Q. What is the equilibrium constant expression for the reaction: aA + bB ⇌ cC + dD?
A.
K = [C]^c [D]^d / [A]^a [B]^b
B.
K = [A]^a [B]^b / [C]^c [D]^d
C.
K = [C]^c [D]^d
D.
K = [A]^a [B]^b
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Solution
The equilibrium constant K is defined as the ratio of the concentration of products to the concentration of reactants, each raised to the power of their coefficients in the balanced equation.
Correct Answer: A — K = [C]^c [D]^d / [A]^a [B]^b
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Q. What is the equivalent of 1 liter in cubic meters?
A.
0.001 m³
B.
0.01 m³
C.
0.1 m³
D.
1 m³
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Solution
1 liter is equal to 0.001 cubic meters.
Correct Answer: A — 0.001 m³
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Q. What is the equivalent resistance of a 10Ω and a 5Ω resistor connected in parallel?
A.
3.33Ω
B.
7.5Ω
C.
15Ω
D.
5Ω
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Solution
R_eq = 1/(1/10 + 1/5) = 3.33Ω.
Correct Answer: A — 3.33Ω
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Q. What is the equivalent resistance of a 6Ω and a 3Ω resistor connected in parallel?
A.
2Ω
B.
4Ω
C.
1.5Ω
D.
9Ω
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Solution
R_eq = 1/(1/6 + 1/3) = 2Ω.
Correct Answer: B — 4Ω
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Q. What is the equivalent resistance of a circuit with a 10 ohm and a 5 ohm resistor in series?
A.
15 ohms
B.
5 ohms
C.
10 ohms
D.
20 ohms
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Solution
For resistors in series, R_eq = R1 + R2 = 10 ohms + 5 ohms = 15 ohms.
Correct Answer: A — 15 ohms
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Q. What is the equivalent resistance of a circuit with two 10Ω resistors in series and one 5Ω resistor in parallel with them?
A.
5Ω
B.
10Ω
C.
15Ω
D.
20Ω
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Solution
R_series = 10Ω + 10Ω = 20Ω. R_parallel = 1/(1/20 + 1/5) = 4Ω. Therefore, R_eq = 4Ω.
Correct Answer: C — 15Ω
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Q. What is the equivalent resistance of a circuit with two resistors R1 = 10Ω and R2 = 10Ω in parallel?
A.
5Ω
B.
10Ω
C.
20Ω
D.
15Ω
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Solution
The equivalent resistance in parallel is given by 1/R_total = 1/R1 + 1/R2 = 1/10 + 1/10 = 1/5. Therefore, R_total = 5Ω.
Correct Answer: A — 5Ω
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Q. What is the equivalent resistance of three resistors of 2 ohms, 3 ohms, and 6 ohms connected in series?
A.
1 ohm
B.
3 ohms
C.
11 ohms
D.
12 ohms
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Solution
In series, the equivalent resistance is the sum of the individual resistances: R_eq = R1 + R2 + R3 = 2 + 3 + 6 = 11 ohms.
Correct Answer: C — 11 ohms
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Q. What is the equivalent resistance of three resistors of 2Ω, 3Ω, and 5Ω connected in parallel?
A.
1Ω
B.
2Ω
C.
0.83Ω
D.
10Ω
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Solution
1/Req = 1/R1 + 1/R2 + 1/R3 = 1/2 + 1/3 + 1/5 = 0.8333, thus Req = 1.2Ω.
Correct Answer: C — 0.83Ω
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Q. What is the equivalent resistance of three resistors of 2Ω, 3Ω, and 6Ω connected in series?
A.
11Ω
B.
10Ω
C.
9Ω
D.
12Ω
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Solution
In series, R_eq = R1 + R2 + R3 = 2 + 3 + 6 = 11Ω.
Correct Answer: A — 11Ω
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Q. What is the equivalent resistance of three resistors of 2Ω, 3Ω, and 6Ω connected in parallel?
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Solution
1/R_eq = 1/R1 + 1/R2 + 1/R3 = 1/2 + 1/3 + 1/6 = 1. Therefore, R_eq = 1Ω.
Correct Answer: A — 1Ω
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Q. What is the equivalent resistance of three resistors of values 2Ω, 3Ω, and 5Ω connected in parallel?
A.
1Ω
B.
2Ω
C.
0.83Ω
D.
10Ω
Show solution
Solution
1/R_eq = 1/R1 + 1/R2 + 1/R3 = 1/2 + 1/3 + 1/5 = 0.8333, thus R_eq = 1.2Ω.
Correct Answer: C — 0.83Ω
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Q. What is the equivalent resistance of three resistors of values 2Ω, 3Ω, and 6Ω connected in parallel?
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Solution
1/Req = 1/R1 + 1/R2 + 1/R3 = 1/2 + 1/3 + 1/6 = 1. Therefore, Req = 1Ω.
Correct Answer: B — 2Ω
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Q. What is the equivalent resistance of three resistors, 2Ω, 3Ω, and 6Ω, connected in series?
Show solution
Solution
In series, the equivalent resistance is the sum of the individual resistances: R_eq = R1 + R2 + R3 = 2Ω + 3Ω + 6Ω = 11Ω.
Correct Answer: A — 11Ω
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Q. What is the equivalent resistance of three resistors, R1, R2, and R3, connected in series?
A.
R1 + R2 + R3
B.
1/(1/R1 + 1/R2 + 1/R3)
C.
R1 * R2 * R3
D.
R1 - R2 - R3
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Solution
In a series connection, the total or equivalent resistance is the sum of the individual resistances.
Correct Answer: A — R1 + R2 + R3
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Q. What is the equivalent resistance of two resistors of 10 ohms and 20 ohms connected in series?
A.
30 ohms
B.
20 ohms
C.
10 ohms
D.
5 ohms
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Solution
In series, the equivalent resistance R_eq = R1 + R2 = 10 ohms + 20 ohms = 30 ohms.
Correct Answer: A — 30 ohms
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Q. What is the equivalent resistance of two resistors of 4Ω and 12Ω connected in parallel?
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Solution
Using the formula for parallel resistors, 1/R_eq = 1/R1 + 1/R2 = 1/4 + 1/12 = 1/3. Therefore, R_eq = 3Ω.
Correct Answer: C — 6Ω
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Q. What is the equivalent resistance of two resistors of 5 ohms and 10 ohms connected in parallel?
A.
3.33 ohms
B.
15 ohms
C.
5 ohms
D.
7.5 ohms
Show solution
Solution
Using the formula for resistors in parallel, 1/R_eq = 1/R1 + 1/R2, we find R_eq = 1 / (1/5 + 1/10) = 3.33 ohms.
Correct Answer: A — 3.33 ohms
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Q. What is the equivalent resistance of two resistors of 5Ω and 10Ω connected in parallel?
A.
3.33Ω
B.
5Ω
C.
7.5Ω
D.
15Ω
Show solution
Solution
1/Req = 1/R1 + 1/R2 = 1/5 + 1/10 = 2/10 + 1/10 = 3/10. Therefore, Req = 10/3 = 3.33Ω.
Correct Answer: A — 3.33Ω
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Q. What is the equivalent resistance of two resistors, 6 ohms and 3 ohms, connected in series?
A.
2 ohms
B.
3 ohms
C.
9 ohms
D.
18 ohms
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Solution
In series, the equivalent resistance is the sum: R_eq = R1 + R2 = 6Ω + 3Ω = 9Ω.
Correct Answer: C — 9 ohms
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Q. What is the equivalent resistance of two resistors, 6Ω and 3Ω, connected in series?
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Solution
In series, the equivalent resistance (R_eq) is the sum of the resistances: R_eq = 6Ω + 3Ω = 9Ω.
Correct Answer: C — 9Ω
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Q. What is the equivalent weight of H2SO4 if its molar mass is 98 g/mol?
A.
49 g
B.
98 g
C.
196 g
D.
24.5 g
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Solution
Equivalent weight = molar mass / number of equivalents = 98 g/mol / 2 = 49 g.
Correct Answer: A — 49 g
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Q. What is the escape velocity for a satellite to leave Earth's gravitational field?
A.
7.9 km/s
B.
11.2 km/s
C.
9.8 km/s
D.
5.0 km/s
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Solution
The escape velocity from the Earth's surface is approximately 11.2 km/s.
Correct Answer: B — 11.2 km/s
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Q. What is the escape velocity for a satellite to leave the Earth's gravitational field?
A.
7.9 km/s
B.
11.2 km/s
C.
9.8 km/s
D.
5.0 km/s
Show solution
Solution
The escape velocity from the Earth's surface is approximately 11.2 km/s.
Correct Answer: B — 11.2 km/s
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Q. What is the escape velocity for a satellite to leave the Earth's gravitational influence?
A.
11.2 km/s
B.
7.9 km/s
C.
9.8 km/s
D.
15.0 km/s
Show solution
Solution
The escape velocity from the Earth's surface is approximately 11.2 km/s.
Correct Answer: A — 11.2 km/s
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Q. What is the escape velocity from the surface of a planet with a radius of 3R and mass 4M?
A.
√(8GM/R)
B.
√(6GM/R)
C.
√(4GM/R)
D.
√(10GM/R)
Show solution
Solution
Escape velocity v = √(2GM/R); here, v = √(2 * 4GM / 3R) = √(8GM/3R).
Correct Answer: A — √(8GM/R)
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Q. What is the escape velocity from the surface of a planet with a radius of 4R and mass 2M?
A.
2√(GM/R)
B.
√(8GM/R)
C.
√(2GM/R)
D.
4√(GM/R)
Show solution
Solution
Escape velocity v = √(2GM/R) = √(2 * 2M / 4R) = √(8GM/4R) = √(8GM/R)
Correct Answer: B — √(8GM/R)
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Q. What is the escape velocity from the surface of a planet with mass M and radius R?
A.
√(2GM/R)
B.
√(GM/R)
C.
√(2R/G)
D.
√(G/R)
Show solution
Solution
Escape velocity is given by v = √(2GM/R).
Correct Answer: A — √(2GM/R)
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Q. What is the escape velocity from the surface of the Earth?
A.
7.9 km/s
B.
11.2 km/s
C.
9.8 km/s
D.
15 km/s
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Solution
The escape velocity from the surface of the Earth is approximately 11.2 km/s.
Correct Answer: B — 11.2 km/s
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Q. What is the escape velocity from the surface of the Earth? (g = 9.8 m/s^2, R = 6.4 x 10^6 m)
A.
7.9 km/s
B.
11.2 km/s
C.
9.8 km/s
D.
5.0 km/s
Show solution
Solution
Escape velocity (v) = sqrt(2gR) = sqrt(2 * 9.8 * 6.4 x 10^6) ≈ 11.2 km/s.
Correct Answer: B — 11.2 km/s
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