "Correct. The worked c... | [
"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_001834 | 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 84 distinct elements? | {
"A": "406481544",
"B": "487777852.8",
"C": "203240772",
"D": "40648155.4"
} | A | 406481544 | Order does not matter, so the count is C(84,6)=84!/[6!(78)!]=406481544. | {
"A": "Correct. The worked calculation gives 406481544.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 406481544, not 487777852.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 406481544, not 203240772.",
"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_006814 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 18 mol H₂ and 3 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "4.5 mol",
"B": "3 mol",
"C": "9 mol",
"D": "6 mol"
} | D | 6 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 18 mol H₂O; O₂ can produce 6 mol H₂O. The limiting condition is O₂; product=6 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 4.5 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 3 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6 mol, not 9 mol.",
"D... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006627 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 1 kg is attached to an ideal spring of force constant 553 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.1701 s",
"B": "3.08505 s",
"C": "0.08505 s",
"D": "1.0085 s"
} | C | 0.08505 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(1/553)=0.08505 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.08505 s, not 0.1701 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.08505 s, not 3.08505 s.",
"C": "Correct. The worked calculation gives 0.08505 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_003982 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 4 m s⁻¹. A constant net force does 5 N of work over 9 m in the direction of motion. Find its final kinetic energy. | {
"A": "202 J",
"B": "151.5 J",
"C": "-101 J",
"D": "101 J"
} | D | 101 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(4)²+(5)(9)=101 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 101 J, not 202 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 101 J, not 151.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 101 J, not -101 J.",
"... | [
"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_005902 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1 atm at 254 K. What is its pressure at 635 K? | {
"A": "2.5 atm",
"B": "4.5 atm",
"C": "3.5 atm",
"D": "5 atm"
} | A | 2.5 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1)(635)/(254)=2.5 atm. | {
"A": "Correct. The worked calculation gives 2.5 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.5 atm, not 4.5 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.5 atm, not 3.5 atm.",
"D": "Incorrect. Substituting the stated va... | [
"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_002972 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(9, -1, 5) and v=(4, -4, -3), calculate u·v. | {
"A": "25",
"B": "23",
"C": "-25",
"D": "24"
} | A | 25 | The dot product is the sum of corresponding component products: (9)(4)+(-1)(-4)+(5)(-3)=25. | {
"A": "Correct. The worked calculation gives 25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 25, not 23.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 25, not -25.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004813 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 9 Ω and 13 Ω are connected in series; this combination is connected in parallel with a 19 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "4.94258 A",
"B": "3.94258 A",
"C": "-0.05742 A",
"D": "2.94258 A"
} | D | 2.94258 A | Series branch resistance=9+13=22 Ω. Parallel equivalent R_eq=(22×19)/(22+19)=10.19512 Ω. Total current I=V/R_eq=30/10.19512=2.94258 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.94258 A, not 4.94258 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.94258 A, not 3.94258 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.94258 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_000786 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio 2. What is the sum of its first 8 terms? | {
"A": "892.5",
"B": "1338.75",
"C": "-1785",
"D": "1785"
} | D | 1785 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(2^8−1)/(2−1)=1785. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1785, not 892.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1785, not 1338.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1785, not -1785.",
"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_007979 | 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 55 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "5.4375 mmol L⁻¹",
"B": "3.4375 mmol L⁻¹",
"C": "1.71875 mmol L⁻¹",
"D": "2.57812 mmol L⁻¹"
} | B | 3.4375 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=55/2^4=3.4375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.4375 mmol L⁻¹, not 5.4375 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 3.4375 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3.4375 mmol L⁻¹, not 1.71875 mmol L⁻¹.",
"D... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001370 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (0x² +4x +5) dx. | {
"A": "66",
"B": "39.6",
"C": "33",
"D": "32"
} | C | 33 | An antiderivative is (0/3)x³+(4/2)x²+(5)x. Evaluating between 0 and 3 gives (0/3)(3)³+(4/2)(3)²+(5)(3)=33. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 33, not 66.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 33, not 39.6.",
"C": "Correct. The worked calculation gives 33.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"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_007593 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 69 mL of 0.10 M HCl is mixed with 14 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "-1.17872",
"B": "-0.82128",
"C": "1.17872",
"D": "4.17872"
} | C | 1.17872 | Excess H⁺ moles=0.10×(69−14)/1000=0.005500 mol. Total volume=0.083 L, so [H⁺]=0.066265 M and pH=−log₁₀[H⁺]=1.17872. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.17872, not -1.17872.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.17872, not -0.82128.",
"C": "Correct. The worked calculation gives 1.17872.",
"D": "Incorrect. Substituting the stated ... | [
"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_001598 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^3 (5x² +8x +1) dx. | {
"A": "67.2",
"B": "86",
"C": "84",
"D": "83"
} | C | 84 | An antiderivative is (5/3)x³+(8/2)x²+(1)x. Evaluating between 0 and 3 gives (5/3)(3)³+(8/2)(3)²+(1)(3)=84. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 84, not 67.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 84, not 86.",
"C": "Correct. The worked calculation gives 84.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"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_005557 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 26 μF capacitor is charged to a potential difference of 22 V. Calculate the energy stored, expressed in μJ. | {
"A": "3146 μJ",
"B": "6292 μJ",
"C": "6290 μJ",
"D": "9438 μJ"
} | B | 6292 μJ | U=½CV². Since C=26 μF, U in μJ is ½×26×(22)²=6292 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6292 μJ, not 3146 μJ.",
"B": "Correct. The worked calculation gives 6292 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6292 μJ, not 6290 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001948 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 11 elements can be selected from a set of 76 distinct elements? | {
"A": "11454320742360",
"B": "5727160371179",
"C": "8590740556770",
"D": "5727160371180"
} | D | 5727160371180 | Order does not matter, so the count is C(76,11)=76!/[11!(65)!]=5727160371180. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5727160371180, not 11454320742360.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5727160371180, not 5727160371179.",
"C": "Incorrect. Substituting the stated values into the governing relation... | [
"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_008531 | chemistry | physical_chemistry | boiling_point_elevation | hard | provisional_template_level_label | single_correct_mcq | A non-volatile solute is dissolved in water to produce a solution of molality 0.35 mol kg⁻¹. If its van't Hoff factor is 3 and K_b for water is 0.52 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.546 K",
"B": "0.273 K",
"C": "1.546 K",
"D": "3.546 K"
} | A | 0.546 K | ΔT_b=iK_bm. Substitution gives ΔT_b=3×0.52×0.35=0.546 K. | {
"A": "Correct. The worked calculation gives 0.546 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.546 K, not 0.273 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.546 K, not 1.546 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_004785 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 4 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 11 Ω resistor across a 24 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.51515 A",
"B": "1.35152 A",
"C": "3.51515 A",
"D": "1.75758 A"
} | C | 3.51515 A | Series branch resistance=4+14=18 Ω. Parallel equivalent R_eq=(18×11)/(18+11)=6.82759 Ω. Total current I=V/R_eq=24/6.82759=3.51515 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.51515 A, not 2.51515 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.51515 A, not 1.35152 A.",
"C": "Correct. The worked calculation gives 3.51515 A.",
"D": "Incorrect. Substituting the... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008787 | 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 0.48 mol L⁻¹ and initially B is absent. At equilibrium, 23% of A has dissociated at constant volume. Find K_c. | {
"A": "0.13191",
"B": "-0.86809",
"C": "0.06595",
"D": "0.26381"
} | A | 0.13191 | Let α=0.23. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.48)(0.23)²/(1−0.23)=0.13191. | {
"A": "Correct. The worked calculation gives 0.13191.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.13191, not -0.86809.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.13191, not 0.06595.",
"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_004291 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.45. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "9.6 N",
"B": "7.2 N",
"C": "-9.6 N",
"D": "14.4 N"
} | A | 9.6 N | Net force=mg(sinθ−μcosθ)=4×10×(0.6−0.45×0.8)=9.6 N. | {
"A": "Correct. The worked calculation gives 9.6 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9.6 N, not 7.2 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9.6 N, not -9.6 N.",
"D": "Incorrect. Substituting the stated values into... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003290 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(5-2i)/(4+11i). What is Re(z), the real part of z? | {
"A": "-0.0146",
"B": "0.0146",
"C": "0.99854",
"D": "-0.0292"
} | A | -0.0146 | Multiply numerator and denominator by the conjugate (4-11i). Then Re(z)=(ac+bd)/(c²+d²)=((5)(4)+(-2)(11))/(4²+(11)²)=-0.0146. | {
"A": "Correct. The worked calculation gives -0.0146.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.0146, not 0.0146.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.0146, not 0.99854.",
"D": "Incorrect. Substituting the stated val... | [
"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_001510 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (-3x² -5x +1) dx. | {
"A": "-16",
"B": "-18",
"C": "-0.6",
"D": "-8"
} | A | -16 | An antiderivative is (-3/3)x³+(-5/2)x²+(1)x. Evaluating between 0 and 2 gives (-3/3)(2)³+(-5/2)(2)²+(1)(2)=-16. | {
"A": "Correct. The worked calculation gives -16.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -16, not -18.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -16, not -0.6.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001594 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (-3x² +7x -5) dx. | {
"A": "4",
"B": "-4",
"C": "-5",
"D": "-3"
} | B | -4 | An antiderivative is (-3/3)x³+(7/2)x²+(-5)x. Evaluating between 0 and 2 gives (-3/3)(2)³+(7/2)(2)²+(-5)(2)=-4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -4, not 4.",
"B": "Correct. The worked calculation gives -4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -4, not -5.",
"D": "Incorrect. Substituting the stated values into the governing re... | [
"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_009494 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_13H_15N_1X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "4.5",
"B": "6",
"C": "8",
"D": "12"
} | B | 6 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×13+2+1−15−2)/2=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.5.",
"B": "Correct. The worked calculation gives 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 8.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003035 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(9-9i)/(6+10i). What is Re(z), the real part of z? | {
"A": "-0.39706",
"B": "-0.26471",
"C": "0.97353",
"D": "-0.52941"
} | B | -0.26471 | Multiply numerator and denominator by the conjugate (6-10i). Then Re(z)=(ac+bd)/(c²+d²)=((9)(6)+(-9)(10))/(6²+(10)²)=-0.26471. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.26471, not -0.39706.",
"B": "Correct. The worked calculation gives -0.26471.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.26471, not 0.97353.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004328 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 49 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.11. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "376.32 N",
"B": "250.88 N",
"C": "252.88 N",
"D": "301.056 N"
} | B | 250.88 N | Net force=mg(sinθ−μcosθ)=49×10×(0.6−0.11×0.8)=250.88 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 250.88 N, not 376.32 N.",
"B": "Correct. The worked calculation gives 250.88 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 250.88 N, not 252.88 N.",
"D": "Incorrect. Substituting the stat... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002516 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 0], [5, 4]]. | {
"A": "12",
"B": "10",
"C": "14",
"D": "13"
} | A | 12 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(4)−(0)(5)=12. | {
"A": "Correct. The worked calculation gives 12.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12, not 10.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12, not 14.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002717 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-5, -5, 0) and v=(-3, 7, 2), calculate u·v. | {
"A": "-16",
"B": "-20",
"C": "-10",
"D": "-24"
} | B | -20 | The dot product is the sum of corresponding component products: (-5)(-3)+(-5)(7)+(0)(2)=-20. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -20, not -16.",
"B": "Correct. The worked calculation gives -20.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -20, not -10.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005360 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 8 μF capacitor is charged to a potential difference of 22 V. Calculate the energy stored, expressed in μJ. | {
"A": "1938 μJ",
"B": "1936 μJ",
"C": "2904 μJ",
"D": "1548.8 μJ"
} | B | 1936 μJ | U=½CV². Since C=8 μF, U in μJ is ½×8×(22)²=1936 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1936 μJ, not 1938 μJ.",
"B": "Correct. The worked calculation gives 1936 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1936 μJ, not 2904 μJ.",
"D": "Incorrect. Substituting the stated va... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002429 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, 6], [5, -3]]. | {
"A": "-33",
"B": "-66",
"C": "-16.5",
"D": "-26.4"
} | A | -33 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(-3)−(6)(5)=-33. | {
"A": "Correct. The worked calculation gives -33.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -33, not -66.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -33, not -16.5.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_007098 | 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 401 K and 2.21 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "536.00672 L",
"B": "267.00336 L",
"C": "268.00336 L",
"D": "27.80034 L"
} | C | 268.00336 L | PV=nRT, so V=nRT/P=(18)(0.082057)(401)/(2.21)=268.00336 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 268.00336 L, not 536.00672 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 268.00336 L, not 267.00336 L.",
"C": "Correct. The worked calculation gives 268.00336 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_008075 | 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 11 A for 15160 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": "-54.86663 g",
"B": "54.86663 g",
"C": "55.86663 g",
"D": "6.48666 g"
} | B | 54.86663 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×15160/(2×96500)=54.86663 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 54.86663 g, not -54.86663 g.",
"B": "Correct. The worked calculation gives 54.86663 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 54.86663 g, not 55.86663 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009012 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.01 V, transfers 1 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.3055 V",
"B": "-1.3055 V",
"C": "4.3055 V",
"D": "-0.6945 V"
} | A | 1.3055 V | Apply the Nernst equation: E=1.01−(0.0591/1)(-5)=1.3055 V. | {
"A": "Correct. The worked calculation gives 1.3055 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.3055 V, not -1.3055 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.3055 V, not 4.3055 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_006383 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 12 kg is attached to an ideal spring of force constant 943 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.22561 s",
"B": "1.22561 s",
"C": "0.45123 s",
"D": "0.16921 s"
} | A | 0.22561 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(12/943)=0.22561 s. | {
"A": "Correct. The worked calculation gives 0.22561 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.22561 s, not 1.22561 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.22561 s, not 0.45123 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_005319 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +2 μC and +8 μC are separated by 7 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "28.38776 N",
"B": "29.38776 N",
"C": "22.04082 N",
"D": "58.77551 N"
} | B | 29.38776 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(2×10⁻⁶)(8×10⁻⁶)/(7×10⁻²)²=29.38776 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 29.38776 N, not 28.38776 N.",
"B": "Correct. The worked calculation gives 29.38776 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 29.38776 N, not 22.04082 N.",
"D": "Incorrect. Substitutin... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003057 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-2+2i)/(6+10i). What is Re(z), the real part of z? | {
"A": "0.11765",
"B": "1.05882",
"C": "0.05882",
"D": "-0.94118"
} | C | 0.05882 | Multiply numerator and denominator by the conjugate (6-10i). Then Re(z)=(ac+bd)/(c²+d²)=((-2)(6)+(2)(10))/(6²+(10)²)=0.05882. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.05882, not 0.11765.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.05882, not 1.05882.",
"C": "Correct. The worked calculation gives 0.05882.",
"D": "Incorrect. Substituting the stated va... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003393 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 110 m s⁻¹ at 40° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "1191.61738 m",
"B": "1189.61738 m",
"C": "1429.94086 m",
"D": "1193.61738 m"
} | A | 1191.61738 m | Range R=u²sin(2θ)/g. Substituting u=110, θ=40° and g=10 gives R=(110)²sin(80°)/10=1191.61738 m. | {
"A": "Correct. The worked calculation gives 1191.61738 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1191.61738 m, not 1189.61738 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1191.61738 m, not 1429.94086 m.",
"D": "Incorrect. S... | [
"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_008779 | 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 1.24 mol L⁻¹ and initially B is absent. At equilibrium, 13% of A has dissociated at constant volume. Find K_c. | {
"A": "0.09635",
"B": "1.00963",
"C": "3.09635",
"D": "2.09635"
} | A | 0.09635 | Let α=0.13. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.24)(0.13)²/(1−0.13)=0.09635. | {
"A": "Correct. The worked calculation gives 0.09635.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.09635, not 1.00963.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.09635, not 3.09635.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005970 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.2 atm at 338 K. What is its pressure at 539 K? | {
"A": "1.91361 atm",
"B": "-1.91361 atm",
"C": "1.19136 atm",
"D": "4.91361 atm"
} | A | 1.91361 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.2)(539)/(338)=1.91361 atm. | {
"A": "Correct. The worked calculation gives 1.91361 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.91361 atm, not -1.91361 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.91361 atm, not 1.19136 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004762 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 6 Ω and 2 Ω are connected in series; this combination is connected in parallel with a 2 Ω resistor across a 30 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.875 A",
"B": "18.75 A",
"C": "16.75 A",
"D": "17.75 A"
} | B | 18.75 A | Series branch resistance=6+2=8 Ω. Parallel equivalent R_eq=(8×2)/(8+2)=1.6 Ω. Total current I=V/R_eq=30/1.6=18.75 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 18.75 A, not 2.875 A.",
"B": "Correct. The worked calculation gives 18.75 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18.75 A, not 16.75 A.",
"D": "Incorrect. Substituting the stated va... | [
"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_006775 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 11 mol H₂ and 27 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "8 mol",
"B": "16.5 mol",
"C": "11 mol",
"D": "10 mol"
} | C | 11 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 11 mol H₂O; O₂ can produce 54 mol H₂O. The limiting condition is H₂; product=11 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11 mol, not 8 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11 mol, not 16.5 mol.",
"C": "Correct. The worked calculation gives 11 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_001938 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 10 elements can be selected from a set of 30 distinct elements? | {
"A": "24036012",
"B": "36054018",
"C": "30045015",
"D": "15022507.5"
} | C | 30045015 | Order does not matter, so the count is C(30,10)=30!/[10!(20)!]=30045015. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 30045015, not 24036012.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 30045015, not 36054018.",
"C": "Correct. The worked calculation gives 30045015.",
"D": "Incorrect. Substituting the stat... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002322 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 7 red, 5 blue and 9 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.31905",
"B": "1.0319",
"C": "0.47857",
"D": "0.15952"
} | A | 0.31905 | Favourable pairs = C(7,2)+C(5,2)+C(9,2)=67. Total pairs=C(21,2)=210. Therefore P=67/210=0.31905. | {
"A": "Correct. The worked calculation gives 0.31905.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.31905, not 1.0319.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31905, not 0.47857.",
"D": "Incorrect. Substituting the stated val... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009556 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_7H_3N_2X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "7",
"B": "6",
"C": "5.25",
"D": "8"
} | A | 7 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+2−3−1)/2=7. | {
"A": "Correct. The worked calculation gives 7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 6.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 5.25.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"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_008863 | 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 1.01 mol L⁻¹ and initially B is absent. At equilibrium, 38% of A has dissociated at constant volume. Find K_c. | {
"A": "1.09409",
"B": "-2.05907",
"C": "0.94093",
"D": "0.47046"
} | C | 0.94093 | Let α=0.38. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.01)(0.38)²/(1−0.38)=0.94093. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.94093, not 1.09409.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.94093, not -2.05907.",
"C": "Correct. The worked calculation gives 0.94093.",
"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_004325 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.42. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "18.48 N",
"B": "22.176 N",
"C": "-18.48 N",
"D": "27.72 N"
} | A | 18.48 N | Net force=mg(sinθ−μcosθ)=7×10×(0.6−0.42×0.8)=18.48 N. | {
"A": "Correct. The worked calculation gives 18.48 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 18.48 N, not 22.176 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 18.48 N, not -18.48 N.",
"D": "Incorrect. Substituting the stated ... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002198 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 5 red, 6 blue and 10 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-0.33333",
"B": "0.33333",
"C": "-1.66667",
"D": "2.33333"
} | B | 0.33333 | Favourable pairs = C(5,2)+C(6,2)+C(10,2)=70. Total pairs=C(21,2)=210. Therefore P=70/210=0.33333. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not -0.33333.",
"B": "Correct. The worked calculation gives 0.33333.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.33333, not -1.66667.",
"D": "Incorrect. Substituting the stated ... | [
"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_001826 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 74 distinct elements? | {
"A": "12081573",
"B": "16108762",
"C": "16108766",
"D": "16108764"
} | D | 16108764 | Order does not matter, so the count is C(74,5)=74!/[5!(69)!]=16108764. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16108764, not 12081573.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16108764, not 16108762.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16108764, not ... | [
"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_003758 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 2 kg block initially moves at 7 m s⁻¹. A constant net force does 24 N of work over 15 m in the direction of motion. Find its final kinetic energy. | {
"A": "407 J",
"B": "327.2 J",
"C": "409 J",
"D": "204.5 J"
} | C | 409 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(2)(7)²+(24)(15)=409 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 409 J, not 407 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 409 J, not 327.2 J.",
"C": "Correct. The worked calculation gives 409 J.",
"D": "Incorrect. Substituting the stated values int... | [
"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_005489 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 26 μF capacitor is charged to a potential difference of 14 V. Calculate the energy stored, expressed in μJ. | {
"A": "2546 μJ",
"B": "1274 μJ",
"C": "2549 μJ",
"D": "2548 μJ"
} | D | 2548 μJ | U=½CV². Since C=26 μF, U in μJ is ½×26×(14)²=2548 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2548 μJ, not 2546 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2548 μJ, not 1274 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2548 μJ, not 2549 ... | [
"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_008357 | 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 1.13 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "2.712 K",
"B": "-2.712 K",
"C": "1.2712 K",
"D": "5.424 K"
} | A | 2.712 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×0.6×1.13=2.712 K. | {
"A": "Correct. The worked calculation gives 2.712 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.712 K, not -2.712 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2.712 K, not 1.2712 K.",
"D": "Incorrect. Substituting the stated ... | [
"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_000659 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -7 and common difference 4. Find the sum of its first 9 terms. | {
"A": "121.5",
"B": "81",
"C": "97.2",
"D": "-81"
} | B | 81 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-7, d=4, n=9: Sₙ=9/2[2(-7)+(9−1)(4)]=81. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 81, not 121.5.",
"B": "Correct. The worked calculation gives 81.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 81, not 97.2.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001748 | 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 48 distinct elements? | {
"A": "194580",
"B": "97290",
"C": "-194580",
"D": "233496"
} | A | 194580 | Order does not matter, so the count is C(48,4)=48!/[4!(44)!]=194580. | {
"A": "Correct. The worked calculation gives 194580.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 194580, not 97290.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 194580, not -194580.",
"D": "Incorrect. Substituting the stated values ... | [
"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_004211 | 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 0.16. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "240.72 N",
"B": "17.048 N",
"C": "160.48 N",
"D": "80.24 N"
} | C | 160.48 N | Net force=mg(sinθ−μcosθ)=34×10×(0.6−0.16×0.8)=160.48 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 160.48 N, not 240.72 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 160.48 N, not 17.048 N.",
"C": "Correct. The worked calculation gives 160.48 N.",
"D": "Incorrect. Substituting the stat... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004057 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 17 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.22. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "72.08 N",
"B": "70.08 N",
"C": "74.08 N",
"D": "108.12 N"
} | A | 72.08 N | Net force=mg(sinθ−μcosθ)=17×10×(0.6−0.22×0.8)=72.08 N. | {
"A": "Correct. The worked calculation gives 72.08 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 72.08 N, not 70.08 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 72.08 N, not 74.08 N.",
"D": "Incorrect. Substituting the stated va... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005185 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +7 μC are separated by 8 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "59.0625 N",
"B": "58.0625 N",
"C": "57.0625 N",
"D": "-59.0625 N"
} | A | 59.0625 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(7×10⁻⁶)/(8×10⁻²)²=59.0625 N. | {
"A": "Correct. The worked calculation gives 59.0625 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 59.0625 N, not 58.0625 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 59.0625 N, not 57.0625 N.",
"D": "Incorrect. Substituting the... | [
"Coulomb's law",
"SI unit conversion",
"inverse-square law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_coulomb | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002059 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 7 red, 12 blue and 4 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.18379",
"B": "0.36759",
"C": "0.27569",
"D": "3.36759"
} | B | 0.36759 | Favourable pairs = C(7,2)+C(12,2)+C(4,2)=93. Total pairs=C(23,2)=253. Therefore P=93/253=0.36759. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.36759, not 0.18379.",
"B": "Correct. The worked calculation gives 0.36759.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.36759, not 0.27569.",
"D": "Incorrect. Substituting the stated va... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006234 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 19 cm in front of a thin convex lens of focal length 12 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "4.71429",
"B": "-1.28571",
"C": "0.71429",
"D": "1.71429"
} | D | 1.71429 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(19)(12)/(19−12)=32.57143 cm. Thus |m|=v/u=32.57143/19=1.71429. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.71429, not 4.71429.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.71429, not -1.28571.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.71429, not 0.71... | [
"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_007317 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 7 mol of gas at 584 K and 0.41 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "981.802 L",
"B": "820.16833 L",
"C": "613.62625 L",
"D": "818.16833 L"
} | D | 818.16833 L | PV=nRT, so V=nRT/P=(7)(0.082057)(584)/(0.41)=818.16833 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 818.16833 L, not 981.802 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 818.16833 L, not 820.16833 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 818.... | [
"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_000866 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 12 and common ratio -2. What is the sum of its first 12 terms? | {
"A": "-16378",
"B": "-16381",
"C": "-32760",
"D": "-16380"
} | D | -16380 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=12(-2^12−1)/(-2−1)=-16380. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -16380, not -16378.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -16380, not -16381.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -16380, not -32760.",
... | [
"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_004233 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 25 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.11. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "192 N",
"B": "256 N",
"C": "128 N",
"D": "96 N"
} | C | 128 N | Net force=mg(sinθ−μcosθ)=25×10×(0.6−0.11×0.8)=128 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 128 N, not 192 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 128 N, not 256 N.",
"C": "Correct. The worked calculation gives 128 N.",
"D": "Incorrect. Substituting the stated values into ... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008969 | 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 1.68 mol L⁻¹ and initially B is absent. At equilibrium, 62% of A has dissociated at constant volume. Find K_c. | {
"A": "3.39891",
"B": "6.79781",
"C": "1.67978",
"D": "9.79781"
} | B | 6.79781 | Let α=0.62. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(1.68)(0.62)²/(1−0.62)=6.79781. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.79781, not 3.39891.",
"B": "Correct. The worked calculation gives 6.79781.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6.79781, not 1.67978.",
"D": "Incorrect. Substituting the stated va... | [
"chemical equilibrium",
"equilibrium constant",
"degree of dissociation"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_equilibrium_alpha | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000657 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 9 and common difference 8. Find the sum of its first 26 terms. | {
"A": "3400.8",
"B": "2832",
"C": "5668",
"D": "2834"
} | D | 2834 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=9, d=8, n=26: Sₙ=26/2[2(9)+(26−1)(8)]=2834. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2834, not 3400.8.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2834, not 2832.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2834, not 5668.",
"D": "Co... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
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