Q. If two resistors of resistivity ρ are connected in series, what is the total resistivity of the combination?
A.
ρ
B.
2ρ
C.
ρ/2
D.
Depends on the configuration
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Solution
Resistivity is a property of the material and does not change with series or parallel connections.
Correct Answer: A — ρ
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Q. If two rigid bodies have the same mass and shape but one is rotating faster than the other, how does their moment of inertia compare?
A.
The same
B.
The faster one has a larger moment of inertia
C.
The slower one has a larger moment of inertia
D.
Cannot be determined
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Solution
The moment of inertia depends only on the mass distribution and shape, not on the angular velocity.
Correct Answer: A — The same
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Q. If two sound waves of the same frequency interfere constructively, what happens to the resultant amplitude?
A.
It decreases
B.
It remains the same
C.
It doubles
D.
It becomes zero
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Solution
In constructive interference, the amplitudes of the waves add up, resulting in a doubled amplitude.
Correct Answer: C — It doubles
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Q. If two waves have a phase difference of π radians, what type of interference occurs?
A.
Constructive interference
B.
Destructive interference
C.
No interference
D.
Complete interference
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Solution
A phase difference of π radians results in destructive interference.
Correct Answer: B — Destructive interference
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Q. If two waves interfere constructively, what is the condition for the path difference?
A.
(n + 1/2)λ
B.
nλ
C.
(n - 1/2)λ
D.
n/2 λ
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Solution
Constructive interference occurs when the path difference is nλ, where n is an integer.
Correct Answer: B — nλ
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Q. If two waves of equal amplitude interfere destructively, what is the phase difference between them?
A.
0 rad
B.
π/2 rad
C.
π rad
D.
3π/2 rad
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Solution
Destructive interference occurs when the phase difference is π rad.
Correct Answer: C — π rad
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Q. If two waves of equal amplitude interfere destructively, what is the resultant amplitude?
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Solution
For destructive interference, the resultant amplitude is zero when two equal amplitudes cancel each other out.
Correct Answer: A — 0
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Q. If two waves of equal amplitude interfere, what is the maximum intensity observed?
A.
A^2
B.
2A^2
C.
4A^2
D.
A
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Solution
Maximum intensity (I_max) = 4A^2 for two waves of equal amplitude A.
Correct Answer: B — 2A^2
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Q. If two waves of the same frequency interfere constructively, what is the result?
A.
A wave of lower amplitude
B.
A wave of higher amplitude
C.
No wave
D.
A standing wave
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Solution
Constructive interference results in a wave of higher amplitude.
Correct Answer: B — A wave of higher amplitude
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Q. If two waves traveling in opposite directions interfere constructively, what is the result?
A.
A smaller amplitude wave
B.
A larger amplitude wave
C.
No wave
D.
A standing wave
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Solution
Constructive interference occurs when two waves meet in phase, resulting in a wave with a larger amplitude.
Correct Answer: B — A larger amplitude wave
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Q. If two wires of the same material are connected in series, how does their combined resistance compare to the individual resistances?
A.
Less than both
B.
Equal to the sum
C.
Greater than both
D.
Depends on length
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Solution
In series, the total resistance is the sum of individual resistances.
Correct Answer: B — Equal to the sum
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Q. If u = (1, 2) and v = (3, 4), what is the dot product u · v?
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Solution
Dot product u · v = 1*3 + 2*4 = 3 + 8 = 11.
Correct Answer: A — 10
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Q. If u = (1, 2) and v = (3, 4), what is u + v?
A.
(4, 6)
B.
(2, 3)
C.
(1, 2)
D.
(3, 4)
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Solution
u + v = (1 + 3, 2 + 4) = (4, 6)
Correct Answer: A — (4, 6)
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Q. If u = (1, 2, 3) and v = (4, 5, 6), what is the dot product u · v?
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Solution
Dot product u · v = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.
Correct Answer: B — 27
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Q. If u = (2, 3, 1) and v = (1, 0, -1), find the dot product u · v.
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Solution
u · v = 2*1 + 3*0 + 1*(-1) = 2 + 0 - 1 = 1.
Correct Answer: A — 5
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Q. If U = {1, 2, 3, 4, 5}, A = {1, 2}, and B = {2, 3}, what is A ∪ B?
A.
{1, 2}
B.
{1, 2, 3}
C.
{1, 2, 3, 4, 5}
D.
{2, 3, 4, 5}
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Solution
The union A ∪ B includes all elements from both sets, which are {1, 2, 3}.
Correct Answer: B — {1, 2, 3}
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Q. If unpolarized light passes through a polarizer, what fraction of the light intensity is transmitted?
A.
0%
B.
25%
C.
50%
D.
100%
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Solution
When unpolarized light passes through a polarizer, 50% of the light intensity is transmitted.
Correct Answer: C — 50%
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Q. If unpolarized light passes through a polarizer, what is the intensity of the transmitted light?
A.
Zero
B.
Half of the original intensity
C.
Equal to the original intensity
D.
Twice the original intensity
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Solution
According to Malus's law, the intensity of transmitted light is half of the original intensity when unpolarized light passes through a polarizer.
Correct Answer: B — Half of the original intensity
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Q. If unpolarized light passes through a polarizer, what percentage of the light intensity will emerge?
A.
0%
B.
25%
C.
50%
D.
100%
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Solution
When unpolarized light passes through a polarizer, 50% of the light intensity will emerge, according to Malus's law.
Correct Answer: C — 50%
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Q. If unpolarized light passes through two polarizers at 90 degrees to each other, what is the intensity of the transmitted light?
A.
Same as incident light
B.
Half of the incident light
C.
Zero
D.
One quarter of the incident light
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Solution
When unpolarized light passes through two polarizers at 90 degrees, no light is transmitted, resulting in zero intensity.
Correct Answer: C — Zero
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Q. If unpolarized light passes through two polarizers, what is the maximum intensity of light transmitted?
A.
Zero
B.
Half of the original intensity
C.
Equal to the original intensity
D.
Dependent on the angle between the polarizers
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Solution
The maximum intensity transmitted through two polarizers is given by Malus's law, which states that I = I0 * cos²(θ), where θ is the angle between the polarizers.
Correct Answer: D — Dependent on the angle between the polarizers
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Q. If vector A = (1, 2, 3) and vector B = (4, 5, 6), what is A + B?
A.
(5, 7, 9)
B.
(4, 5, 6)
C.
(1, 2, 3)
D.
(0, 0, 0)
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Solution
A + B = (1+4, 2+5, 3+6) = (5, 7, 9).
Correct Answer: A — (5, 7, 9)
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Q. If vector A = (1, 2, 3) and vector B = (4, 5, 6), what is the angle between them?
A.
0 degrees
B.
30 degrees
C.
60 degrees
D.
90 degrees
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Solution
Cosine of angle θ = (A . B) / (|A| |B|) = (1*4 + 2*5 + 3*6) / (√14 * √77) = 0, hence θ = 90 degrees.
Correct Answer: D — 90 degrees
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Q. If vector A = (1, 2, 3) and vector B = (4, 5, 6), what is the vector A - B?
A.
(-3, -3, -3)
B.
(3, 3, 3)
C.
(5, 7, 9)
D.
(0, 0, 0)
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Solution
A - B = (1-4, 2-5, 3-6) = (-3, -3, -3).
Correct Answer: A — (-3, -3, -3)
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Q. If vector A = (2, 2, 2) and vector B = (1, 1, 1), what is the scalar triple product A . (B × A)?
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Solution
A . (B × A) = 0, since B × A = 0.
Correct Answer: A — 0
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Q. If vector A = (3, -2, 1) and vector B = (1, 4, -3), what is the cross product A × B?
A.
(-5, -10, 14)
B.
(5, 10, -14)
C.
(10, 14, 5)
D.
(14, -5, 10)
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Solution
A × B = |i j k|\n|3 -2 1|\n|1 4 -3| = (-5, -10, 14).
Correct Answer: A — (-5, -10, 14)
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Q. If vectors A = (x, 2, 3) and B = (1, y, 4) are perpendicular, what is the value of x + y?
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Solution
A · B = x*1 + 2*y + 3*4 = 0. Thus, x + 2y + 12 = 0. Solving gives x + y = -6.
Correct Answer: B — 2
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Q. If vectors A = 3i + 4j and B = 2i - j, what is the scalar product A · B?
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Solution
A · B = (3)(2) + (4)(-1) = 6 - 4 = 2.
Correct Answer: C — 10
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Q. If x + 2y = 10 and 2x - y = 3, what is the value of x?
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Solution
From the first equation, x = 10 - 2y. Substituting into the second gives 2(10 - 2y) - y = 3, solving gives y = 4, x = 2.
Correct Answer: C — 3
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Q. If x + 4 = 10, what is the value of x?
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Solution
Subtracting 4 from both sides gives x = 6.
Correct Answer: B — 6
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