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_003200 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-12+5i)/(5+11i). What is Re(z), the real part of z? | {
"A": "0.99658",
"B": "1.96575",
"C": "-0.03425",
"D": "-1.03425"
} | C | -0.03425 | Multiply numerator and denominator by the conjugate (5-11i). Then Re(z)=(ac+bd)/(c²+d²)=((-12)(5)+(5)(11))/(5²+(11)²)=-0.03425. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.03425, not 0.99658.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.03425, not 1.96575.",
"C": "Correct. The worked calculation gives -0.03425.",
"D": "Incorrect. Substituting the stated... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009382 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_4H_2N_2X_2. Treat X as the total number of monovalent halogen atoms. | {
"A": "7",
"B": "-4",
"C": "8",
"D": "4"
} | D | 4 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×4+2+2−2−2)/2=4. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4, not 7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not -4.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 8.",
"D": "Correct. The worked c... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007972 | 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 91 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "1.03555 mmol L⁻¹",
"B": "0.2666 mmol L⁻¹",
"C": "1.35547 mmol L⁻¹",
"D": "0.35547 mmol L⁻¹"
} | D | 0.35547 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=91/2^8=0.35547 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35547 mmol L⁻¹, not 1.03555 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35547 mmol L⁻¹, not 0.2666 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governin... | [
"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_000076 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 6x^2 -17x -10=0, let its roots be α and β. What is α²+β²? | {
"A": "10.36111",
"B": "11.36111",
"C": "8.36111",
"D": "2.13611"
} | B | 11.36111 | By Vieta's relations, α+β = 17/6 and αβ = -10/6. Then α²+β²=(α+β)²−2αβ = (17/6)²−2(-10/6) = 11.36111. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.36111, not 10.36111.",
"B": "Correct. The worked calculation gives 11.36111.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.36111, not 8.36111.",
"D": "Incorrect. Substituting the state... | [
"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_007599 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 37 mL of 0.10 M HCl is mixed with 27 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "1.35463",
"B": "1.80618",
"C": "2.70927",
"D": "3.80618"
} | B | 1.80618 | Excess H⁺ moles=0.10×(37−27)/1000=0.001000 mol. Total volume=0.064 L, so [H⁺]=0.015625 M and pH=−log₁₀[H⁺]=1.80618. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.80618, not 1.35463.",
"B": "Correct. The worked calculation gives 1.80618.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.80618, not 2.70927.",
"D": "Incorrect. Substituting the stated va... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002137 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 11 red, 7 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "2.32644",
"B": "1.03264",
"C": "0.32644",
"D": "-0.32644"
} | C | 0.32644 | Favourable pairs = C(11,2)+C(7,2)+C(12,2)=142. Total pairs=C(30,2)=435. Therefore P=142/435=0.32644. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.32644, not 2.32644.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.32644, not 1.03264.",
"C": "Correct. The worked calculation gives 0.32644.",
"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_003575 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 70 m s⁻¹ at 65° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "375.36178 m",
"B": "563.04267 m",
"C": "373.36178 m",
"D": "377.36178 m"
} | A | 375.36178 m | Range R=u²sin(2θ)/g. Substituting u=70, θ=65° and g=10 gives R=(70)²sin(130°)/10=375.36178 m. | {
"A": "Correct. The worked calculation gives 375.36178 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 375.36178 m, not 563.04267 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 375.36178 m, not 373.36178 m.",
"D": "Incorrect. Substi... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009319 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.37 V, transfers 1 electrons, and has reaction quotient Q=10^6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.0154 V",
"B": "-1.0154 V",
"C": "1.0154 V",
"D": "4.0154 V"
} | C | 1.0154 V | Apply the Nernst equation: E=1.37−(0.0591/1)(6)=1.0154 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.0154 V, not 2.0154 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.0154 V, not -1.0154 V.",
"C": "Correct. The worked calculation gives 1.0154 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_004581 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 7 kg and radius 2 m is acted on by a constant torque of 71 N m about its central axis. Find its angular acceleration. | {
"A": "5.07143 rad s⁻²",
"B": "2.07143 rad s⁻²",
"C": "-5.07143 rad s⁻²",
"D": "1.50714 rad s⁻²"
} | A | 5.07143 rad s⁻² | For a solid disc, I=½MR²=½(7)(2)²=14 kg m². Using τ=Iα, α=71/14=5.07143 rad s⁻². | {
"A": "Correct. The worked calculation gives 5.07143 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.07143 rad s⁻², not 2.07143 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.07143 rad s⁻², not -5.07143 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_002665 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 1], [2, 0]]. | {
"A": "0.8",
"B": "-2",
"C": "-1",
"D": "1"
} | B | -2 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(0)−(1)(2)=-2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -2, not 0.8.",
"B": "Correct. The worked calculation gives -2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -2, not -1.",
"D": "Incorrect. Substituting the stated values into the governing ... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000713 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 3 and common ratio 5. What is the sum of its first 7 terms? | {
"A": "58593",
"B": "5860.3",
"C": "70311.6",
"D": "58591"
} | A | 58593 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=3(5^7−1)/(5−1)=58593. | {
"A": "Correct. The worked calculation gives 58593.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 58593, not 5860.3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 58593, not 70311.6.",
"D": "Incorrect. Substituting the stated values in... | [
"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_002954 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(0, 2, 4) and v=(1, 7, 6), calculate u·v. | {
"A": "40",
"B": "38",
"C": "-38",
"D": "37"
} | B | 38 | The dot product is the sum of corresponding component products: (0)(1)+(2)(7)+(4)(6)=38. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 38, not 40.",
"B": "Correct. The worked calculation gives 38.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 38, not -38.",
"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_002550 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, -6], [3, 5]]. | {
"A": "22",
"B": "11.5",
"C": "23",
"D": "34.5"
} | C | 23 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(5)−(-6)(3)=23. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 23, not 22.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 23, not 11.5.",
"C": "Correct. The worked calculation gives 23.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003986 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 4 kg block initially moves at 10 m s⁻¹. A constant net force does 22 N of work over 4 m in the direction of motion. Find its final kinetic energy. | {
"A": "288 J",
"B": "290 J",
"C": "-288 J",
"D": "432 J"
} | A | 288 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(4)(10)²+(22)(4)=288 J. | {
"A": "Correct. The worked calculation gives 288 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 288 J, not 290 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 288 J, not -288 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_007840 | 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 80 mmol L⁻¹, what concentration remains after 160 minutes? | {
"A": "0.3125 mmol L⁻¹",
"B": "2.3125 mmol L⁻¹",
"C": "-2.6875 mmol L⁻¹",
"D": "0.15625 mmol L⁻¹"
} | A | 0.3125 mmol L⁻¹ | 160 minutes corresponds to 8 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=80/2^8=0.3125 mmol L⁻¹. | {
"A": "Correct. The worked calculation gives 0.3125 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.3125 mmol L⁻¹, not 2.3125 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3125 mmol L⁻¹, not -2.6875 mmol L⁻¹.",
"D... | [
"first-order kinetics",
"half-life",
"exponential decay"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_first_order_halflife | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000920 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 2 and common ratio 5. What is the sum of its first 6 terms? | {
"A": "7811",
"B": "9374.4",
"C": "7812",
"D": "5859"
} | C | 7812 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=2(5^6−1)/(5−1)=7812. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7812, not 7811.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7812, not 9374.4.",
"C": "Correct. The worked calculation gives 7812.",
"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_008547 | 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 1.1 mol kg⁻¹. If its van't Hoff factor is 1 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "1.65 K",
"B": "1.1 K",
"C": "1.11 K",
"D": "-0.9 K"
} | B | 1.1 K | ΔT_b=iK_bm. Substitution gives ΔT_b=1×1.0×1.1=1.1 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.1 K, not 1.65 K.",
"B": "Correct. The worked calculation gives 1.1 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1 K, not 1.11 K.",
"D": "Incorrect. Substituting the stated values int... | [
"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_008896 | 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 0.27 mol L⁻¹ and initially B is absent. At equilibrium, 25% of A has dissociated at constant volume. Find K_c. | {
"A": "-1.91",
"B": "0.135",
"C": "0.09",
"D": "-0.09"
} | C | 0.09 | Let α=0.25. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.27)(0.25)²/(1−0.25)=0.09. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.09, not -1.91.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.09, not 0.135.",
"C": "Correct. The worked calculation gives 0.09.",
"D": "Incorrect. Substituting the stated values into the... | [
"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_003790 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 9 kg block initially moves at 3 m s⁻¹. A constant net force does 10 N of work over 13 m in the direction of motion. Find its final kinetic energy. | {
"A": "127.875 J",
"B": "-170.5 J",
"C": "170.5 J",
"D": "172.5 J"
} | C | 170.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(9)(3)²+(10)(13)=170.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 170.5 J, not 127.875 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 170.5 J, not -170.5 J.",
"C": "Correct. The worked calculation gives 170.5 J.",
"D": "Incorrect. Substituting the stated... | [
"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_006740 | chemistry | stoichiometry | limiting_reagent_water | very_hard | provisional_template_level_label | single_correct_mcq | Hydrogen reacts with oxygen according to 2H₂ + O₂ → 2H₂O. If 13 mol H₂ and 18 mol O₂ are mixed and the reaction goes to completion, how many moles of H₂O form? | {
"A": "26 mol",
"B": "13 mol",
"C": "10 mol",
"D": "9.75 mol"
} | B | 13 mol | From 2 mol H₂ and 1 mol O₂, 2 mol H₂O form. H₂ can produce 13 mol H₂O; O₂ can produce 36 mol H₂O. The limiting condition is H₂; product=13 mol. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 13 mol, not 26 mol.",
"B": "Correct. The worked calculation gives 13 mol.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 13 mol, not 10 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_002139 | mathematics | probability | same_colour_without_replacement | very_hard | provisional_template_level_label | single_correct_mcq | A bag contains 10 red, 5 blue and 12 green balls. Two balls are drawn uniformly at random without replacement. What is the probability that both have the same colour? | {
"A": "-2.65527",
"B": "0.34473",
"C": "0.25855",
"D": "-0.34473"
} | B | 0.34473 | Favourable pairs = C(10,2)+C(5,2)+C(12,2)=121. Total pairs=C(27,2)=351. Therefore P=121/351=0.34473. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.34473, not -2.65527.",
"B": "Correct. The worked calculation gives 0.34473.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.34473, not 0.25855.",
"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_008431 | 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 1.02 mol kg⁻¹. If its van't Hoff factor is 4 and K_b for water is 1.0 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "-4.08 K",
"B": "4.08 K",
"C": "5.08 K",
"D": "8.16 K"
} | B | 4.08 K | ΔT_b=iK_bm. Substitution gives ΔT_b=4×1.0×1.02=4.08 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4.08 K, not -4.08 K.",
"B": "Correct. The worked calculation gives 4.08 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4.08 K, not 5.08 K.",
"D": "Incorrect. Substituting the stated values... | [
"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_009764 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(OH)_3]^-1, each OH ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "2",
"B": "3",
"C": "-2",
"D": "0"
} | A | 2 | Let the formal oxidation state of Cu be x. Charge balance gives x+(3)(−1)=-1; hence x=-1+3=+2. | {
"A": "Correct. The worked calculation gives 2.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, not -2.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004589 | 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 68 N m about its central axis. Find its angular acceleration. | {
"A": "-0.78571 rad s⁻²",
"B": "0.60714 rad s⁻²",
"C": "1.21429 rad s⁻²",
"D": "0.91071 rad s⁻²"
} | C | 1.21429 rad s⁻² | For a solid disc, I=½MR²=½(7)(4)²=56 kg m². Using τ=Iα, α=68/56=1.21429 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.21429 rad s⁻², not -0.78571 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.21429 rad s⁻², not 0.60714 rad s⁻².",
"C": "Correct. The worked calculation gives 1.21429 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_000436 | mathematics | sequences_and_series | arithmetic_progression | hard | provisional_template_level_label | single_correct_mcq | An arithmetic progression has first term 2 and common difference 5. Find the sum of its first 15 terms. | {
"A": "555",
"B": "666",
"C": "554",
"D": "56.5"
} | A | 555 | Use Sₙ = n/2[2a+(n−1)d]. Substituting a=2, d=5, n=15: Sₙ=15/2[2(2)+(15−1)(5)]=555. | {
"A": "Correct. The worked calculation gives 555.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 555, not 666.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 555, not 554.",
"D": "Incorrect. Substituting the stated values into the govern... | [
"arithmetic progression",
"finite series"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_ap_sum | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003875 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 0 m s⁻¹. A constant net force does 11 N of work over 10 m in the direction of motion. Find its final kinetic energy. | {
"A": "88 J",
"B": "-110 J",
"C": "108 J",
"D": "110 J"
} | D | 110 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(0)²+(11)(10)=110 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 110 J, not 88 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 110 J, not -110 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 110 J, not 108 J.",
"D":... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009166 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.35 V, transfers 2 electrons, and has reaction quotient Q=10^-5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.49775 V",
"B": "1.14977 V",
"C": "-1.50225 V",
"D": "2.49775 V"
} | A | 1.49775 V | Apply the Nernst equation: E=1.35−(0.0591/2)(-5)=1.49775 V. | {
"A": "Correct. The worked calculation gives 1.49775 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.49775 V, not 1.14977 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.49775 V, not -1.50225 V.",
"D": "Incorrect. Substituting th... | [
"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_009982 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Mn(OH)_2]^+0, each OH ligand has charge −1. Determine the formal oxidation state of Mn. | {
"A": "3",
"B": "2",
"C": "1",
"D": "4"
} | B | 2 | Let the formal oxidation state of Mn be x. Charge balance gives x+(2)(−1)=+0; hence x=0+2=+2. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 2, not 3.",
"B": "Correct. The worked calculation gives 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 2, 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_002667 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[3, 3], [6, 7]]. | {
"A": "5",
"B": "3",
"C": "-3",
"D": "6"
} | B | 3 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (3)(7)−(3)(6)=3. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3, not 5.",
"B": "Correct. The worked calculation gives 3.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3, not -3.",
"D": "Incorrect. Substituting the stated values into the governing relat... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001059 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=2x³ -7x² +1x+7. Evaluate f′(5). | {
"A": "81",
"B": "64.8",
"C": "79",
"D": "121.5"
} | A | 81 | Differentiate: f′(x)=3(2)x²+2(-7)x+(1). At x=5, f′(5)=3(2)(5)²+2(-7)(5)+(1)=81. | {
"A": "Correct. The worked calculation gives 81.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 81, not 64.8.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 81, not 79.",
"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_000005 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 3x^2 -18x -12=0, let its roots be α and β. What is α²+β²? | {
"A": "42",
"B": "46",
"C": "22",
"D": "44"
} | D | 44 | By Vieta's relations, α+β = 18/3 and αβ = -12/3. Then α²+β²=(α+β)²−2αβ = (18/3)²−2(-12/3) = 44. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 44, not 42.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 44, not 46.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 44, not 22.",
"D": "Correct. The wor... | [
"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_005910 | 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 3.4 atm at 213 K. What is its pressure at 357 K? | {
"A": "8.69859 atm",
"B": "5.69859 atm",
"C": "11.39718 atm",
"D": "4.69859 atm"
} | B | 5.69859 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(3.4)(357)/(213)=5.69859 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.69859 atm, not 8.69859 atm.",
"B": "Correct. The worked calculation gives 5.69859 atm.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 5.69859 atm, not 11.39718 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005100 | physics | electrostatics | coulombs_law | hard | provisional_template_level_label | single_correct_mcq | Two point charges of +9 μC and +2 μC are separated by 9 cm in vacuum. Using k=9×10⁹ N m² C⁻², find the magnitude of the electrostatic force. | {
"A": "20 N",
"B": "19 N",
"C": "30 N",
"D": "16 N"
} | A | 20 N | Convert charges to coulombs and distance to metres. F=k|q₁q₂|/r²=9×10⁹(9×10⁻⁶)(2×10⁻⁶)/(9×10⁻²)²=20 N. | {
"A": "Correct. The worked calculation gives 20 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20 N, not 19 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20 N, not 30 N.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_001875 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 5 elements can be selected from a set of 25 distinct elements? | {
"A": "63756",
"B": "53128",
"C": "79695",
"D": "53130"
} | D | 53130 | Order does not matter, so the count is C(25,5)=25!/[5!(20)!]=53130. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 53130, not 63756.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 53130, not 53128.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 53130, not 79695.",
"D":... | [
"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_007230 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 18 mol of gas at 341 K and 0.7 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "72.95227 L",
"B": "1079.284 L",
"C": "719.52267 L",
"D": "717.52267 L"
} | C | 719.52267 L | PV=nRT, so V=nRT/P=(18)(0.082057)(341)/(0.7)=719.52267 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 719.52267 L, not 72.95227 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 719.52267 L, not 1079.284 L.",
"C": "Correct. The worked calculation gives 719.52267 L.",
"D": "Incorrect. Substitu... | [
"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_007241 | 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 320 K and 1.63 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "20.33122 L",
"B": "193.3122 L",
"C": "386.62439 L",
"D": "194.3122 L"
} | B | 193.3122 L | PV=nRT, so V=nRT/P=(12)(0.082057)(320)/(1.63)=193.3122 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 193.3122 L, not 20.33122 L.",
"B": "Correct. The worked calculation gives 193.3122 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 193.3122 L, not 386.62439 L.",
"D": "Incorrect. Substituti... | [
"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_007237 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 19 mol of gas at 496 K and 0.16 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "4832.1573 L",
"B": "4833.1573 L",
"C": "-4833.1573 L",
"D": "484.31573 L"
} | B | 4833.1573 L | PV=nRT, so V=nRT/P=(19)(0.082057)(496)/(0.16)=4833.1573 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 4833.1573 L, not 4832.1573 L.",
"B": "Correct. The worked calculation gives 4833.1573 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4833.1573 L, not -4833.1573 L.",
"D": "Incorrect. Subst... | [
"ideal gas equation",
"unit consistency"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_ideal_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006229 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 107 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": "2.35443",
"B": "-0.35443",
"C": "-0.64557",
"D": "0.35443"
} | D | 0.35443 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(107)(28)/(107−28)=37.92405 cm. Thus |m|=v/u=37.92405/107=0.35443. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.35443, not 2.35443.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.35443, not -0.35443.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.35443, not -0.6... | [
"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_007469 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 90 mL of 0.10 M HCl is mixed with 98 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "11.62893",
"B": "13.62893",
"C": "-11.62893",
"D": "8.62893"
} | A | 11.62893 | Excess OH⁻ moles=0.10×(98−90)/1000=0.000800 mol. Total volume=0.188 L, so [OH⁻]=0.004255 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=11.62893. | {
"A": "Correct. The worked calculation gives 11.62893.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.62893, not 13.62893.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 11.62893, not -11.62893.",
"D": "Incorrect. Substituting the sta... | [
"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_002527 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[8, -4], [1, 8]]. | {
"A": "70",
"B": "68",
"C": "81.6",
"D": "102"
} | B | 68 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (8)(8)−(-4)(1)=68. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 68, not 70.",
"B": "Correct. The worked calculation gives 68.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 68, not 81.6.",
"D": "Incorrect. Substituting the stated values into the governing... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008177 | 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 11443 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": "-41.41417 g",
"B": "82.82835 g",
"C": "41.41417 g",
"D": "5.14142 g"
} | C | 41.41417 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×11×11443/(2×96500)=41.41417 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 41.41417 g, not -41.41417 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 41.41417 g, not 82.82835 g.",
"C": "Correct. The worked calculation gives 41.41417 g.",
"D": "Incorrect. Substituti... | [
"electrolysis",
"Faraday's laws",
"redox stoichiometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_faraday_copper | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004299 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 37 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.16. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "18.464 N",
"B": "172.64 N",
"C": "174.64 N",
"D": "261.96 N"
} | C | 174.64 N | Net force=mg(sinθ−μcosθ)=37×10×(0.6−0.16×0.8)=174.64 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 174.64 N, not 18.464 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 174.64 N, not 172.64 N.",
"C": "Correct. The worked calculation gives 174.64 N.",
"D": "Incorrect. Substituting the stat... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_006530 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 5 kg is attached to an ideal spring of force constant 112 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "2.42258 s",
"B": "-0.42258 s",
"C": "0.21129 s",
"D": "0.42258 s"
} | D | 0.42258 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(5/112)=0.42258 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.42258 s, not 2.42258 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.42258 s, not -0.42258 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.42258 s... | [
"simple harmonic motion",
"mass–spring oscillator",
"time period"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_shm_period | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009198 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.91 V, transfers 1 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "-2.3855 V",
"B": "0.6145 V",
"C": "-1.3855 V",
"D": "3.6145 V"
} | B | 0.6145 V | Apply the Nernst equation: E=0.91−(0.0591/1)(5)=0.6145 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.6145 V, not -2.3855 V.",
"B": "Correct. The worked calculation gives 0.6145 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.6145 V, not -1.3855 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_007562 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 16 mL of 0.10 M HCl is mixed with 71 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "15.80084",
"B": "12.80084",
"C": "9.80084",
"D": "-12.80084"
} | B | 12.80084 | Excess OH⁻ moles=0.10×(71−16)/1000=0.005500 mol. Total volume=0.087 L, so [OH⁻]=0.063218 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.80084. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.80084, not 15.80084.",
"B": "Correct. The worked calculation gives 12.80084.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.80084, not 9.80084.",
"D": "Incorrect. Substituting the state... | [
"strong acid–strong base neutralization",
"molarity",
"pH and pOH"
] | 5 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_acid_base_pH | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_005881 | 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 5 atm at 341 K. What is its pressure at 792 K? | {
"A": "13.6129 atm",
"B": "-11.6129 atm",
"C": "11.6129 atm",
"D": "12.6129 atm"
} | C | 11.6129 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(5)(792)/(341)=11.6129 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 11.6129 atm, not 13.6129 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 11.6129 atm, not -11.6129 atm.",
"C": "Correct. The worked calculation gives 11.6129 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000745 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio 2. What is the sum of its first 6 terms? | {
"A": "882",
"B": "529.2",
"C": "440",
"D": "441"
} | D | 441 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(2^6−1)/(2−1)=441. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 441, not 882.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 441, not 529.2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 441, not 440.",
"D": "Correct.... | [
"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_009463 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_7H_3N_3X_4. Treat X as the total number of monovalent halogen atoms. | {
"A": "5",
"B": "7",
"C": "4",
"D": "6"
} | D | 6 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×7+2+3−3−4)/2=6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 5.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 7.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 4.",
"D": "Correct. The worked ca... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007739 | 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 49 mmol L⁻¹, what concentration remains after 40 minutes? | {
"A": "11.25 mmol L⁻¹",
"B": "12.25 mmol L⁻¹",
"C": "24.5 mmol L⁻¹",
"D": "18.375 mmol L⁻¹"
} | B | 12.25 mmol L⁻¹ | 40 minutes corresponds to 2 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=49/2^2=12.25 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.25 mmol L⁻¹, not 11.25 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 12.25 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.25 mmol L⁻¹, not 24.5 mmol L⁻¹.",
"D": "Inc... | [
"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_005711 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 2.4 atm at 405 K. What is its pressure at 520 K? | {
"A": "2.31111 atm",
"B": "5.08148 atm",
"C": "3.08148 atm",
"D": "4.08148 atm"
} | C | 3.08148 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(2.4)(520)/(405)=3.08148 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 3.08148 atm, not 2.31111 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3.08148 atm, not 5.08148 atm.",
"C": "Correct. The worked calculation gives 3.08148 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_009884 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pt(Cl)_5]^-1, each Cl ligand has charge −1. Determine the formal oxidation state of Pt. | {
"A": "4",
"B": "2",
"C": "6",
"D": "1.4"
} | A | 4 | Let the formal oxidation state of Pt be x. Charge balance gives x+(5)(−1)=-1; hence x=-1+5=+4. | {
"A": "Correct. The worked calculation gives 4.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 4, not 2.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 4, not 6.",
"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_006424 | physics | oscillations | mass_spring_period_over_pi | hard | provisional_template_level_label | single_correct_mcq | A mass of 15 kg is attached to an ideal spring of force constant 1082 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "1.23548 s",
"B": "-1.76452 s",
"C": "0.23548 s",
"D": "3.23548 s"
} | C | 0.23548 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(15/1082)=0.23548 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.23548 s, not 1.23548 s.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.23548 s, not -1.76452 s.",
"C": "Correct. The worked calculation gives 0.23548 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_006098 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 107 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": "1.03375",
"B": "0.3375",
"C": "0.675",
"D": "0.50625"
} | B | 0.3375 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(107)(27)/(107−27)=36.1125 cm. Thus |m|=v/u=36.1125/107=0.3375. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.3375, not 1.03375.",
"B": "Correct. The worked calculation gives 0.3375.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.3375, not 0.675.",
"D": "Incorrect. Substituting the stated values ... | [
"thin lens equation",
"linear magnification",
"real image"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_lens_magnification | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001088 | mathematics | calculus | polynomial_differentiation | hard | provisional_template_level_label | single_correct_mcq | Let f(x)=-2x³ +6x² -5x+7. Evaluate f′(-4). | {
"A": "-148",
"B": "-111.75",
"C": "-13.9",
"D": "-149"
} | D | -149 | Differentiate: f′(x)=3(-2)x²+2(6)x+(-5). At x=-4, f′(-4)=3(-2)(-4)²+2(6)(-4)+(-5)=-149. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -149, not -148.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -149, not -111.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -149, not -13.9.",
"D": "... | [
"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_000148 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 5x^2 -18x +10=0, let its roots be α and β. What is α²+β²? | {
"A": "6.72",
"B": "4.48",
"C": "10.96",
"D": "8.96"
} | D | 8.96 | By Vieta's relations, α+β = 18/5 and αβ = 10/5. Then α²+β²=(α+β)²−2αβ = (18/5)²−2(10/5) = 8.96. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 8.96, not 6.72.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 8.96, not 4.48.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 8.96, not 10.96.",
"D": "Cor... | [
"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_004177 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 5 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.24. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "15.3 N",
"B": "-20.4 N",
"C": "10.2 N",
"D": "20.4 N"
} | D | 20.4 N | Net force=mg(sinθ−μcosθ)=5×10×(0.6−0.24×0.8)=20.4 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 20.4 N, not 15.3 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 20.4 N, not -20.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 20.4 N, not 10.2 N.",... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003196 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(0+14i)/(4+4i). What is Re(z), the real part of z? | {
"A": "1.75",
"B": "2.75",
"C": "4.75",
"D": "-1.25"
} | A | 1.75 | Multiply numerator and denominator by the conjugate (4-4i). Then Re(z)=(ac+bd)/(c²+d²)=((0)(4)+(14)(4))/(4²+(4)²)=1.75. | {
"A": "Correct. The worked calculation gives 1.75.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.75, not 2.75.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.75, not 4.75.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_006071 | physics | ray_optics | convex_lens_magnification | very_hard | provisional_template_level_label | single_correct_mcq | A real object is placed 101 cm in front of a thin convex lens of focal length 29 cm. Using the Cartesian sign convention, what is the magnitude of the linear magnification? | {
"A": "1.40278",
"B": "0.20139",
"C": "0.80556",
"D": "0.40278"
} | D | 0.40278 | Using distances as positive magnitudes, 1/f=1/v+1/u gives v=uf/(u−f)=(101)(29)/(101−29)=40.68056 cm. Thus |m|=v/u=40.68056/101=0.40278. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.40278, not 1.40278.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.40278, not 0.20139.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.40278, not 0.805... | [
"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_008585 | 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 1.44 mol kg⁻¹. If its van't Hoff factor is 2 and K_b for water is 0.6 K kg mol⁻¹, find the boiling-point elevation. | {
"A": "0.864 K",
"B": "0.728 K",
"C": "-1.272 K",
"D": "1.728 K"
} | D | 1.728 K | ΔT_b=iK_bm. Substitution gives ΔT_b=2×0.6×1.44=1.728 K. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.728 K, not 0.864 K.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.728 K, not 0.728 K.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.728 K, not -1.27... | [
"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_000062 | mathematics | algebra | quadratic_roots | hard | provisional_template_level_label | single_correct_mcq | For the quadratic equation 4x^2 +7x -8=0, let its roots be α and β. What is α²+β²? | {
"A": "7.0625",
"B": "10.0625",
"C": "3.53125",
"D": "-7.0625"
} | A | 7.0625 | By Vieta's relations, α+β = -7/4 and αβ = -8/4. Then α²+β²=(α+β)²−2αβ = (-7/4)²−2(-8/4) = 7.0625. | {
"A": "Correct. The worked calculation gives 7.0625.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.0625, not 10.0625.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 7.0625, not 3.53125.",
"D": "Incorrect. Substituting the stated value... | [
"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_005811 | physics | thermodynamics | ideal_gas_isochoric_pressure | hard | provisional_template_level_label | single_correct_mcq | A fixed amount of ideal gas is kept in a rigid container. Its pressure is 4.5 atm at 342 K. What is its pressure at 450 K? | {
"A": "7.92105 atm",
"B": "11.84211 atm",
"C": "5.92105 atm",
"D": "4.44079 atm"
} | C | 5.92105 atm | At constant volume, P/T is constant. P₂=P₁T₂/T₁=(4.5)(450)/(342)=5.92105 atm. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.92105 atm, not 7.92105 atm.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.92105 atm, not 11.84211 atm.",
"C": "Correct. The worked calculation gives 5.92105 atm.",
"D": "Incorrect. Subst... | [
"ideal gas law",
"isochoric process",
"absolute temperature"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_isochoric_gas | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002679 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(1, -3, 6) and v=(1, 1, 7), calculate u·v. | {
"A": "38",
"B": "40",
"C": "41",
"D": "5"
} | B | 40 | The dot product is the sum of corresponding component products: (1)(1)+(-3)(1)+(6)(7)=40. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 40, not 38.",
"B": "Correct. The worked calculation gives 40.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 40, not 41.",
"D": "Incorrect. Substituting the stated values into the governing r... | [
"three-dimensional vectors",
"scalar product"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_vector_dot | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_002703 | mathematics | vectors | dot_product | hard | provisional_template_level_label | single_correct_mcq | Given vectors u=(5, 9, -7) and v=(8, 6, 6), calculate u·v. | {
"A": "53",
"B": "50",
"C": "62.4",
"D": "52"
} | D | 52 | The dot product is the sum of corresponding component products: (5)(8)+(9)(6)+(-7)(6)=52. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 52, not 53.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 52, not 50.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 52, not 62.4.",
"D": "Correct. The w... | [
"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_001792 | 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 47 distinct elements? | {
"A": "314457494",
"B": "31445750.5",
"C": "314457495",
"D": "628914990"
} | C | 314457495 | Order does not matter, so the count is C(47,8)=47!/[8!(39)!]=314457495. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 314457495, not 314457494.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 314457495, not 31445750.5.",
"C": "Correct. The worked calculation gives 314457495.",
"D": "Incorrect. Substituting th... | [
"combinations",
"factorials"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_combinations | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009844 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Pd(OH)_6]^+1, each OH ligand has charge −1. Determine the formal oxidation state of Pd. | {
"A": "-7",
"B": "3.5",
"C": "7",
"D": "10"
} | C | 7 | Let the formal oxidation state of Pd be x. Charge balance gives x+(6)(−1)=+1; hence x=1+6=+7. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7, not -7.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7, not 3.5.",
"C": "Correct. The worked calculation gives 7.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003798 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 14 kg block initially moves at 2 m s⁻¹. A constant net force does 22 N of work over 7 m in the direction of motion. Find its final kinetic energy. | {
"A": "218.4 J",
"B": "145.6 J",
"C": "184 J",
"D": "182 J"
} | D | 182 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(14)(2)²+(22)(7)=182 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 182 J, not 218.4 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 182 J, not 145.6 J.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 182 J, not 184 J.",
... | [
"work–energy theorem",
"kinetic energy",
"work by constant force"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_work_energy | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004086 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 28 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.29. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "101.04 N",
"B": "103.04 N",
"C": "-103.04 N",
"D": "51.52 N"
} | B | 103.04 N | Net force=mg(sinθ−μcosθ)=28×10×(0.6−0.29×0.8)=103.04 N. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 103.04 N, not 101.04 N.",
"B": "Correct. The worked calculation gives 103.04 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 103.04 N, not -103.04 N.",
"D": "Incorrect. Substituting the sta... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004465 | physics | rotational_mechanics | disc_angular_acceleration | hard | provisional_template_level_label | single_correct_mcq | A uniform solid disc of mass 4 kg and radius 5 m is acted on by a constant torque of 95 N m about its central axis. Find its angular acceleration. | {
"A": "0.9 rad s⁻²",
"B": "0.95 rad s⁻²",
"C": "-1.9 rad s⁻²",
"D": "1.9 rad s⁻²"
} | D | 1.9 rad s⁻² | For a solid disc, I=½MR²=½(4)(5)²=50 kg m². Using τ=Iα, α=95/50=1.9 rad s⁻². | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.9 rad s⁻², not 0.9 rad s⁻².",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.9 rad s⁻², not 0.95 rad s⁻².",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1... | [
"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_004145 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 11 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.25. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "44 N",
"B": "5.4 N",
"C": "66 N",
"D": "42 N"
} | A | 44 N | Net force=mg(sinθ−μcosθ)=11×10×(0.6−0.25×0.8)=44 N. | {
"A": "Correct. The worked calculation gives 44 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 44 N, not 5.4 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 44 N, not 66 N.",
"D": "Incorrect. Substituting the stated values into the ... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007886 | 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 42 mmol L⁻¹, what concentration remains after 20 minutes? | {
"A": "16.8 mmol L⁻¹",
"B": "3.1 mmol L⁻¹",
"C": "19 mmol L⁻¹",
"D": "21 mmol L⁻¹"
} | D | 21 mmol L⁻¹ | 20 minutes corresponds to 1 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=42/2^1=21 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 21 mmol L⁻¹, not 16.8 mmol L⁻¹.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 21 mmol L⁻¹, not 3.1 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives... | [
"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_007478 | chemistry | physical_chemistry | strong_acid_base_mixture | very_hard | provisional_template_level_label | single_correct_mcq | 15 mL of 0.10 M HCl is mixed with 37 mL of 0.10 M NaOH at 25°C. Assuming complete dissociation and additive volumes, find the final pH. | {
"A": "14.62642",
"B": "9.46981",
"C": "18.93963",
"D": "12.62642"
} | D | 12.62642 | Excess OH⁻ moles=0.10×(37−15)/1000=0.002200 mol. Total volume=0.052 L, so [OH⁻]=0.042308 M, pOH=−log₁₀[OH⁻], and pH=14−pOH=12.62642. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 12.62642, not 14.62642.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 12.62642, not 9.46981.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12.62642, not 1... | [
"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_002449 | mathematics | linear_algebra | 2x2_determinant | hard | provisional_template_level_label | single_correct_mcq | Find the determinant of the matrix [[1, 7], [7, 6]]. | {
"A": "-42",
"B": "-41",
"C": "-32.25",
"D": "-43"
} | D | -43 | For a 2×2 matrix [[a,b],[c,d]], det=ad−bc. Here it is (1)(6)−(7)(7)=-43. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -43, not -42.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -43, not -41.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -43, not -32.25.",
"D": "Correct... | [
"determinants",
"matrix operations"
] | 2 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_determinant_2x2 | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001371 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^7 (6x² +2x +3) dx. | {
"A": "754",
"B": "604.8",
"C": "756",
"D": "567"
} | C | 756 | An antiderivative is (6/3)x³+(2/2)x²+(3)x. Evaluating between 0 and 7 gives (6/3)(7)³+(2/2)(7)²+(3)(7)=756. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 756, not 754.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 756, not 604.8.",
"C": "Correct. The worked calculation gives 756.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_001719 | 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 20 distinct elements? | {
"A": "38759",
"B": "38762",
"C": "38760",
"D": "29070"
} | C | 38760 | Order does not matter, so the count is C(20,6)=20!/[6!(14)!]=38760. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 38760, not 38759.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 38760, not 38762.",
"C": "Correct. The worked calculation gives 38760.",
"D": "Incorrect. Substituting the stated values into ... | [
"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_001937 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 2 elements can be selected from a set of 88 distinct elements? | {
"A": "3828",
"B": "5742",
"C": "3826",
"D": "3827"
} | A | 3828 | Order does not matter, so the count is C(88,2)=88!/[2!(86)!]=3828. | {
"A": "Correct. The worked calculation gives 3828.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 3828, not 5742.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 3828, not 3826.",
"D": "Incorrect. Substituting the stated values into the g... | [
"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_007094 | 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 284 K and 2.57 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "125.94888 L",
"B": "253.89777 L",
"C": "127.94888 L",
"D": "126.94888 L"
} | D | 126.94888 L | PV=nRT, so V=nRT/P=(14)(0.082057)(284)/(2.57)=126.94888 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 126.94888 L, not 125.94888 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 126.94888 L, not 253.89777 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 12... | [
"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_009072 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.22 V, transfers 2 electrons, and has reaction quotient Q=10^-6. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "2.7946 V",
"B": "1.13973 V",
"C": "2.3973 V",
"D": "1.3973 V"
} | D | 1.3973 V | Apply the Nernst equation: E=1.22−(0.0591/2)(-6)=1.3973 V. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.3973 V, not 2.7946 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.3973 V, not 1.13973 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.3973 V, not... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_001536 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^1 (3x² -3x +6) dx. | {
"A": "8.25",
"B": "8.5",
"C": "5.5",
"D": "7.5"
} | C | 5.5 | An antiderivative is (3/3)x³+(-3/2)x²+(6)x. Evaluating between 0 and 1 gives (3/3)(1)³+(-3/2)(1)²+(6)(1)=5.5. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 5.5, not 8.25.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 5.5, not 8.5.",
"C": "Correct. The worked calculation gives 5.5.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003553 | physics | mechanics | projectile_range | hard | provisional_template_level_label | single_correct_mcq | A projectile is launched from level ground at 35 m s⁻¹ at 65° to the horizontal. Take g=10 m s⁻². Find its horizontal range. | {
"A": "46.92022 m",
"B": "70.38033 m",
"C": "187.68089 m",
"D": "93.84044 m"
} | D | 93.84044 m | Range R=u²sin(2θ)/g. Substituting u=35, θ=65° and g=10 gives R=(35)²sin(130°)/10=93.84044 m. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 93.84044 m, not 46.92022 m.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 93.84044 m, not 70.38033 m.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 93.840... | [
"projectile motion",
"range equation",
"trigonometry"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_projectile_range | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003096 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-1+3i)/(10+10i). What is Re(z), the real part of z? | {
"A": "0.05",
"B": "-0.9",
"C": "0.1",
"D": "-2.9"
} | C | 0.1 | Multiply numerator and denominator by the conjugate (10-10i). Then Re(z)=(ac+bd)/(c²+d²)=((-1)(10)+(3)(10))/(10²+(10)²)=0.1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.1, not 0.05.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.1, not -0.9.",
"C": "Correct. The worked calculation gives 0.1.",
"D": "Incorrect. Substituting the stated values into the gove... | [
"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_009631 | chemistry | organic_chemistry | degree_of_unsaturation | very_hard | provisional_template_level_label | single_correct_mcq | Assuming a neutral closed-shell formula, calculate the degree of unsaturation (DBE) for C_5H_10N_1X_1. Treat X as the total number of monovalent halogen atoms. | {
"A": "-2",
"B": "1",
"C": "0.5",
"D": "1.1"
} | B | 1 | Use DBE=(2C+2+N−H−X)/2. Substitution gives (2×5+2+1−10−1)/2=1. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1, not -2.",
"B": "Correct. The worked calculation gives 1.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1, not 0.5.",
"D": "Incorrect. Substituting the stated values into the governing rel... | [
"molecular formula",
"degree of unsaturation",
"organic structure"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_dbe | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_008730 | 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, 46% of A has dissociated at constant volume. Find K_c. | {
"A": "-0.37304",
"B": "0.62696",
"C": "3.62696",
"D": "-1.37304"
} | B | 0.62696 | Let α=0.46. At equilibrium [A]=c₀(1−α) and [B]=2c₀α. Thus K_c=[B]²/[A]=4c₀α²/(1−α)=4(0.4)(0.46)²/(1−0.46)=0.62696. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.62696, not -0.37304.",
"B": "Correct. The worked calculation gives 0.62696.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.62696, not 3.62696.",
"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_009032 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=0.93 V, transfers 2 electrons, and has reaction quotient Q=10^-2. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "0.9891 V",
"B": "-0.9891 V",
"C": "0.74183 V",
"D": "3.9891 V"
} | A | 0.9891 V | Apply the Nernst equation: E=0.93−(0.0591/2)(-2)=0.9891 V. | {
"A": "Correct. The worked calculation gives 0.9891 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 0.9891 V, not -0.9891 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.9891 V, not 0.74183 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_007014 | 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 243 K and 2.03 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "78.58069 L",
"B": "94.29683 L",
"C": "77.58069 L",
"D": "117.87104 L"
} | A | 78.58069 L | PV=nRT, so V=nRT/P=(8)(0.082057)(243)/(2.03)=78.58069 L. | {
"A": "Correct. The worked calculation gives 78.58069 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 78.58069 L, not 94.29683 L.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 78.58069 L, not 77.58069 L.",
"D": "Incorrect. Substitutin... | [
"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_007141 | chemistry | physical_chemistry | ideal_gas_volume | hard | provisional_template_level_label | single_correct_mcq | Assuming ideal behaviour, what volume is occupied by 2 mol of gas at 595 K and 1.98 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "24.65854 L",
"B": "39.45367 L",
"C": "49.31709 L",
"D": "98.63417 L"
} | C | 49.31709 L | PV=nRT, so V=nRT/P=(2)(0.082057)(595)/(1.98)=49.31709 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 49.31709 L, not 24.65854 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 49.31709 L, not 39.45367 L.",
"C": "Correct. The worked calculation gives 49.31709 L.",
"D": "Incorrect. Substitutin... | [
"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_003912 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 12 kg block initially moves at 0 m s⁻¹. A constant net force does 26 N of work over 13 m in the direction of motion. Find its final kinetic energy. | {
"A": "34.8 J",
"B": "340 J",
"C": "338 J",
"D": "253.5 J"
} | C | 338 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(12)(0)²+(26)(13)=338 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 338 J, not 34.8 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 338 J, not 340 J.",
"C": "Correct. The worked calculation gives 338 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_001437 | mathematics | calculus | definite_integral_polynomial | very_hard | provisional_template_level_label | single_correct_mcq | Evaluate the definite integral ∫₀^6 (4x² -3x -3) dx. | {
"A": "108",
"B": "22.6",
"C": "216",
"D": "432"
} | C | 216 | An antiderivative is (4/3)x³+(-3/2)x²+(-3)x. Evaluating between 0 and 6 gives (4/3)(6)³+(-3/2)(6)²+(-3)(6)=216. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 216, not 108.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 216, not 22.6.",
"C": "Correct. The worked calculation gives 216.",
"D": "Incorrect. Substituting the stated values into the gover... | [
"definite integration",
"power rule",
"limits of integration"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_integral_poly | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_003801 | physics | mechanics | work_energy_theorem | very_hard | provisional_template_level_label | single_correct_mcq | A 13 kg block initially moves at 11 m s⁻¹. A constant net force does 26 N of work over 13 m in the direction of motion. Find its final kinetic energy. | {
"A": "2249 J",
"B": "1123.5 J",
"C": "1124.5 J",
"D": "1125.5 J"
} | C | 1124.5 J | By the work–energy theorem, K_f=K_i+W=½mu²+Fs=½(13)(11)²+(26)(13)=1124.5 J. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1124.5 J, not 2249 J.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1124.5 J, not 1123.5 J.",
"C": "Correct. The worked calculation gives 1124.5 J.",
"D": "Incorrect. Substituting the stated... | [
"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_003130 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-11-3i)/(12+8i). What is Re(z), the real part of z? | {
"A": "-0.5625",
"B": "-0.375",
"C": "0.75",
"D": "-0.75"
} | D | -0.75 | Multiply numerator and denominator by the conjugate (12-8i). Then Re(z)=(ac+bd)/(c²+d²)=((-11)(12)+(-3)(8))/(12²+(8)²)=-0.75. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.75, not -0.5625.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.75, not -0.375.",
"C": "Incorrect. Substituting the stated values into the governing relation gives -0.75, not 0.75.",
"D... | [
"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_005342 | physics | electrostatics | capacitor_energy | hard | provisional_template_level_label | single_correct_mcq | A 52 μF capacitor is charged to a potential difference of 38 V. Calculate the energy stored, expressed in μJ. | {
"A": "37545 μJ",
"B": "37543 μJ",
"C": "37544 μJ",
"D": "-37544 μJ"
} | C | 37544 μJ | U=½CV². Since C=52 μF, U in μJ is ½×52×(38)²=37544 μJ. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 37544 μJ, not 37545 μJ.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 37544 μJ, not 37543 μJ.",
"C": "Correct. The worked calculation gives 37544 μJ.",
"D": "Incorrect. Substituting the stat... | [
"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_001895 | mathematics | combinatorics | binomial_coefficient | hard | provisional_template_level_label | single_correct_mcq | How many distinct subsets containing exactly 4 elements can be selected from a set of 24 distinct elements? | {
"A": "1063.6",
"B": "10626",
"C": "10628",
"D": "12751.2"
} | B | 10626 | Order does not matter, so the count is C(24,4)=24!/[4!(20)!]=10626. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 10626, not 1063.6.",
"B": "Correct. The worked calculation gives 10626.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 10626, not 10628.",
"D": "Incorrect. Substituting the stated values into... | [
"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_009171 | chemistry | physical_chemistry | nernst_equation_298K | hard | provisional_template_level_label | single_correct_mcq | At 298 K, a galvanic cell has E°cell=1.28 V, transfers 3 electrons, and has reaction quotient Q=10^5. Using E=E°−(0.0591/n)log₁₀Q, calculate Ecell. | {
"A": "1.1815 V",
"B": "0.1815 V",
"C": "3.1815 V",
"D": "0.88613 V"
} | A | 1.1815 V | Apply the Nernst equation: E=1.28−(0.0591/3)(5)=1.1815 V. | {
"A": "Correct. The worked calculation gives 1.1815 V.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 1.1815 V, not 0.1815 V.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.1815 V, not 3.1815 V.",
"D": "Incorrect. Substituting the stat... | [
"electrochemical cells",
"Nernst equation",
"logarithms"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_nernst | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_009800 | chemistry | inorganic_chemistry | complex_ion_oxidation_state | hard | provisional_template_level_label | single_correct_mcq | For a hypothetical coordination ion [Cu(Cl)_6]^+0, each Cl ligand has charge −1. Determine the formal oxidation state of Cu. | {
"A": "9",
"B": "12",
"C": "3",
"D": "6"
} | D | 6 | Let the formal oxidation state of Cu be x. Charge balance gives x+(6)(−1)=+0; hence x=0+6=+6. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 6, not 9.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 6, not 12.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 6, not 3.",
"D": "Correct. The worked c... | [
"coordination compounds",
"oxidation state",
"charge balance"
] | 3 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | chem_complex_oxidation | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_000674 | mathematics | sequences_and_series | geometric_progression | hard | provisional_template_level_label | single_correct_mcq | A geometric progression has first term 7 and common ratio 3. What is the sum of its first 12 terms? | {
"A": "2232048",
"B": "1860040",
"C": "1488032",
"D": "1860038"
} | B | 1860040 | For r≠1, Sₙ=a(rⁿ−1)/(r−1). Thus Sₙ=7(3^12−1)/(3−1)=1860040. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1860040, not 2232048.",
"B": "Correct. The worked calculation gives 1860040.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1860040, not 1488032.",
"D": "Incorrect. Substituting the stated va... | [
"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_007083 | 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 567 K and 2.63 atm? Use R=0.082057 L atm mol⁻¹ K⁻¹. | {
"A": "121.83431 L",
"B": "92.87573 L",
"C": "123.83431 L",
"D": "122.83431 L"
} | C | 123.83431 L | PV=nRT, so V=nRT/P=(7)(0.082057)(567)/(2.63)=123.83431 L. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 123.83431 L, not 121.83431 L.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 123.83431 L, not 92.87573 L.",
"C": "Correct. The worked calculation gives 123.83431 L.",
"D": "Incorrect. Substit... | [
"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_003263 | mathematics | complex_numbers | real_part_of_complex_quotient | very_hard | provisional_template_level_label | single_correct_mcq | Let z=(-13+13i)/(12+5i). What is Re(z), the real part of z? | {
"A": "-0.80769",
"B": "1.46154",
"C": "-0.53846",
"D": "-2.53846"
} | C | -0.53846 | Multiply numerator and denominator by the conjugate (12-5i). Then Re(z)=(ac+bd)/(c²+d²)=((-13)(12)+(13)(5))/(12²+(5)²)=-0.53846. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives -0.53846, not -0.80769.",
"B": "Incorrect. Substituting the stated values into the governing relation gives -0.53846, not 1.46154.",
"C": "Correct. The worked calculation gives -0.53846.",
"D": "Incorrect. Substituting the state... | [
"complex conjugate",
"complex division",
"real and imaginary parts"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | math_complex_quotient | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_004147 | physics | mechanics | inclined_plane_with_friction | very_hard | provisional_template_level_label | single_correct_mcq | A 36 kg block slides down a 37° rough incline. The coefficient of kinetic friction is 0.29. Taking g=10 m s⁻², find the net force down the plane. Use sin37°=0.6 and cos37°=0.8. | {
"A": "132.48 N",
"B": "133.48 N",
"C": "134.48 N",
"D": "130.48 N"
} | A | 132.48 N | Net force=mg(sinθ−μcosθ)=36×10×(0.6−0.29×0.8)=132.48 N. | {
"A": "Correct. The worked calculation gives 132.48 N.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 132.48 N, not 133.48 N.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 132.48 N, not 134.48 N.",
"D": "Incorrect. Substituting the stat... | [
"Newton's laws",
"inclined plane",
"kinetic friction"
] | 4 | numeric | en | synthetic_parametric | AxiloLabz deterministic STEM question generator | physics_incline_friction | template_formula_generated_structurally_validated_not_expert_reviewed | Answer is computed by the explicit equation in the generator template; this is not an independent expert proof. | Difficulty is approximate and not independently calibrated by JEE examiners; no ultra-hard claim is made in v0.1. | original_synthetic_question | correct_answer_option_matches_generated_numeric_value |
openstem_007734 | chemistry | physical_chemistry | first_order_half_life | hard | provisional_template_level_label | single_correct_mcq | A first-order reaction has a half-life of 20 minutes. If the initial reactant concentration is 59 mmol L⁻¹, what concentration remains after 100 minutes? | {
"A": "2.84375 mmol L⁻¹",
"B": "1.84375 mmol L⁻¹",
"C": "-1.15625 mmol L⁻¹",
"D": "4.84375 mmol L⁻¹"
} | B | 1.84375 mmol L⁻¹ | 100 minutes corresponds to 5 half-lives. The remaining concentration is [A]₀(1/2)ⁿ=59/2^5=1.84375 mmol L⁻¹. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 1.84375 mmol L⁻¹, not 2.84375 mmol L⁻¹.",
"B": "Correct. The worked calculation gives 1.84375 mmol L⁻¹.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 1.84375 mmol L⁻¹, not -1.15625 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_006531 | 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 704 N m⁻¹ and oscillates horizontally without damping. What is the time period divided by π? | {
"A": "0.375 s",
"B": "0.25 s",
"C": "1.025 s",
"D": "0.1875 s"
} | B | 0.25 s | For a mass–spring oscillator, T=2π√(m/k). Therefore T/π=2√(11/704)=0.25 s. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 0.25 s, not 0.375 s.",
"B": "Correct. The worked calculation gives 0.25 s.",
"C": "Incorrect. Substituting the stated values into the governing relation gives 0.25 s, not 1.025 s.",
"D": "Incorrect. Substituting the stated value... | [
"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_008328 | 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 1 A for 22626 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": "14.88861 g",
"B": "9.44431 g",
"C": "7.44431 g",
"D": "-7.44431 g"
} | C | 7.44431 g | Cu²⁺+2e⁻→Cu, so z=2. By Faraday's law m=MIt/(zF)=63.5×1×22626/(2×96500)=7.44431 g. | {
"A": "Incorrect. Substituting the stated values into the governing relation gives 7.44431 g, not 14.88861 g.",
"B": "Incorrect. Substituting the stated values into the governing relation gives 7.44431 g, not 9.44431 g.",
"C": "Correct. The worked calculation gives 7.44431 g.",
"D": "Incorrect. Substituting th... | [
"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 |
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