Q. If the inductance of a coil is 0.5H and the frequency is 60Hz, what is the inductive reactance? (2023)
A.
31.42 ohms
B.
18.85 ohms
C.
37.70 ohms
D.
25.13 ohms
Show solution
Solution
Xl = 2πfL = 2π × 60 × 0.5 = 31.42 ohms.
Correct Answer:
A
— 31.42 ohms
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Q. If the inductive reactance of a coil is 30Ω and the resistance is 10Ω, what is the total impedance? (2018)
A.
10Ω
B.
30Ω
C.
33.33Ω
D.
40Ω
Show solution
Solution
Total impedance Z = √(R² + (XL)²) = √(10² + 30²) = √(100 + 900) = √1000 = 31.62Ω.
Correct Answer:
C
— 33.33Ω
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Q. If the latent heat of fusion of ice is 334 J/g, how much heat is required to melt 50 g of ice? (2019)
A.
1670 J
B.
3340 J
C.
5000 J
D.
1000 J
Show solution
Solution
Heat required = mass × latent heat = 50 g × 334 J/g = 16700 J.
Correct Answer:
A
— 1670 J
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Q. If the latent heat of vaporization of water is 2260 kJ/kg, how much energy is required to convert 0.5 kg of water at 100°C to steam at 100°C?
A.
1130 kJ
B.
2260 kJ
C.
3390 kJ
D.
4520 kJ
Show solution
Solution
Energy required = mass * latent heat = 0.5 kg * 2260 kJ/kg = 1130 kJ.
Correct Answer:
A
— 1130 kJ
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Q. If the line 2x + 3y = 6 intersects the x-axis, what is the point of intersection?
A.
(3, 0)
B.
(0, 2)
C.
(0, 3)
D.
(2, 0)
Show solution
Solution
Setting y = 0 gives 2x = 6, thus x = 3. The point of intersection is (3, 0).
Correct Answer:
A
— (3, 0)
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Q. If the line 2x + 3y = 6 intersects the x-axis, what is the x-coordinate of the intersection point?
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Solution
Setting y = 0 gives 2x = 6, thus x = 3. The x-coordinate of the intersection point is 3.
Correct Answer:
B
— 2
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Q. If the line 3x + 4y = 12 intersects the y-axis, what is the point of intersection? (2021)
A.
(0, 3)
B.
(0, 4)
C.
(0, 2)
D.
(0, 1)
Show solution
Solution
Setting x = 0 gives 4y = 12, thus y = 3. The point of intersection is (0, 3).
Correct Answer:
A
— (0, 3)
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Q. If the line 3x - 4y + 12 = 0 intersects the x-axis, what is the x-coordinate of the intersection point? (2021)
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Solution
Setting y = 0 in the equation gives 3x + 12 = 0, thus x = -4.
Correct Answer:
A
— -4
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Q. If the line 3x - 4y + 12 = 0 intersects the y-axis, what is the point of intersection?
A.
(0, 3)
B.
(0, -3)
C.
(0, 4)
D.
(0, -4)
Show solution
Solution
Setting x = 0 gives -4y + 12 = 0, thus y = -3. The point of intersection is (0, -3).
Correct Answer:
D
— (0, -4)
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Q. If the line 3x - 4y + 12 = 0 is parallel to another line, what is the slope of the parallel line?
A.
3/4
B.
-3/4
C.
4/3
D.
-4/3
Show solution
Solution
Rearranging gives y = (3/4)x + 3. The slope of the line is 3/4, so the slope of the parallel line is -3/4.
Correct Answer:
B
— -3/4
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Q. If the line 3x - 4y + 12 = 0 is parallel to which of the following lines?
A.
6x - 8y + 24 = 0
B.
3x + 4y - 12 = 0
C.
x + 2y - 5 = 0
D.
2x - 3y + 6 = 0
Show solution
Solution
Parallel lines have the same slope. The slope of the given line is 3/4, which is the same as the slope of 6x - 8y + 24 = 0.
Correct Answer:
A
— 6x - 8y + 24 = 0
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Q. If the line 7x + 2y = 14 is transformed to slope-intercept form, what is the slope?
A.
-7/2
B.
7/2
C.
2/7
D.
-2/7
Show solution
Solution
Rearranging to y = -7/2x + 7 shows that the slope is -7/2.
Correct Answer:
A
— -7/2
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Q. If the magnetic field strength is doubled, what happens to the force experienced by a current-carrying conductor in that field? (2022)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
Show solution
Solution
The force experienced by a current-carrying conductor in a magnetic field is directly proportional to the magnetic field strength. Therefore, if the magnetic field strength is doubled, the force also doubles.
Correct Answer:
A
— It doubles
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Q. If the magnetic field strength is doubled, what happens to the force experienced by a current-carrying conductor? (2022)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
Show solution
Solution
The force experienced by a current-carrying conductor in a magnetic field is directly proportional to the magnetic field strength. Therefore, if the magnetic field strength is doubled, the force also doubles.
Correct Answer:
A
— It doubles
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Q. If the magnetic field strength is doubled, what happens to the force on a current-carrying conductor in that field? (2022)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
Show solution
Solution
The force on a current-carrying conductor is directly proportional to the magnetic field strength, so if the field strength is doubled, the force also doubles.
Correct Answer:
A
— It doubles
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Q. If the magnetic field strength is doubled, what happens to the force on a current-carrying conductor? (2022)
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
Show solution
Solution
The force on a current-carrying conductor is directly proportional to the magnetic field strength, so if the magnetic field strength is doubled, the force also doubles.
Correct Answer:
A
— It doubles
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Q. If the magnetic flux through a coil changes from 0.2 Wb to 0.5 Wb in 2 seconds, what is the average induced EMF? (2021)
A.
150 V
B.
100 V
C.
75 V
D.
50 V
Show solution
Solution
Average induced EMF = -ΔΦ/Δt = -(0.5 Wb - 0.2 Wb) / 2 s = -0.15 Wb/s = 150 V.
Correct Answer:
B
— 100 V
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Q. If the magnetic flux through a coil changes from 0.2 Wb to 0.5 Wb in 2 seconds, what is the average induced EMF in the coil? (2021)
A.
150 V
B.
100 V
C.
75 V
D.
50 V
Show solution
Solution
Average induced EMF (ε) = -ΔΦ/Δt = -(0.5 Wb - 0.2 Wb) / 2 s = -0.3 Wb / 2 s = -0.15 V. The absolute value is 0.15 V or 150 mV.
Correct Answer:
B
— 100 V
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Q. If the mass of an object is measured in kilograms and its volume in cubic meters, what is the unit of density? (2022)
A.
kg/m
B.
kg/m^3
C.
m^3/kg
D.
m/kg
Show solution
Solution
Density is defined as mass per unit volume, so the unit of density is kg/m³.
Correct Answer:
B
— kg/m^3
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Q. If the mass of an object is tripled and the distance from the center of the Earth is halved, how does the gravitational force change?
A.
It triples
B.
It increases by a factor of 6
C.
It increases by a factor of 9
D.
It decreases
Show solution
Solution
F ∝ m/r²; if m is tripled and r is halved, F = 3m/(1/4) = 12m, so it increases by a factor of 9.
Correct Answer:
C
— It increases by a factor of 9
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Q. If the mass of the Earth were to double, what would happen to the gravitational force experienced by an object on its surface?
A.
It doubles
B.
It halves
C.
It quadruples
D.
It remains the same
Show solution
Solution
Gravitational force is directly proportional to mass. If mass doubles, force also doubles.
Correct Answer:
A
— It doubles
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Q. If the perimeter of a square is 40 cm, what is the length of one side? (2018)
A.
10 cm
B.
15 cm
C.
20 cm
D.
25 cm
Show solution
Solution
Perimeter = 4 × side, so side = 40/4 = 10 cm.
Correct Answer:
A
— 10 cm
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Q. If the pH of a solution is 3, what is the concentration of H+ ions? (2023)
A.
0.001 M
B.
0.01 M
C.
0.1 M
D.
0.0001 M
Show solution
Solution
pH = 3 means [H+] = 10^-3 M = 0.001 M.
Correct Answer:
B
— 0.01 M
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Q. If the pKa of acetic acid is 4.76, what is the pH of a 0.1 M solution?
A.
4.76
B.
5.76
C.
6.76
D.
3.76
Show solution
Solution
For a weak acid, pH ≈ pKa for a 0.1 M solution, so pH ≈ 4.76.
Correct Answer:
A
— 4.76
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Q. If the power factor of an AC circuit is 0.8, what is the angle between the current and voltage? (2021)
A.
36.87°
B.
53.13°
C.
60°
D.
45°
Show solution
Solution
The angle θ can be found using cos(θ) = power factor. Thus, θ = cos⁻¹(0.8) ≈ 36.87°.
Correct Answer:
B
— 53.13°
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Q. If the pressure of a gas is increased while keeping the temperature constant, what happens to its volume? (2020)
A.
It increases
B.
It decreases
C.
It remains the same
D.
It becomes zero
Show solution
Solution
According to Boyle's Law, P * V = constant at constant temperature, so if P increases, V must decrease.
Correct Answer:
B
— It decreases
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Q. If the quadratic equation x² + 5x + k = 0 has roots -2 and -3, find k. (2020)
Show solution
Solution
The product of the roots gives k = (-2)(-3) = 6.
Correct Answer:
A
— 6
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Q. If the radius of a circle is 4 cm, what is the length of a chord that is 3 cm from the center? (2014)
A.
5 cm
B.
6 cm
C.
7 cm
D.
8 cm
Show solution
Solution
Using Pythagoras theorem: chord length = 2√(r² - d²) = 2√(4² - 3²) = 2√(16 - 9) = 2√7 ≈ 5.29 cm.
Correct Answer:
A
— 5 cm
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Q. If the radius of a circle is 7 cm, what is its circumference? (Use π = 22/7) (2014)
A.
44 cm
B.
22 cm
C.
14 cm
D.
28 cm
Show solution
Solution
Circumference = 2πr = 2 × (22/7) × 7 = 44 cm.
Correct Answer:
A
— 44 cm
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Q. If the radius of a circle is decreased by 2 cm, how does the area change? (Original radius is 10 cm) (2021)
A.
Decreases by 12.56 cm²
B.
Decreases by 25.12 cm²
C.
Decreases by 31.4 cm²
D.
Decreases by 50.24 cm²
Show solution
Solution
Original area = π(10)² = 314 cm²; New area = π(8)² = 201.06 cm². Change = 314 - 201.06 = 112.94 cm².
Correct Answer:
B
— Decreases by 25.12 cm²
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