Q. What is the vapor pressure of a solution containing 1 mole of solute in 3 moles of solvent, assuming ideal behavior?
-
A.
0.25 P0
-
B.
0.75 P0
-
C.
0.5 P0
-
D.
P0
Solution
Using Raoult's law, the vapor pressure of the solution = (moles of solvent / total moles) * P0 = (3 / (3 + 1)) * P0 = 0.75 P0.
Correct Answer: B — 0.75 P0
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Q. What is the vapor pressure of a solution containing a non-volatile solute compared to the pure solvent?
-
A.
Higher than the pure solvent
-
B.
Lower than the pure solvent
-
C.
Equal to the pure solvent
-
D.
Unpredictable
Solution
The vapor pressure of a solution containing a non-volatile solute is lower than that of the pure solvent due to the presence of solute particles.
Correct Answer: B — Lower than the pure solvent
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Q. What is the variance of the data set {4, 8, 6, 5, 3}?
Solution
Mean = 5.2; Variance = [(4-5.2)² + (8-5.2)² + (6-5.2)² + (5-5.2)² + (3-5.2)²] / 5 = 2.56.
Correct Answer: A — 2.5
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Q. What is the variance of the data set: 1, 2, 3, 4, 5?
Solution
Mean = 3. Variance = [(1-3)² + (2-3)² + (3-3)² + (4-3)² + (5-3)²] / 5 = 2.
Correct Answer: B — 1.5
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Q. What is the variance of the data set: 2, 4, 4, 4, 5, 5, 7, 9?
-
A.
2.5
-
B.
3.5
-
C.
4.5
-
D.
5.5
Solution
Mean = 5.0; Variance = [(2-5)^2 + (4-5)^2 + (4-5)^2 + (4-5)^2 + (5-5)^2 + (5-5)^2 + (7-5)^2 + (9-5)^2] / 8 = 2.5.
Correct Answer: A — 2.5
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Q. What is the variance of the following data set: {5, 7, 8, 9, 10}?
Solution
Mean = 7.8, Variance = [(5-7.8)² + (7-7.8)² + (8-7.8)² + (9-7.8)² + (10-7.8)²] / 5 = 3.
Correct Answer: B — 3
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Q. What is the vertex of the parabola defined by the equation y = -2(x - 1)^2 + 4?
-
A.
(1, 4)
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B.
(1, -4)
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C.
(4, 1)
-
D.
(-1, 4)
Solution
The vertex form of a parabola is y = a(x - h)^2 + k. Here, h = 1 and k = 4, so the vertex is (1, 4).
Correct Answer: A — (1, 4)
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Q. What is the vertex of the parabola given by the equation y = -2(x - 1)^2 + 4?
-
A.
(1, 4)
-
B.
(1, -4)
-
C.
(4, 1)
-
D.
(-1, 4)
Solution
The vertex form of a parabola is y = a(x - h)^2 + k. Here, h = 1 and k = 4, so the vertex is (1, 4).
Correct Answer: A — (1, 4)
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Q. What is the vertex of the parabola represented by the equation y = -2(x - 1)^2 + 4?
-
A.
(1, 4)
-
B.
(1, -4)
-
C.
(-1, 4)
-
D.
(-1, -4)
Solution
The vertex form of a parabola is y = a(x - h)^2 + k. Here, h = 1 and k = 4, so the vertex is (1, 4).
Correct Answer: A — (1, 4)
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Q. What is the vertex of the parabola represented by the equation y = 2x^2 - 8x + 5?
-
A.
(2, -3)
-
B.
(2, -7)
-
C.
(4, -3)
-
D.
(4, -7)
Solution
The vertex can be found using x = -b/(2a) = 4. Substituting x = 4 into the equation gives y = -3.
Correct Answer: A — (2, -3)
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Q. What is the viscosity of water at 20°C?
-
A.
0.001 Pa·s
-
B.
0.01 Pa·s
-
C.
0.1 Pa·s
-
D.
1 Pa·s
Solution
The viscosity of water at 20°C is approximately 0.001 Pa·s.
Correct Answer: A — 0.001 Pa·s
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Q. What is the voltage across a 10 ohm resistor carrying a current of 0.5 A?
-
A.
5 V
-
B.
10 V
-
C.
15 V
-
D.
20 V
Solution
Using Ohm's law, V = I * R = 0.5 A * 10 Ω = 5 V.
Correct Answer: A — 5 V
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Q. What is the voltage drop across a 3 ohm resistor carrying a current of 2 A?
-
A.
3 V
-
B.
6 V
-
C.
9 V
-
D.
12 V
Solution
Using Ohm's law, V = I * R = 2 A * 3 ohms = 6 V.
Correct Answer: B — 6 V
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Q. What is the voltage drop across a 5 ohm resistor carrying a current of 2 A?
-
A.
5 V
-
B.
10 V
-
C.
15 V
-
D.
20 V
Solution
Using Ohm's law, V = I * R = 2 A * 5 ohms = 10 V.
Correct Answer: B — 10 V
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Q. What is the voltage drop across a 5 ohm resistor carrying a current of 3 A?
-
A.
15 V
-
B.
10 V
-
C.
5 V
-
D.
20 V
Solution
Using Ohm's law, V = I * R = 3 A * 5Ω = 15 V.
Correct Answer: A — 15 V
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Q. What is the voltage drop across a 5Ω resistor carrying a current of 3A?
-
A.
5V
-
B.
10V
-
C.
15V
-
D.
20V
Solution
Using Ohm's law, V = I * R = 3A * 5Ω = 15V.
Correct Answer: C — 15V
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Q. What is the volume occupied by 1 mole of an ideal gas at STP (Standard Temperature and Pressure)?
-
A.
22.4 L
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B.
24.0 L
-
C.
18.0 L
-
D.
20.0 L
Solution
At STP, 1 mole of an ideal gas occupies 22.4 liters.
Correct Answer: A — 22.4 L
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Q. What is the volume occupied by 1 mole of an ideal gas at STP?
-
A.
22.4 L
-
B.
24 L
-
C.
20 L
-
D.
18 L
Solution
At STP, 1 mole of an ideal gas occupies 22.4 liters.
Correct Answer: A — 22.4 L
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Q. What is the volume occupied by 4 moles of an ideal gas at STP?
-
A.
22.4 L
-
B.
44.8 L
-
C.
67.2 L
-
D.
89.6 L
Solution
At STP, 1 mole of gas occupies 22.4 L. Therefore, 4 moles occupy 4 x 22.4 L = 89.6 L.
Correct Answer: B — 44.8 L
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Q. What is the volume of 1 liter in cubic meters?
-
A.
0.001
-
B.
0.01
-
C.
1
-
D.
1000
Solution
1 liter is equal to 0.001 cubic meters.
Correct Answer: A — 0.001
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Q. What is the volume of 1 M NaOH solution required to obtain 0.5 moles of NaOH?
-
A.
0.5 L
-
B.
1 L
-
C.
2 L
-
D.
0.25 L
Solution
Using the formula M = moles/volume, Volume = moles/M = 0.5 moles / 1 M = 0.5 L.
Correct Answer: A — 0.5 L
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Q. What is the volume of 1 mole of an ideal gas at STP (Standard Temperature and Pressure)?
-
A.
22.4 L
-
B.
24.0 L
-
C.
18.0 L
-
D.
20.0 L
Solution
At STP, 1 mole of an ideal gas occupies 22.4 liters.
Correct Answer: A — 22.4 L
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Q. What is the volume of 1 mole of an ideal gas at STP?
-
A.
22.4 L
-
B.
24 L
-
C.
10 L
-
D.
1 L
Solution
At STP (Standard Temperature and Pressure), 1 mole of an ideal gas occupies 22.4 liters.
Correct Answer: A — 22.4 L
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Q. What is the volume of 1 mole of gas at STP?
-
A.
22.4 L
-
B.
24 L
-
C.
20 L
-
D.
18 L
Solution
At STP, 1 mole of gas occupies 22.4 liters.
Correct Answer: A — 22.4 L
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Q. What is the volume of 4 moles of an ideal gas at STP?
-
A.
22.4 L
-
B.
44.8 L
-
C.
89.6 L
-
D.
112 L
Solution
Volume = moles x volume per mole = 4 moles x 22.4 L/mole = 89.6 L.
Correct Answer: C — 89.6 L
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Q. What is the volume of a 2 M solution that contains 4 moles of solute?
-
A.
2 L
-
B.
4 L
-
C.
1 L
-
D.
0.5 L
Solution
Volume = moles of solute / molarity = 4 moles / 2 M = 2 L.
Correct Answer: B — 4 L
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Q. What is the volume of a cube with a side length of 2 meters?
-
A.
4 m³
-
B.
6 m³
-
C.
8 m³
-
D.
10 m³
Solution
Volume = side³ = 2³ = 8 m³.
Correct Answer: C — 8 m³
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Q. What is the volume of a cube with a side length of 3 cm?
-
A.
9 cm³
-
B.
18 cm³
-
C.
27 cm³
-
D.
36 cm³
Solution
The volume of a cube is given by side³, so 3 cm³ = 27 cm³.
Correct Answer: C — 27 cm³
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Q. What is the volume of CO2 produced at STP when 2 moles of C2H5OH are completely combusted?
-
A.
22.4 L
-
B.
44.8 L
-
C.
67.2 L
-
D.
89.6 L
Solution
C2H5OH + 3O2 → 2CO2 + 3H2O. 2 moles of C2H5OH produce 4 moles of CO2. Volume = 4 * 22.4 L = 89.6 L.
Correct Answer: B — 44.8 L
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Q. What is the volume percent concentration of a solution containing 30 mL of ethanol in 150 mL of solution?
-
A.
20%
-
B.
25%
-
C.
30%
-
D.
15%
Solution
Volume percent = (volume of solute / total volume) x 100 = (30 mL / 150 mL) x 100 = 20%.
Correct Answer: B — 25%
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