Q. What is the solution to the inequality 5 - 2x < 1?
-
A.
x > 2
-
B.
x < 2
-
C.
x > 3
-
D.
x < 3
Solution
Subtract 5 from both sides: -2x < -4. Then divide by -2 (reverse the inequality): x > 2.
Correct Answer:
A
— x > 2
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Q. What is the solution to the inequality 5 - 2x ≤ 1?
-
A.
x ≥ 2
-
B.
x ≤ 2
-
C.
x < 2
-
D.
x > 2
Solution
5 - 2x ≤ 1 => -2x ≤ -4 => x ≥ 2.
Correct Answer:
A
— x ≥ 2
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Q. What is the solution to the inequality 5 - 2x ≤ 3?
-
A.
x ≥ 1
-
B.
x ≤ 1
-
C.
x > 1
-
D.
x < 1
Solution
5 - 2x ≤ 3 => -2x ≤ -2 => x ≥ 1.
Correct Answer:
B
— x ≤ 1
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Q. What is the solution to the inequality 6 - 3x ≥ 0?
-
A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
6 - 3x ≥ 0 => -3x ≥ -6 => x ≤ 2.
Correct Answer:
C
— x ≤ 2
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Q. What is the solution to the inequality 6x + 2 < 14?
-
A.
x < 2
-
B.
x > 2
-
C.
x < 3
-
D.
x > 3
Solution
6x + 2 < 14 => 6x < 12 => x < 2.
Correct Answer:
A
— x < 2
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Q. What is the solution to the inequality 6x + 2 ≤ 14?
-
A.
x ≤ 2
-
B.
x < 2
-
C.
x ≥ 2
-
D.
x > 2
Solution
6x + 2 ≤ 14 => 6x ≤ 12 => x ≤ 2.
Correct Answer:
A
— x ≤ 2
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Q. What is the solution to the inequality 6x + 4 < 2x + 20?
-
A.
x < 4
-
B.
x > 4
-
C.
x ≤ 4
-
D.
x ≥ 4
Solution
6x + 4 < 2x + 20 => 4x < 16 => x < 4.
Correct Answer:
A
— x < 4
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Q. What is the solution to the inequality 6x + 4 ≤ 2x + 16?
-
A.
x ≤ 3
-
B.
x ≥ 3
-
C.
x ≤ 4
-
D.
x ≥ 4
Solution
6x + 4 ≤ 2x + 16 => 4x ≤ 12 => x ≤ 3.
Correct Answer:
B
— x ≥ 3
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Q. What is the solution to the inequality 7 - 3x > 1?
-
A.
x < 2
-
B.
x > 2
-
C.
x < 3
-
D.
x > 3
Solution
7 - 3x > 1 => -3x > -6 => x < 2.
Correct Answer:
A
— x < 2
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Q. What is the solution to the inequality 7 - 3x < 1?
-
A.
x > 2
-
B.
x < 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
7 - 3x < 1 => -3x < -6 => x > 2.
Correct Answer:
A
— x > 2
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Q. What is the solution to the inequality 7x + 2 > 5?
-
A.
x > 0.5
-
B.
x < 0.5
-
C.
x ≥ 0.5
-
D.
x ≤ 0.5
Solution
7x + 2 > 5 => 7x > 3 => x > 0.5.
Correct Answer:
A
— x > 0.5
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Q. What is the solution to the inequality 7x + 2 > 5x + 6?
-
A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
7x + 2 > 5x + 6 => 2x > 4 => x > 2.
Correct Answer:
B
— x > 2
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Q. What is the solution to the inequality 7x + 2 < 5?
-
A.
x < -1
-
B.
x > -1
-
C.
x < 1
-
D.
x > 1
Solution
7x + 2 < 5 => 7x < 3 => x < -1.
Correct Answer:
A
— x < -1
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Q. What is the solution to the inequality 7x + 3 > 24?
-
A.
x < 3
-
B.
x > 3
-
C.
x ≤ 3
-
D.
x ≥ 3
Solution
7x + 3 > 24 => 7x > 21 => x > 3.
Correct Answer:
B
— x > 3
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Q. What is the solution to the inequality 7x + 5 < 2x + 20?
-
A.
x < 3
-
B.
x > 3
-
C.
x < 4
-
D.
x > 4
Solution
7x + 5 < 2x + 20 => 5x < 15 => x < 3.
Correct Answer:
A
— x < 3
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Q. What is the solution to the inequality 7x - 4 < 3x + 8?
-
A.
x < 3
-
B.
x > 3
-
C.
x < 2
-
D.
x > 2
Solution
7x - 4 < 3x + 8 => 4x < 12 => x < 3.
Correct Answer:
B
— x > 3
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Q. What is the solution to the inequality 8 - 2x > 0?
-
A.
x < 4
-
B.
x > 4
-
C.
x < 2
-
D.
x > 2
Solution
8 - 2x > 0 => -2x > -8 => x < 4.
Correct Answer:
B
— x > 4
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Q. What is the solution to the inequality x/2 - 1 ≤ 3?
-
A.
x ≤ 8
-
B.
x ≥ 8
-
C.
x ≤ 6
-
D.
x ≥ 6
Solution
x/2 - 1 ≤ 3 => x/2 ≤ 4 => x ≤ 8.
Correct Answer:
A
— x ≤ 8
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Q. What is the solution to the inequality x/3 - 2 ≤ 1?
-
A.
x ≤ 9
-
B.
x ≥ 9
-
C.
x < 9
-
D.
x > 9
Solution
x/3 - 2 ≤ 1 => x/3 ≤ 3 => x ≤ 9.
Correct Answer:
A
— x ≤ 9
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Q. What is the solution to the initial value problem dy/dx = 4y, y(1) = 2?
-
A.
y = 2e^(4x)
-
B.
y = 2e^(4x-4)
-
C.
y = e^(4x)
-
D.
y = 4e^(x)
Solution
The general solution is y = Ce^(4x). Using y(1) = 2, we find C = 2e^(-4).
Correct Answer:
B
— y = 2e^(4x-4)
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Q. What is the specific heat at constant volume (Cv) for a monatomic ideal gas? (2019)
-
A.
3R/2
-
B.
5R/2
-
C.
R
-
D.
2R
Solution
For a monatomic ideal gas, the specific heat at constant volume (Cv) is 3R/2.
Correct Answer:
A
— 3R/2
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Q. What is the specific heat capacity at constant volume (Cv) for a monatomic ideal gas?
-
A.
3/2 R
-
B.
5/2 R
-
C.
R
-
D.
2 R
Solution
The specific heat capacity at constant volume for a monatomic ideal gas is Cv = 3/2 R.
Correct Answer:
A
— 3/2 R
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Q. What is the specific heat capacity of a substance if 500 J of heat is required to raise the temperature of 2 kg of the substance by 10°C? (2021)
-
A.
25 J/kg°C
-
B.
50 J/kg°C
-
C.
75 J/kg°C
-
D.
100 J/kg°C
Solution
Specific heat capacity (c) = Q / (m * ΔT) = 500 J / (2 kg * 10°C) = 25 J/kg°C.
Correct Answer:
B
— 50 J/kg°C
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Q. What is the specific heat capacity of a substance if it requires 500 J to raise the temperature of 2 kg of the substance by 5°C? (2021)
-
A.
20 J/kg°C
-
B.
50 J/kg°C
-
C.
100 J/kg°C
-
D.
200 J/kg°C
Solution
Specific heat capacity (c) = Q / (m * ΔT) = 500 J / (2 kg * 5°C) = 50 J/kg°C.
Correct Answer:
B
— 50 J/kg°C
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Q. What is the specific heat capacity of a substance if it requires 500 J to raise the temperature of 2 kg of the substance by 10°C? (2021)
-
A.
25 J/kg°C
-
B.
50 J/kg°C
-
C.
100 J/kg°C
-
D.
200 J/kg°C
Solution
Specific heat capacity (c) = Q / (m * ΔT) = 500 J / (2 kg * 10°C) = 25 J/kg°C.
Correct Answer:
B
— 50 J/kg°C
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Q. What is the specific heat capacity of a substance if it takes 500 J to raise the temperature of 2 kg of the substance by 5°C? (2021)
-
A.
20 J/kg°C
-
B.
50 J/kg°C
-
C.
100 J/kg°C
-
D.
200 J/kg°C
Solution
Specific heat capacity (c) = Q / (m * ΔT) = 500 J / (2 kg * 5°C) = 50 J/kg°C
Correct Answer:
B
— 50 J/kg°C
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Q. What is the specific heat capacity of a substance?
-
A.
The amount of heat required to change its temperature by 1 degree Celsius
-
B.
The amount of heat required to change its state
-
C.
The heat required to raise the temperature of a unit mass by 1 degree Celsius
-
D.
The heat required to cool a substance
Solution
The specific heat capacity of a substance is defined as the amount of heat required to raise the temperature of a unit mass by 1 degree Celsius.
Correct Answer:
C
— The heat required to raise the temperature of a unit mass by 1 degree Celsius
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Q. What is the specific heat capacity of air at constant pressure? (2022)
-
A.
1.005 J/kg·K
-
B.
0.718 J/kg·K
-
C.
4.186 J/kg·K
-
D.
2.093 J/kg·K
Solution
The specific heat capacity of air at constant pressure is approximately 1.005 J/kg·K.
Correct Answer:
A
— 1.005 J/kg·K
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Q. What is the specific heat capacity of air? (2022)
-
A.
1.005 J/kg·K
-
B.
4.18 J/kg·K
-
C.
2.09 J/kg·K
-
D.
0.9 J/kg·K
Solution
The specific heat capacity of air is approximately 1.005 J/kg·K.
Correct Answer:
A
— 1.005 J/kg·K
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Q. What is the specific heat capacity of iron? (2023)
-
A.
0.45 J/g·K
-
B.
1.00 J/g·K
-
C.
2.00 J/g·K
-
D.
4.18 J/g·K
Solution
The specific heat capacity of iron is approximately 0.45 J/g·K.
Correct Answer:
A
— 0.45 J/g·K
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