Q. If a 6Ω and a 3Ω resistor are connected in parallel, what is the equivalent resistance? (2022)
-
A.
2Ω
-
B.
4Ω
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C.
1.5Ω
-
D.
9Ω
Solution
Using the formula for parallel resistors: 1/R_eq = 1/R1 + 1/R2 = 1/6 + 1/3 = 1/6 + 2/6 = 3/6. Therefore, R_eq = 2Ω.
Correct Answer: A — 2Ω
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Q. If a 6Ω resistor is connected in parallel with a 3Ω resistor, what is the equivalent resistance? (2023)
-
A.
2Ω
-
B.
1.5Ω
-
C.
4Ω
-
D.
9Ω
Solution
Using the formula 1/R_eq = 1/R1 + 1/R2, we get 1/R_eq = 1/6 + 1/3 = 1/6 + 2/6 = 3/6, thus R_eq = 2Ω.
Correct Answer: A — 2Ω
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Q. If a 9V battery is connected to a 3Ω resistor, what is the current flowing through it? (2021)
Solution
Using Ohm's law, I = V/R = 9V / 3Ω = 3A.
Correct Answer: B — 2A
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Q. If a 9V battery is connected to a 3Ω resistor, what is the energy consumed in 10 seconds? (2023)
-
A.
30J
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B.
90J
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C.
60J
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D.
45J
Solution
Power (P) = V²/R = 9²/3 = 27W. Energy (E) = P * t = 27W * 10s = 270J.
Correct Answer: B — 90J
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Q. If a 9V battery is connected to a 3Ω resistor, what is the power dissipated in the resistor? (2023)
Solution
Power (P) can be calculated using P = V²/R = (9V)² / 3Ω = 81 / 3 = 27W.
Correct Answer: A — 3W
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Q. If a 9V battery is connected to a 3Ω resistor, what is the voltage drop across the resistor? (2023)
Solution
The voltage drop across the resistor is equal to the battery voltage, which is 9V.
Correct Answer: C — 9V
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Q. If a = 2 and b = 3, what is the value of a^3 + b^3? (2021)
Solution
a^3 = 2^3 = 8 and b^3 = 3^3 = 27, so 8 + 27 = 35.
Correct Answer: A — 35
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Q. If A = 2i + 3j and B = 3i + 4j, what is the angle between A and B? (2021)
-
A.
0 degrees
-
B.
45 degrees
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C.
90 degrees
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D.
180 degrees
Solution
cos(θ) = (A · B) / (|A||B|) = (2*3 + 3*4) / (√(2^2 + 3^2) * √(3^2 + 4^2)) = 0.7071, θ = 45 degrees.
Correct Answer: B — 45 degrees
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Q. If a = 3 and b = 4, what is a^2 + b^2? (2017)
Solution
a^2 = 9 and b^2 = 16, so 9 + 16 = 25.
Correct Answer: A — 25
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Q. If a = 3 and b = 4, what is the value of a^2 + b^2? (2019)
Solution
a^2 = 9 and b^2 = 16, so 9 + 16 = 25.
Correct Answer: A — 25
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Q. If A = 3i + 4j and B = 2i - j, what is A + B? (2021)
-
A.
5i + 3j
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B.
5i + 5j
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C.
1i + 5j
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D.
1i + 3j
Solution
A + B = (3i + 4j) + (2i - j) = (3 + 2)i + (4 - 1)j = 5i + 3j.
Correct Answer: A — 5i + 3j
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Q. If a = 4 and b = 2, what is the value of a^2 + b^2? (2020)
Solution
a^2 = 16 and b^2 = 4, so 16 + 4 = 20.
Correct Answer: A — 20
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Q. If A = 4i + 2j and B = -i + 3j, what is the scalar triple product A · (B × A)? (2023)
Solution
B × A = |i j k| |-1 3 0| |4 2 0| = 0, hence A · (B × A) = 0.
Correct Answer: A — 0
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Q. If A = 5i + 12j, what is the unit vector in the direction of A? (2021)
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A.
(5/13)i + (12/13)j
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B.
(12/13)i + (5/13)j
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C.
(5/12)i + (12/5)j
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D.
(12/5)i + (5/12)j
Solution
Unit vector = A / |A| = (5i + 12j) / √(5^2 + 12^2) = (5/13)i + (12/13)j.
Correct Answer: A — (5/13)i + (12/13)j
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Q. If A = i + 2j + 3k and B = 4i + 5j + 6k, what is A - B? (2023)
-
A.
-3i - 3j - 3k
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B.
-3i - 3j + 3k
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C.
3i + 3j + 3k
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D.
3i + 3j - 3k
Solution
A - B = (1 - 4)i + (2 - 5)j + (3 - 6)k = -3i - 3j - 3k.
Correct Answer: A — -3i - 3j - 3k
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Q. If A = {2, 4, 6} and B = {1, 2, 3}, what is A ∩ B?
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A.
{2}
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B.
{4, 6}
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C.
{1, 2, 3}
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D.
{}
Solution
The intersection A ∩ B includes elements that are in both A and B. Here, A ∩ B = {2}.
Correct Answer: A — {2}
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Q. If A = {x | x is a prime number less than 10}, what is A?
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A.
{2, 3, 5, 7}
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B.
{1, 2, 3, 4}
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C.
{2, 4, 6, 8}
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D.
{3, 5, 7, 9}
Solution
The prime numbers less than 10 are 2, 3, 5, and 7. Therefore, A = {2, 3, 5, 7}.
Correct Answer: A — {2, 3, 5, 7}
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Q. If A = {x | x is an even number} and B = {x | x is a multiple of 3}, what is A ∪ B?
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A.
{0, 2, 4, 6, ...}
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B.
{0, 3, 6, 9, ...}
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C.
{0, 2, 3, 4, 6, 9, ...}
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D.
{0, 1, 2, 3, ...}
Solution
The union A ∪ B includes all even numbers and all multiples of 3. Thus, A ∪ B = {0, 2, 3, 4, 6, 9, ...}.
Correct Answer: C — {0, 2, 3, 4, 6, 9, ...}
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Q. If a bag contains 4 green and 6 yellow marbles, what is the probability of picking a green marble?
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A.
2/5
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B.
4/10
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C.
4/6
-
D.
1/3
Solution
Total marbles = 4 + 6 = 10. Probability of green marble = 4/10 = 2/5.
Correct Answer: A — 2/5
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Q. If a bag contains 4 green and 6 yellow marbles, what is the probability of picking a yellow marble?
-
A.
2/5
-
B.
3/5
-
C.
4/5
-
D.
1/5
Solution
Total marbles = 4 + 6 = 10. Probability of yellow = 6/10 = 3/5.
Correct Answer: B — 3/5
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Q. If a body is moving in a circular path with a constant speed, what is its acceleration? (2023)
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A.
Zero
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B.
Tangential
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C.
Centripetal
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D.
Radial
Solution
The body experiences centripetal acceleration directed towards the center of the circular path.
Correct Answer: C — Centripetal
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Q. If a body is moving in a circular path with a constant speed, what type of acceleration does it experience?
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A.
Centripetal acceleration
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B.
Linear acceleration
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C.
Angular acceleration
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D.
No acceleration
Solution
A body moving in a circular path experiences centripetal acceleration directed towards the center of the circle.
Correct Answer: A — Centripetal acceleration
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Q. If a capacitor is charged to 12V and has a capacitance of 6μF, what is the stored energy? (2022)
-
A.
0.432 mJ
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B.
0.072 mJ
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C.
0.864 mJ
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D.
0.216 mJ
Solution
Energy = 0.5 × C × V² = 0.5 × 6 × 10^-6 × 12² = 0.432 mJ.
Correct Answer: A — 0.432 mJ
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Q. If a car accelerates from rest to a speed of 20 m/s, and its mass is 1000 kg, what is the kinetic energy of the car at that speed? (2020)
-
A.
200 J
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B.
1000 J
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C.
2000 J
-
D.
4000 J
Solution
Kinetic Energy = 0.5 × mass × velocity² = 0.5 × 1000 kg × (20 m/s)² = 200000 J = 2000 J
Correct Answer: C — 2000 J
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Q. If a car accelerates from rest to a speed of 20 m/s, and its mass is 1000 kg, what is the kinetic energy gained by the car? (2021)
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A.
200,000 J
-
B.
100,000 J
-
C.
50,000 J
-
D.
400,000 J
Solution
Kinetic Energy (KE) = 0.5 × mass (m) × velocity² (v²). KE = 0.5 × 1000 kg × (20 m/s)² = 200,000 J.
Correct Answer: B — 100,000 J
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Q. If a car accelerates from rest to a speed of 20 m/s, what is the kinetic energy of the car if its mass is 1000 kg?
-
A.
200,000 J
-
B.
100,000 J
-
C.
50,000 J
-
D.
400,000 J
Solution
Kinetic Energy = 0.5 × mass × velocity² = 0.5 × 1000 kg × (20 m/s)² = 200,000 J
Correct Answer: B — 100,000 J
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Q. If a car travels at a speed of 60 km/h, how far will it travel in 2 hours? (2022)
-
A.
120 km
-
B.
100 km
-
C.
150 km
-
D.
90 km
Solution
Distance = Speed × Time = 60 km/h × 2 h = 120 km.
Correct Answer: A — 120 km
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Q. If a car with a mass of 1200 kg is moving at a speed of 15 m/s, what is its kinetic energy? (2021)
-
A.
13500 J
-
B.
9000 J
-
C.
18000 J
-
D.
27000 J
Solution
Kinetic Energy = 0.5 × mass × velocity² = 0.5 × 1200 kg × (15 m/s)² = 13500 J
Correct Answer: A — 13500 J
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Q. If a charge of +2μC is placed in an electric field of 1000 N/C, what is the force experienced by the charge? (2023)
-
A.
2 N
-
B.
0.002 N
-
C.
2000 N
-
D.
0.2 N
Solution
The force (F) on a charge in an electric field is given by F = qE. Here, F = 2μC * 1000 N/C = 2 N.
Correct Answer: A — 2 N
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Q. If a charge of +2μC is placed in an electric field of 500 N/C, what is the force experienced by the charge? (2022)
-
A.
1000 N
-
B.
250 N
-
C.
500 N
-
D.
2000 N
Solution
The force (F) on a charge in an electric field is given by F = qE. Here, F = 2μC * 500 N/C = 1000 N.
Correct Answer: A — 1000 N
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