Q. A jar contains 4 red, 5 green, and 6 blue marbles. If one marble is drawn at random, what is the probability that it is not green?
A.
1/3
B.
2/3
C.
1/2
D.
5/11
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Solution
Total marbles = 4 + 5 + 6 = 15. Non-green marbles = 4 + 6 = 10. Probability = 10/15 = 2/3.
Correct Answer: B — 2/3
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Q. A jar contains 4 red, 5 green, and 6 blue marbles. What is the probability of drawing a green marble?
A.
1/3
B.
5/15
C.
5/15
D.
1/5
Show solution
Solution
Total marbles = 4 + 5 + 6 = 15. Probability of green = 5/15 = 1/3.
Correct Answer: A — 1/3
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Q. A jar contains 4 red, 5 green, and 6 blue marbles. What is the probability of picking a green marble?
A.
5/15
B.
1/3
C.
1/5
D.
1/2
Show solution
Solution
The total number of marbles is 4 + 5 + 6 = 15. The probability of picking a green marble is 5/15 = 1/3.
Correct Answer: B — 1/3
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Q. A jar contains 4 red, 5 green, and 6 blue marbles. What is the probability of randomly selecting a green marble?
A.
1/3
B.
5/15
C.
5/15
D.
1/5
Show solution
Solution
The total number of marbles is 4 + 5 + 6 = 15. The probability of selecting a green marble is 5/15 = 1/3.
Correct Answer: A — 1/3
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Q. A jar contains 5 green, 3 yellow, and 2 blue marbles. If one marble is drawn at random, what is the probability that it is either green or yellow?
A.
1/2
B.
2/5
C.
4/5
D.
3/5
Show solution
Solution
Total marbles = 5 + 3 + 2 = 10. Green or yellow = 5 + 3 = 8. Probability = (Green + Yellow) / Total = 8/10 = 4/5.
Correct Answer: D — 3/5
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Q. A jar contains 5 green, 7 yellow, and 8 blue marbles. If one marble is drawn at random, what is the probability that it is either green or yellow?
A.
1/3
B.
5/20
C.
12/20
D.
1/2
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Solution
Total marbles = 5 + 7 + 8 = 20. Green or yellow = 5 + 7 = 12. Probability = 12/20 = 3/5.
Correct Answer: C — 12/20
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Q. A jar contains 5 red, 3 blue, and 2 yellow marbles. If one marble is drawn, what is the probability that it is either red or yellow?
A.
1/2
B.
2/5
C.
4/10
D.
7/10
Show solution
Solution
Total marbles = 5 + 3 + 2 = 10. Probability of red or yellow = (Number of red + Number of yellow) / Total = (5 + 2) / 10 = 7/10.
Correct Answer: D — 7/10
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Q. A jar contains 5 red, 3 blue, and 2 yellow marbles. What is the probability of drawing a yellow marble?
A.
1/5
B.
1/10
C.
1/4
D.
1/6
Show solution
Solution
Total marbles = 5 + 3 + 2 = 10. Probability of drawing a yellow marble = Number of yellow marbles / Total marbles = 2/10 = 1/5.
Correct Answer: B — 1/10
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Q. A jar contains 5 red, 3 blue, and 2 yellow marbles. What is the probability of picking a yellow marble? (2023)
A.
1/5
B.
1/10
C.
1/4
D.
1/2
Show solution
Solution
Total marbles = 5 + 3 + 2 = 10. Probability of picking a yellow marble = Number of yellow marbles / Total marbles = 2/10 = 1/5.
Correct Answer: B — 1/10
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Q. A jar contains 5 red, 3 green, and 2 blue marbles. If one marble is drawn at random, what is the probability that it is either red or green?
A.
1/2
B.
2/5
C.
4/5
D.
3/5
Show solution
Solution
Total marbles = 5 + 3 + 2 = 10. Favorable outcomes (red or green) = 5 + 3 = 8. Probability = 8/10 = 4/5.
Correct Answer: C — 4/5
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Q. A jar contains 5 red, 3 green, and 2 blue marbles. What is the probability of drawing a green marble?
A.
1/5
B.
1/4
C.
3/10
D.
1/2
Show solution
Solution
Total marbles = 5 + 3 + 2 = 10. Probability of green = 3/10.
Correct Answer: C — 3/10
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Q. A jar contains 5 red, 3 green, and 2 yellow marbles. If one marble is drawn at random, what is the probability that it is either red or green?
A.
1/2
B.
4/5
C.
2/5
D.
3/5
Show solution
Solution
The total number of marbles is 5 + 3 + 2 = 10. The number of favorable outcomes (red or green) is 5 + 3 = 8. Thus, the probability is 8/10 = 4/5.
Correct Answer: B — 4/5
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Q. A jar contains 6 green and 4 yellow marbles. What is the probability of picking a yellow marble?
A.
2/5
B.
1/2
C.
4/10
D.
3/5
Show solution
Solution
Total marbles = 6 + 4 = 10. Probability of yellow marble = 4/10 = 2/5.
Correct Answer: A — 2/5
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Q. A jar contains 7 red, 5 blue, and 8 green marbles. What is the probability of selecting a blue marble?
A.
5/20
B.
1/4
C.
1/5
D.
1/3
Show solution
Solution
Total marbles = 7 + 5 + 8 = 20. Probability of blue marble = 5/20 = 1/4.
Correct Answer: A — 5/20
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Q. A jar contains 8 red and 4 blue marbles. What is the probability of selecting a blue marble?
A.
1/3
B.
1/2
C.
1/4
D.
1/5
Show solution
Solution
Total marbles = 8 + 4 = 12. Probability of blue marble = 4/12 = 1/3.
Correct Answer: A — 1/3
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Q. A jar contains 8 red, 6 blue, and 4 green marbles. What is the probability of selecting a blue marble?
A.
1/3
B.
1/4
C.
2/5
D.
3/10
Show solution
Solution
Total marbles = 8 + 6 + 4 = 18. Probability of blue marble = 6/18 = 1/3.
Correct Answer: D — 3/10
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Q. A kite is flying at a height of 100 m. If the angle of elevation from a point on the ground to the kite is 30 degrees, how far is the point from the base of the kite?
A.
100 m
B.
200 m
C.
300 m
D.
400 m
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Solution
Using tan(30°) = height/distance, we have 1/√3 = 100/distance. Therefore, distance = 100√3 ≈ 173.2 m.
Correct Answer: B — 200 m
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Q. A kite is flying at a height of 100 meters. If the angle of depression from the kite to a point on the ground is 30 degrees, how far is the point from the point directly below the kite?
A.
50 m
B.
60 m
C.
70 m
D.
80 m
Show solution
Solution
Using tan(30°) = 100/distance, we have 1/√3 = 100/distance. Therefore, distance = 100√3 ≈ 173.21 m.
Correct Answer: A — 50 m
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Q. A kite is flying at a height of 30 m. If the angle of elevation from a point on the ground to the kite is 60 degrees, how far is the point from the base of the kite?
A.
15√3 m
B.
30 m
C.
10√3 m
D.
20 m
Show solution
Solution
Using tan(60°) = height/distance, we have distance = height/tan(60°) = 30/√3 = 15√3 m.
Correct Answer: A — 15√3 m
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Q. A kite is flying at a height of 30 meters. If the angle of elevation from a point on the ground to the kite is 45 degrees, how far is the point from the base of the kite?
A.
15 m
B.
30 m
C.
45 m
D.
60 m
Show solution
Solution
Using tan(45°) = height/distance, we have 1 = 30/distance. Therefore, distance = 30 m.
Correct Answer: B — 30 m
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Q. A kite is flying at a height of 50 m. If the angle of elevation from a point on the ground to the kite is 60 degrees, how far is the point from the base of the kite? (2021)
A.
25 m
B.
50 m
C.
75 m
D.
100 m
Show solution
Solution
Distance = height / tan(angle) = 50 / tan(60) = 50 / √3 ≈ 25 m.
Correct Answer: A — 25 m
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Q. A kite is flying at a height of 50 m. If the angle of elevation from a point on the ground to the kite is 45 degrees, how far is the point from the base of the kite? (2020)
A.
50 m
B.
70 m
C.
100 m
D.
30 m
Show solution
Solution
Using tan(45) = 1, distance = height = 50 m.
Correct Answer: A — 50 m
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Q. A kite is flying at a height of 50 meters. If the angle of elevation from a point on the ground to the kite is 30 degrees, how far is the point from the base of the kite?
A.
50√3 meters
B.
25√3 meters
C.
100 meters
D.
75 meters
Show solution
Solution
Distance = height / tan(angle) = 50 / (1/√3) = 50√3 meters.
Correct Answer: B — 25√3 meters
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Q. A ladder 10 m long reaches a window 8 m above the ground. What is the angle of elevation of the ladder from the ground?
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
75 degrees
Show solution
Solution
Using sin(θ) = opposite/hypotenuse, we have sin(θ) = 8/10. Therefore, θ = sin⁻¹(0.8) ≈ 53.13 degrees.
Correct Answer: C — 60 degrees
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Q. A ladder 10 m long reaches a window 8 m high. What is the angle of elevation of the ladder from the ground? (2019)
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
75 degrees
Show solution
Solution
Using sin(θ) = opposite/hypotenuse, sin(θ) = 8/10, θ = sin⁻¹(0.8) ≈ 53.13 degrees.
Correct Answer: C — 60 degrees
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Q. A ladder 15 m long reaches a window 12 m above the ground. What is the angle of elevation of the ladder from the ground? (2019)
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
75 degrees
Show solution
Solution
Using sin(θ) = opposite/hypotenuse = 12/15, θ = sin⁻¹(0.8) ≈ 53.13 degrees, which is closest to 60 degrees.
Correct Answer: C — 60 degrees
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Q. A ladder 15 meters long reaches a window 12 meters above the ground. What is the angle of elevation of the ladder from the ground?
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
75 degrees
Show solution
Solution
Using sin(θ) = opposite/hypotenuse, we have sin(θ) = 12/15. Therefore, θ = sin⁻¹(0.8) ≈ 53.13 degrees.
Correct Answer: C — 60 degrees
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Q. A ladder is leaning against a wall. The foot of the ladder is 12 meters away from the wall, and the angle between the ladder and the ground is 60 degrees. What is the height at which the ladder touches the wall?
A.
12√3 m
B.
6 m
C.
12 m
D.
24 m
Show solution
Solution
Using sin(60°) = height/hypotenuse, we find the height = 12 * tan(60°) = 12√3 m.
Correct Answer: A — 12√3 m
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Q. A ladder leans against a wall and is in equilibrium. What forces are acting on the ladder?
A.
Weight, normal force from the ground, and friction
B.
Only weight and normal force
C.
Only weight and friction
D.
Only normal force and friction
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Solution
The ladder experiences weight, a normal force from the ground, and friction at the base.
Correct Answer: A — Weight, normal force from the ground, and friction
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Q. A length is measured as 100 m with a possible error of 1 m. What is the percentage error?
A.
1%
B.
0.5%
C.
2%
D.
0.1%
Show solution
Solution
Percentage error = (Absolute error / True value) * 100 = (1 / 100) * 100 = 1%.
Correct Answer: A — 1%
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