Undergraduate
Q. What is the vertex of the parabola represented by the equation y = x² - 4x + 3? (2022)
-
A.
(2, -1)
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B.
(2, 1)
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C.
(1, 2)
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D.
(3, 0)
Solution
The vertex can be found using the formula x = -b/2a. Here, x = 2, and substituting back gives y = -1.
Correct Answer: A — (2, -1)
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Q. What is the vertex of the parabola represented by the equation y = x² - 6x + 8? (2023)
-
A.
(3, -1)
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B.
(3, -5)
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C.
(2, -4)
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D.
(2, -2)
Solution
The vertex can be found using the formula x = -b/2a = 6/2 = 3. Substituting x = 3 into the equation gives y = -1.
Correct Answer: A — (3, -1)
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Q. What is the voltage across a 10Ω resistor carrying a current of 2A? (2022)
-
A.
5V
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B.
10V
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C.
15V
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D.
20V
Solution
Using Ohm's law, V = I * R = 2A * 10Ω = 20V.
Correct Answer: B — 10V
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Q. What is the voltage across a 10Ω resistor carrying a current of 3A? (2022)
-
A.
30V
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B.
20V
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C.
10V
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D.
15V
Solution
Using Ohm's law, V = IR = 3A * 10Ω = 30V.
Correct Answer: A — 30V
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Q. What is the voltage across a 12Ω resistor carrying a current of 1.5A? (2023)
-
A.
18V
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B.
12V
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C.
6V
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D.
24V
Solution
Using Ohm's law, V = IR = 1.5A * 12Ω = 18V.
Correct Answer: A — 18V
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Q. What is the voltage across a 12Ω resistor carrying a current of 3A? (2023)
-
A.
36V
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B.
24V
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C.
12V
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D.
18V
Solution
Using Ohm's law, V = IR = 3A * 12Ω = 36V.
Correct Answer: A — 36V
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Q. What is the voltage across a 5Ω resistor carrying a current of 3A? (2023)
-
A.
15V
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B.
10V
-
C.
5V
-
D.
20V
Solution
Using Ohm's law, V = IR = 3A * 5Ω = 15V.
Correct Answer: A — 15V
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Q. What is the voltage across a 5Ω resistor if a current of 3A flows through it? (2020)
-
A.
15V
-
B.
10V
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C.
5V
-
D.
20V
Solution
Using Ohm's law, V = IR = 3A * 5Ω = 15V.
Correct Answer: A — 15V
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Q. What is the volume of 0.2 M NaOH required to neutralize 0.1 M HCl in 250 mL? (2020)
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A.
125 mL
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B.
250 mL
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C.
500 mL
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D.
100 mL
Solution
Using the formula M1V1 = M2V2, (0.1 M)(0.25 L) = (0.2 M)(V2). V2 = 0.125 L = 125 mL.
Correct Answer: A — 125 mL
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Q. What is the volume of 1 M HCl solution needed to obtain 0.5 moles of HCl? (2022)
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A.
0.5 L
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B.
1 L
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C.
2 L
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D.
0.25 L
Solution
Volume = moles / molarity = 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? (2019) 2019
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A.
22.4 L
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B.
24 L
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C.
1 L
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D.
10 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 a 2 M NaOH solution needed to obtain 4 moles of NaOH? (2021) 2021
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A.
2 L
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B.
1 L
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C.
0.5 L
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D.
4 L
Solution
Volume (L) = moles / molarity = 4 moles / 2 M = 2 L.
Correct Answer: A — 2 L
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Q. What is the volume of a cube with side length 3 units? (2023)
Solution
Volume = side³ = 3³ = 27 cubic units.
Correct Answer: B — 27
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Q. What is the volume of a cylinder with radius 2 and height 5? (2023)
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A.
20π
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B.
10π
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C.
15π
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D.
25π
Solution
Volume = πr²h = π(2²)(5) = 20π cubic units.
Correct Answer: A — 20π
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Q. What is the volume of a sphere with radius 5 units? (2021)
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A.
500/3π
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B.
125/3π
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C.
100/3π
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D.
200/3π
Solution
Volume = (4/3)πr³ = (4/3)π(5)³ = (4/3)π(125) = 500/3π cubic units.
Correct Answer: A — 500/3π
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Q. What is the work done by an ideal gas during an isobaric expansion if it expands from 2 L to 5 L at a pressure of 3 atm? (2022)
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A.
9 J
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B.
12 J
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C.
15 J
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D.
18 J
Solution
Work done (W) = P * ΔV = 3 atm * (5 L - 2 L) = 3 atm * 3 L = 9 atm·L = 15 J (1 atm·L = 101.325 J)
Correct Answer: C — 15 J
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Q. What is the work done by an ideal gas during an isothermal expansion from volume V1 to V2 at temperature T? (2021)
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A.
nRT ln(V2/V1)
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B.
nRT (V2 - V1)
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C.
PV
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D.
0
Solution
The work done during an isothermal expansion is given by W = nRT ln(V2/V1).
Correct Answer: A — nRT ln(V2/V1)
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Q. What is the work done by an ideal gas during isothermal expansion? (2021)
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A.
0
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B.
nRT ln(Vf/Vi)
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C.
nRT (Vf - Vi)
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D.
nR (Tf - Ti)
Solution
For an ideal gas undergoing isothermal expansion, the work done is given by W = nRT ln(Vf/Vi).
Correct Answer: B — nRT ln(Vf/Vi)
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Q. What is the work done on a gas when it is compressed from 4 L to 2 L at a constant pressure of 2 atm?
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A.
4 L·atm
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B.
2 L·atm
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C.
8 L·atm
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D.
0 L·atm
Solution
Work done (W) = P * ΔV = 2 atm * (2 L - 4 L) = 2 atm * (-2 L) = -4 L·atm (work done on the gas is positive).
Correct Answer: A — 4 L·atm
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Q. What is the work done on a gas when it is compressed from 5 L to 2 L at a constant pressure of 200 kPa? (2022)
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A.
600 J
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B.
800 J
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C.
1000 J
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D.
1200 J
Solution
Work done (W) = P * ΔV = 200 kPa * (2 L - 5 L) = 200 kPa * (-3 L) = -600 J (work done on the gas).
Correct Answer: C — 1000 J
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Q. What is the work done when 1 mole of an ideal gas expands isothermally from 10 L to 20 L at 300 K? (2022)
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A.
300 J
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B.
600 J
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C.
150 J
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D.
0 J
Solution
Work done W = nRT ln(Vf/Vi) = 1 * 8.314 * 300 * ln(20/10) = 600 J.
Correct Answer: B — 600 J
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Q. What is the work done when 1 mole of an ideal gas expands isothermally from 10 L to 20 L at 300 K? (R = 8.31 J/mol·K) (2023)
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A.
0 J
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B.
830 J
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C.
1660 J
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D.
2490 J
Solution
Work done = nRT ln(Vf/Vi) = 1 mol × 8.31 J/mol·K × 300 K × ln(20/10) = 1660 J.
Correct Answer: C — 1660 J
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Q. What is the work done when a 50 N force moves an object 3 m in the direction of the force?
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A.
150 J
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B.
100 J
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C.
50 J
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D.
200 J
Solution
Work done (W) = F × d = 50 N × 3 m = 150 J.
Correct Answer: A — 150 J
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Q. What is the work done when a force of 10 N moves an object 5 m in the direction of the force? (2016)
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A.
50 J
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B.
25 J
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C.
10 J
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D.
5 J
Solution
Work done (W) = Force × Distance = 10 N × 5 m = 50 J.
Correct Answer: A — 50 J
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Q. What is the work done when a force of 15 N moves an object 3 m at an angle of 0 degrees to the direction of motion?
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A.
45 J
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B.
30 J
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C.
60 J
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D.
75 J
Solution
Work = Force * Distance * cos(θ) = 15 N * 3 m * cos(0°) = 45 J.
Correct Answer: A — 45 J
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Q. What is the work done when a force of 15 N moves an object 4 m in the direction of the force?
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A.
60 J
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B.
30 J
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C.
45 J
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D.
75 J
Solution
Work done = Force × Distance = 15 N × 4 m = 60 J
Correct Answer: A — 60 J
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Q. What is the x-intercept of the line 5x - 2y + 10 = 0?
Solution
Setting y = 0 in the equation gives 5x + 10 = 0, thus x = -2.
Correct Answer: B — 2
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Q. What is the x-intercept of the line 6x - 2y = 12?
Solution
Setting y = 0 in the equation gives 6x = 12, thus x = 2. The x-intercept is 2.
Correct Answer: B — 3
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Q. What is the y-intercept of the line 3x - 2y = 6? (2020) 2020
Solution
Setting x = 0, we get -2y = 6, so y = -3.
Correct Answer: A — 3
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Q. What is the y-intercept of the line 3x - 4y = 12? (2023)
Solution
Setting x = 0, we get -4y = 12, so y = -3.
Correct Answer: A — 3
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