Q. If a 4 kg object is moving with a speed of 5 m/s, what is its kinetic energy?
-
A.
50 J
-
B.
40 J
-
C.
100 J
-
D.
80 J
Solution
Kinetic Energy (KE) = 0.5 × m × v² = 0.5 × 4 kg × (5 m/s)² = 0.5 × 4 × 25 = 50 J.
Correct Answer: D — 80 J
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Q. If a 5 kg object is dropped from a height of 10 m, what is its potential energy just before it hits the ground? (g = 9.8 m/s²)
-
A.
490 J
-
B.
980 J
-
C.
245 J
-
D.
2450 J
Solution
Potential Energy (PE) = m × g × h = 5 kg × 9.8 m/s² × 10 m = 490 J.
Correct Answer: B — 980 J
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Q. If a 5 kg object is dropped from a height of 10 m, what is its potential energy just before it hits the ground? (2021)
-
A.
50 J
-
B.
100 J
-
C.
150 J
-
D.
200 J
Solution
PE = m × g × h = 5 kg × 9.8 m/s² × 10 m = 490 J.
Correct Answer: B — 100 J
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Q. If a 5 kg object is moving with a speed of 10 m/s, what is its total mechanical energy assuming no potential energy?
-
A.
250 J
-
B.
500 J
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C.
100 J
-
D.
50 J
Solution
Total Mechanical Energy = Kinetic Energy = 0.5 * m * v² = 0.5 * 5 kg * (10 m/s)² = 250 J.
Correct Answer: B — 500 J
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Q. If a 5 kg object is moving with a velocity of 3 m/s, what is its kinetic energy? (2023)
-
A.
22.5 J
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B.
30 J
-
C.
45 J
-
D.
60 J
Solution
Kinetic Energy = 0.5 × mass × velocity² = 0.5 × 5 kg × (3 m/s)² = 22.5 J
Correct Answer: C — 45 J
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Q. If a 5 kg object is moving with a velocity of 3 m/s, what is its momentum? (2023)
-
A.
5 kg·m/s
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B.
10 kg·m/s
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C.
15 kg·m/s
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D.
20 kg·m/s
Solution
Momentum p = mv = 5 kg * 3 m/s = 15 kg·m/s.
Correct Answer: C — 15 kg·m/s
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Q. If a 5 kg object is subjected to a net force of 20 N, what is its acceleration? (2023)
-
A.
2 m/s²
-
B.
4 m/s²
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C.
5 m/s²
-
D.
10 m/s²
Solution
Using F = ma, we find a = F/m = 20 N / 5 kg = 4 m/s².
Correct Answer: B — 4 m/s²
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Q. If a 5Ω resistor is connected in series with a 10Ω resistor, what is the total resistance? (2022)
-
A.
15Ω
-
B.
5Ω
-
C.
10Ω
-
D.
20Ω
Solution
In series, R_eq = R1 + R2 = 5Ω + 10Ω = 15Ω.
Correct Answer: A — 15Ω
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Q. If a 5Ω resistor is connected to a 10V source, what is the power dissipated? (2023)
-
A.
2W
-
B.
5W
-
C.
10W
-
D.
20W
Solution
Power P = V²/R = (10V)² / 5Ω = 100 / 5 = 20W.
Correct Answer: C — 10W
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Q. If a 6Ω and a 3Ω resistor are connected in parallel, what is the equivalent resistance? (2022)
-
A.
2Ω
-
B.
4Ω
-
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 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
-
C.
90 degrees
-
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
-
C.
1i + 5j
-
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)
-
A.
(5/13)i + (12/13)j
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B.
(12/13)i + (5/13)j
-
C.
(5/12)i + (12/5)j
-
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
-
C.
3i + 3j + 3k
-
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?
-
A.
{2}
-
B.
{4, 6}
-
C.
{1, 2, 3}
-
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?
-
A.
{2, 3, 5, 7}
-
B.
{1, 2, 3, 4}
-
C.
{2, 4, 6, 8}
-
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?
-
A.
{0, 2, 4, 6, ...}
-
B.
{0, 3, 6, 9, ...}
-
C.
{0, 2, 3, 4, 6, 9, ...}
-
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?
-
A.
2/5
-
B.
4/10
-
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)
-
A.
Zero
-
B.
Tangential
-
C.
Centripetal
-
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?
-
A.
Centripetal acceleration
-
B.
Linear acceleration
-
C.
Angular acceleration
-
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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