Q. What is the critical mass in nuclear fission?
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A.
Mass required for a chain reaction
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B.
Mass of a single nucleus
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C.
Mass of the entire reactor
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D.
Mass of fuel rods
Solution
Critical mass is the minimum mass of fissile material needed to maintain a sustained nuclear chain reaction.
Correct Answer: A — Mass required for a chain reaction
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Q. What is the critical mass in nuclear physics?
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A.
Mass required for a stable nucleus
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B.
Mass required to sustain a nuclear chain reaction
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C.
Mass of a neutron
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D.
Mass of a proton
Solution
Critical mass is the minimum mass of fissile material needed to maintain a nuclear chain reaction.
Correct Answer: B — Mass required to sustain a nuclear chain reaction
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Q. What is the critical point in a phase diagram?
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A.
The point where solid and liquid coexist
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B.
The point where liquid and gas coexist
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C.
The point beyond which gas cannot be liquefied
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D.
The point of maximum pressure
Solution
The critical point is where the liquid and gas phases become indistinguishable.
Correct Answer: C — The point beyond which gas cannot be liquefied
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Q. What is the critical point of f(x) = x^3 - 3x^2 + 4?
Solution
Setting f'(x) = 3x^2 - 6x = 0 gives x(x - 2) = 0, so critical points are x = 0 and x = 2.
Correct Answer: B — 2
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Q. What is the critical point of f(x) = x^3 - 6x^2 + 9x?
Solution
Setting f'(x) = 0 gives critical points at x = 1, 2, and 3.
Correct Answer: C — 2
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Q. What is the critical temperature for a superconductor?
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A.
The temperature at which it becomes a perfect conductor
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B.
The temperature at which it loses all resistance
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C.
The temperature at which it becomes a perfect insulator
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D.
The temperature at which it becomes a normal conductor
Solution
The critical temperature is the temperature below which a material exhibits superconductivity, losing all electrical resistance.
Correct Answer: B — The temperature at which it loses all resistance
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Q. What is the critical temperature of a gas?
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A.
The temperature above which a gas cannot be liquefied
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B.
The temperature at which a gas condenses
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C.
The temperature at which a gas expands
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D.
The temperature at which a gas is at its maximum density
Solution
The critical temperature is the temperature above which a gas cannot be liquefied, regardless of the pressure applied.
Correct Answer: A — The temperature above which a gas cannot be liquefied
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Q. What is the critical temperature of a substance?
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A.
The temperature at which a substance boils
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B.
The temperature above which a gas cannot be liquefied
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C.
The temperature at which a substance freezes
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D.
The temperature at which a substance condenses
Solution
The critical temperature is the temperature above which a gas cannot be liquefied.
Correct Answer: B — The temperature above which a gas cannot be liquefied
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Q. What is the cross product of the vectors (1, 0, 0) and (0, 1, 0)?
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A.
(0, 0, 1)
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B.
(1, 1, 0)
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C.
(0, 0, 0)
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D.
(1, 0, 0)
Solution
Cross product = (1, 0, 0) × (0, 1, 0) = (0, 0, 1).
Correct Answer: A — (0, 0, 1)
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Q. What is the cross product of the vectors (1, 2, 3) and (4, 5, 6)?
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A.
(-3, 6, -3)
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B.
(-3, 6, 3)
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C.
(3, -6, 3)
-
D.
(3, 6, -3)
Solution
Cross product = |i j k| |1 2 3| |4 5 6| = (-3, 6, -3).
Correct Answer: A — (-3, 6, -3)
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Q. What is the cross product of u = (1, 2, 3) and v = (4, 5, 6)?
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A.
(-3, 6, -3)
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B.
(0, 0, 0)
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C.
(3, -6, 3)
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D.
(1, 2, 3)
Solution
u × v = |i j k| |1 2 3| |4 5 6| = (-3, 6, -3)
Correct Answer: A — (-3, 6, -3)
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Q. What is the cross product of vectors (1, 2, 3) and (4, 5, 6)?
-
A.
(-3, 6, -3)
-
B.
(0, 0, 0)
-
C.
(3, -6, 3)
-
D.
(1, 2, 3)
Solution
Cross product = |i j k| |1 2 3| |4 5 6| = (-3, 6, -3)
Correct Answer: A — (-3, 6, -3)
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Q. What is the cross product of vectors A = (1, 2, 3) and B = (4, 5, 6)?
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A.
(-3, 6, -3)
-
B.
(0, 0, 0)
-
C.
(3, -6, 3)
-
D.
(1, -2, 1)
Solution
Cross product A × B = |i j k| |1 2 3| |4 5 6| = (-3, 6, -3).
Correct Answer: A — (-3, 6, -3)
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Q. What is the current flowing through a 10 ohm resistor connected to a 20V battery?
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A.
2 A
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B.
1 A
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C.
0.5 A
-
D.
0.2 A
Solution
Using Ohm's law, I = V/R = 20V / 10 ohms = 2 A.
Correct Answer: A — 2 A
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Q. What is the current flowing through a 15Ω resistor connected to a 45V battery?
Solution
Using Ohm's law, I = V/R = 45V / 15Ω = 3A.
Correct Answer: C — 3A
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Q. What is the current through a 10 ohm resistor connected across a 20V battery?
-
A.
0.5 A
-
B.
2 A
-
C.
1 A
-
D.
5 A
Solution
Using Ohm's law, I = V/R, we have I = 20V / 10 ohms = 2 A.
Correct Answer: B — 2 A
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Q. What is the current through a 10 ohm resistor connected to a 20V battery?
-
A.
2 A
-
B.
0.5 A
-
C.
20 A
-
D.
10 A
Solution
Using Ohm's law, I = V/R, we have I = 20V / 10 ohms = 2 A.
Correct Answer: A — 2 A
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Q. What is the current through a 10Ω resistor connected to a 50V power supply?
Solution
Using Ohm's law, I = V/R = 50V/10Ω = 5A.
Correct Answer: A — 5A
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Q. What is the current through a 12Ω resistor connected to a 24V source?
Solution
Using Ohm's law, I = V/R = 24V/12Ω = 2A.
Correct Answer: B — 2A
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Q. What is the current through a 12Ω resistor connected to a 36V battery?
Solution
Using Ohm's Law, I = V / R = 36V / 12Ω = 3A.
Correct Answer: C — 3A
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Q. What is the damping ratio for critically damped oscillation?
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A.
Less than 1
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B.
Equal to 1
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C.
Greater than 1
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D.
Zero
Solution
A critically damped system has a damping ratio equal to 1, which allows it to return to equilibrium without oscillating.
Correct Answer: B — Equal to 1
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Q. What is the de Broglie wavelength of an electron moving with a velocity of 1.5 x 10^6 m/s? (mass of electron = 9.11 x 10^-31 kg)
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A.
4.86 x 10^-10 m
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B.
2.42 x 10^-10 m
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C.
1.33 x 10^-10 m
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D.
6.63 x 10^-10 m
Solution
The de Broglie wavelength λ = h/p = h/(mv). Using h = 6.63 x 10^-34 J.s, we find λ = 6.63 x 10^-34 / (9.11 x 10^-31 * 1.5 x 10^6) = 2.42 x 10^-10 m.
Correct Answer: B — 2.42 x 10^-10 m
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Q. What is the decibel level of a sound that is 10 times more intense than the reference level?
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A.
10 dB
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B.
20 dB
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C.
30 dB
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D.
40 dB
Solution
Every increase of 10 dB represents a tenfold increase in intensity, so 10 times more intense is 20 dB.
Correct Answer: B — 20 dB
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Q. What is the definition of Young's modulus?
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A.
The ratio of tensile stress to tensile strain
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B.
The ratio of compressive stress to compressive strain
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C.
The ratio of shear stress to shear strain
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D.
The ratio of bulk stress to bulk strain
Solution
Young's modulus is defined as the ratio of tensile stress to tensile strain, which measures the stiffness of a solid material.
Correct Answer: A — The ratio of tensile stress to tensile strain
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Q. What is the derivative of f(x) = 3x^2 + 5x - 7?
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A.
3x + 5
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B.
6x + 5
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C.
6x - 5
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D.
3x^2 + 5
Solution
The derivative f'(x) = d/dx(3x^2 + 5x - 7) = 6x + 5.
Correct Answer: B — 6x + 5
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Q. What is the derivative of f(x) = 3x^3 - 5x + 2?
-
A.
9x^2 - 5
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B.
3x^2 - 5
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C.
9x^2 + 5
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D.
3x^2 + 5
Solution
f'(x) = 9x^2 - 5.
Correct Answer: A — 9x^2 - 5
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Q. What is the derivative of f(x) = 5x^4 - 3x + 2?
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A.
20x^3 - 3
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B.
20x^3 + 3
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C.
15x^3 - 3
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D.
5x^3 - 3
Solution
The derivative f'(x) = d/dx(5x^4 - 3x + 2) = 20x^3 - 3.
Correct Answer: A — 20x^3 - 3
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Q. What is the derivative of f(x) = e^x?
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A.
e^x
-
B.
x*e^x
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C.
1
-
D.
0
Solution
The derivative of e^x is e^x.
Correct Answer: A — e^x
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Q. What is the derivative of f(x) = ln(x^2 + 1) at x = 0?
-
A.
0
-
B.
1
-
C.
2
-
D.
undefined
Solution
f'(x) = (2x)/(x^2 + 1), thus f'(0) = 0.
Correct Answer: A — 0
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Q. What is the derivative of f(x) = ln(x^2 + 1) at x = 1?
Solution
f'(x) = (2x)/(x^2 + 1). At x = 1, f'(1) = (2*1)/(1^2 + 1) = 1.
Correct Answer: B — 1
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