Engineering Entrance
Q. If z = 3 + 4i, what is the imaginary part of z? (2022) 2022
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Solution
The imaginary part of the complex number z = 3 + 4i is 4.
Correct Answer: B — 4
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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 z = 5 + 12i, what is the argument of z? (2022)
A.
arctan(12/5)
B.
arctan(5/12)
C.
π/2
D.
0
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Solution
The argument of z = 5 + 12i is given by arctan(12/5).
Correct Answer: A — arctan(12/5)
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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 buffer solution, which component resists changes in pH? (2020)
A.
Strong acid
B.
Weak acid and its salt
C.
Strong base
D.
Water
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Solution
A buffer solution typically consists of a weak acid and its conjugate base (salt), which helps to resist changes in pH when small amounts of acid or base are added.
Correct Answer: B — Weak acid and its salt
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Q. In a Carnot engine operating between temperatures of 500 K and 300 K, what is the efficiency of the engine? (2023)
A.
40%
B.
50%
C.
60%
D.
70%
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Solution
Efficiency (η) = 1 - (T_cold / T_hot) = 1 - (300 K / 500 K) = 0.4 or 40%.
Correct Answer: C — 60%
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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 Carnot engine, the efficiency depends on which of the following? (2023)
A.
Temperature of the hot reservoir
B.
Temperature of the cold reservoir
C.
Both temperatures
D.
Type of working substance
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Solution
The efficiency of a Carnot engine is determined by the temperatures of the hot and cold reservoirs, given by the formula η = 1 - (T_c/T_h).
Correct Answer: C — Both temperatures
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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 current flowing through the resistor? (2023)
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Solution
Using Ohm's law, I = V/R = 9V / 3Ω = 3A.
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 by the resistor? (2021)
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Solution
Power is given by P = V²/R = (9V)² / 3Ω = 81V² / 3Ω = 27W.
Correct Answer: B — 9W
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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 circuit, if the current is doubled while the resistance remains constant, what happens to the power consumed? (2020)
A.
It doubles
B.
It triples
C.
It remains the same
D.
It halves
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Solution
Power is given by P = I²R. If I is doubled, P becomes (2I)²R = 4I²R, which means power quadruples.
Correct Answer: A — It doubles
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Q. In a circuit, if the resistance is halved while the voltage remains constant, what happens to the current? (2022)
A.
It halves
B.
It doubles
C.
It remains the same
D.
It quadruples
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Solution
According to Ohm's law, I = V/R. If R is halved, I will double.
Correct Answer: B — It doubles
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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 closed system, if 100 J of heat is added and 40 J of work is done by the system, what is the change in internal energy? (2022)
A.
60 J
B.
40 J
C.
100 J
D.
Zero
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Solution
According to the First Law of Thermodynamics, ΔU = Q - W. Here, ΔU = 100 J - 40 J = 60 J.
Correct Answer: A — 60 J
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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 damped harmonic oscillator, what happens to the amplitude over time? (2023)
A.
Increases
B.
Decreases
C.
Remains constant
D.
Oscillates
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Solution
In a damped harmonic oscillator, the amplitude decreases over time due to energy loss.
Correct Answer: B — Decreases
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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 double-slit experiment, if the wavelength of light is halved, what happens to the fringe width? (2020)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
Fringe width (β) is given by β = λD/d. If λ is halved, β will also be halved.
Correct Answer: A — It doubles
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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 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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