Engineering Entrance
Q. In an RLC series circuit, if the inductive reactance is greater than the capacitive reactance, the circuit is said to be: (2022)
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A.
Resonant
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B.
Inductive
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C.
Capacitive
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D.
Purely resistive
Solution
If the inductive reactance (XL) is greater than the capacitive reactance (XC), the circuit is inductive.
Correct Answer: B — Inductive
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Q. In an RLC series circuit, if the resistance is 10 Ω, inductance is 0.1 H, and capacitance is 100 μF, what is the resonant frequency? (2023)
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A.
50 Hz
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B.
100 Hz
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C.
159 Hz
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D.
200 Hz
Solution
The resonant frequency f0 = 1/(2π√(LC)) = 1/(2π√(0.1 * 100e-6)) = 159 Hz.
Correct Answer: C — 159 Hz
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Q. In an RLC series circuit, if the total impedance is 50 ohms and the resistance is 30 ohms, what is the reactance? (2020)
-
A.
40 ohms
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B.
30 ohms
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C.
20 ohms
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D.
10 ohms
Solution
Using Z = √(R² + X²), we find X = √(Z² - R²) = √(50² - 30²) = √(2500 - 900) = √1600 = 40 ohms.
Correct Answer: A — 40 ohms
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Q. In electrolysis, if 1 mole of electrons is transferred, how many grams of copper can be deposited from Cu²⁺?
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A.
63.5 g
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B.
31.75 g
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C.
127 g
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D.
159 g
Solution
1 mole of Cu²⁺ deposits 63.5 g of copper.
Correct Answer: A — 63.5 g
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Q. In electrolysis, if the current is 2 A and the time is 30 minutes, how many moles of electrons are transferred?
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A.
0.1 mol
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B.
0.2 mol
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C.
0.3 mol
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D.
0.4 mol
Solution
Using the formula: moles = (current × time) / (n × F), where n=1 for electrons and F=96500 C/mol.
Correct Answer: B — 0.2 mol
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Q. In electrolysis, the process of oxidation occurs at the: (2023)
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A.
Anode
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B.
Cathode
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C.
Electrolyte
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D.
None of the above
Solution
In electrolysis, oxidation occurs at the anode.
Correct Answer: A — Anode
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Q. In electrolysis, the process of oxidation occurs at the: (2023) 2023
-
A.
Anode
-
B.
Cathode
-
C.
Electrolyte
-
D.
None of the above
Solution
In electrolysis, oxidation occurs at the anode.
Correct Answer: A — Anode
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Q. In electrolysis, what is produced at the anode when NaCl solution is electrolyzed? (2022)
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A.
Hydrogen gas
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B.
Chlorine gas
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C.
Sodium metal
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D.
Oxygen gas
Solution
Chlorine gas is produced at the anode during the electrolysis of NaCl solution.
Correct Answer: B — Chlorine gas
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Q. In how many ways can 3 prizes be awarded to 5 students? (2021)
-
A.
60
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B.
100
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C.
120
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D.
80
Solution
The number of ways to award 3 prizes to 5 students is 5P3 = 60.
Correct Answer: C — 120
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Q. In how many ways can 4 different flags be arranged on a pole? (2015)
Solution
The number of arrangements of 4 distinct flags is 4! = 24.
Correct Answer: A — 24
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Q. In how many ways can 4 different fruits be selected from 10 fruits?
-
A.
210
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B.
120
-
C.
240
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D.
300
Solution
The number of ways to choose 4 fruits from 10 is C(10, 4) = 210.
Correct Answer: A — 210
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Q. In how many ways can 4 different prizes be distributed among 10 students? (2023)
-
A.
5040
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B.
10000
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C.
2400
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D.
120
Solution
The number of ways to distribute 4 different prizes among 10 students is 10P4 = 5040.
Correct Answer: A — 5040
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Q. In how many ways can 4 prizes be distributed among 10 students?
-
A.
210
-
B.
5040
-
C.
10000
-
D.
1001
Solution
The number of ways to distribute 4 prizes among 10 students is 10P4 = 5040.
Correct Answer: B — 5040
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Q. In how many ways can 4 students be seated in a row of 6 chairs? (2021)
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A.
360
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B.
720
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C.
120
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D.
240
Solution
Choose 4 chairs from 6 (6C4) and arrange 4 students (4!). Total = 15 * 24 = 360.
Correct Answer: B — 720
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Q. In how many ways can 5 different books be arranged on a shelf? (2021)
-
A.
60
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B.
120
-
C.
240
-
D.
720
Solution
The number of arrangements of 5 distinct books is 5! = 120.
Correct Answer: D — 720
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Q. In how many ways can 5 different colored balls be arranged in a line?
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A.
60
-
B.
120
-
C.
240
-
D.
720
Solution
The number of ways to arrange 5 different colored balls is 5! = 120.
Correct Answer: D — 720
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Q. In how many ways can 6 different colored balls be arranged in a row? (2018)
-
A.
720
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B.
600
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C.
480
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D.
360
Solution
The number of arrangements of 6 distinct balls is 6! = 720.
Correct Answer: A — 720
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Q. In how many ways can 6 people be seated in a row?
-
A.
720
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B.
600
-
C.
480
-
D.
360
Solution
The number of arrangements of 6 people is 6! = 720.
Correct Answer: A — 720
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Q. In how many ways can 7 people be divided into 3 groups if one group must have 3 people?
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A.
210
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B.
300
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C.
420
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D.
560
Solution
Choose 3 people from 7: C(7, 3) = 35. The remaining 4 can be divided into 2 groups in 2 ways. Total = 35 * 2 = 70.
Correct Answer: B — 300
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Q. In the expansion of (2x + 3)^4, what is the coefficient of x^0?
Solution
The coefficient of x^0 is given by 4C4 * (2x)^0 * (3)^4 = 1 * 81 = 81.
Correct Answer: A — 81
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Q. In the expansion of (2x - 5)^5, what is the coefficient of x^2? (2021)
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A.
-300
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B.
-600
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C.
600
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D.
300
Solution
The coefficient of x^2 is C(5,2) * (2)^2 * (-5)^3 = 10 * 4 * (-125) = -5000.
Correct Answer: A — -300
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Q. In the expansion of (2x - 5)^6, what is the coefficient of x^2? (2021)
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A.
-150
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B.
-300
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C.
300
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D.
150
Solution
The coefficient of x^2 is C(6,2) * (2)^2 * (-5)^4 = 15 * 4 * 625 = -37500.
Correct Answer: A — -150
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Q. In the expansion of (2x - 5)^6, what is the coefficient of x^3? (2020)
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A.
-600
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B.
-720
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C.
720
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D.
600
Solution
The coefficient of x^3 is C(6,3)(2)^3(-5)^3 = 20 * 8 * -125 = -20000.
Correct Answer: B — -720
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Q. In the expansion of (3x - 2)^6, what is the coefficient of x^4? (2022)
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A.
540
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B.
810
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C.
729
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D.
486
Solution
The coefficient of x^4 is given by 6C4 * (3)^4 * (-2)^2 = 15 * 81 * 4 = 4860.
Correct Answer: A — 540
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Q. In the expansion of (3x - 4)^4, what is the coefficient of x^2? (2023)
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A.
-144
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B.
-216
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C.
216
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D.
144
Solution
The coefficient of x^2 is C(4,2)(3)^2(-4)^2 = 6 * 9 * 16 = -864.
Correct Answer: B — -216
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Q. In the expansion of (x + 3)^4, what is the coefficient of x^3? (2023)
Solution
The coefficient of x^3 is C(4,3) * (3)^1 = 4 * 3 = 12.
Correct Answer: A — 36
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Q. In the expansion of (x - 1)^5, what is the coefficient of x^3?
Solution
The coefficient of x^3 is C(5,3) * (-1)^2 = 10.
Correct Answer: A — -10
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Q. In the reaction 2Ag+ + Zn → 2Ag + Zn2+, what is the oxidation state of zinc after the reaction?
Solution
Zinc (Zn) is oxidized to Zn2+, so its oxidation state is +2.
Correct Answer: B — +2
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Q. In the reaction 2Fe + 3Cl2 → 2FeCl3, which element is oxidized?
-
A.
Fe
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B.
Cl2
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C.
FeCl3
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D.
None of the above
Solution
Iron (Fe) is oxidized as it loses electrons to form FeCl3.
Correct Answer: A — Fe
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Q. In the reaction 2Fe2O3 + 3C → 4Fe + 3CO2, what is being reduced? (2020) 2020
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A.
Fe2O3
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B.
C
-
C.
CO2
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D.
Fe
Solution
Fe2O3 is reduced to Fe, as it gains electrons during the reaction.
Correct Answer: A — Fe2O3
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