Engineering Entrance
Q. What is the capacitance of a capacitor that stores 10 µC of charge at a potential difference of 5 V?
-
A.
2 µF
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B.
5 µF
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C.
10 µF
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D.
20 µF
Solution
C = Q/V = 10 × 10^-6 C / 5 V = 2 × 10^-6 F = 2 µF.
Correct Answer: A — 2 µF
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Q. What is the capacitive reactance of a capacitor of 10μF at a frequency of 60 Hz? (2016)
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A.
265.26Ω
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B.
159.15Ω
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C.
100Ω
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D.
50Ω
Solution
Capacitive reactance Xc = 1 / (2πfC) = 1 / (2π * 60 * 10e-6) = 265.26Ω.
Correct Answer: A — 265.26Ω
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Q. What is the capacitive reactance of a capacitor with a capacitance of 10μF at a frequency of 50Hz? (2020)
-
A.
318.31 ohms
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B.
159.15 ohms
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C.
31.83 ohms
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D.
15.92 ohms
Solution
Xc = 1 / (2πfC) = 1 / (2π × 50 × 10 × 10^-6) = 318.31 ohms.
Correct Answer: A — 318.31 ohms
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Q. What is the cell potential of a Daniell cell at standard conditions?
-
A.
1.10 V
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B.
1.96 V
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C.
0.76 V
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D.
0.34 V
Solution
The standard cell potential of a Daniell cell is 1.10 V.
Correct Answer: A — 1.10 V
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Q. What is the cell potential of a galvanic cell with E° = 1.5 V and Q = 10?
-
A.
1.2 V
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B.
1.0 V
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C.
1.3 V
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D.
1.4 V
Solution
Using the Nernst equation, E = E° - (RT/nF)lnQ, we find E ≈ 1.0 V.
Correct Answer: B — 1.0 V
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Q. What is the change in internal energy (ΔU) for an ideal gas that expands isothermally? (2022)
-
A.
0
-
B.
nRT
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C.
nRΔT
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D.
PV
Solution
For an isothermal process, the change in internal energy ΔU = 0 for an ideal gas.
Correct Answer: A — 0
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Q. What is the change in internal energy for an ideal gas that expands isothermally? (2019)
-
A.
nRT
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B.
0
-
C.
-nRT
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D.
nR(Tf - Ti)
Solution
For an isothermal process, the change in internal energy (ΔU) for an ideal gas is zero, as ΔU depends only on temperature.
Correct Answer: B — 0
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Q. What is the change in internal energy of a gas that absorbs 300 J of heat and does 100 J of work on the surroundings? (2020)
-
A.
200 J
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B.
300 J
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C.
400 J
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D.
500 J
Solution
Change in internal energy (ΔU) = Q - W = 300 J - 100 J = 200 J.
Correct Answer: A — 200 J
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Q. What is the change in internal energy of a system if 200 J of heat is added and 50 J of work is done by the system?
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A.
150 J
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B.
250 J
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C.
200 J
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D.
100 J
Solution
Using the first law of thermodynamics, ΔU = Q - W = 200 J - 50 J = 150 J.
Correct Answer: A — 150 J
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Q. What is the change in internal energy of a system if 300 J of heat is added and 100 J of work is done by the system? (2021)
-
A.
200 J
-
B.
300 J
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C.
400 J
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D.
500 J
Solution
Using the first law of thermodynamics: ΔU = Q - W = 300 J - 100 J = 200 J.
Correct Answer: A — 200 J
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Q. What is the change in internal energy of an ideal gas when it expands isothermally? (2021)
-
A.
Zero
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B.
Positive
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C.
Negative
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D.
Depends on the gas
Solution
In an isothermal process for an ideal gas, the internal energy remains constant, hence the change in internal energy is zero.
Correct Answer: A — Zero
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Q. What is the change in internal energy of an ideal gas when it is heated at constant volume? (2021) 2021
-
A.
Zero
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B.
Equal to heat added
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C.
Equal to work done
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D.
Equal to pressure times volume
Solution
At constant volume, the change in internal energy (ΔU) is equal to the heat added (Q). Therefore, ΔU = Q.
Correct Answer: B — Equal to heat added
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Q. What is the chemical formula for sodium chloride? (2023) 2023
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A.
NaCl
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B.
Na2Cl
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C.
NaCl2
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D.
Na2Cl2
Solution
The chemical formula for sodium chloride is NaCl.
Correct Answer: A — NaCl
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Q. What is the chemical formula for table salt? (2019)
-
A.
NaCl
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B.
KCl
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C.
CaCl2
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D.
MgCl2
Solution
Table salt is chemically known as sodium chloride, which has the formula NaCl.
Correct Answer: A — NaCl
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Q. What is the coefficient of x^0 in the expansion of (2x - 3)^5? (2022)
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A.
-243
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B.
243
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C.
-81
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D.
81
Solution
The constant term is C(5,5)(-3)^5 = -243.
Correct Answer: A — -243
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Q. What is the coefficient of x^0 in the expansion of (3x + 2)^5? (2022)
Solution
The coefficient of x^0 is C(5,5) * (3x)^0 * (2)^5 = 1 * 32 = 32.
Correct Answer: C — 64
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Q. What is the coefficient of x^0 in the expansion of (x + 1/x)^8? (2021)
Solution
The coefficient of x^0 occurs when k=4, which gives us 8C4 = 70.
Correct Answer: C — 70
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Q. What is the coefficient of x^1 in the expansion of (x + 1)^10? (2021)
Solution
The coefficient of x^1 is C(10,1)(1)^9 = 10.
Correct Answer: A — 10
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Q. What is the coefficient of x^1 in the expansion of (x - 1)^5?
Solution
The coefficient of x^1 is given by 5C1 * (-1)^4 = 5 * 1 = 5.
Correct Answer: A — -5
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Q. What is the coefficient of x^2 in the expansion of (2x - 1)^5? (2021)
Solution
The coefficient of x^2 is C(5,2) * (2)^2 * (-1)^3 = 10 * 4 * (-1) = -40.
Correct Answer: B — 20
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Q. What is the coefficient of x^2 in the expansion of (x + 5)^4?
-
A.
50
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B.
100
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C.
150
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D.
200
Solution
The coefficient of x^2 is C(4,2) * (5)^2 = 6 * 25 = 150.
Correct Answer: B — 100
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Q. What is the coefficient of x^2 in the expansion of (x - 2)^5?
-
A.
-40
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B.
-20
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C.
20
-
D.
40
Solution
The coefficient of x^2 is given by 5C2 * (-2)^3 = 10 * (-8) = -80.
Correct Answer: A — -40
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Q. What is the coefficient of x^3 in the expansion of (5x + 2)^6? (2000) 2000
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A.
600
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B.
720
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C.
800
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D.
900
Solution
The coefficient of x^3 is C(6,3) * (5)^3 * (2)^3 = 20 * 125 * 8 = 20000.
Correct Answer: B — 720
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Q. What is the coefficient of x^3 in the expansion of (x + 5)^8?
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A.
2800
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B.
3360
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C.
4000
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D.
4200
Solution
The coefficient of x^3 is given by 8C3 * (5)^5 = 56 * 3125 = 175000.
Correct Answer: B — 3360
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Q. What is the coefficient of x^3 in the expansion of (x - 1)^5? (2022)
Solution
The coefficient of x^3 is C(5,3)(-1)^2 = 10.
Correct Answer: A — -10
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Q. What is the coefficient of x^4 in the expansion of (3x + 2)^6?
-
A.
540
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B.
720
-
C.
810
-
D.
900
Solution
The coefficient of x^4 is C(6,4) * (3)^4 * (2)^2 = 15 * 81 * 4 = 4860.
Correct Answer: B — 720
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Q. What is the coefficient of x^4 in the expansion of (x + 1)^8? (2020)
Solution
The coefficient of x^4 is C(8,4) = 70.
Correct Answer: B — 56
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Q. What is the coefficient of x^5 in the expansion of (2x - 1)^6?
Solution
The coefficient of x^5 is C(6,5) * (2)^5 * (-1)^1 = 6 * 32 * (-1) = -192.
Correct Answer: D — 80
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Q. What is the coefficient of x^5 in the expansion of (x + 4)^7? (2020)
-
A.
672
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B.
6720
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C.
1680
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D.
840
Solution
The coefficient of x^5 is C(7,5) * (4)^2 = 21 * 16 = 336.
Correct Answer: C — 1680
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Q. What is the coefficient of x^6 in the expansion of (x + 3)^8? (2020)
-
A.
56
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B.
84
-
C.
112
-
D.
128
Solution
The coefficient of x^6 is C(8,6) * (3)^2 = 28 * 9 = 252.
Correct Answer: B — 84
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