Q. If the mixed graph indicates a peak at a certain point, what does this suggest about the data? (2023)
A.
The data is at its highest point of performance.
B.
The data is experiencing a decline.
C.
The data is stable at that point.
D.
The data is irrelevant beyond that point.
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Solution
A peak in the graph indicates that the data has reached its highest performance level at that point.
Correct Answer:
A
— The data is at its highest point of performance.
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Q. If the mixed graph indicates a seasonal trend, which of the following statements is most accurate? (2023)
A.
The data is consistent across all seasons.
B.
There are peaks and troughs corresponding to seasonal changes.
C.
The seasonal trend is irrelevant to the overall analysis.
D.
The trend is only visible in one season.
Show solution
Solution
The graph shows clear peaks and troughs that align with seasonal changes.
Correct Answer:
B
— There are peaks and troughs corresponding to seasonal changes.
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Q. If the mixed graph shows a decline in one variable while the other remains stable, what can be inferred?
A.
The stable variable is influencing the decline.
B.
There is no relationship between the two variables.
C.
The decline is a result of external factors.
D.
The stable variable is likely a control factor.
Show solution
Solution
A stable variable may act as a control, indicating that the decline is not influenced by it.
Correct Answer:
D
— The stable variable is likely a control factor.
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Q. If the mixed graph shows a downward trend, what can be inferred about the relationship between the variables? (2023)
A.
As one variable increases, the other decreases.
B.
Both variables are increasing together.
C.
There is no relationship between the variables.
D.
The variables are inversely related.
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Solution
A downward trend indicates that as one variable increases, the other decreases.
Correct Answer:
A
— As one variable increases, the other decreases.
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Q. If the mixed graph shows a steep increase followed by a gradual decrease, what could this suggest about consumer behavior?
A.
Consumers are consistently purchasing more.
B.
There was a temporary spike in interest followed by a decline.
C.
Consumers are becoming more loyal to the product.
D.
The market is saturated.
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Solution
A steep increase followed by a decrease often indicates a temporary spike in interest.
Correct Answer:
B
— There was a temporary spike in interest followed by a decline.
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Q. If the mode of a data set is 5, which of the following statements is true?
A.
5 occurs most frequently
B.
5 is the average
C.
5 is the middle value
D.
5 is the least value
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Solution
Mode is the value that appears most frequently in a data set.
Correct Answer:
A
— 5 occurs most frequently
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Q. If the mode of the data set 1, 2, 2, 3, 4, 4, 4, 5 is removed, what will be the new mode?
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Solution
New mode = 2 (as 4 is removed, 2 is the next most frequent).
Correct Answer:
A
— 2
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Q. If the mode of the data set 1, 2, 2, 3, 4, 4, 4, 5 is?
Show solution
Solution
Mode is the number that appears most frequently. Here, 4 appears 3 times.
Correct Answer:
D
— 4
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Q. If the mode of the data set 2, 3, 3, 5, 7, 8 is 3, what is the mode of the data set 1, 1, 2, 2, 3, 3, 3, 4?
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Solution
Mode = 3 (most frequent value).
Correct Answer:
C
— 3
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Q. If the mode of the data set 2, 3, 4, 4, 5, 5, 5, 6 is removed, what is the new mode?
A.
4
B.
5
C.
6
D.
No mode
Show solution
Solution
Removing 5 leaves 2, 3, 4, 4, 6. The new mode is 4.
Correct Answer:
D
— No mode
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Q. If the mode of the data set 2, 3, 4, 4, 5, 5, 5, 6 is?
Show solution
Solution
Mode is the value that appears most frequently. Here, 5 appears 3 times.
Correct Answer:
C
— 5
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Q. If the mode of the data set 3, 4, 4, 5, 6, 6, 6, 7 is removed, what is the new mode?
Show solution
Solution
Removing mode 6 leaves 3, 4, 4, 5, 7. New mode = 4.
Correct Answer:
A
— 4
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Q. If the mode of the data set 3, 7, 7, 2, 5, 7, 8 is x, what is the value of x?
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Solution
Mode is the most frequent value. Here, 7 appears most frequently.
Correct Answer:
C
— 7
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Q. If the mode of the data set {1, 2, 2, 3, 4, 4, 4, 5} is removed, what is the new mode?
Show solution
Solution
Removing mode 4 leaves {1, 2, 2, 3, 5}. New mode = 2.
Correct Answer:
B
— 2
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Q. If the mode of the data set {3, 5, 7, 3, 9, 3, 5} is x, what is the value of x?
Show solution
Solution
Mode is the number that appears most frequently. Here, 3 appears 3 times.
Correct Answer:
A
— 3
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Q. If the mode of the following numbers: 3, 3, 4, 5, 5, 5, 6, 7 is removed, what will be the new mode? (2019)
Show solution
Solution
Removing 5, which is the mode, leaves 3 as the new mode since it appears twice.
Correct Answer:
A
— 3
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Q. If the mode of the following set of numbers: 1, 2, 2, 3, 4, 4, 4, 5 is increased by 1, what will be the new mode? (2022)
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Solution
The original mode is 4. Increasing it by 1 gives a new mode of 5.
Correct Answer:
C
— 4
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Q. If the molar mass of a gas is doubled, how does its RMS speed change?
A.
Increases by sqrt(2)
B.
Decreases by sqrt(2)
C.
Remains the same
D.
Increases by 2
Show solution
Solution
RMS speed is inversely proportional to the square root of molar mass, so if M is doubled, v_rms decreases by sqrt(2).
Correct Answer:
B
— Decreases by sqrt(2)
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Q. If the molar mass of a gas is doubled, how does the RMS speed change?
A.
Increases by sqrt(2)
B.
Decreases by sqrt(2)
C.
Remains the same
D.
Increases by 2
Show solution
Solution
The RMS speed is inversely proportional to the square root of the molar mass. If M is doubled, v_rms decreases by sqrt(2).
Correct Answer:
B
— Decreases by sqrt(2)
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Q. If the molar mass of a gas is halved, what happens to its RMS speed?
A.
Increases by a factor of sqrt(2)
B.
Increases by a factor of 2
C.
Decreases by a factor of sqrt(2)
D.
Remains the same
Show solution
Solution
If the molar mass is halved, the RMS speed increases by a factor of sqrt(2) because RMS speed is inversely proportional to the square root of molar mass.
Correct Answer:
A
— Increases by a factor of sqrt(2)
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Q. If the mole fraction of a solute in a solution is 0.2, what is the mole fraction of the solvent?
A.
0.8
B.
0.2
C.
0.5
D.
0.6
Show solution
Solution
Mole fraction of solvent = 1 - mole fraction of solute = 1 - 0.2 = 0.8.
Correct Answer:
A
— 0.8
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Q. If the mole fraction of a solvent in a solution is 0.75, what is the vapor pressure of the solvent if its pure vapor pressure is 100 mmHg?
A.
75 mmHg
B.
100 mmHg
C.
25 mmHg
D.
50 mmHg
Show solution
Solution
According to Raoult's Law, the vapor pressure of the solvent in the solution is 0.75 * 100 mmHg = 75 mmHg.
Correct Answer:
A
— 75 mmHg
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Q. If the mole fraction of a solvent in a solution is 0.8, what is the mole fraction of the solute?
A.
0.2
B.
0.8
C.
0.5
D.
0.1
Show solution
Solution
The mole fraction of the solute is 1 - X_solvent = 1 - 0.8 = 0.2.
Correct Answer:
A
— 0.2
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Q. If the mole fraction of solute in a solution is 0.2, what is the mole fraction of the solvent?
A.
0.8
B.
0.2
C.
0.5
D.
0.6
Show solution
Solution
The mole fraction of the solvent is 1 - X_solute = 1 - 0.2 = 0.8.
Correct Answer:
A
— 0.8
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Q. If the moment of inertia of a body is 10 kg m², what is the angular momentum when it rotates with an angular velocity of 5 rad/s?
A.
50 kg m²/s
B.
10 kg m²/s
C.
5 kg m²/s
D.
2 kg m²/s
Show solution
Solution
Angular momentum L = Iω = 10 kg m² * 5 rad/s = 50 kg m²/s.
Correct Answer:
A
— 50 kg m²/s
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Q. If the moment of inertia of a body is 10 kg m², what is the rotational kinetic energy when it rotates with an angular velocity of 5 rad/s?
A.
125 J
B.
50 J
C.
100 J
D.
75 J
Show solution
Solution
Rotational kinetic energy is given by KE = 1/2 I ω² = 1/2 * 10 * 5² = 125 J.
Correct Answer:
A
— 125 J
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Q. If the moment of inertia of a body is 10 kg·m² and it is subjected to a torque of 20 N·m, what is the angular acceleration?
A.
2 rad/s²
B.
0.5 rad/s²
C.
5 rad/s²
D.
10 rad/s²
Show solution
Solution
Using τ = Iα, we have α = τ/I = 20 N·m / 10 kg·m² = 2 rad/s².
Correct Answer:
A
— 2 rad/s²
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Q. If the moment of inertia of a body is doubled while keeping the angular velocity constant, what happens to its angular momentum? (2019)
A.
It doubles
B.
It remains the same
C.
It halves
D.
It quadruples
Show solution
Solution
Angular momentum L = Iω, so if I is doubled and ω remains constant, L also doubles.
Correct Answer:
A
— It doubles
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Q. If the moment of inertia of a body is doubled, what happens to its rotational kinetic energy if the angular velocity remains constant?
A.
Doubles
B.
Halves
C.
Remains the same
D.
Quadruples
Show solution
Solution
Rotational kinetic energy is given by KE = 1/2 I ω^2. If I is doubled and ω remains constant, KE also doubles.
Correct Answer:
A
— Doubles
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Q. If the moment of inertia of a body is doubled, what will be the effect on its angular acceleration if the torque applied remains constant?
A.
Doubles
B.
Halves
C.
Remains the same
D.
Increases by a factor of four
Show solution
Solution
Angular acceleration α = τ/I. If I is doubled and τ remains constant, α is halved.
Correct Answer:
B
— Halves
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