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_007131 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 14 mol of gas at 213 K and 0.76 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "321.96576 L",
"B": "322.96576 L",
"C": "241.47432 L",
"D": "643.93151 L"
} | A | 321.96576 L | PV=nRT, so V=nRT/P=(14)(0.082057)(213)/(0.76)=321.96576 L. | {
"A": "Correct. The worked calculation gives 321.96576 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 321.96576 L, not 322.96576 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 321.96576 L, not 241.47432 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_000707 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 12 and common ratio 5. What is the sum of its first 9 terms? | {
"A": "7031246.4",
"B": "11718744",
"C": "5859372",
"D": "5859371"
} | C | 5859372 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=12(5^9−1)/(5−1)=5859372. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5859372, not 7031246.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5859372, not 11718744.",
"C": "Correct. The worked calculation gives 5859372.",
"D": "Incorrect. Substituting the stated... | [
"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_007129 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 6 mol of gas at 462 K and 2.89 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "78.70658 L",
"B": "-78.70658 L",
"C": "157.41315 L",
"D": "94.44789 L"
} | A | 78.70658 L | PV=nRT, so V=nRT/P=(6)(0.082057)(462)/(2.89)=78.70658 L. | {
"A": "Correct. The worked calculation gives 78.70658 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 78.70658 L, not -78.70658 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 78.70658 L, not 157.41315 L.",
"D": "Incorrect. Substitut... | [
"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_000628 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 6 and common difference 10. Find the sum of its first 26 terms. | {
"A": "3408",
"B": "-3406",
"C": "3406",
"D": "341.6"
} | C | 3406 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=6, d=10, n=26: Sₙ=26/2[2(6)+(26−1)(10)]=3406. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3406, not 3408.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3406, not -3406.",
"C": "Correct. The worked calculation gives 3406.",
"D": "Incorrect. Substituting the stated values into the ... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002340 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, -1], [4, 4]]. | {
"A": "28",
"B": "29",
"C": "14",
"D": "27"
} | A | 28 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(4)−(-1)(4)=28. | {
"A": "Correct. The worked calculation gives 28.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28, not 29.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28, 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_000421 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 6 and common difference 4. Find the sum of its first 16 terms. | {
"A": "574",
"B": "-576",
"C": "1152",
"D": "576"
} | D | 576 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=6, d=4, n=16: Sₙ=16/2[2(6)+(16−1)(4)]=576. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 576, not 574.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 576, not -576.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 576, not 1152.",
"D": "Correct.... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007296 | 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 465 K and 2.27 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "94.13059 L",
"B": "176.49485 L",
"C": "235.32646 L",
"D": "117.66323 L"
} | D | 117.66323 L | PV=nRT, so V=nRT/P=(7)(0.082057)(465)/(2.27)=117.66323 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 117.66323 L, not 94.13059 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 117.66323 L, not 176.49485 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 117... | [
"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_004931 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 10 Ω and 10 Ω are connected in series; this combination is connected in parallel with a 4 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "8.4 A",
"B": "5.4 A",
"C": "2.7 A",
"D": "8.1 A"
} | B | 5.4 A | Series branch resistance=10+10=20 Ω. Parallel equivalent R_eq=(20×4)/(20+4)=3.33333 Ω. Total current I=V/R_eq=18/3.33333=5.4 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.4 A, not 8.4 A.",
"B": "Correct. The worked calculation gives 5.4 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.4 A, not 2.7 A.",
"D": "Incorrect. Substituting the stated values into ... | [
"series resistors",
"parallel resistors",
"Ohm's law"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_series_parallel | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007634 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 45 mL of 0.10 M HCl is mixed with 64 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.24133",
"B": "13.24133",
"C": "24.48265",
"D": "9.181"
} | A | 12.24133 | Excess OH⁻ moles=0.10×(64−45)/1000=0.001900 mol. Total volume=0.109 L, so [OH⁻]=0.017431 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.24133. | {
"A": "Correct. The worked calculation gives 12.24133.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.24133, not 13.24133.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.24133, not 24.48265.",
"D": "Incorrect. Substituting the stat... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002607 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, 5], [5, 7]]. | {
"A": "0",
"B": "-3",
"C": "6",
"D": "3"
} | D | 3 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(7)−(5)(5)=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 0.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3, not -3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not 6.",
"D": "Correct. The worked c... | [
"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_000955 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 10 and common ratio 4. What is the sum of its first 8 terms? | {
"A": "21846",
"B": "218452",
"C": "218450",
"D": "262140"
} | C | 218450 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=10(4^8−1)/(4−1)=218450. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 218450, not 21846.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 218450, not 218452.",
"C": "Correct. The worked calculation gives 218450.",
"D": "Incorrect. Substituting the stated values i... | [
"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_003155 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(8+10i)/(8+1i). What is Re(z), the real part of z? | {
"A": "2.13846",
"B": "1.13846",
"C": "0.85385",
"D": "0.56923"
} | B | 1.13846 | Multiply numerator and denominator by the conjugate (8-1i). Then Re(z)=(ac+bd)/(c²+d²)=((8)(8)+(10)(1))/(8²+(1)²)=1.13846. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.13846, not 2.13846.",
"B": "Correct. The worked calculation gives 1.13846.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.13846, not 0.85385.",
"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_003152 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(11+13i)/(4+1i). What is Re(z), the real part of z? | {
"A": "5.02941",
"B": "1.67647",
"C": "3.35294",
"D": "1.33529"
} | C | 3.35294 | Multiply numerator and denominator by the conjugate (4-1i). Then Re(z)=(ac+bd)/(c²+d²)=((11)(4)+(13)(1))/(4²+(1)²)=3.35294. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.35294, not 5.02941.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.35294, not 1.67647.",
"C": "Correct. The worked calculation gives 3.35294.",
"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_008315 | chemistry | physical_chemistry | faradays_law_copper | very_hard | provisional_template_level_label | single_correct_mcq | An aqueous Cu²⁺ solution is electrolysed using a current of 15 A for 29041 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": "143.32411 g",
"B": "144.32411 g",
"C": "142.32411 g",
"D": "114.65928 g"
} | A | 143.32411 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×15×29041/(2×96500)=143.32411 g. | {
"A": "Correct. The worked calculation gives 143.32411 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 143.32411 g, not 144.32411 g.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 143.32411 g, not 142.32411 g.",
"D": "Incorrect. Substi... | [
"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_001588 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (4x² -3x +6) dx. | {
"A": "33.33333",
"B": "16.66667",
"C": "8.33333",
"D": "17.66667"
} | B | 16.66667 | An antiderivative is (4/3)x³+(-3/2)x²+(6)x. Evaluating between 0 and 2 gives (4/3)(2)³+(-3/2)(2)²+(6)(2)=16.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16.66667, not 33.33333.",
"B": "Correct. The worked calculation gives 16.66667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 16.66667, not 8.33333.",
"D": "Incorrect. Substituting the state... | [
"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_009238 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.94 V, transfers 1 electrons, and has reaction quotient Q=10^2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-0.8218 V",
"B": "3.8218 V",
"C": "0.8218 V",
"D": "0.61635 V"
} | C | 0.8218 V | Apply the Nernst equation: E=0.94−(0.0591/1)(2)=0.8218 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.8218 V, not -0.8218 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.8218 V, not 3.8218 V.",
"C": "Correct. The worked calculation gives 0.8218 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_004385 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 10 kg and radius 4 m is acted on by a constant torque of 48 N m about its central axis. Find its angular acceleration. | {
"A": "-0.6 rad s⁻²",
"B": "1.6 rad s⁻²",
"C": "0.6 rad s⁻²",
"D": "2.6 rad s⁻²"
} | C | 0.6 rad s⁻² | For a solid disc, I=½MR²=½(10)(4)²=80 kg m². Using τ=Iα, α=48/80=0.6 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6 rad s⁻², not -0.6 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.6 rad s⁻², not 1.6 rad s⁻².",
"C": "Correct. The worked calculation gives 0.6 rad s⁻².",
"D": "Incorrect. Subst... | [
"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_009669 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(Cl)_3]^-1, each Cl ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "0",
"B": "2",
"C": "1.5",
"D": "3"
} | B | 2 | Let the formal oxidation state of Pd be x. Charge balance gives x+(3)(−1)=-1; hence x=-1+3=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 0.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not 1.5.",
"D": "Incorrect. Substituting the stated values into the governing rela... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004611 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 2 m is acted on by a constant torque of 27 N m about its central axis. Find its angular acceleration. | {
"A": "13.5 rad s⁻²",
"B": "-6.75 rad s⁻²",
"C": "1.675 rad s⁻²",
"D": "6.75 rad s⁻²"
} | D | 6.75 rad s⁻² | For a solid disc, I=½MR²=½(2)(2)²=4 kg m². Using τ=Iα, α=27/4=6.75 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.75 rad s⁻², not 13.5 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.75 rad s⁻², not -6.75 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation giv... | [
"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_005456 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 44 μF capacitor is charged to a potential difference of 36 V. Calculate the energy stored, expressed in μJ. | {
"A": "28512 μJ",
"B": "21384 μJ",
"C": "2852.2 μJ",
"D": "-28512 μJ"
} | A | 28512 μJ | U=½CV². Since C=44 μF, U in μJ is ½×44×(36)²=28512 μJ. | {
"A": "Correct. The worked calculation gives 28512 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 28512 μJ, not 21384 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 28512 μJ, not 2852.2 μJ.",
"D": "Incorrect. Substituting the sta... | [
"capacitance",
"energy stored in a capacitor"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_capacitor_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007965 | 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 92 mmol L⁻¹, what concentration remains after 80 minutes? | {
"A": "5.75 mmol L⁻¹",
"B": "11.5 mmol L⁻¹",
"C": "4.3125 mmol L⁻¹",
"D": "7.75 mmol L⁻¹"
} | A | 5.75 mmol L⁻¹ | 80 minutes corresponds to 4 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=92/2^4=5.75 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 5.75 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.75 mmol L⁻¹, not 11.5 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.75 mmol L⁻¹, not 4.3125 mmol L⁻¹.",
"D": "Incor... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004584 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 5 kg and radius 5 m is acted on by a constant torque of 8 N m about its central axis. Find its angular acceleration. | {
"A": "0.064 rad s⁻²",
"B": "0.128 rad s⁻²",
"C": "0.192 rad s⁻²",
"D": "-0.128 rad s⁻²"
} | B | 0.128 rad s⁻² | For a solid disc, I=½MR²=½(5)(5)²=62.5 kg m². Using τ=Iα, α=8/62.5=0.128 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.128 rad s⁻², not 0.064 rad s⁻².",
"B": "Correct. The worked calculation gives 0.128 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.128 rad s⁻², not 0.192 rad s⁻².",
"D": "Incorre... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001782 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 39 distinct elements? | {
"A": "61523748",
"B": "61523747",
"C": "92285622",
"D": "6152375.8"
} | A | 61523748 | Order does not matter, so the count is C(39,8)=39!/[8!(31)!]=61523748. | {
"A": "Correct. The worked calculation gives 61523748.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 61523748, not 61523747.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 61523748, not 92285622.",
"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_000613 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -3 and common difference 3. Find the sum of its first 29 terms. | {
"A": "565.5",
"B": "1131",
"C": "1129",
"D": "1132"
} | B | 1131 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-3, d=3, n=29: Sₙ=29/2[2(-3)+(29−1)(3)]=1131. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1131, not 565.5.",
"B": "Correct. The worked calculation gives 1131.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1131, not 1129.",
"D": "Incorrect. Substituting the stated values into the ... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001164 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=0x³ -7x² +2x+7. Evaluate f′(3). | {
"A": "-42",
"B": "-40",
"C": "-38",
"D": "-48"
} | B | -40 | Differentiate: f′(x)=3(0)x²+2(-7)x+(2). At x=3, f′(3)=3(0)(3)²+2(-7)(3)+(2)=-40. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -40, not -42.",
"B": "Correct. The worked calculation gives -40.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -40, not -38.",
"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_002761 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(5, 1, -1) and v=(-7, -4, 6), calculate u·v. | {
"A": "-22.5",
"B": "-45",
"C": "45",
"D": "-47"
} | B | -45 | The dot product is the sum of corresponding component products: (5)(-7)+(1)(-4)+(-1)(6)=-45. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -45, not -22.5.",
"B": "Correct. The worked calculation gives -45.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -45, not 45.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_002221 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 7 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": "-1.68376",
"B": "0.31624",
"C": "2.31624",
"D": "0.15812"
} | B | 0.31624 | Favourable pairs = C(10,2)+C(7,2)+C(10,2)=111. Total pairs=C(27,2)=351. Therefore P=111/351=0.31624. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31624, not -1.68376.",
"B": "Correct. The worked calculation gives 0.31624.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31624, not 2.31624.",
"D": "Incorrect. Substituting the stated v... | [
"classical probability",
"combinations",
"without replacement"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_probability_colours | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006240 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 105 cm in front of a thin convex lens of focal length 21 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.125",
"B": "0.25",
"C": "-1.75",
"D": "-0.25"
} | B | 0.25 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(105)(21)/(105−21)=26.25 cm. Thus |m|=v/u=26.25/105=0.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25, not 0.125.",
"B": "Correct. The worked calculation gives 0.25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25, not -1.75.",
"D": "Incorrect. Substituting the stated values into the... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002496 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, 2], [6, -7]]. | {
"A": "-54",
"B": "-55",
"C": "-27",
"D": "-108"
} | A | -54 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(-7)−(2)(6)=-54. | {
"A": "Correct. The worked calculation gives -54.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -54, not -55.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -54, not -27.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002318 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 6 red, 8 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-2.67333",
"B": "0.32667",
"C": "0.245",
"D": "0.49"
} | B | 0.32667 | Favourable pairs = C(6,2)+C(8,2)+C(11,2)=98. Total pairs=C(25,2)=300. Therefore P=98/300=0.32667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32667, not -2.67333.",
"B": "Correct. The worked calculation gives 0.32667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.32667, not 0.245.",
"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_006486 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 11 kg is attached to an ideal spring of force constant 393 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.3346 s",
"B": "0.1673 s",
"C": "1.03346 s",
"D": "1.3346 s"
} | A | 0.3346 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(11/393)=0.3346 s. | {
"A": "Correct. The worked calculation gives 0.3346 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3346 s, not 0.1673 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3346 s, not 1.03346 s.",
"D": "Incorrect. Substituting the sta... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009296 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.83 V, transfers 3 electrons, and has reaction quotient Q=10^2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.7906 V",
"B": "-0.7906 V",
"C": "-1.2094 V",
"D": "3.7906 V"
} | A | 0.7906 V | Apply the Nernst equation: E=0.83−(0.0591/3)(2)=0.7906 V. | {
"A": "Correct. The worked calculation gives 0.7906 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.7906 V, not -0.7906 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.7906 V, not -1.2094 V.",
"D": "Incorrect. Substituting the st... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001770 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 9 elements can be selected from a set of 69 distinct elements? | {
"A": "45337659910.4",
"B": "56672074890",
"C": "56672074888",
"D": "56672074889"
} | C | 56672074888 | Order does not matter, so the count is C(69,9)=69!/[9!(60)!]=56672074888. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 56672074888, not 45337659910.4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 56672074888, not 56672074890.",
"C": "Correct. The worked calculation gives 56672074888.",
"D": "Incorrect. Subs... | [
"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_004982 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 5 Ω and 7 Ω are connected in series; this combination is connected in parallel with a 6 Ω resistor across a 18 V ideal battery. Find the total current supplied by the battery. | {
"A": "1.45 A",
"B": "2.5 A",
"C": "-4.5 A",
"D": "4.5 A"
} | D | 4.5 A | Series branch resistance=5+7=12 Ω. Parallel equivalent R_eq=(12×6)/(12+6)=4 Ω. Total current I=V/R_eq=18/4=4.5 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.5 A, not 1.45 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4.5 A, not 2.5 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.5 A, not -4.5 A.",
"D... | [
"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_001461 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (-4x² -5x +5) dx. | {
"A": "-346",
"B": "-261",
"C": "348",
"D": "-348"
} | D | -348 | An antiderivative is (-4/3)x³+(-5/2)x²+(5)x. Evaluating between 0 and 6 gives (-4/3)(6)³+(-5/2)(6)²+(5)(6)=-348. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -348, not -346.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -348, not -261.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -348, not 348.",
"D": "Corre... | [
"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_006017 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 28 cm in front of a thin convex lens of focal length 9 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "-2.52632",
"B": "0.47368",
"C": "-0.52632",
"D": "-0.47368"
} | B | 0.47368 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(28)(9)/(28−9)=13.26316 cm. Thus |m|=v/u=13.26316/28=0.47368. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.47368, not -2.52632.",
"B": "Correct. The worked calculation gives 0.47368.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.47368, not -0.52632.",
"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_007145 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 16 mol of gas at 478 K and 2.61 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "288.53882 L",
"B": "239.44902 L",
"C": "25.0449 L",
"D": "240.44902 L"
} | D | 240.44902 L | PV=nRT, so V=nRT/P=(16)(0.082057)(478)/(2.61)=240.44902 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 240.44902 L, not 288.53882 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 240.44902 L, not 239.44902 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 24... | [
"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_002618 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[6, 4], [5, -8]]. | {
"A": "-68",
"B": "-70",
"C": "-102",
"D": "-67"
} | A | -68 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (6)(-8)−(4)(5)=-68. | {
"A": "Correct. The worked calculation gives -68.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -68, not -70.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -68, not -102.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"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_008052 | 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 16831 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": "61.91427 g",
"B": "73.09712 g",
"C": "60.91427 g",
"D": "121.82853 g"
} | C | 60.91427 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×16831/(2×96500)=60.91427 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 60.91427 g, not 61.91427 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 60.91427 g, not 73.09712 g.",
"C": "Correct. The worked calculation gives 60.91427 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_001320 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-3x³ +10x² -5x+7. Evaluate f′(2). | {
"A": "-1",
"B": "0.9",
"C": "-0.5",
"D": "0"
} | A | -1 | Differentiate: f′(x)=3(-3)x²+2(10)x+(-5). At x=2, f′(2)=3(-3)(2)²+2(10)(2)+(-5)=-1. | {
"A": "Correct. The worked calculation gives -1.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1, not 0.9.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1, not -0.5.",
"D": "Incorrect. Substituting the stated values into the governin... | [
"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_005299 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +6 μC and +9 μC are separated by 11 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "48.19835 N",
"B": "60.24793 N",
"C": "40.16529 N",
"D": "80.33058 N"
} | C | 40.16529 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(6×10⁻⁶)(9×10⁻⁶)/(11×10⁻²)²=40.16529 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 40.16529 N, not 48.19835 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 40.16529 N, not 60.24793 N.",
"C": "Correct. The worked calculation gives 40.16529 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_005975 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.9 atm at 382 K. What is its pressure at 540 K? | {
"A": "0.68586 atm",
"B": "4.0288 atm",
"C": "2.68586 atm",
"D": "1.26859 atm"
} | C | 2.68586 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.9)(540)/(382)=2.68586 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2.68586 atm, not 0.68586 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2.68586 atm, not 4.0288 atm.",
"C": "Correct. The worked calculation gives 2.68586 atm.",
"D": "Incorrect. Substit... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007077 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 13 mol of gas at 438 K and 0.35 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "1001.21262 L",
"B": "134.49502 L",
"C": "1334.95017 L",
"D": "2669.90033 L"
} | C | 1334.95017 L | PV=nRT, so V=nRT/P=(13)(0.082057)(438)/(0.35)=1334.95017 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1334.95017 L, not 1001.21262 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1334.95017 L, not 134.49502 L.",
"C": "Correct. The worked calculation gives 1334.95017 L.",
"D": "Incorrect. Su... | [
"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_000032 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 7x^2 -4x -5=0, let its roots be α and β. What is α²+β²? | {
"A": "3.5102",
"B": "1.17551",
"C": "0.87755",
"D": "1.7551"
} | D | 1.7551 | By Vieta's relations, α+β = 4/7 and αβ = -5/7. Then α²+β²=(α+β)²−2αβ = (4/7)²−2(-5/7) = 1.7551. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.7551, not 3.5102.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.7551, not 1.17551.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.7551, not 0.87755."... | [
"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_006772 | 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 22 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "44 mol",
"B": "22 mol",
"C": "33 mol",
"D": "66 mol"
} | A | 44 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 44 mol H₂O; O₂ can produce 44 mol H₂O. The limiting condition is neither; stoichiometric; product=44 mol. | {
"A": "Correct. The worked calculation gives 44 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 44 mol, not 22 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 44 mol, not 33 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_003179 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-13-14i)/(7+9i). What is Re(z), the real part of z? | {
"A": "-1.66923",
"B": "-4.66923",
"C": "-1.25192",
"D": "-2.50385"
} | A | -1.66923 | Multiply numerator and denominator by the conjugate (7-9i). Then Re(z)=(ac+bd)/(c²+d²)=((-13)(7)+(-14)(9))/(7²+(9)²)=-1.66923. | {
"A": "Correct. The worked calculation gives -1.66923.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -1.66923, not -4.66923.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -1.66923, not -1.25192.",
"D": "Incorrect. Substituting the stat... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000887 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 9 and common ratio 4. What is the sum of its first 11 terms? | {
"A": "-12582909",
"B": "18874363.5",
"C": "12582909",
"D": "10066327.2"
} | C | 12582909 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=9(4^11−1)/(4−1)=12582909. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12582909, not -12582909.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12582909, not 18874363.5.",
"C": "Correct. The worked calculation gives 12582909.",
"D": "Incorrect. Substituting the s... | [
"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_006262 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 90 cm in front of a thin convex lens of focal length 27 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "2.42857",
"B": "-1.57143",
"C": "0.42857",
"D": "1.42857"
} | C | 0.42857 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(90)(27)/(90−27)=38.57143 cm. Thus |m|=v/u=38.57143/90=0.42857. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.42857, not 2.42857.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.42857, not -1.57143.",
"C": "Correct. The worked calculation gives 0.42857.",
"D": "Incorrect. Substituting the stated v... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001754 | 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 10 distinct elements? | {
"A": "210",
"B": "212",
"C": "252",
"D": "105"
} | A | 210 | Order does not matter, so the count is C(10,6)=10!/[6!(4)!]=210. | {
"A": "Correct. The worked calculation gives 210.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 210, not 212.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 210, not 252.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"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_005976 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 3.5 atm at 208 K. What is its pressure at 749 K? | {
"A": "14.60337 atm",
"B": "12.60337 atm",
"C": "9.60337 atm",
"D": "25.20673 atm"
} | B | 12.60337 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.5)(749)/(208)=12.60337 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.60337 atm, not 14.60337 atm.",
"B": "Correct. The worked calculation gives 12.60337 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.60337 atm, not 9.60337 atm.",
"D": "Incorrect. Su... | [
"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_002242 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 3 red, 3 blue and 11 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "0.89706",
"B": "1.44853",
"C": "0.44853",
"D": "2.44853"
} | C | 0.44853 | Favourable pairs = C(3,2)+C(3,2)+C(11,2)=61. Total pairs=C(17,2)=136. Therefore P=61/136=0.44853. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.44853, not 0.89706.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.44853, not 1.44853.",
"C": "Correct. The worked calculation gives 0.44853.",
"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_006723 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 38 mol H₂ and 10 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "19 mol",
"B": "-20 mol",
"C": "20 mol",
"D": "3 mol"
} | C | 20 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 38 mol H₂O; O₂ can produce 20 mol H₂O. The limiting condition is O₂; product=20 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20 mol, not 19 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20 mol, not -20 mol.",
"C": "Correct. The worked calculation gives 20 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_005889 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 1.9 atm at 219 K. What is its pressure at 650 K? | {
"A": "5.63927 atm",
"B": "-5.63927 atm",
"C": "8.4589 atm",
"D": "8.63927 atm"
} | A | 5.63927 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(1.9)(650)/(219)=5.63927 atm. | {
"A": "Correct. The worked calculation gives 5.63927 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.63927 atm, not -5.63927 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.63927 atm, not 8.4589 atm.",
"D": "Incorrect. Substi... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007514 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 25 mL of 0.10 M HCl is mixed with 57 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "12.59134",
"B": "18.887",
"C": "9.59134",
"D": "14.59134"
} | A | 12.59134 | Excess OH⁻ moles=0.10×(57−25)/1000=0.003200 mol. Total volume=0.082 L, so [OH⁻]=0.039024 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.59134. | {
"A": "Correct. The worked calculation gives 12.59134.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.59134, not 18.887.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.59134, not 9.59134.",
"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_004965 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 5 Ω and 8 Ω are connected in series; this combination is connected in parallel with a 14 Ω resistor across a 9 V ideal battery. Find the total current supplied by the battery. | {
"A": "2.00275 A",
"B": "1.33516 A",
"C": "4.33516 A",
"D": "-1.33516 A"
} | B | 1.33516 A | Series branch resistance=5+8=13 Ω. Parallel equivalent R_eq=(13×14)/(13+14)=6.74074 Ω. Total current I=V/R_eq=9/6.74074=1.33516 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.33516 A, not 2.00275 A.",
"B": "Correct. The worked calculation gives 1.33516 A.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.33516 A, not 4.33516 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_007084 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 8 mol of gas at 389 K and 2.62 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "146.19927 L",
"B": "48.73309 L",
"C": "99.46618 L",
"D": "97.46618 L"
} | D | 97.46618 L | PV=nRT, so V=nRT/P=(8)(0.082057)(389)/(2.62)=97.46618 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 97.46618 L, not 146.19927 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 97.46618 L, not 48.73309 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 97.46... | [
"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_005396 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 21 μF capacitor is charged to a potential difference of 10 V. Calculate the energy stored, expressed in μJ. | {
"A": "1052 μJ",
"B": "1051 μJ",
"C": "1050 μJ",
"D": "787.5 μJ"
} | C | 1050 μJ | U=½CV². Since C=21 μF, U in μJ is ½×21×(10)²=1050 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1050 μJ, not 1052 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1050 μJ, not 1051 μJ.",
"C": "Correct. The worked calculation gives 1050 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_002955 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(-4, 2, -1) and v=(4, 2, -4), calculate u·v. | {
"A": "-10",
"B": "-11",
"C": "-8",
"D": "-5"
} | C | -8 | The dot product is the sum of corresponding component products: (-4)(4)+(2)(2)+(-1)(-4)=-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 -11.",
"C": "Correct. The worked calculation gives -8.",
"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_001368 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (4x² -3x +2) dx. | {
"A": "10.66667",
"B": "13",
"C": "8.66667",
"D": "-8.66667"
} | C | 8.66667 | An antiderivative is (4/3)x³+(-3/2)x²+(2)x. Evaluating between 0 and 2 gives (4/3)(2)³+(-3/2)(2)²+(2)(2)=8.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.66667, not 10.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.66667, not 13.",
"C": "Correct. The worked calculation gives 8.66667.",
"D": "Incorrect. Substituting the stated values... | [
"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_000568 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 4 and common difference 13. Find the sum of its first 19 terms. | {
"A": "2301",
"B": "2299",
"C": "2297",
"D": "1724.25"
} | B | 2299 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=4, d=13, n=19: Sₙ=19/2[2(4)+(19−1)(13)]=2299. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2299, not 2301.",
"B": "Correct. The worked calculation gives 2299.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2299, not 2297.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006377 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 17 kg is attached to an ideal spring of force constant 1046 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.25497 s",
"B": "2.25497 s",
"C": "3.25497 s",
"D": "0.12748 s"
} | A | 0.25497 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(17/1046)=0.25497 s. | {
"A": "Correct. The worked calculation gives 0.25497 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.25497 s, not 2.25497 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25497 s, not 3.25497 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_004638 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 4 m is acted on by a constant torque of 79 N m about its central axis. Find its angular acceleration. | {
"A": "2.82143 rad s⁻²",
"B": "1.41071 rad s⁻²",
"C": "3.41071 rad s⁻²",
"D": "1.14107 rad s⁻²"
} | B | 1.41071 rad s⁻² | For a solid disc, I=½MR²=½(7)(4)²=56 kg m². Using τ=Iα, α=79/56=1.41071 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.41071 rad s⁻², not 2.82143 rad s⁻².",
"B": "Correct. The worked calculation gives 1.41071 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.41071 rad s⁻², not 3.41071 rad s⁻².",
"D"... | [
"moment of inertia",
"rotational dynamics",
"torque"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_disc_torque | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007124 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 13 mol of gas at 537 K and 0.17 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "3367.64657 L",
"B": "3371.64657 L",
"C": "3369.64657 L",
"D": "4043.57588 L"
} | C | 3369.64657 L | PV=nRT, so V=nRT/P=(13)(0.082057)(537)/(0.17)=3369.64657 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3369.64657 L, not 3367.64657 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3369.64657 L, not 3371.64657 L.",
"C": "Correct. The worked calculation gives 3369.64657 L.",
"D": "Incorrect. S... | [
"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_002383 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[9, -2], [9, -8]]. | {
"A": "-40.5",
"B": "-27",
"C": "-54",
"D": "-81"
} | C | -54 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (9)(-8)−(-2)(9)=-54. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -54, not -40.5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -54, not -27.",
"C": "Correct. The worked calculation gives -54.",
"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_006396 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 14 kg is attached to an ideal spring of force constant 1132 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.33363 s",
"B": "0.22242 s",
"C": "-0.77758 s",
"D": "-0.22242 s"
} | B | 0.22242 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(14/1132)=0.22242 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.22242 s, not 0.33363 s.",
"B": "Correct. The worked calculation gives 0.22242 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.22242 s, not -0.77758 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_001010 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=2x³ +1x² +0x+7. Evaluate f′(3). | {
"A": "60",
"B": "58",
"C": "45",
"D": "61"
} | A | 60 | Differentiate: f′(x)=3(2)x²+2(1)x+(0). At x=3, f′(3)=3(2)(3)²+2(1)(3)+(0)=60. | {
"A": "Correct. The worked calculation gives 60.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 60, not 58.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 60, not 45.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006791 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 4 mol H₂ and 22 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "4 mol",
"B": "2 mol",
"C": "8 mol",
"D": "3 mol"
} | A | 4 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 4 mol H₂O; O₂ can produce 44 mol H₂O. The limiting condition is H₂; product=4 mol. | {
"A": "Correct. The worked calculation gives 4 mol.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4 mol, not 2 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4 mol, not 8 mol.",
"D": "Incorrect. Substituting the stated values into ... | [
"balanced chemical equations",
"limiting reagent",
"mole ratios"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_limiting_reagent | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007045 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 17 mol of gas at 467 K and 2.01 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "323.10474 L",
"B": "324.10474 L",
"C": "388.92569 L",
"D": "322.10474 L"
} | B | 324.10474 L | PV=nRT, so V=nRT/P=(17)(0.082057)(467)/(2.01)=324.10474 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 324.10474 L, not 323.10474 L.",
"B": "Correct. The worked calculation gives 324.10474 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 324.10474 L, not 388.92569 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_005110 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +3 μC and +7 μC are separated by 12 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "14.125 N",
"B": "13.125 N",
"C": "6.5625 N",
"D": "15.125 N"
} | B | 13.125 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(3×10⁻⁶)(7×10⁻⁶)/(12×10⁻²)²=13.125 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13.125 N, not 14.125 N.",
"B": "Correct. The worked calculation gives 13.125 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13.125 N, not 6.5625 N.",
"D": "Incorrect. Substituting the stat... | [
"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_004501 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 2 kg and radius 1 m is acted on by a constant torque of 50 N m about its central axis. Find its angular acceleration. | {
"A": "25 rad s⁻²",
"B": "50 rad s⁻²",
"C": "48 rad s⁻²",
"D": "100 rad s⁻²"
} | B | 50 rad s⁻² | For a solid disc, I=½MR²=½(2)(1)²=1 kg m². Using τ=Iα, α=50/1=50 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 50 rad s⁻², not 25 rad s⁻².",
"B": "Correct. The worked calculation gives 50 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 50 rad s⁻², not 48 rad s⁻².",
"D": "Incorrect. Substitutin... | [
"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_009317 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.50 V, transfers 1 electrons, and has reaction quotient Q=10^3. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.3227 V",
"B": "1.3227 V",
"C": "1.13227 V",
"D": "0.99202 V"
} | B | 1.3227 V | Apply the Nernst equation: E=1.50−(0.0591/1)(3)=1.3227 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.3227 V, not 2.3227 V.",
"B": "Correct. The worked calculation gives 1.3227 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.3227 V, not 1.13227 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_003987 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 7 kg block initially moves at 1 m s⁻¹. A constant net force does 22 N of work over 6 m in the direction of motion. Find its final kinetic energy. | {
"A": "134.5 J",
"B": "162.6 J",
"C": "14.55 J",
"D": "135.5 J"
} | D | 135.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(7)(1)²+(22)(6)=135.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 135.5 J, not 134.5 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 135.5 J, not 162.6 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 135.5 J, not 14.55... | [
"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_000222 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 2x^2 -11x -5=0, let its roots be α and β. What is α²+β²? | {
"A": "28.2",
"B": "37.25",
"C": "35.25",
"D": "34.25"
} | C | 35.25 | By Vieta's relations, α+β = 11/2 and αβ = -5/2. Then α²+β²=(α+β)²−2αβ = (11/2)²−2(-5/2) = 35.25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 35.25, not 28.2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 35.25, not 37.25.",
"C": "Correct. The worked calculation gives 35.25.",
"D": "Incorrect. Substituting the stated values into t... | [
"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_005728 | 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 300 K. What is its pressure at 528 K? | {
"A": "4.584 atm",
"B": "3.168 atm",
"C": "1.584 atm",
"D": "0.792 atm"
} | C | 1.584 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(0.9)(528)/(300)=1.584 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.584 atm, not 4.584 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.584 atm, not 3.168 atm.",
"C": "Correct. The worked calculation gives 1.584 atm.",
"D": "Incorrect. Substituting the... | [
"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_004468 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 11 kg and radius 1 m is acted on by a constant torque of 32 N m about its central axis. Find its angular acceleration. | {
"A": "4.36364 rad s⁻²",
"B": "8.81818 rad s⁻²",
"C": "4.81818 rad s⁻²",
"D": "5.81818 rad s⁻²"
} | D | 5.81818 rad s⁻² | For a solid disc, I=½MR²=½(11)(1)²=5.5 kg m². Using τ=Iα, α=32/5.5=5.81818 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.81818 rad s⁻², not 4.36364 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.81818 rad s⁻², not 8.81818 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing r... | [
"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_005624 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 60 μF capacitor is charged to a potential difference of 18 V. Calculate the energy stored, expressed in μJ. | {
"A": "-9720 μJ",
"B": "973 μJ",
"C": "9718 μJ",
"D": "9720 μJ"
} | D | 9720 μJ | U=½CV². Since C=60 μF, U in μJ is ½×60×(18)²=9720 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9720 μJ, not -9720 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9720 μJ, not 973 μJ.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9720 μJ, not 9718 ... | [
"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_000378 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 10 and common difference 11. Find the sum of its first 29 terms. | {
"A": "4755",
"B": "4756",
"C": "3567",
"D": "4758"
} | B | 4756 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=10, d=11, n=29: Sₙ=29/2[2(10)+(29−1)(11)]=4756. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4756, not 4755.",
"B": "Correct. The worked calculation gives 4756.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4756, not 3567.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009811 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(Cl)_3]^-3, each Cl ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "0",
"B": "2",
"C": "1",
"D": "-2"
} | A | 0 | Let the formal oxidation state of Mn be x. Charge balance gives x+(3)(−1)=-3; hence x=-3+3=+0. | {
"A": "Correct. The worked calculation gives 0.",
"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": "Incorrect. Substituting the stated values into the governing relati... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001887 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 8 elements can be selected from a set of 50 distinct elements? | {
"A": "536878650",
"B": "536878651",
"C": "644254380",
"D": "1073757300"
} | A | 536878650 | Order does not matter, so the count is C(50,8)=50!/[8!(42)!]=536878650. | {
"A": "Correct. The worked calculation gives 536878650.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 536878650, not 536878651.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 536878650, not 644254380.",
"D": "Incorrect. Substituting the... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001486 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (1x² -1x +2) dx. | {
"A": "103.83333",
"B": "51.91667",
"C": "102.83333",
"D": "207.66667"
} | A | 103.83333 | An antiderivative is (1/3)x³+(-1/2)x²+(2)x. Evaluating between 0 and 7 gives (1/3)(7)³+(-1/2)(7)²+(2)(7)=103.83333. | {
"A": "Correct. The worked calculation gives 103.83333.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 103.83333, not 51.91667.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 103.83333, not 102.83333.",
"D": "Incorrect. Substituting 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_000578 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -12 and common difference 6. Find the sum of its first 30 terms. | {
"A": "2250",
"B": "1125",
"C": "2248",
"D": "226"
} | A | 2250 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-12, d=6, n=30: Sₙ=30/2[2(-12)+(30−1)(6)]=2250. | {
"A": "Correct. The worked calculation gives 2250.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2250, not 1125.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2250, not 2248.",
"D": "Incorrect. Substituting the stated values into the g... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000520 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term -3 and common difference 11. Find the sum of its first 31 terms. | {
"A": "5022",
"B": "5024",
"C": "4017.6",
"D": "5020"
} | A | 5022 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=-3, d=11, n=31: Sₙ=31/2[2(-3)+(31−1)(11)]=5022. | {
"A": "Correct. The worked calculation gives 5022.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5022, not 5024.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5022, not 4017.6.",
"D": "Incorrect. Substituting the stated values into the... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009956 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(Cl)_6]^+3, each Cl ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "11",
"B": "13.5",
"C": "7",
"D": "9"
} | D | 9 | Let the formal oxidation state of Mn be x. Charge balance gives x+(6)(−1)=+3; hence x=3+6=+9. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 9, not 11.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 9, not 13.5.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 9, not 7.",
"D": "Correct. The worke... | [
"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_007157 | 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 321 K and 1.72 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "106.19888 L",
"B": "108.19888 L",
"C": "107.19888 L",
"D": "128.63866 L"
} | C | 107.19888 L | PV=nRT, so V=nRT/P=(7)(0.082057)(321)/(1.72)=107.19888 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 107.19888 L, not 106.19888 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 107.19888 L, not 108.19888 L.",
"C": "Correct. The worked calculation gives 107.19888 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_001848 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 9 elements can be selected from a set of 54 distinct elements? | {
"A": "5317936260",
"B": "5317936261",
"C": "5317936262",
"D": "531793627"
} | A | 5317936260 | Order does not matter, so the count is C(54,9)=54!/[9!(45)!]=5317936260. | {
"A": "Correct. The worked calculation gives 5317936260.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5317936260, not 5317936261.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5317936260, not 5317936262.",
"D": "Incorrect. Substitutin... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003852 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block initially moves at 1 m s⁻¹. A constant net force does 30 N of work over 15 m in the direction of motion. Find its final kinetic energy. | {
"A": "453.5 J",
"B": "455.5 J",
"C": "364.4 J",
"D": "46.55 J"
} | B | 455.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(11)(1)²+(30)(15)=455.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 455.5 J, not 453.5 J.",
"B": "Correct. The worked calculation gives 455.5 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 455.5 J, not 364.4 J.",
"D": "Incorrect. Substituting the stated va... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002633 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, -1], [3, 1]]. | {
"A": "14",
"B": "8",
"C": "3.5",
"D": "7"
} | D | 7 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(1)−(-1)(3)=7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not 14.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7, not 3.5.",
"D": "Correct. The worked... | [
"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_003943 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 9 m s⁻¹. A constant net force does 27 N of work over 16 m in the direction of motion. Find its final kinetic energy. | {
"A": "593 J",
"B": "60.4 J",
"C": "594 J",
"D": "592 J"
} | C | 594 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(9)²+(27)(16)=594 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 594 J, not 593 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 594 J, not 60.4 J.",
"C": "Correct. The worked calculation gives 594 J.",
"D": "Incorrect. Substituting the stated values into... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008770 | 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 0.4 mol L⁻¹ and initially B is absent. At equilibrium, 30% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.20571",
"B": "0.20571",
"C": "1.20571",
"D": "-2.79429"
} | B | 0.20571 | Let α=0.3. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.4)(0.3)²/(1−0.3)=0.20571. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.20571, not -0.20571.",
"B": "Correct. The worked calculation gives 0.20571.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.20571, not 1.20571.",
"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_008342 | 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 1.69 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.512 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-0.26944 K",
"B": "-1.73056 K",
"C": "1.73056 K",
"D": "0.86528 K"
} | C | 1.73056 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.512×1.69=1.73056 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.73056 K, not -0.26944 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.73056 K, not -1.73056 K.",
"C": "Correct. The worked calculation gives 1.73056 K.",
"D": "Incorrect. Substituting t... | [
"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_000927 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio 4. What is the sum of its first 5 terms? | {
"A": "2387",
"B": "2864.4",
"C": "4774",
"D": "2389"
} | A | 2387 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(4^5−1)/(4−1)=2387. | {
"A": "Correct. The worked calculation gives 2387.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2387, not 2864.4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2387, not 4774.",
"D": "Incorrect. Substituting the stated values into the... | [
"geometric progression",
"finite geometric sum"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_gp_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007323 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 12 mol of gas at 513 K and 0.45 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "561.26988 L",
"B": "898.03181 L",
"C": "2245.07952 L",
"D": "1122.53976 L"
} | D | 1122.53976 L | PV=nRT, so V=nRT/P=(12)(0.082057)(513)/(0.45)=1122.53976 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1122.53976 L, not 561.26988 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1122.53976 L, not 898.03181 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives ... | [
"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_004789 | physics | electricity | series_parallel_circuit | very_hard | provisional_template_level_label | single_correct_mcq | Resistors 7 Ω and 14 Ω are connected in series; this combination is connected in parallel with a 3 Ω resistor across a 36 V ideal battery. Find the total current supplied by the battery. | {
"A": "11.71429 A",
"B": "12.71429 A",
"C": "13.71429 A",
"D": "14.71429 A"
} | C | 13.71429 A | Series branch resistance=7+14=21 Ω. Parallel equivalent R_eq=(21×3)/(21+3)=2.625 Ω. Total current I=V/R_eq=36/2.625=13.71429 A. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13.71429 A, not 11.71429 A.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 13.71429 A, not 12.71429 A.",
"C": "Correct. The worked calculation gives 13.71429 A.",
"D": "Incorrect. Substitutin... | [
"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_006167 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 90 cm in front of a thin convex lens of focal length 28 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "0.67742",
"B": "1.04516",
"C": "0.45161",
"D": "-0.45161"
} | C | 0.45161 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(90)(28)/(90−28)=40.64516 cm. Thus |m|=v/u=40.64516/90=0.45161. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.45161, not 0.67742.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.45161, not 1.04516.",
"C": "Correct. The worked calculation gives 0.45161.",
"D": "Incorrect. Substituting the stated va... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001286 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=5x³ +3x² -3x+7. Evaluate f′(2). | {
"A": "69",
"B": "-69",
"C": "71",
"D": "68"
} | A | 69 | Differentiate: f′(x)=3(5)x²+2(3)x+(-3). At x=2, f′(2)=3(5)(2)²+2(3)(2)+(-3)=69. | {
"A": "Correct. The worked calculation gives 69.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 69, not -69.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 69, not 71.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"power rule",
"polynomial derivative"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_derivative_cubic | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002651 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[7, -4], [8, -1]]. | {
"A": "50",
"B": "25",
"C": "20",
"D": "26"
} | B | 25 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (7)(-1)−(-4)(8)=25. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 25, not 50.",
"B": "Correct. The worked calculation gives 25.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 25, not 20.",
"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_002455 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[4, -1], [8, 2]]. | {
"A": "2.6",
"B": "8",
"C": "16",
"D": "12.8"
} | C | 16 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (4)(2)−(-1)(8)=16. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 16, not 2.6.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 16, not 8.",
"C": "Correct. The worked calculation gives 16.",
"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_002332 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 12 blue and 8 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "1.31954",
"B": "0.31954",
"C": "0.15977",
"D": "0.23966"
} | B | 0.31954 | Favourable pairs = C(10,2)+C(12,2)+C(8,2)=139. Total pairs=C(30,2)=435. Therefore P=139/435=0.31954. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.31954, not 1.31954.",
"B": "Correct. The worked calculation gives 0.31954.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.31954, not 0.15977.",
"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_007996 | 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 70 mmol L⁻¹, what concentration remains after 120 minutes? | {
"A": "1.09375 mmol L⁻¹",
"B": "-0.90625 mmol L⁻¹",
"C": "0.09375 mmol L⁻¹",
"D": "-1.09375 mmol L⁻¹"
} | A | 1.09375 mmol L⁻¹ | 120 minutes corresponds to 6 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=70/2^6=1.09375 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 1.09375 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.09375 mmol L⁻¹, not -0.90625 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.09375 mmol L⁻¹, not 0.09375 mmol L⁻¹.",... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001411 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^2 (1x² +5x -3) dx. | {
"A": "8.66667",
"B": "4.66667",
"C": "6.66667",
"D": "3.66667"
} | C | 6.66667 | An antiderivative is (1/3)x³+(5/2)x²+(-3)x. Evaluating between 0 and 2 gives (1/3)(2)³+(5/2)(2)²+(-3)(2)=6.66667. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6.66667, not 8.66667.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6.66667, not 4.66667.",
"C": "Correct. The worked calculation gives 6.66667.",
"D": "Incorrect. Substituting the stated va... | [
"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 |
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