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Q. If z = 2 + 2i, what is |z|^2? (2021)
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Solution
|z|^2 = (2^2 + 2^2) = 4 + 4 = 8.
Correct Answer: A — 8
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Q. If z = 2 - 3i, what is the conjugate of z? (2020)
A.
2 + 3i
B.
2 - 3i
C.
-2 + 3i
D.
-2 - 3i
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Solution
The conjugate of z = 2 - 3i is 2 + 3i.
Correct Answer: A — 2 + 3i
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Q. If z = 3 + 4i, what is the value of z + z* (where z* is the conjugate of z)? (2017)
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Solution
z + z* = (3 + 4i) + (3 - 4i) = 6.
Correct Answer: B — 8
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Q. If z = 3 + 4i, what is the value of z + z̅? (2022)
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Solution
z + z̅ = (3 + 4i) + (3 - 4i) = 6.
Correct Answer: B — 8
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Q. If z = 4 + 3i, what is the real part of z? (2023)
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Solution
The real part of the complex number z = 4 + 3i is 4.
Correct Answer: A — 4
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Q. If \( B = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \), what is \( |B| \)? (2022)
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Solution
The determinant of \( B \) is \( 2*4 - 3*1 = 8 - 3 = 5 \).
Correct Answer: A — 5
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Q. In a Carnot engine operating between temperatures T1 and T2, what is the efficiency (η) of the engine? (2023)
A.
1 - T2/T1
B.
T1/T2
C.
T2/T1
D.
T1 - T2
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Solution
The efficiency of a Carnot engine is given by η = 1 - T2/T1.
Correct Answer: A — 1 - T2/T1
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Q. In a circuit with a 24V battery and two 8Ω resistors in series, what is the total current? (2022)
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Solution
Total resistance R = 8Ω + 8Ω = 16Ω. Current I = V/R = 24V / 16Ω = 1.5A.
Correct Answer: B — 2A
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Q. In a circuit with a 9V battery and a 3Ω resistor, what is the power dissipated in the resistor? (2023)
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Solution
Power P = V²/R = (9V)² / 3Ω = 81 / 3 = 27W.
Correct Answer: B — 9W
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Q. In a class of 30 students, 18 are girls. What is the probability of randomly selecting a boy? (2021)
A.
3/5
B.
2/5
C.
1/2
D.
1/3
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Solution
Number of boys = 30 - 18 = 12. Probability = 12/30 = 2/5.
Correct Answer: B — 2/5
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Q. In a concentration cell, if the concentration of one half-cell is 0.1 M and the other is 1 M, what is the cell potential?
A.
0.059 V
B.
0.118 V
C.
0.0591 V
D.
0.1181 V
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Solution
Using the Nernst equation, E = (0.0591/n) log([C1/C2]), where n=1.
Correct Answer: B — 0.118 V
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Q. In a cyclic process, the net work done is equal to: (2020)
A.
Net heat added
B.
Change in internal energy
C.
Zero
D.
Net heat removed
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Solution
In a cyclic process, the net work done is equal to the net heat added to the system, as the internal energy returns to its initial state.
Correct Answer: A — Net heat added
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Q. In a Daniell cell, which metal acts as the anode?
A.
Copper
B.
Zinc
C.
Silver
D.
Lead
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Solution
In a Daniell cell, Zinc acts as the anode.
Correct Answer: B — Zinc
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Q. In a first-order reaction, if the concentration of reactant decreases from 0.8 M to 0.2 M in 20 minutes, what is the rate constant? (2022)
A.
0.0347 min⁻¹
B.
0.0693 min⁻¹
C.
0.1 min⁻¹
D.
0.2 min⁻¹
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Solution
Using the first-order rate equation, k = (ln[A₀] - ln[A]) / t. Here, k = (ln(0.8) - ln(0.2)) / 20 = 0.0347 min⁻¹.
Correct Answer: A — 0.0347 min⁻¹
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Q. In a first-order reaction, if the rate constant k is 0.03 min⁻¹, what is the time required for the concentration to decrease to half? (2020)
A.
23.1 min
B.
10.0 min
C.
20.0 min
D.
15.0 min
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Solution
t₁/₂ = 0.693 / k = 0.693 / 0.03 = 23.1 min.
Correct Answer: A — 23.1 min
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Q. In a galvanic cell, if the anode reaction is 2Ag⁺ + 2e⁻ → 2Ag, what is the cathode reaction? (2022)
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 reaction, and Cu²⁺ + 2e⁻ → Cu is a common cathode reaction.
Correct Answer: A — Cu²⁺ + 2e⁻ → Cu
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Q. In a galvanic cell, if the anode reaction is 2H₂ → 4H⁺ + 4e⁻, what is the cathode reaction?
A.
O₂ + 4e⁻ + 4H⁺ → 2H₂O
B.
2H₂O + 4e⁻ → 2H₂ + O₂
C.
4H⁺ + 4e⁻ → 2H₂
D.
2H₂ + O₂ → 2H₂O
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Solution
The cathode reaction is O₂ + 4e⁻ + 4H⁺ → 2H₂O.
Correct Answer: A — O₂ + 4e⁻ + 4H⁺ → 2H₂O
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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 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 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 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 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 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 an AC circuit, if the voltage is 120V and the current is 10A, what is the power factor if the real power is 600W? (2022)
A.
0.5
B.
0.6
C.
0.8
D.
1.0
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Solution
Power factor = Real Power / (Voltage x Current) = 600 / (120 x 10) = 600 / 1200 = 0.5.
Correct Answer: B — 0.6
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