answer string | choices dict | id string | kind string | lang string | question string | steps list | subject string | text string | topic string |
|---|---|---|---|---|---|---|---|---|---|
The voltage is 84 V. | {
"A": "72 V",
"B": "84 V",
"C": "96 V",
"D": "108 V"
} | eng_0051 | multiple_choice | en | Current 7 A flows through 12 Ω. What is the voltage? | [
"I = 7 A, R = 12 Ω.",
"V = IR = 84 V.",
"Select option B (84 V)."
] | engineering | Answer: 84 V.
Steps:
1. I = 7 A, R = 12 Ω.
2. V = IR = 84 V.
3. Select option B (84 V).
Answer: (B) | circuits |
Steady-state error is 10%. | {
"A": "12%",
"B": "8%",
"C": "10%",
"D": "15%"
} | eng_0052 | multiple_choice | en | Type-0 loop has position constant Kp = 9. What is step steady-state error? | [
"Kp = 9 (dimensionless).",
"ess = 100/10 = 10%.",
"Select option C (10%)."
] | engineering | Answer: 10%.
Steps:
1. Kp = 9 (dimensionless).
2. ess = 100/10 = 10%.
3. Select option C (10%).
Answer: (C) | control |
Dynamický tlak je 375 Pa. | null | eng_0053 | worked_example | cs | Vzduch (ρ = 1,2 kg/m³) letí 25 m/s. Jaký je dynamický tlak? | [
"ρ = 1.2 kg/m³, v = 25 m/s.",
"q = ½ρv² = 375 Pa.",
"Result 375 Pa."
] | engineering | Answer: 375 Pa.
Steps:
1. ρ = 1.2 kg/m³, v = 25 m/s.
2. q = ½ρv² = 375 Pa.
3. Result 375 Pa. | fluids |
The mass is 39.25 kg. | null | eng_0054 | worked_example | en | Steel part volume 0.005 m³ (ρ = 7850 kg/m³). What is its mass? | [
"V = 0.005 m³, ρ = 7850 kg/m³.",
"m = ρV = 39.25 kg.",
"Result 39.25 kg."
] | engineering | Answer: 39.25 kg.
Steps:
1. V = 0.005 m³, ρ = 7850 kg/m³.
2. m = ρV = 39.25 kg.
3. Result 39.25 kg. | materials |
The net moment is 1460 N·m clockwise. | null | eng_0055 | worked_example | en | 500 N at 4 m clockwise, 180 N at 3 m counter-clockwise. What is the net moment? | [
"M1 = 500×4 = 2000 N·m.",
"M2 = 180×3 = 540 N·m.",
"Net 1460 N·m."
] | engineering | Answer: 1460 N·m.
Steps:
1. M1 = 500×4 = 2000 N·m.
2. M2 = 180×3 = 540 N·m.
3. Net 1460 N·m. | statics |
Carnot efficiency is 50%. | {
"A": "55%",
"B": "45%",
"C": "50%",
"D": "60%"
} | eng_0056 | multiple_choice | en | Carnot engine between 300 K and 600 K. What is its efficiency? | [
"Tc = 300 K, Th = 600 K.",
"η = 1 − 300/600 = 50%.",
"Select option C (50%)."
] | engineering | Answer: 50%.
Steps:
1. Tc = 300 K, Th = 600 K.
2. η = 1 − 300/600 = 50%.
3. Select option C (50%).
Answer: (C) | thermodynamics |
The power is 1840 W. | {
"A": "1610 W",
"B": "2070 W",
"C": "1840 W",
"D": "1955 W"
} | eng_0057 | multiple_choice | en | A 230 V appliance draws 8 A. What is its power? | [
"V = 230 V, I = 8 A.",
"P = VI = 1840 W.",
"Select option C (1840 W)."
] | engineering | Answer: 1840 W.
Steps:
1. V = 230 V, I = 8 A.
2. P = VI = 1840 W.
3. Select option C (1840 W).
Answer: (C) | circuits |
The controller output is 40 V. | {
"A": "30 V",
"B": "50 V",
"C": "60 V",
"D": "40 V"
} | eng_0058 | multiple_choice | en | P-controller with Kp = 2 V/V sees error 20 units. What is the output? | [
"Kp = 2 V/V, e = 20 units.",
"u = Kp·e = 40 V.",
"Select option D (40 V)."
] | engineering | Answer: 40 V.
Steps:
1. Kp = 2 V/V, e = 20 units.
2. u = Kp·e = 40 V.
3. Select option D (40 V).
Answer: (D) | control |
Archimedes' principle says buoyancy equals the weight of displaced fluid. | null | eng_0059 | concept | en | What is Archimedes' principle? | [
"Volume under.",
"Times rho g.",
"Floats if light."
] | engineering | Answer: Displaced weight.
Steps:
1. Volume under.
2. Times rho g.
3. Floats if light. | fluids |
Napětí je vnitřní síla na plochu, v pascalech či megapascalech. | null | eng_0060 | concept | cs | Co je napětí v materiálu? | [
"N na m².",
"MPa šikovné.",
"Tah kladný."
] | engineering | Answer: Síla na plochu.
Steps:
1. N na m².
2. MPa šikovné.
3. Tah kladný. | materials |
Rameno je 14 m. | null | eng_0061 | worked_example | cs | Moment 2100 N·m dělá síla 150 N. Jaké je rameno? | [
"M = 2100 N·m, F = 150 N.",
"d = M/F = 14 m.",
"Result 14 m."
] | engineering | Answer: 14 m.
Steps:
1. M = 2100 N·m, F = 150 N.
2. d = M/F = 14 m.
3. Result 14 m. | statics |
The heat required is 66.88 kJ. | {
"A": "76.88 kJ",
"B": "56.88 kJ",
"C": "86.88 kJ",
"D": "66.88 kJ"
} | eng_0062 | multiple_choice | en | 2 kg of water warms by 8 K (c = 4.18 kJ/(kg·K)). How much heat? | [
"m = 2 kg, ΔT = 8 K.",
"Q = mcΔT = 66.88 kJ.",
"Select option D (66.88 kJ)."
] | engineering | Answer: 66.88 kJ.
Steps:
1. m = 2 kg, ΔT = 8 K.
2. Q = mcΔT = 66.88 kJ.
3. Select option D (66.88 kJ).
Answer: (D) | thermodynamics |
The stored charge is 3000 μC. | null | eng_0063 | worked_example | en | Capacitor 300 μF charged to 10 V. What charge is stored? | [
"C = 300 μF, V = 10 V.",
"Q = CV = 3000 μC.",
"Result 3000 μC."
] | engineering | Answer: 3000 μC.
Steps:
1. C = 300 μF, V = 10 V.
2. Q = CV = 3000 μC.
3. Result 3000 μC. | circuits |
PID control sums proportional, integral, and derivative terms on the error. | null | eng_0064 | concept | en | What is PID control? | [
"P reacts now.",
"I removes offset.",
"D damps."
] | engineering | Answer: P plus I plus D.
Steps:
1. P reacts now.
2. I removes offset.
3. D damps. | control |
The volume is 14 m³. | null | eng_0065 | worked_example | en | Tank base area 2 m², depth 7 m. What is the water volume? | [
"A = 2 m², h = 7 m.",
"V = Ah = 14 m³.",
"Result 14 m³."
] | engineering | Answer: 14 m³.
Steps:
1. A = 2 m², h = 7 m.
2. V = Ah = 14 m³.
3. Result 14 m³. | fluids |
Elongation is 2.5 mm. | {
"A": "3.5 mm",
"B": "1.5 mm",
"C": "4.5 mm",
"D": "2.5 mm"
} | eng_0066 | multiple_choice | en | Force 25 kN on 2 m steel bar (A = 100 mm², E = 200 GPa). What is elongation? | [
"F = 25 kN, L = 2 m.",
"ΔL = FL/AE = 2.5 mm.",
"Select option D (2.5 mm)."
] | engineering | Answer: 2.5 mm.
Steps:
1. F = 25 kN, L = 2 m.
2. ΔL = FL/AE = 2.5 mm.
3. Select option D (2.5 mm).
Answer: (D) | materials |
The horizontal component is 240 N. | null | eng_0067 | worked_example | en | Force 400 N pulls at a 3-4-5 angle. What is the horizontal component? | [
"F = 400 N, cos = 3/5.",
"Fx = 0.6×400 = 240 N.",
"Result 240 N."
] | engineering | Answer: 240 N.
Steps:
1. F = 400 N, cos = 3/5.
2. Fx = 0.6×400 = 240 N.
3. Result 240 N. | statics |
Internal energy rises 50 kJ. | {
"A": "50 kJ",
"B": "55 kJ",
"C": "45 kJ",
"D": "60 kJ"
} | eng_0068 | multiple_choice | en | System gains 90 kJ of heat and does 40 kJ of work. What is internal energy change? | [
"Q = 90 kJ, W = 40 kJ.",
"ΔU = Q−W = 50 kJ.",
"Select option A (50 kJ)."
] | engineering | Answer: 50 kJ.
Steps:
1. Q = 90 kJ, W = 40 kJ.
2. ΔU = Q−W = 50 kJ.
3. Select option A (50 kJ).
Answer: (A) | thermodynamics |
Total resistance is 1000 Ω. | {
"A": "900 Ω",
"B": "1100 Ω",
"C": "1050 Ω",
"D": "1000 Ω"
} | eng_0069 | multiple_choice | en | Resistors 100 Ω and 900 Ω in series. What is total resistance? | [
"R1 = 100 Ω, R2 = 900 Ω.",
"R = 1000 Ω.",
"Select option D (1000 Ω)."
] | engineering | Answer: 1000 Ω.
Steps:
1. R1 = 100 Ω, R2 = 900 Ω.
2. R = 1000 Ω.
3. Select option D (1000 Ω).
Answer: (D) | circuits |
P pushes with error, I clears steady offset, and D brakes on fast change. | null | eng_0070 | concept | en | What do P, I, D terms do? | [
"P gain now.",
"I sums past.",
"D rates change."
] | engineering | Answer: Push clear brake.
Steps:
1. P gain now.
2. I sums past.
3. D rates change. | control |
Continuity says mass flow is constant, so area times velocity stays fixed. | null | eng_0071 | concept | en | What is the continuity equation? | [
"Narrow pipe.",
"Faster flow.",
"Q constant."
] | engineering | Answer: Area times velocity.
Steps:
1. Narrow pipe.
2. Faster flow.
3. Q constant. | fluids |
Young's modulus is stiffness, stress over strain in gigapascals. | null | eng_0072 | concept | en | What is Young's modulus? | [
"Steel 200 GPa.",
"Alu 70 GPa.",
"Steeper stiffer."
] | engineering | Answer: Stiffness slope.
Steps:
1. Steel 200 GPa.
2. Alu 70 GPa.
3. Steeper stiffer. | materials |
The moment is 800 N·m. | {
"A": "700 N·m",
"B": "900 N·m",
"C": "800 N·m",
"D": "850 N·m"
} | eng_0073 | multiple_choice | en | Force 400 N acts at 2 m from a pivot. What is the moment? | [
"F = 400 N, d = 2 m.",
"M = Fd = 800 N·m.",
"Select option C (800 N·m)."
] | engineering | Answer: 800 N·m.
Steps:
1. F = 400 N, d = 2 m.
2. M = Fd = 800 N·m.
3. Select option C (800 N·m).
Answer: (C) | statics |
The first law states energy is conserved: heat added equals internal rise plus work done. | null | eng_0074 | concept | en | What is the first law of thermodynamics? | [
"Heat in J.",
"Work in J.",
"Internal stores."
] | engineering | Answer: Energy conserved.
Steps:
1. Heat in J.
2. Work in J.
3. Internal stores. | thermodynamics |
Ztrátový výkon je 120 W. | null | eng_0075 | worked_example | cs | Proud 2 A odporem 30 Ω. Jaký je ztrátový výkon? | [
"I = 2 A, R = 30 Ω.",
"P = I²R = 120 W.",
"Result 120 W."
] | engineering | Answer: 120 W.
Steps:
1. I = 2 A, R = 30 Ω.
2. P = I²R = 120 W.
3. Result 120 W. | circuits |
PID regulace sčítá složky P, I a D z regulační odchylky. | null | eng_0076 | concept | cs | Co je PID regulace? | [
"P tlačí hned.",
"I maže trvalou.",
"D tlumí."
] | engineering | Answer: P plus I plus D.
Steps:
1. P tlačí hned.
2. I maže trvalou.
3. D tlumí. | control |
The flow rate is 8 L/s. | {
"A": "6 L/s",
"B": "10 L/s",
"C": "8 L/s",
"D": "12 L/s"
} | eng_0077 | multiple_choice | en | Pipe area 20 cm², velocity 4 m/s. What is flow in litres per second? | [
"A = 20 cm², v = 4 m/s.",
"Q = Av = 8 L/s.",
"Select option C (8 L/s)."
] | engineering | Answer: 8 L/s.
Steps:
1. A = 20 cm², v = 4 m/s.
2. Q = Av = 8 L/s.
3. Select option C (8 L/s).
Answer: (C) | fluids |
The modulus is 62.1 GPa. | null | eng_0078 | worked_example | en | Composite with fibre fraction 0.3 (Ef = 200 GPa, Em = 3 GPa). What is the modulus? | [
"Vf = 0.3, Ef = 200 GPa.",
"E = VfEf+VmEm = 62.1 GPa.",
"Result 62.1 GPa."
] | engineering | Answer: 62.1 GPa.
Steps:
1. Vf = 0.3, Ef = 200 GPa.
2. E = VfEf+VmEm = 62.1 GPa.
3. Result 62.1 GPa. | materials |
Max friction is 450 N. | {
"A": "500 N",
"B": "400 N",
"C": "550 N",
"D": "450 N"
} | eng_0079 | multiple_choice | en | Normal force 900 N, friction coefficient 0.5. What is max friction? | [
"μ = 0.5 (dimensionless), N = 900 N.",
"F = μN = 450 N.",
"Select option D (450 N)."
] | engineering | Answer: 450 N.
Steps:
1. μ = 0.5 (dimensionless), N = 900 N.
2. F = μN = 450 N.
3. Select option D (450 N).
Answer: (D) | statics |
Teplota je 87 °C. | null | eng_0080 | worked_example | cs | Teplota je 360 K. Kolik je to stupňů Celsia? | [
"T = 360 K.",
"C = 360 − 273 = 87 °C.",
"Result 87 °C."
] | engineering | Answer: 87 °C.
Steps:
1. T = 360 K.
2. C = 360 − 273 = 87 °C.
3. Result 87 °C. | thermodynamics |
The current is 8 A. | null | eng_0081 | worked_example | en | Voltage 48 V across 6 Ω. What is the current? | [
"V = 48 V, R = 6 Ω.",
"I = V/R = 8 A.",
"Result 8 A."
] | engineering | Answer: 8 A.
Steps:
1. V = 48 V, R = 6 Ω.
2. I = V/R = 8 A.
3. Result 8 A. | circuits |
Stability means bounded inputs give bounded outputs without runaway. | null | eng_0082 | concept | en | What is stability? | [
"Poles left.",
"No blowup.",
"Margin kept."
] | engineering | Answer: Bounded stays bounded.
Steps:
1. Poles left.
2. No blowup.
3. Margin kept. | control |
The Reynolds number is 100000. | {
"A": "75000 (dimensionless)",
"B": "125000 (dimensionless)",
"C": "150000 (dimensionless)",
"D": "100000 (dimensionless)"
} | eng_0083 | multiple_choice | en | Water at 2 m/s in 0.05 m pipe (μ = 0.001 Pa·s). What is the Reynolds number? | [
"ρ = 1000 kg/m³, v = 2 m/s, D = 0.05 m.",
"Re = ρvD/μ = 100000 (dimensionless).",
"Select option D (100000 (dimensionless))."
] | engineering | Answer: 100000 (dimensionless).
Steps:
1. ρ = 1000 kg/m³, v = 2 m/s, D = 0.05 m.
2. Re = ρvD/μ = 100000 (dimensionless).
3. Select option D (100000 (dimensionless)).
Answer: (D) | fluids |
The shear stress is 32 MPa. | null | eng_0084 | worked_example | en | Shear force 16 kN on 500 mm² section. What is the shear stress? | [
"F = 16 kN, A = 500 mm².",
"τ = F/A = 32 MPa.",
"Result 32 MPa."
] | engineering | Answer: 32 MPa.
Steps:
1. F = 16 kN, A = 500 mm².
2. τ = F/A = 32 MPa.
3. Result 32 MPa. | materials |
The vertical component is 360 N. | null | eng_0085 | worked_example | en | Force 450 N pulls at a 3-4-5 angle. What is the vertical component? | [
"F = 450 N, sin = 4/5.",
"Fy = 0.8×450 = 360 N.",
"Result 360 N."
] | engineering | Answer: 360 N.
Steps:
1. F = 450 N, sin = 4/5.
2. Fy = 0.8×450 = 360 N.
3. Result 360 N. | statics |
The temperature is 318 K. | {
"A": "313 K",
"B": "318 K",
"C": "323 K",
"D": "328 K"
} | eng_0086 | multiple_choice | en | Temperature is 45 °C. What is it in kelvin? | [
"T = 45 °C.",
"K = 45 + 273 = 318 K.",
"Select option B (318 K)."
] | engineering | Answer: 318 K.
Steps:
1. T = 45 °C.
2. K = 45 + 273 = 318 K.
3. Select option B (318 K).
Answer: (B) | thermodynamics |
The equivalent is 50 Ω. | {
"A": "50 Ω",
"B": "55 Ω",
"C": "45 Ω",
"D": "60 Ω"
} | eng_0087 | multiple_choice | en | Two 100 Ω resistors in parallel. What is the equivalent? | [
"R = 100 Ω each.",
"Req = R/2 = 50 Ω.",
"Select option A (50 Ω)."
] | engineering | Answer: 50 Ω.
Steps:
1. R = 100 Ω each.
2. Req = R/2 = 50 Ω.
3. Select option A (50 Ω).
Answer: (A) | circuits |
The total gain is 14. | {
"A": "14 (dimensionless)",
"B": "12 (dimensionless)",
"C": "16 (dimensionless)",
"D": "18 (dimensionless)"
} | eng_0088 | multiple_choice | en | Two series blocks have gains 2 and 7. What is the total gain? | [
"K1 = 2, K2 = 7 (dimensionless).",
"K = 14 (dimensionless).",
"Select option A (14 (dimensionless))."
] | engineering | Answer: 14 (dimensionless).
Steps:
1. K1 = 2, K2 = 7 (dimensionless).
2. K = 14 (dimensionless).
3. Select option A (14 (dimensionless)).
Answer: (A) | control |
Hydraulic power is 1962 W. | null | eng_0089 | worked_example | en | Pump lifts 0.02 m³/s of water 10 m. What hydraulic power is needed? | [
"Q = 0.02 m³/s, H = 10 m.",
"P = ρgQH = 1962 W.",
"Result 1962 W."
] | engineering | Answer: 1962 W.
Steps:
1. Q = 0.02 m³/s, H = 10 m.
2. P = ρgQH = 1962 W.
3. Result 1962 W. | fluids |
Thermal stress is 108 MPa. | null | eng_0090 | worked_example | en | Steel bar (E = 200 GPa, α = 12e-6/K) cools 45 K constrained. What thermal stress arises? | [
"E = 200 GPa, ΔT = 45 K.",
"σ = EαΔT = 108 MPa.",
"Result 108 MPa."
] | engineering | Answer: 108 MPa.
Steps:
1. E = 200 GPa, ΔT = 45 K.
2. σ = EαΔT = 108 MPa.
3. Result 108 MPa. | materials |
The balancing reaction is 650 N upward. | {
"A": "650 N",
"B": "700 N",
"C": "600 N",
"D": "750 N"
} | eng_0091 | multiple_choice | en | Downward forces 260 N and 390 N act on a beam. What upward reaction balances them? | [
"F1 = 260 N, F2 = 390 N.",
"R = 260+390 = 650 N.",
"Select option A (650 N)."
] | engineering | Answer: 650 N.
Steps:
1. F1 = 260 N, F2 = 390 N.
2. R = 260+390 = 650 N.
3. Select option A (650 N).
Answer: (A) | statics |
The second law says entropy of an isolated system never decreases and heat flows hot to cold. | null | eng_0092 | concept | en | What is the second law of thermodynamics? | [
"Hot to cold.",
"No free lunch.",
"Irreversible."
] | engineering | Answer: Entropy never falls.
Steps:
1. Hot to cold.
2. No free lunch.
3. Irreversible. | thermodynamics |
The resistance is 11 Ω. | null | eng_0093 | worked_example | en | Voltage 33 V drives 3 A. What is the resistance? | [
"V = 33 V, I = 3 A.",
"R = V/I = 11 Ω.",
"Result 11 Ω."
] | engineering | Answer: 11 Ω.
Steps:
1. V = 33 V, I = 3 A.
2. R = V/I = 11 Ω.
3. Result 11 Ω. | circuits |
Stabilita znamená, že omezený vstup dá omezený výstup. | null | eng_0094 | concept | cs | Co je stabilita systému? | [
"Póly vlevo.",
"Bez úletu.",
"Rezerva drží."
] | engineering | Answer: Omezené drží.
Steps:
1. Póly vlevo.
2. Bez úletu.
3. Rezerva drží. | control |
The buoyant force is 58860 N. | {
"A": "58860 N",
"B": "49050 N",
"C": "68670 N",
"D": "78480 N"
} | eng_0095 | multiple_choice | en | A hull displaces 6 m³ of water. What is the buoyant force? | [
"V = 6 m³, ρ = 1000 kg/m³.",
"F = ρgV = 58860 N.",
"Select option A (58860 N)."
] | engineering | Answer: 58860 N.
Steps:
1. V = 6 m³, ρ = 1000 kg/m³.
2. F = ρgV = 58860 N.
3. Select option A (58860 N).
Answer: (A) | fluids |
Deformace je poměrné prodloužení, bezrozměrné, často v mikrostrainu. | null | eng_0096 | concept | cs | Co je deformace (strain)? | [
"Delta L lomeno L.",
"Bez jednotek.",
"Mikro škála."
] | engineering | Answer: Poměrné protažení.
Steps:
1. Delta L lomeno L.
2. Bez jednotek.
3. Mikro škála. | materials |
Síla je vektor s velikostí a směrem, měří se v newtonech. | null | eng_0097 | concept | cs | Co je síla? | [
"Velikost v N.",
"Směr platí.",
"Sčítá vektory."
] | engineering | Answer: Vektor v newtonech.
Steps:
1. Velikost v N.
2. Směr platí.
3. Sčítá vektory. | statics |
The specific volume is 4 m³/kg. | null | eng_0098 | worked_example | en | Gas fills 16 m³ with mass 4 kg. What is the specific volume? | [
"V = 16 m³, m = 4 kg.",
"v = V/m = 4 m³/kg.",
"Result 4 m³/kg."
] | engineering | Answer: 4 m³/kg.
Steps:
1. V = 16 m³, m = 4 kg.
2. v = V/m = 4 m³/kg.
3. Result 4 m³/kg. | thermodynamics |
Kirchhoff's current law says currents entering a node equal those leaving it. | null | eng_0099 | concept | en | What is Kirchhoff's current law? | [
"Sum in amps.",
"In equals out.",
"Charge conserves."
] | engineering | Answer: Currents balance.
Steps:
1. Sum in amps.
2. In equals out.
3. Charge conserves. | circuits |
The error is 35 units. | null | eng_0100 | worked_example | en | Setpoint 350 units, measurement 315 units. What is the error? | [
"r = 350 units, y = 315 units.",
"e = r−y = 35 units.",
"Result 35 units."
] | engineering | Answer: 35 units.
Steps:
1. r = 350 units, y = 315 units.
2. e = r−y = 35 units.
3. Result 35 units. | control |
Bernoulli's equation trades pressure, velocity, and height energy along a streamline. | null | eng_0101 | concept | en | What is Bernoulli's equation? | [
"Fast means low p.",
"High means low v.",
"Steady ideal."
] | engineering | Answer: Energy tradeoff.
Steps:
1. Fast means low p.
2. High means low v.
3. Steady ideal. | fluids |
Příčná deformace je -780 mikrostrainu. | null | eng_0102 | worked_example | cs | Tyč se natáhne o 2600 mikrostrainu, Poisson 0,3. Jaká je příčná deformace? | [
"εa = 2600 microstrain, ν = 0.3.",
"εt = −νεa = -780 microstrain.",
"Result -780 microstrain."
] | engineering | Answer: -780 microstrain.
Steps:
1. εa = 2600 microstrain, ν = 0.3.
2. εt = −νεa = -780 microstrain.
3. Result -780 microstrain. | materials |
The reaction at B is 1000 N. | null | eng_0103 | worked_example | en | Beam 6 m, load 1500 N at 4 m from A. What is reaction at B? | [
"F = 1500 N, span 6 m.",
"RB = 1500×4/6 = 1000 N.",
"Result 1000 N."
] | engineering | Answer: 1000 N.
Steps:
1. F = 1500 N, span 6 m.
2. RB = 1500×4/6 = 1000 N.
3. Result 1000 N. | statics |
The work done is 220 kJ. | {
"A": "200 kJ",
"B": "240 kJ",
"C": "220 kJ",
"D": "260 kJ"
} | eng_0104 | multiple_choice | en | Gas expands at 200 kPa by 1.1 m³. What work is done? | [
"p = 200 kPa, ΔV = 1.1 m³.",
"W = pΔV = 220 kJ.",
"Select option C (220 kJ)."
] | engineering | Answer: 220 kJ.
Steps:
1. p = 200 kPa, ΔV = 1.1 m³.
2. W = pΔV = 220 kJ.
3. Select option C (220 kJ).
Answer: (C) | thermodynamics |
Ohmův zákon říká, že napětí je proud krát odpor, U rovná IR. | null | eng_0105 | concept | cs | Co je Ohmův zákon? | [
"U ve voltech.",
"I v ampérech.",
"R v ohmech."
] | engineering | Answer: U rovná IR.
Steps:
1. U ve voltech.
2. I v ampérech.
3. R v ohmech. | circuits |
Ustálená hodnota je 30 jednotek. | {
"A": "25 units",
"B": "30 units",
"C": "35 units",
"D": "40 units"
} | eng_0106 | multiple_choice | cs | Soustava K/(10s+1) s K = 30 dostane jednotkový skok. Jaká je ustálená hodnota? | [
"DC gain K = 30 (dimensionless).",
"Step final = 30 units.",
"Vyber možnost B (30 units)."
] | engineering | Answer: 30 units.
Steps:
1. DC gain K = 30 (dimensionless).
2. Step final = 30 units.
3. Vyber možnost B (30 units).
Answer: (B) | control |
Přetlak je 68.67 kPa. | {
"A": "63.67 kPa",
"B": "68.67 kPa",
"C": "73.67 kPa",
"D": "78.67 kPa"
} | eng_0107 | multiple_choice | cs | Hloubka vody je 7 m. Jaký je přetlak? | [
"ρ = 1000 kg/m³, h = 7 m.",
"p = ρgh = 68.67 kPa.",
"Vyber možnost B (68.67 kPa)."
] | engineering | Answer: 68.67 kPa.
Steps:
1. ρ = 1000 kg/m³, h = 7 m.
2. p = ρgh = 68.67 kPa.
3. Vyber možnost B (68.67 kPa).
Answer: (B) | fluids |
Estimated strength is 980 MPa. | null | eng_0108 | worked_example | en | Steel hardness 280 HB. Estimate tensile strength (UTS ≈ 3.5·HB). | [
"Hardness = 280 HB.",
"UTS ≈ 3.5×280 = 980 MPa.",
"Result 980 MPa."
] | engineering | Answer: 980 MPa.
Steps:
1. Hardness = 280 HB.
2. UTS ≈ 3.5×280 = 980 MPa.
3. Result 980 MPa. | materials |
Moment dvojice je 420 N·m. | {
"A": "450 N·m",
"B": "420 N·m",
"C": "390 N·m",
"D": "480 N·m"
} | eng_0109 | multiple_choice | cs | Dvojice sil 140 N má rameno 3 m. Jaký je její moment? | [
"F = 140 N, d = 3 m.",
"M = Fd = 420 N·m.",
"Vyber možnost B (420 N·m)."
] | engineering | Answer: 420 N·m.
Steps:
1. F = 140 N, d = 3 m.
2. M = Fd = 420 N·m.
3. Vyber možnost B (420 N·m).
Answer: (B) | statics |
The power is 500 W. | null | eng_0110 | worked_example | en | Work 5000 J is done in 10 s. What is the power? | [
"W = 5000 J, t = 10 s.",
"P = W/t = 500 W.",
"Result 500 W."
] | engineering | Answer: 500 W.
Steps:
1. W = 5000 J, t = 10 s.
2. P = W/t = 500 W.
3. Result 500 W. | thermodynamics |
Energy used is 1100 Wh. | {
"A": "1000 Wh",
"B": "1100 Wh",
"C": "1200 Wh",
"D": "1150 Wh"
} | eng_0111 | multiple_choice | en | A 550 W bulb burns 2 h. How much energy is used? | [
"P = 550 W, t = 2 h.",
"E = Pt = 1100 Wh.",
"Select option B (1100 Wh)."
] | engineering | Answer: 1100 Wh.
Steps:
1. P = 550 W, t = 2 h.
2. E = Pt = 1100 Wh.
3. Select option B (1100 Wh).
Answer: (B) | circuits |
Settling time is about 32 s. | {
"A": "28 s",
"B": "36 s",
"C": "32 s",
"D": "40 s"
} | eng_0112 | multiple_choice | en | First-order system has time constant 8 s. What is 2% settling time? | [
"τ = 8 s.",
"ts ≈ 4τ = 32 s.",
"Select option C (32 s)."
] | engineering | Answer: 32 s.
Steps:
1. τ = 8 s.
2. ts ≈ 4τ = 32 s.
3. Select option C (32 s).
Answer: (C) | control |
Outlet velocity is 16 m/s. | {
"A": "14 m/s",
"B": "18 m/s",
"C": "16 m/s",
"D": "20 m/s"
} | eng_0113 | multiple_choice | en | Pipe narrows from 0.02 m² to 0.01 m², inlet velocity 8 m/s. What is outlet velocity? | [
"A1v1 = 0.02×8 m³/s.",
"v2 = 16 m/s.",
"Select option C (16 m/s)."
] | engineering | Answer: 16 m/s.
Steps:
1. A1v1 = 0.02×8 m³/s.
2. v2 = 16 m/s.
3. Select option C (16 m/s).
Answer: (C) | fluids |
The factor of safety is 2. | {
"A": "2 (dimensionless)",
"B": "2.5 (dimensionless)",
"C": "1.5 (dimensionless)",
"D": "3 (dimensionless)"
} | eng_0114 | multiple_choice | en | Yield 300 MPa, working stress 150 MPa. What is the factor of safety? | [
"σy = 300 MPa, σw = 150 MPa.",
"n = 2 (dimensionless).",
"Select option A (2 (dimensionless))."
] | engineering | Answer: 2 (dimensionless).
Steps:
1. σy = 300 MPa, σw = 150 MPa.
2. n = 2 (dimensionless).
3. Select option A (2 (dimensionless)).
Answer: (A) | materials |
Newton's first law says a body keeps its velocity unless a net force acts on it. | null | eng_0115 | concept | en | What is Newton's first law? | [
"No net force.",
"No acceleration.",
"Inertia rules."
] | engineering | Answer: Keep velocity.
Steps:
1. No net force.
2. No acceleration.
3. Inertia rules. | statics |
Carnotova účinnost je 60 %. | {
"A": "65%",
"B": "55%",
"C": "70%",
"D": "60%"
} | eng_0116 | multiple_choice | cs | Carnotův stroj mezi 300 K a 750 K. Jaká je jeho účinnost? | [
"Tc = 300 K, Th = 750 K.",
"η = 1 − 300/750 = 60%.",
"Vyber možnost D (60%)."
] | engineering | Answer: 60%.
Steps:
1. Tc = 300 K, Th = 750 K.
2. η = 1 − 300/750 = 60%.
3. Vyber možnost D (60%).
Answer: (D) | thermodynamics |
Kirchhoff's voltage law says voltages around any loop sum to zero. | null | eng_0117 | concept | en | What is Kirchhoff's voltage law? | [
"Add volts.",
"Rises equal drops.",
"Energy conserves."
] | engineering | Answer: Loop sums zero.
Steps:
1. Add volts.
2. Rises equal drops.
3. Energy conserves. | circuits |
Konečná hodnota je 24 jednotek. | null | eng_0118 | worked_example | cs | Soustava se zesílením 8 dostane skok 3. Jaká je konečná hodnota? | [
"K = 8 (dimensionless), step 3 units.",
"Final = 3×8 = 24 units.",
"Result 24 units."
] | engineering | Answer: 24 units.
Steps:
1. K = 8 (dimensionless), step 3 units.
2. Final = 3×8 = 24 units.
3. Result 24 units. | control |
The flow rate is 18 L/s. | {
"A": "16 L/s",
"B": "20 L/s",
"C": "22 L/s",
"D": "18 L/s"
} | eng_0119 | multiple_choice | en | Pipe area 20 cm², velocity 9 m/s. What is flow in litres per second? | [
"A = 20 cm², v = 9 m/s.",
"Q = Av = 18 L/s.",
"Select option D (18 L/s)."
] | engineering | Answer: 18 L/s.
Steps:
1. A = 20 cm², v = 9 m/s.
2. Q = Av = 18 L/s.
3. Select option D (18 L/s).
Answer: (D) | fluids |
The stress is 70 MPa. | {
"A": "60 MPa",
"B": "70 MPa",
"C": "80 MPa",
"D": "90 MPa"
} | eng_0120 | multiple_choice | en | Tensile force 7 kN on 100 mm² bar. What is the stress? | [
"F = 7 kN, A = 100 mm².",
"σ = F/A = 70 MPa.",
"Select option B (70 MPa)."
] | engineering | Answer: 70 MPa.
Steps:
1. F = 7 kN, A = 100 mm².
2. σ = F/A = 70 MPa.
3. Select option B (70 MPa).
Answer: (B) | materials |
Each end reaction is 700 N. | null | eng_0121 | worked_example | en | Uniform beam weighs 1400 N over 8 m. What is each end reaction? | [
"W = 1400 N, midspan 4 m.",
"R = W/2 = 700 N.",
"Result 700 N."
] | engineering | Answer: 700 N.
Steps:
1. W = 1400 N, midspan 4 m.
2. R = W/2 = 700 N.
3. Result 700 N. | statics |
Potřebné teplo je 108.68 kJ. | {
"A": "108.68 kJ",
"B": "118.68 kJ",
"C": "98.68 kJ",
"D": "128.68 kJ"
} | eng_0122 | multiple_choice | cs | 2 kg vody se ohřejí o 13 K (c = 4,18 kJ/(kg·K)). Kolik tepla? | [
"m = 2 kg, ΔT = 13 K.",
"Q = mcΔT = 108.68 kJ.",
"Vyber možnost A (108.68 kJ)."
] | engineering | Answer: 108.68 kJ.
Steps:
1. m = 2 kg, ΔT = 13 K.
2. Q = mcΔT = 108.68 kJ.
3. Vyber možnost A (108.68 kJ).
Answer: (A) | thermodynamics |
Series resistors add directly, so total resistance is the sum in ohms. | null | eng_0123 | concept | en | How do series resistors combine? | [
"Same current.",
"Voltages split.",
"R sums."
] | engineering | Answer: Add in series.
Steps:
1. Same current.
2. Voltages split.
3. R sums. | circuits |
Settling time is about 27 s. | null | eng_0124 | worked_example | en | Time constant 9 s. What is 5% settling time? | [
"τ = 9 s.",
"ts ≈ 3τ = 27 s.",
"Result 27 s."
] | engineering | Answer: 27 s.
Steps:
1. τ = 9 s.
2. ts ≈ 3τ = 27 s.
3. Result 27 s. | control |
The Reynolds number is 225000. | {
"A": "225000 (dimensionless)",
"B": "200000 (dimensionless)",
"C": "250000 (dimensionless)",
"D": "275000 (dimensionless)"
} | eng_0125 | multiple_choice | en | Water at 4.5 m/s in 0.05 m pipe (μ = 0.001 Pa·s). What is the Reynolds number? | [
"ρ = 1000 kg/m³, v = 4.5 m/s, D = 0.05 m.",
"Re = ρvD/μ = 225000 (dimensionless).",
"Select option A (225000 (dimensionless))."
] | engineering | Answer: 225000 (dimensionless).
Steps:
1. ρ = 1000 kg/m³, v = 4.5 m/s, D = 0.05 m.
2. Re = ρvD/μ = 225000 (dimensionless).
3. Select option A (225000 (dimensionless)).
Answer: (A) | fluids |
Yield strength is the stress where permanent deformation begins. | null | eng_0126 | concept | en | What is yield strength? | [
"Below elastic.",
"Above stays bent.",
"Design limit."
] | engineering | Answer: Plastic onset.
Steps:
1. Below elastic.
2. Above stays bent.
3. Design limit. | materials |
The resultant is 550 N. | {
"A": "500 N",
"B": "600 N",
"C": "550 N",
"D": "650 N"
} | eng_0127 | multiple_choice | en | Forces 330 N east and 440 N north act on a bolt. What is the resultant? | [
"Fx = 330 N, Fy = 440 N.",
"R = √(330²+440²) = 550 N.",
"Select option C (550 N)."
] | engineering | Answer: 550 N.
Steps:
1. Fx = 330 N, Fy = 440 N.
2. R = √(330²+440²) = 550 N.
3. Select option C (550 N).
Answer: (C) | statics |
Internal energy rises 75 kJ. | {
"A": "80 kJ",
"B": "75 kJ",
"C": "70 kJ",
"D": "85 kJ"
} | eng_0128 | multiple_choice | en | System gains 140 kJ of heat and does 65 kJ of work. What is internal energy change? | [
"Q = 140 kJ, W = 65 kJ.",
"ΔU = Q−W = 75 kJ.",
"Select option B (75 kJ)."
] | engineering | Answer: 75 kJ.
Steps:
1. Q = 140 kJ, W = 65 kJ.
2. ΔU = Q−W = 75 kJ.
3. Select option B (75 kJ).
Answer: (B) | thermodynamics |
The tap voltage is 13 V. | null | eng_0129 | worked_example | en | Divider with two 1000 Ω resistors fed 26 V. What is the tap voltage? | [
"Vin = 26 V, halves.",
"Vout = 13 V.",
"Result 13 V."
] | engineering | Answer: 13 V.
Steps:
1. Vin = 26 V, halves.
2. Vout = 13 V.
3. Result 13 V. | circuits |
Steady-state error is the lasting gap between setpoint and output. | null | eng_0130 | concept | en | What is steady-state error? | [
"Wait long.",
"Read offset.",
"Type sets it."
] | engineering | Answer: Lasting gap.
Steps:
1. Wait long.
2. Read offset.
3. Type sets it. | control |
Viscosity is a fluid's resistance to shearing flow. | null | eng_0131 | concept | en | What is viscosity? | [
"Honey high.",
"Water low.",
"Pa·s unit."
] | engineering | Answer: Flow resistance.
Steps:
1. Honey high.
2. Water low.
3. Pa·s unit. | fluids |
The mass is 86.35 kg. | null | eng_0132 | worked_example | en | Steel part volume 0.011 m³ (ρ = 7850 kg/m³). What is its mass? | [
"V = 0.011 m³, ρ = 7850 kg/m³.",
"m = ρV = 86.35 kg.",
"Result 86.35 kg."
] | engineering | Answer: 86.35 kg.
Steps:
1. V = 0.011 m³, ρ = 7850 kg/m³.
2. m = ρV = 86.35 kg.
3. Result 86.35 kg. | materials |
Moment je 1300 N·m. | {
"A": "1200 N·m",
"B": "1400 N·m",
"C": "1350 N·m",
"D": "1300 N·m"
} | eng_0133 | multiple_choice | cs | Síla 650 N působí 2 m od čepu. Jaký je moment? | [
"F = 650 N, d = 2 m.",
"M = Fd = 1300 N·m.",
"Vyber možnost D (1300 N·m)."
] | engineering | Answer: 1300 N·m.
Steps:
1. F = 650 N, d = 2 m.
2. M = Fd = 1300 N·m.
3. Vyber možnost D (1300 N·m).
Answer: (D) | statics |
The efficiency is 19%. | null | eng_0134 | worked_example | en | Engine turns 190 J of 1000 J heat into work. What is the efficiency? | [
"W = 190 J, Q = 1000 J.",
"η = W/Q = 19%.",
"Result 19%."
] | engineering | Answer: 19%.
Steps:
1. W = 190 J, Q = 1000 J.
2. η = W/Q = 19%.
3. Result 19%. | thermodynamics |
The leaving current is 14 A. | null | eng_0135 | worked_example | en | Currents 2 A and 12 A enter a node. What current leaves? | [
"I1 = 2 A, I2 = 12 A.",
"I3 = 14 A.",
"Result 14 A."
] | engineering | Answer: 14 A.
Steps:
1. I1 = 2 A, I2 = 12 A.
2. I3 = 14 A.
3. Result 14 A. | circuits |
Steady-state error is 20%. | {
"A": "22%",
"B": "18%",
"C": "25%",
"D": "20%"
} | eng_0136 | multiple_choice | en | Type-0 loop has position constant Kp = 4. What is step steady-state error? | [
"Kp = 4 (dimensionless).",
"ess = 100/5 = 20%.",
"Select option D (20%)."
] | engineering | Answer: 20%.
Steps:
1. Kp = 4 (dimensionless).
2. ess = 100/5 = 20%.
3. Select option D (20%).
Answer: (D) | control |
Tlak u dna je 107.91 kPa. | null | eng_0137 | worked_example | cs | Sloupec klidné vody 11 m. Jaký je tlak u dna? | [
"ρ = 1000 kg/m³, h = 11 m.",
"p = ρgh = 107.91 kPa.",
"Result 107.91 kPa."
] | engineering | Answer: 107.91 kPa.
Steps:
1. ρ = 1000 kg/m³, h = 11 m.
2. p = ρgh = 107.91 kPa.
3. Result 107.91 kPa. | fluids |
The modulus is 81.8 GPa. | null | eng_0138 | worked_example | en | Composite with fibre fraction 0.4 (Ef = 200 GPa, Em = 3 GPa). What is the modulus? | [
"Vf = 0.4, Ef = 200 GPa.",
"E = VfEf+VmEm = 81.8 GPa.",
"Result 81.8 GPa."
] | engineering | Answer: 81.8 GPa.
Steps:
1. Vf = 0.4, Ef = 200 GPa.
2. E = VfEf+VmEm = 81.8 GPa.
3. Result 81.8 GPa. | materials |
Newton's third law says every action has an equal and opposite reaction. | null | eng_0139 | concept | en | What is Newton's third law? | [
"Push object.",
"Object pushes back.",
"Pair acts."
] | engineering | Answer: Equal opposite reaction.
Steps:
1. Push object.
2. Object pushes back.
3. Pair acts. | statics |
The new volume is 8 m³. | null | eng_0140 | worked_example | en | Gas 3 m³ at 300 K warms to 800 K at constant pressure. What is the new volume? | [
"V1 = 3 m³, T1 = 300 K.",
"V2 = 3×800/300 = 8 m³.",
"Result 8 m³."
] | engineering | Answer: 8 m³.
Steps:
1. V1 = 3 m³, T1 = 300 K.
2. V2 = 3×800/300 = 8 m³.
3. Result 8 m³. | thermodynamics |
The voltage is 144 V. | {
"A": "132 V",
"B": "156 V",
"C": "144 V",
"D": "168 V"
} | eng_0141 | multiple_choice | en | Current 12 A flows through 12 Ω. What is the voltage? | [
"I = 12 A, R = 12 Ω.",
"V = IR = 144 V.",
"Select option C (144 V)."
] | engineering | Answer: 144 V.
Steps:
1. I = 12 A, R = 12 Ω.
2. V = IR = 144 V.
3. Select option C (144 V).
Answer: (C) | circuits |
The controller output is 90 V. | {
"A": "90 V",
"B": "80 V",
"C": "100 V",
"D": "110 V"
} | eng_0142 | multiple_choice | en | P-controller with Kp = 2 V/V sees error 45 units. What is the output? | [
"Kp = 2 V/V, e = 45 units.",
"u = Kp·e = 90 V.",
"Select option A (90 V)."
] | engineering | Answer: 90 V.
Steps:
1. Kp = 2 V/V, e = 45 units.
2. u = Kp·e = 90 V.
3. Select option A (90 V).
Answer: (A) | control |
The buoyant force is 107910 N. | {
"A": "98100 N",
"B": "107910 N",
"C": "117720 N",
"D": "127530 N"
} | eng_0143 | multiple_choice | en | A hull displaces 11 m³ of water. What is the buoyant force? | [
"V = 11 m³, ρ = 1000 kg/m³.",
"F = ρgV = 107910 N.",
"Select option B (107910 N)."
] | engineering | Answer: 107910 N.
Steps:
1. V = 11 m³, ρ = 1000 kg/m³.
2. F = ρgV = 107910 N.
3. Select option B (107910 N).
Answer: (B) | fluids |
The shear stress is 56 MPa. | null | eng_0144 | worked_example | en | Shear force 28 kN on 500 mm² section. What is the shear stress? | [
"F = 28 kN, A = 500 mm².",
"τ = F/A = 56 MPa.",
"Result 56 MPa."
] | engineering | Answer: 56 MPa.
Steps:
1. F = 28 kN, A = 500 mm².
2. τ = F/A = 56 MPa.
3. Result 56 MPa. | materials |
Max friction is 700 N. | {
"A": "700 N",
"B": "750 N",
"C": "650 N",
"D": "800 N"
} | eng_0145 | multiple_choice | en | Normal force 1400 N, friction coefficient 0.5. What is max friction? | [
"μ = 0.5 (dimensionless), N = 1400 N.",
"F = μN = 700 N.",
"Select option A (700 N)."
] | engineering | Answer: 700 N.
Steps:
1. μ = 0.5 (dimensionless), N = 1400 N.
2. F = μN = 700 N.
3. Select option A (700 N).
Answer: (A) | statics |
The pressure is 1300 kPa. | null | eng_0146 | worked_example | en | Gas 13 m³ at 100 kPa is squeezed to 1 m³ at constant temperature. What is the pressure? | [
"p1 = 100 kPa, V1 = 13 m³.",
"p2 = 100×13 = 1300 kPa.",
"Result 1300 kPa."
] | engineering | Answer: 1300 kPa.
Steps:
1. p1 = 100 kPa, V1 = 13 m³.
2. p2 = 100×13 = 1300 kPa.
3. Result 1300 kPa. | thermodynamics |
Příkon je 2990 W. | {
"A": "2760 W",
"B": "3220 W",
"C": "3105 W",
"D": "2990 W"
} | eng_0147 | multiple_choice | cs | Spotřebič na 230 V odebírá 13 A. Jaký je jeho příkon? | [
"V = 230 V, I = 13 A.",
"P = VI = 2990 W.",
"Vyber možnost D (2990 W)."
] | engineering | Answer: 2990 W.
Steps:
1. V = 230 V, I = 13 A.
2. P = VI = 2990 W.
3. Vyber možnost D (2990 W).
Answer: (D) | circuits |
Integrační výstup je 45 V. | null | eng_0148 | worked_example | cs | Chyba 2 jednotky trvá 45 s při Ki = 0,5 1/s. Jaký je integrační výstup? | [
"e = 2 units, t = 45 s.",
"u = 0.5×2×45 = 45 V.",
"Result 45 V."
] | engineering | Answer: 45 V.
Steps:
1. e = 2 units, t = 45 s.
2. u = 0.5×2×45 = 45 V.
3. Result 45 V. | control |
Laminar flow is smooth layered motion while turbulent flow is chaotic mixing. | null | eng_0149 | concept | en | How do laminar and turbulent flow differ? | [
"Low Re calm.",
"High Re wild.",
"Drag differs."
] | engineering | Answer: Smooth versus chaotic.
Steps:
1. Low Re calm.
2. High Re wild.
3. Drag differs. | fluids |
Thermal stress is 180 MPa. | null | eng_0150 | worked_example | en | Steel bar (E = 200 GPa, α = 12e-6/K) cools 75 K constrained. What thermal stress arises? | [
"E = 200 GPa, ΔT = 75 K.",
"σ = EαΔT = 180 MPa.",
"Result 180 MPa."
] | engineering | Answer: 180 MPa.
Steps:
1. E = 200 GPa, ΔT = 75 K.
2. σ = EαΔT = 180 MPa.
3. Result 180 MPa. | materials |
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