Q. What is the critical angle for light traveling from glass (n = 1.5) to air (n = 1)? (2019)
A.
30 degrees
B.
41.8 degrees
C.
48.6 degrees
D.
60 degrees
Show solution
Solution
Using the formula sin(c) = n2/n1, we find sin(c) = 1/1.5, thus c = sin^(-1)(2/3) ≈ 41.8 degrees.
Correct Answer:
B
— 41.8 degrees
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Q. What is the critical angle for total internal reflection from glass to air if the refractive index of glass is 1.5?
A.
30 degrees
B.
41.8 degrees
C.
48.6 degrees
D.
60 degrees
Show solution
Solution
Critical angle (C) is given by sin(C) = n2/n1. Thus, sin(C) = 1/1.5, C = sin^(-1)(0.6667) ≈ 41.8 degrees.
Correct Answer:
B
— 41.8 degrees
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Q. What is the critical angle for total internal reflection from water (n = 1.33) to air (n = 1)?
A.
48.6 degrees
B.
53.1 degrees
C.
60 degrees
D.
90 degrees
Show solution
Solution
The critical angle (θc) can be calculated using sin(θc) = n2/n1. Thus, sin(θc) = 1/1.33, giving θc ≈ 53.1 degrees.
Correct Answer:
B
— 53.1 degrees
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Q. What is the critical angle for total internal reflection from water to air (n_water = 1.33, n_air = 1)?
A.
48.6 degrees
B.
90 degrees
C.
30.0 degrees
D.
60.0 degrees
Show solution
Solution
The critical angle θ_c can be calculated using sin(θ_c) = n2/n1 = 1/1.33, which gives θ_c ≈ 48.6 degrees.
Correct Answer:
A
— 48.6 degrees
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Q. What is the critical angle for total internal reflection from water to air (n_water = 1.33, n_air = 1.00)?
A.
48.6 degrees
B.
90 degrees
C.
42.0 degrees
D.
60 degrees
Show solution
Solution
The critical angle θ_c can be calculated using sin(θ_c) = n2/n1 = 1.00/1.33, which gives θ_c ≈ 48.6 degrees.
Correct Answer:
A
— 48.6 degrees
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Q. What is the critical angle for total internal reflection if the refractive index of the medium is 1.5?
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
90 degrees
Show solution
Solution
The critical angle (θc) can be calculated using sin(θc) = 1/n. Here, n = 1.5, so θc = sin^(-1)(1/1.5) ≈ 41.81 degrees, which is approximately 42 degrees.
Correct Answer:
C
— 60 degrees
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Q. What is the critical angle for total internal reflection in a medium with a refractive index of 1.5?
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
90 degrees
Show solution
Solution
The critical angle (θc) can be calculated using sin(θc) = 1/n. For n = 1.5, sin(θc) = 1/1.5 = 2/3. Therefore, θc = sin^(-1)(2/3) which is approximately 41.81 degrees, closest to 45 degrees.
Correct Answer:
C
— 60 degrees
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Q. What is the critical angle for total internal reflection when light travels from water (n=1.33) to air (n=1.00)?
A.
48.6 degrees
B.
41.8 degrees
C.
53.1 degrees
D.
60.0 degrees
Show solution
Solution
The critical angle θc can be calculated using sin(θc) = n2/n1 = 1.00/1.33, which gives θc ≈ 48.6 degrees.
Correct Answer:
A
— 48.6 degrees
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Q. What is the critical angle for total internal reflection when light travels from water (n = 1.33) to air (n = 1)?
A.
48.6 degrees
B.
53.1 degrees
C.
60 degrees
D.
90 degrees
Show solution
Solution
The critical angle (θc) can be calculated using sin(θc) = n2/n1. Here, n1 = 1.33 (water) and n2 = 1 (air). Thus, sin(θc) = 1/1.33, giving θc ≈ 53.1 degrees.
Correct Answer:
B
— 53.1 degrees
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Q. What is the critical angle for total internal reflection when light travels from glass (n = 1.5) to air (n = 1)?
A.
30 degrees
B.
41.8 degrees
C.
48.6 degrees
D.
60 degrees
Show solution
Solution
The critical angle θc is given by sin(θc) = n2/n1. Thus, θc = sin^(-1)(1/1.5) ≈ 41.8 degrees.
Correct Answer:
B
— 41.8 degrees
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Q. What is the critical mass in nuclear fission?
A.
Mass required for a chain reaction
B.
Mass of a single nucleus
C.
Mass of the entire reactor
D.
Mass of fuel rods
Show solution
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?
A.
Mass required for a stable nucleus
B.
Mass required to sustain a nuclear chain reaction
C.
Mass of a neutron
D.
Mass of a proton
Show solution
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?
A.
The point where solid and liquid coexist
B.
The point where liquid and gas coexist
C.
The point beyond which gas cannot be liquefied
D.
The point of maximum pressure
Show solution
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^2 - 4x + 4? (2022)
Show solution
Solution
Set f'(x) = 2x - 4 = 0; solving gives x = 2.
Correct Answer:
B
— 2
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Q. What is the critical point of f(x) = x^3 - 3x^2 + 4?
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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?
Show solution
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 point of the function f(x) = x^2 - 4x + 4? (2022)
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Solution
Find f'(x) = 2x - 4. Set f'(x) = 0, giving 2x - 4 = 0, hence x = 2.
Correct Answer:
B
— 2
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Q. What is the critical point of the function f(x) = x^4 - 4x^3 + 6? (2023)
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Solution
First derivative f'(x) = 4x^3 - 12x^2. Setting f'(x) = 0 gives x = 0, 1, 3.
Correct Answer:
B
— 1
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Q. What is the critical temperature for a superconductor?
A.
The temperature at which it becomes a perfect conductor
B.
The temperature at which it loses all resistance
C.
The temperature at which it becomes a perfect insulator
D.
The temperature at which it becomes a normal conductor
Show solution
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?
A.
The temperature above which a gas cannot be liquefied
B.
The temperature at which a gas condenses
C.
The temperature at which a gas expands
D.
The temperature at which a gas is at its maximum density
Show solution
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?
A.
The temperature at which a substance boils
B.
The temperature above which a gas cannot be liquefied
C.
The temperature at which a substance freezes
D.
The temperature at which a substance condenses
Show solution
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)?
A.
(0, 0, 1)
B.
(1, 1, 0)
C.
(0, 0, 0)
D.
(1, 0, 0)
Show solution
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)?
A.
(-3, 6, -3)
B.
(-3, 6, 3)
C.
(3, -6, 3)
D.
(3, 6, -3)
Show solution
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)?
A.
(-3, 6, -3)
B.
(0, 0, 0)
C.
(3, -6, 3)
D.
(1, 2, 3)
Show solution
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)
Show solution
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)?
A.
(-3, 6, -3)
B.
(0, 0, 0)
C.
(3, -6, 3)
D.
(1, -2, 1)
Show solution
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 cross product of vectors A = i + 2j + 3k and B = 4i + 5j + 6k?
A.
-3i + 6j - 3k
B.
-3i + 6j + 3k
C.
3i - 6j + 3k
D.
3i + 6j - 3k
Show solution
Solution
A × B = |i j k| |1 2 3| |4 5 6| = -3i + 6j - 3k.
Correct Answer:
A
— -3i + 6j - 3k
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Q. What is the cross product of vectors A = i + 2j and B = 3i + 4j? (2021)
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Solution
A × B = |i j k| |1 2 0| |3 4 0| = (0 - 0)i - (0 - 0)j + (4 - 6)k = -2k.
Correct Answer:
A
— -2k
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Q. What is the cross product of vectors A = i + j and B = j + k? (2022)
A.
i + k
B.
i - k
C.
j - i
D.
k - j
Show solution
Solution
A × B = |i j k| |1 1 0| |0 1 1| = i(1*1 - 0*1) - j(1*1 - 0*0) + k(1*0 - 1*0) = i - j.
Correct Answer:
A
— i + k
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Q. What is the cross product of vectors E = i + 2j and F = 3i + 4j?
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Solution
E × F = |i j k| |1 2 0| |3 4 0| = (0 - 0)i - (0 - 0)j + (1*4 - 2*3)k = -2k.
Correct Answer:
A
— -2k
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