Q. What is the equation of the tangent line to the curve y = x^2 + 2x at the point where x = 1?
A.
y = 3x - 2
B.
y = 2x + 1
C.
y = 2x + 2
D.
y = x + 3
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Solution
f'(x) = 2x + 2. At x = 1, f'(1) = 4. The point is (1, 3). The tangent line is y - 3 = 4(x - 1) => y = 4x - 1.
Correct Answer: A — y = 3x - 2
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Q. What is the equation of the tangent line to the curve y = x^2 + 2x at the point (1, 3)?
A.
y = 2x + 1
B.
y = 2x + 2
C.
y = 3x
D.
y = x + 2
Show solution
Solution
f'(x) = 2x + 2. At x = 1, f'(1) = 4. The tangent line is y - 3 = 4(x - 1) => y = 4x - 1.
Correct Answer: A — y = 2x + 1
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Q. What is the equilibrium constant (K) for the dissociation of acetic acid (CH3COOH) in water? (2023)
A.
1.8 x 10^-5
B.
1.0
C.
10
D.
100
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Solution
The dissociation constant (K) for acetic acid is approximately 1.8 x 10^-5, indicating it is a weak acid.
Correct Answer: A — 1.8 x 10^-5
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Q. What is the equilibrium constant (Kc) expression for the reaction: 2A + B ⇌ C?
A.
Kc = [C] / ([A]^2[B])
B.
Kc = [A]^2[B] / [C]
C.
Kc = [C] / [A]^2
D.
Kc = [A]^2 / ([B][C])
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Solution
The equilibrium constant Kc 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. For the reaction 2A + B ⇌ C, Kc = [C] / ([A]^2[B]).
Correct Answer: A — Kc = [C] / ([A]^2[B])
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Q. What is the equilibrium constant (Kc) for the reaction 2A + B ⇌ C? (2022)
A.
Kc = [C] / ([A]^2[B])
B.
Kc = [A]^2[B] / [C]
C.
Kc = [B] / ([A]^2[C])
D.
Kc = [C] / ([B][A])
Show solution
Solution
The equilibrium constant Kc is defined as the concentration of the products raised to the power of their coefficients divided by the concentration of the reactants raised to the power of their coefficients. For the reaction 2A + B ⇌ C, Kc = [C] / ([A]^2[B]).
Correct Answer: A — Kc = [C] / ([A]^2[B])
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Q. What is the equilibrium constant (Kc) for the reaction: A + B ⇌ C + D? (2022)
A.
Kc = [C][D]/[A][B]
B.
Kc = [A][B]/[C][D]
C.
Kc = [C][D][A][B]
D.
Kc = [A][B][C][D]
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Solution
The equilibrium constant Kc is defined as the ratio of the concentrations of the products to the reactants, each raised to the power of their coefficients in the balanced equation.
Correct Answer: A — Kc = [C][D]/[A][B]
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Q. What is the equilibrium constant (Kc) for the reaction: N2(g) + 3H2(g) ⇌ 2NH3(g)? (2022) 2022
A.
1.0 × 10^-5
B.
1.0 × 10^-2
C.
1.0 × 10^2
D.
1.0 × 10^5
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Solution
The equilibrium constant Kc for the formation of ammonia from nitrogen and hydrogen is typically around 1.0 × 10^5 at standard conditions.
Correct Answer: D — 1.0 × 10^5
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Q. What is the equilibrium constant expression for the reaction N2(g) + 3H2(g) ⇌ 2NH3(g)?
A.
Kc = [NH3]^2 / ([N2][H2]^3)
B.
Kc = [N2][H2]^3 / [NH3]^2
C.
Kc = [NH3]^2 / [N2][H2]
D.
Kc = [N2][H2] / [NH3]^2
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Solution
The equilibrium constant Kc is given by the ratio of the concentration of products to reactants, raised to the power of their coefficients.
Correct Answer: A — Kc = [NH3]^2 / ([N2][H2]^3)
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Q. What is the equilibrium constant expression for the reaction: 2A + B ⇌ C?
A.
[C]/([A]^2[B])
B.
[A]^2[B]/[C]
C.
[C]/[A][B]
D.
[A][B]/[C]
Show solution
Solution
The equilibrium constant K is given by the expression K = [C]/([A]^2[B]) for the reaction 2A + B ⇌ C.
Correct Answer: A — [C]/([A]^2[B])
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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
Show solution
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
Show solution
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 each connected in series? (2020)
A.
2 ohms
B.
4 ohms
C.
6 ohms
D.
8 ohms
Show solution
Solution
In series, the equivalent resistance is the sum of the individual resistances: R_eq = R1 + R2 + R3 = 2 + 2 + 2 = 6 ohms.
Correct Answer: C — 6 ohms
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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
Show solution
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
Show solution
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 parallel?
Show solution
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 2Ω, 3Ω, and 6Ω connected in series?
A.
11Ω
B.
10Ω
C.
9Ω
D.
12Ω
Show solution
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 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?
Show solution
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
Show solution
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 10Ω resistors connected in series? (2022)
A.
5Ω
B.
10Ω
C.
20Ω
D.
15Ω
Show solution
Solution
In series, R_eq = R1 + R2 = 10 + 10 = 20Ω.
Correct Answer: C — 20Ω
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Q. What is the equivalent resistance of two 12Ω resistors connected in series? (2019)
A.
6Ω
B.
12Ω
C.
24Ω
D.
18Ω
Show solution
Solution
In series, R_eq = R1 + R2 = 12Ω + 12Ω = 24Ω.
Correct Answer: C — 24Ω
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Q. What is the equivalent resistance of two 4Ω resistors in parallel? (2019)
Show solution
Solution
Using the formula 1/R_eq = 1/R1 + 1/R2, we get 1/R_eq = 1/4 + 1/4 = 1/2, thus R_eq = 2Ω.
Correct Answer: A — 2Ω
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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
Show solution
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 4 ohms and 6 ohms connected in series?
A.
10 ohms
B.
24 ohms
C.
2.4 ohms
D.
0.67 ohms
Show solution
Solution
In series, the equivalent resistance is the sum: R_eq = R1 + R2 = 4 Ω + 6 Ω = 10 Ω.
Correct Answer: A — 10 ohms
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