Engineering Entrance
Q. In a galvanic cell, if the anode reaction is Ag⁺ + e⁻ → Ag, what is the cathode reaction?
A.
Cu²⁺ + 2e⁻ → Cu
B.
Zn²⁺ + 2e⁻ → Zn
C.
Fe²⁺ + 2e⁻ → Fe
D.
Pb²⁺ + 2e⁻ → Pb
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Solution
The cathode reaction must be a reduction; Ag⁺ + e⁻ → Ag is the anode reaction.
Correct Answer: A — Cu²⁺ + 2e⁻ → Cu
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Q. In a galvanic cell, if the anode reaction is Zn → Zn²⁺ + 2e⁻, what is the cathode reaction if the cathode is Cu²⁺ + 2e⁻ → Cu?
A.
Cu → Cu²⁺ + 2e⁻
B.
Zn²⁺ + 2e⁻ → Zn
C.
Zn + Cu²⁺ → Zn²⁺ + Cu
D.
Cu²⁺ + 2e⁻ → Cu
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Solution
The cathode reaction is Cu²⁺ + 2e⁻ → Cu.
Correct Answer: D — Cu²⁺ + 2e⁻ → Cu
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Q. In a group of 50 people, 20 are smokers. What is the probability of selecting a non-smoker? (2022)
A.
2/5
B.
3/5
C.
1/2
D.
1/4
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Solution
Number of non-smokers = 50 - 20 = 30. Probability = 30/50 = 3/5.
Correct Answer: B — 3/5
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Q. In a group of 50 people, 20 are smokers. What is the probability that a randomly selected person is a non-smoker? (2021)
A.
1/2
B.
3/5
C.
2/5
D.
1/5
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Solution
There are 50 - 20 = 30 non-smokers. The probability is 30/50 = 3/5.
Correct Answer: B — 3/5
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Q. In a harmonic oscillator, if the mass is doubled while keeping the spring constant the same, how does the frequency change? (2021)
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
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Solution
Frequency (f) = (1/2π)√(k/m). If mass (m) is doubled, frequency decreases.
Correct Answer: B — Decreases
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Q. In a heat engine, if the input heat is 500 J and the work done is 300 J, what is the efficiency? (2023) 2023
A.
60%
B.
50%
C.
40%
D.
70%
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Solution
Efficiency (η) = Work done / Input heat = 300 J / 500 J = 0.6 or 60%.
Correct Answer: A — 60%
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Q. In a lottery, there are 10 tickets, and 2 are winning tickets. What is the probability of picking a winning ticket?
A.
1/5
B.
1/10
C.
1/2
D.
2/10
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Solution
Probability = Number of winning tickets / Total tickets = 2/10 = 1/5.
Correct Answer: A — 1/5
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Q. In a lottery, there are 10 tickets, and 3 are winning tickets. What is the probability of picking a winning ticket? (2022)
A.
1/3
B.
1/4
C.
1/5
D.
1/2
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Solution
Probability = Number of winning tickets / Total tickets = 3/10.
Correct Answer: A — 1/3
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Q. In a parallel circuit with two resistors of 6Ω and 3Ω, what is the total current if a 12V battery is connected? (2021)
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Solution
First, find the equivalent resistance: 1/R_eq = 1/6 + 1/3 = 1/2, so R_eq = 2Ω. Then, I = V/R_eq = 12V / 2Ω = 6A.
Correct Answer: C — 6A
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Q. In a parallel circuit with two resistors of 6Ω and 3Ω, what is the total resistance? (2019)
A.
2Ω
B.
4Ω
C.
1.5Ω
D.
9Ω
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Solution
Using the formula 1/R_eq = 1/R1 + 1/R2, we get 1/R_eq = 1/6 + 1/3 = 1/6 + 2/6 = 3/6, thus R_eq = 2Ω.
Correct Answer: B — 4Ω
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Q. In a parallel circuit, if one branch has a resistance of 4Ω and another has 8Ω, what is the equivalent resistance? (2020)
A.
2.67Ω
B.
3Ω
C.
4Ω
D.
6Ω
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Solution
1/R_eq = 1/4 + 1/8 = 2/8 + 1/8 = 3/8, so R_eq = 8/3Ω ≈ 2.67Ω.
Correct Answer: A — 2.67Ω
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Q. In a parallel RLC circuit, if R = 50 ohms, L = 0.2H, and C = 50μF, what is the total admittance? (2023)
A.
0.02 S
B.
0.04 S
C.
0.06 S
D.
0.08 S
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Solution
Y = 1/R + j(ωC - 1/ωL); calculate Y for given values.
Correct Answer: C — 0.06 S
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Q. In a parallel RLC circuit, if R = 50Ω, L = 0.2 H, and C = 50μF, what is the quality factor Q? (2015)
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Solution
Quality factor Q = (1/R) * √(L/C) = (1/50) * √(0.2/50e-6) = 2.
Correct Answer: B — 2
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Q. In a purely capacitive AC circuit, the current leads the voltage by how many degrees? (2022)
A.
0°
B.
90°
C.
180°
D.
270°
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Solution
In a purely capacitive circuit, the current leads the voltage by 90°.
Correct Answer: B — 90°
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Q. In a purely capacitive AC circuit, the current leads the voltage by how much phase angle? (2023)
A.
0 degrees
B.
90 degrees
C.
180 degrees
D.
270 degrees
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Solution
In a purely capacitive circuit, the current leads the voltage by 90 degrees.
Correct Answer: B — 90 degrees
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Q. In a reaction A → B, if the concentration of A decreases from 0.8 M to 0.4 M in 20 minutes, what is the average rate of reaction? (2019)
A.
0.02 M/min
B.
0.04 M/min
C.
0.1 M/min
D.
0.05 M/min
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Solution
Average rate = Δ[A]/Δt = (0.8 - 0.4) / 20 = 0.02 M/min.
Correct Answer: D — 0.05 M/min
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Q. In a reaction, if the concentration of reactant A is halved, and the rate constant remains the same, how does the rate change for a first-order reaction? (2021)
A.
Doubles
B.
Halves
C.
Remains the same
D.
Quadruples
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Solution
For a first-order reaction, if [A] is halved, the rate also halves.
Correct Answer: B — Halves
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Q. In a reaction, if the concentration of reactant A is halved, and the rate of reaction decreases to one-fourth, what is the order of the reaction? (2020)
A.
Zero
B.
First
C.
Second
D.
Third
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Solution
If the rate decreases to one-fourth when concentration is halved, the reaction is second-order.
Correct Answer: C — Second
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Q. In a reversible reaction, if the concentration of products increases, what happens to the equilibrium position? (2021) 2021
A.
It shifts to the left
B.
It shifts to the right
C.
It remains unchanged
D.
It shifts to the center
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Solution
According to Le Chatelier's principle, if the concentration of products increases, the equilibrium will shift to the left to counteract the change.
Correct Answer: A — It shifts to the left
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Q. In a reversible reaction, if the concentration of products increases, what happens to the rate of the forward reaction? (2021)
A.
It increases
B.
It decreases
C.
It remains constant
D.
It becomes zero
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Solution
According to Le Chatelier's principle, if the concentration of products increases, the system will shift to the left, decreasing the rate of the forward reaction.
Correct Answer: B — It decreases
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Q. In a reversible reaction, if the concentration of products increases, what happens to the equilibrium position? (2021)
A.
It shifts to the left
B.
It shifts to the right
C.
It remains unchanged
D.
It shifts to the center
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Solution
According to Le Chatelier's principle, if the concentration of products increases, the equilibrium will shift to the left to counteract the change.
Correct Answer: A — It shifts to the left
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Q. In a reversible reaction, if the concentration of reactants is increased, what will happen to the position of equilibrium? (2021)
A.
It will shift to the right
B.
It will shift to the left
C.
It will remain unchanged
D.
It will shift to the center
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Solution
According to Le Chatelier's principle, increasing the concentration of reactants will shift the equilibrium position to the right to favor the formation of products.
Correct Answer: A — It will shift to the right
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Q. In a reversible reaction, if the concentration of reactants is increased, what will happen to the equilibrium position? (2021)
A.
It will shift to the right
B.
It will shift to the left
C.
It will remain unchanged
D.
It will shift to the center
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Solution
According to Le Chatelier's principle, if the concentration of reactants is increased, the equilibrium will shift to the right to favor the formation of products.
Correct Answer: A — It will shift to the right
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Q. In a second-order reaction, if the initial concentration is 0.1 M and the rate constant is 0.05 M⁻¹s⁻¹, what is the time taken to reach half the initial concentration? (2020)
A.
10 s
B.
20 s
C.
5 s
D.
15 s
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Solution
For a second-order reaction, t₁/₂ = 1 / (k[A₀]) = 1 / (0.05 * 0.1) = 200 s.
Correct Answer: B — 20 s
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Q. In a series RLC circuit, if R = 10 ohms, L = 0.1H, and C = 100μF, what is the resonant frequency? (2021)
A.
159.15 Hz
B.
100 Hz
C.
50 Hz
D.
200 Hz
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Solution
f0 = 1 / (2π√(LC)) = 1 / (2π√(0.1 × 100 × 10^-6)) = 159.15 Hz.
Correct Answer: A — 159.15 Hz
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Q. In a series RLC circuit, if R = 20Ω, L = 0.1 H, and C = 100μF, what is the resonant frequency? (2020)
A.
50 Hz
B.
100 Hz
C.
159.15 Hz
D.
200 Hz
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Solution
Resonant frequency f₀ = 1 / (2π√(LC)) = 1 / (2π√(0.1 * 100e-6)) = 159.15 Hz.
Correct Answer: C — 159.15 Hz
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Q. In a series RLC circuit, if the inductive reactance is greater than the capacitive reactance, the circuit is said to be: (2019)
A.
Resonant
B.
Capacitive
C.
Inductive
D.
Purely resistive
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Solution
If inductive reactance (XL) is greater than capacitive reactance (XC), the circuit is inductive.
Correct Answer: C — Inductive
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Q. In a series RLC circuit, if the resistance is 10 ohms, inductance is 0.1 H, and capacitance is 100 μF, what is the resonant frequency? (2021)
A.
50 Hz
B.
100 Hz
C.
159 Hz
D.
200 Hz
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Solution
Resonant frequency f = 1/(2π√(LC)) = 1/(2π√(0.1 * 100e-6)) = 159.15 Hz.
Correct Answer: C — 159 Hz
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Q. In a series RLC circuit, if the resistance is 10Ω, inductance is 0.1H, and capacitance is 100μF, what is the resonant frequency? (2021)
A.
50Hz
B.
100Hz
C.
159Hz
D.
200Hz
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Solution
Resonant frequency f0 = 1/(2π√(LC)) = 1/(2π√(0.1*100e-6)) ≈ 159Hz.
Correct Answer: C — 159Hz
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Q. In a series RLC circuit, if the resistance is 4 ohms, inductance is 0.1 H, and capacitance is 100 μF, what is the resonant frequency? (2023)
A.
50 Hz
B.
100 Hz
C.
159.15 Hz
D.
200 Hz
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Solution
Resonant frequency f = 1/(2π√(LC)) = 1/(2π√(0.1 * 100e-6)) = 159.15 Hz.
Correct Answer: C — 159.15 Hz
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