Q. What is the median of the following data set: 3, 5, 7, 9, 11, 13, 15?
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Solution
Median = 9 (middle value).
Correct Answer: C — 9
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Q. What is the median of the following numbers: 1, 3, 3, 6, 7, 8, 9?
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Solution
Median = 6 (middle value of the ordered set).
Correct Answer: B — 6
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Q. What is the median of the following numbers: 12, 15, 14, 10, 18?
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Solution
Arranging the numbers: 10, 12, 14, 15, 18. Median = 14.
Correct Answer: B — 14
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Q. What is the median of the following numbers: 3, 1, 4, 2, 5?
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Solution
Arranging in order: 1, 2, 3, 4, 5. Median = 3.
Correct Answer: B — 3
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Q. What is the median of the following numbers: 3, 7, 8, 12, 14?
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Solution
Median = 8 (middle value in ordered list).
Correct Answer: B — 8
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Q. What is the median of the following numbers: 7, 9, 12, 15, 18, 20?
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Solution
Median = (12 + 15) / 2 = 27 / 2 = 13.5.
Correct Answer: A — 12
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Q. What is the middle term in the expansion of (x + 2)^8?
A.
128
B.
112
C.
256
D.
64
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Solution
The middle term is T(5) = C(8,4) * (2)^4 = 70 * 16 = 1120.
Correct Answer: A — 128
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Q. What is the midpoint of the line segment joining the points (1, 2) and (3, 4)?
A.
(2, 3)
B.
(1, 2)
C.
(3, 4)
D.
(4, 6)
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Solution
Midpoint = ((1+3)/2, (2+4)/2) = (2, 3).
Correct Answer: A — (2, 3)
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Q. What is the midpoint of the line segment joining the points (2, 3) and (4, 7)?
A.
(3, 5)
B.
(2, 5)
C.
(4, 3)
D.
(5, 7)
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Solution
Midpoint = ((2+4)/2, (3+7)/2) = (3, 5).
Correct Answer: A — (3, 5)
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Q. What is the minimum energy required to remove an electron from the surface of a metal called?
A.
Work function
B.
Ionization energy
C.
Binding energy
D.
Threshold energy
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Solution
The minimum energy required to remove an electron from the surface of a metal is known as the work function.
Correct Answer: A — Work function
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Q. What is the minimum frequency of light required to eject electrons from a metal surface in the photoelectric effect?
A.
It depends on the intensity of light
B.
It is constant for all metals
C.
It depends on the work function of the metal
D.
It is equal to the energy of the incident photons
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Solution
The minimum frequency required to eject electrons is determined by the work function of the metal, given by the equation E = hf, where E is the work function, h is Planck's constant, and f is the frequency.
Correct Answer: C — It depends on the work function of the metal
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Q. What is the minimum speed required for a satellite to achieve a low Earth orbit?
A.
7.9 km/s
B.
11.2 km/s
C.
5.0 km/s
D.
9.8 km/s
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Solution
The minimum speed required for a satellite to achieve a low Earth orbit is approximately 7.9 km/s.
Correct Answer: A — 7.9 km/s
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Q. What is the minimum speed required for a satellite to maintain a low Earth orbit?
A.
7.9 km/s
B.
11.2 km/s
C.
5.0 km/s
D.
9.8 km/s
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Solution
The minimum speed required for a satellite in low Earth orbit is approximately 7.9 km/s.
Correct Answer: A — 7.9 km/s
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Q. What is the minimum thickness of a soap bubble for which the first order of bright fringe appears for light of wavelength 550 nm?
A.
275 nm
B.
550 nm
C.
1100 nm
D.
2200 nm
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Solution
For the first order bright fringe, thickness t = λ/2 = 550 nm / 2 = 275 nm.
Correct Answer: A — 275 nm
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Q. What is the minimum thickness of a soap bubble for which the first order of constructive interference occurs for light of wavelength 550 nm?
A.
275 nm
B.
550 nm
C.
1100 nm
D.
825 nm
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Solution
For constructive interference, the minimum thickness t = λ/2 = 550 nm / 2 = 275 nm.
Correct Answer: A — 275 nm
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Q. What is the minimum thickness of a soap bubble for which the first order of constructive interference occurs for light of wavelength 600 nm?
A.
100 nm
B.
200 nm
C.
300 nm
D.
400 nm
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Solution
For constructive interference in a soap bubble, the minimum thickness t = λ/2 = 600 nm / 2 = 300 nm.
Correct Answer: B — 200 nm
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Q. What is the minimum thickness of a soap bubble that appears black in reflected light?
A.
λ/4
B.
λ/2
C.
λ
D.
3λ/4
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Solution
A soap bubble appears black in reflected light when the thickness is λ/4, leading to destructive interference.
Correct Answer: A — λ/4
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Q. What is the minimum thickness of a soap bubble that will appear black in reflected light?
A.
λ/4
B.
λ/2
C.
λ
D.
3λ/4
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Solution
A soap bubble appears black in reflected light when the thickness is λ/4, leading to destructive interference.
Correct Answer: A — λ/4
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Q. What is the minimum thickness of a soap bubble that will appear black when viewed in white light?
A.
λ/4
B.
λ/2
C.
λ
D.
3λ/4
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Solution
A soap bubble appears black when the thickness is λ/4 due to destructive interference of light reflected from the top and bottom surfaces.
Correct Answer: A — λ/4
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Q. What is the minimum thickness of a soap film that appears dark in reflected light for a wavelength of 600 nm?
A.
150 nm
B.
300 nm
C.
600 nm
D.
1200 nm
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Solution
For destructive interference in reflected light, the minimum thickness t = λ/2n, where n is the refractive index (approximately 1.5 for soap). Thus, t = 600 nm / (2 * 1.5) = 200 nm.
Correct Answer: B — 300 nm
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Q. What is the minimum thickness of a soap film that appears dark when illuminated by white light?
A.
λ/4
B.
λ/2
C.
λ
D.
3λ/4
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Solution
For destructive interference in a soap film, the minimum thickness should be λ/2, considering the phase change upon reflection.
Correct Answer: B — λ/2
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Q. What is the minimum thickness of a soap film that appears dark when viewed in reflected light?
A.
λ/4
B.
λ/2
C.
λ
D.
3λ/4
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Solution
For destructive interference in reflected light, the minimum thickness of the film must be λ/2.
Correct Answer: B — λ/2
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Q. What is the minimum value of the function f(x) = 2x^2 - 8x + 10?
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Solution
The vertex form gives the minimum at x = 2. f(2) = 2(2^2) - 8(2) + 10 = 6.
Correct Answer: B — 4
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Q. What is the minimum value of the function f(x) = x^2 - 4x + 5?
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Solution
The vertex form gives the minimum at x = 2. f(2) = 2^2 - 4(2) + 5 = 1.
Correct Answer: A — 1
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Q. What is the minimum value of the function f(x) = x^4 - 8x^2 + 16?
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Solution
f'(x) = 4x^3 - 16x. Setting f'(x) = 0 gives x(x^2 - 4) = 0, so x = 0, 2, -2. f(0) = 16, f(2) = 0, f(-2) = 0. Minimum value is 0.
Correct Answer: A — 0
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Q. What is the mode of heat transfer that occurs through a fluid due to density differences?
A.
Conduction
B.
Convection
C.
Radiation
D.
Insulation
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Solution
Convection is the mode of heat transfer that occurs through a fluid due to density differences.
Correct Answer: B — Convection
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Q. What is the mode of heat transfer that occurs through a fluid without any movement of the fluid itself?
A.
Conduction
B.
Convection
C.
Radiation
D.
Diffusion
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Solution
Conduction is the mode of heat transfer that occurs through a solid or stationary fluid without any movement of the fluid itself.
Correct Answer: A — Conduction
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Q. What is the mode of the data set: 1, 2, 2, 3, 4, 4, 4, 5?
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Solution
The mode is the number that appears most frequently, which is 4.
Correct Answer: D — 4
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Q. What is the mode of the data set: 1, 2, 2, 3, 4?
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Solution
Mode is the number that appears most frequently. Here, mode = 2.
Correct Answer: B — 2
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Q. What is the mode of the data set: 5, 1, 2, 5, 3, 5, 4?
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Solution
Mode is the number that appears most frequently. Here, mode = 5.
Correct Answer: C — 5
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