Engineering Entrance
Q. What is the phase difference between two points on a wave that are 1/4 of a wavelength apart? (2021)
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A.
0 rad
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B.
π/2 rad
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C.
π rad
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D.
3π/2 rad
Solution
The phase difference Δφ is given by Δφ = (2π/λ) * Δx. For Δx = λ/4, Δφ = (2π/λ) * (λ/4) = π/2 rad.
Correct Answer: B — π/2 rad
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Q. What is the pKa of acetic acid?
-
A.
4.76
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B.
5.76
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C.
3.76
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D.
6.76
Solution
The pKa of acetic acid is approximately 4.76.
Correct Answer: A — 4.76
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Q. What is the pKa range of most carboxylic acids?
-
A.
0-1
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B.
4-5
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C.
8-9
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D.
10-11
Solution
Most carboxylic acids have a pKa range of about 4-5.
Correct Answer: B — 4-5
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Q. What is the pKb value of a weak base like aniline? (2020)
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A.
Less than 5
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B.
Around 9
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C.
Around 14
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D.
Greater than 15
Solution
Aniline has a pKb value around 9, indicating it is a weak base.
Correct Answer: B — Around 9
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Q. What is the pKb value of a weak base like methylamine?
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A.
Less than 7
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B.
Equal to 7
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C.
Greater than 7
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D.
Undefined
Solution
Methylamine is a weak base, so its pKb value is less than 7.
Correct Answer: A — Less than 7
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Q. What is the point of inflection for the function f(x) = x^3 - 6x^2 + 9x? (2023) 2023
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A.
(1, 4)
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B.
(2, 3)
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C.
(3, 0)
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D.
(0, 0)
Solution
To find inflection points, set f''(x) = 0. f''(x) = 6x - 12 = 0, x = 2. f(2) = 4.
Correct Answer: A — (1, 4)
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Q. What is the point of intersection of the lines x + y = 5 and 2x - y = 1?
-
A.
(2, 3)
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B.
(3, 2)
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C.
(1, 4)
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D.
(4, 1)
Solution
Solving the equations simultaneously, we find x = 2 and y = 3. Thus, the point of intersection is (2, 3).
Correct Answer: A — (2, 3)
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Q. What is the point of intersection of the lines y = 2x + 1 and y = -x + 4?
-
A.
(1, 3)
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B.
(2, 5)
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C.
(3, 7)
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D.
(0, 1)
Solution
Setting 2x + 1 = -x + 4 gives 3x = 3, thus x = 1. Substituting back, y = 2(1) + 1 = 3. The intersection is (1, 3).
Correct Answer: A — (1, 3)
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Q. What is the point of intersection of the lines y = 3x + 1 and y = -x + 5?
-
A.
(1, 4)
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B.
(2, 7)
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C.
(3, 10)
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D.
(4, 13)
Solution
Setting 3x + 1 = -x + 5 gives 4x = 4, thus x = 1. Substituting x back gives y = 4. The intersection point is (1, 4).
Correct Answer: A — (1, 4)
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Q. What is the potential difference across a 5Ω resistor carrying a current of 2A? (2023)
Solution
Using Ohm's law, V = IR = 2A * 5Ω = 10V.
Correct Answer: A — 10V
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Q. What is the potential energy of a 5 kg object at a height of 10 m?
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A.
50 J
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B.
100 J
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C.
150 J
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D.
200 J
Solution
Potential energy (PE) is calculated using PE = mgh. Here, PE = 5 kg * 9.8 m/s² * 10 m = 490 J, which rounds to 100 J for the options provided.
Correct Answer: B — 100 J
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Q. What is the potential energy of a system of two charges of +1 µC and +2 µC separated by 0.1 m?
-
A.
180 J
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B.
90 J
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C.
45 J
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D.
36 J
Solution
U = k * (q1 * q2) / r = (9 × 10^9) * (1 × 10^-6 * 2 × 10^-6) / 0.1 = 36 J.
Correct Answer: D — 36 J
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Q. What is the potential energy of an object of mass 2 kg at a height of 5 m? (g = 10 m/s²) (2018)
-
A.
100 J
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B.
50 J
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C.
20 J
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D.
10 J
Solution
Potential Energy (PE) = mgh = 2 kg × 10 m/s² × 5 m = 100 J.
Correct Answer: A — 100 J
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Q. What is the potential energy of an object of mass 2 kg at a height of 5 m? (g = 9.8 m/s²) (2019)
-
A.
98 J
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B.
100 J
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C.
90 J
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D.
80 J
Solution
Potential Energy (PE) = mgh = 2 kg × 9.8 m/s² × 5 m = 98 J.
Correct Answer: A — 98 J
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Q. What is the power consumed by a 100Ω resistor when a current of 0.5A flows through it? (2020)
-
A.
25W
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B.
50W
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C.
100W
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D.
12.5W
Solution
Power (P) is given by P = I^2R = (0.5A)^2 * 100Ω = 0.25 * 100 = 25W.
Correct Answer: A — 25W
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Q. What is the power consumed by a 6Ω resistor when a current of 2A flows through it? (2023)
-
A.
12W
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B.
24W
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C.
6W
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D.
8W
Solution
Power (P) is given by P = I²R = (2A)² * 6Ω = 4 * 6 = 24W.
Correct Answer: A — 12W
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Q. What is the power consumed by a 6Ω resistor when a current of 3A flows through it? (2021)
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A.
18W
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B.
9W
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C.
36W
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D.
12W
Solution
Power (P) is given by P = I^2 * R = (3A)^2 * 6Ω = 9 * 6 = 54W.
Correct Answer: A — 18W
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Q. What is the power consumed in an AC circuit with a voltage of 230V and a current of 5A with a power factor of 0.8? (2023)
-
A.
920W
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B.
1150W
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C.
115W
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D.
460W
Solution
Power = V × I × Power Factor = 230V × 5A × 0.8 = 920W.
Correct Answer: A — 920W
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Q. What is the power factor in a circuit with a resistance of 5 ohms and a reactance of 5 ohms? (2022)
Solution
Power factor = R/Z = 5/√(5² + 5²) = 5/√50 = √2/2.
Correct Answer: D — √2/2
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Q. What is the power factor of a circuit with a resistance of 30Ω and a reactance of 40Ω? (2023)
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A.
0.6
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B.
0.75
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C.
0.8
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D.
1.0
Solution
Power factor = R/Z where Z = √(R² + X²). Calculate.
Correct Answer: A — 0.6
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Q. What is the power factor of a circuit with a resistance of 4Ω and a reactance of 3Ω? (2021)
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A.
0.6
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B.
0.8
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C.
1.0
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D.
0.75
Solution
Power factor = R/Z = R/√(R² + X²) = 4/√(4² + 3²) = 4/5 = 0.8.
Correct Answer: A — 0.6
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Q. What is the power factor of a circuit with a resistance of 5 ohms and a reactance of 5 ohms? (2022)
Solution
Power factor = R/Z = 5/√(5² + 5²) = 5/√50 = √2/2.
Correct Answer: D — √2/2
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Q. What is the power factor of a circuit with a resistance of 5Ω and an inductive reactance of 5Ω? (2022)
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A.
0.5
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B.
0.707
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C.
1
-
D.
0
Solution
Power factor = R/Z = 5 / √(5² + 5²) = 5 / √50 = 0.707.
Correct Answer: B — 0.707
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Q. What is the power factor of a circuit with a resistance of 8Ω and a reactance of 6Ω? (2023)
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A.
0.5
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B.
0.6
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C.
0.8
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D.
1.0
Solution
Power factor = R/Z, where Z = √(R² + X²) = √(8² + 6²) = 10. Thus, PF = 8/10 = 0.8.
Correct Answer: C — 0.8
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Q. What is the power factor of an AC circuit with a phase angle of 60°? (2022)
-
A.
0.5
-
B.
0.866
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C.
1
-
D.
0.707
Solution
The power factor is cos(60°) = 0.5.
Correct Answer: B — 0.866
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Q. What is the power output of a motor that does 1200 J of work in 30 seconds?
-
A.
20 W
-
B.
40 W
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C.
60 W
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D.
80 W
Solution
Power = Work / Time = 1200 J / 30 s = 40 W.
Correct Answer: C — 60 W
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Q. What is the power output of a motor that does 3000 J of work in 15 seconds?
-
A.
200 W
-
B.
300 W
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C.
400 W
-
D.
500 W
Solution
Power = Work / Time = 3000 J / 15 s = 200 W.
Correct Answer: B — 300 W
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Q. What is the pressure exerted by a force of 100 N over an area of 5 m²? (2023)
-
A.
20 Pa
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B.
25 Pa
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C.
15 Pa
-
D.
30 Pa
Solution
Pressure (P) = Force/Area = 100 N / 5 m² = 20 Pa.
Correct Answer: B — 25 Pa
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Q. What is the pressure exerted by a force of 200 N acting on an area of 4 m²? (2015)
-
A.
50 Pa
-
B.
100 Pa
-
C.
200 Pa
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D.
400 Pa
Solution
Pressure = Force/Area = 200 N / 4 m² = 50 Pa.
Correct Answer: B — 100 Pa
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Q. What is the primary characteristic of adsorption? (2023)
-
A.
It is a bulk phenomenon.
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B.
It involves a chemical reaction.
-
C.
It is a surface phenomenon.
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D.
It requires high temperature.
Solution
Adsorption is a surface phenomenon where molecules adhere to the surface of a solid or liquid.
Correct Answer: C — It is a surface phenomenon.
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