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Q. A boat can travel at 10 km/h in still water. If the current of the river is 2 km/h, what is the speed of the boat downstream?
A.
8 km/h
B.
10 km/h
C.
12 km/h
D.
14 km/h
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Solution
Speed downstream = speed of boat + speed of current = 10 + 2 = 12 km/h.
Correct Answer: C — 12 km/h
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Q. A boat can travel at 12 km/h in still water. If it is going downstream in a river flowing at 4 km/h, what is the speed of the boat relative to the riverbank?
A.
8 km/h
B.
12 km/h
C.
16 km/h
D.
20 km/h
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Solution
Speed of boat downstream = Speed of boat + Speed of river = 12 km/h + 4 km/h = 16 km/h.
Correct Answer: C — 16 km/h
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Q. A boat can travel at 12 km/h in still water. If it is moving downstream in a river flowing at 4 km/h, what is the speed of the boat relative to the riverbank?
A.
8 km/h
B.
12 km/h
C.
16 km/h
D.
4 km/h
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Solution
Speed of boat relative to riverbank = Speed of boat + Speed of river = 12 km/h + 4 km/h = 16 km/h.
Correct Answer: C — 16 km/h
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Q. A boat can travel at 12 km/h in still water. If it travels downstream in a river flowing at 3 km/h, what is its speed relative to the riverbank?
A.
9 km/h
B.
12 km/h
C.
15 km/h
D.
18 km/h
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Solution
Speed downstream = Speed of boat + Speed of river = 12 km/h + 3 km/h = 15 km/h.
Correct Answer: C — 15 km/h
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Q. A boat can travel at 15 km/h in still water. If it takes 2 hours to go upstream and 1 hour to return downstream, what is the speed of the current?
A.
3 km/h
B.
4 km/h
C.
5 km/h
D.
6 km/h
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Solution
Let speed of current = x. Upstream speed = 15 - x, Downstream speed = 15 + x. Distance = speed × time. 2(15 - x) = 1(15 + x). Solving gives x = 5 km/h.
Correct Answer: C — 5 km/h
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Q. A boat can travel at a speed of 10 km/h in still water. If the speed of the current is 2 km/h, what is the speed of the boat downstream?
A.
8 km/h
B.
10 km/h
C.
12 km/h
D.
14 km/h
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Solution
Speed downstream = speed of boat + speed of current = 10 + 2 = 12 km/h.
Correct Answer: C — 12 km/h
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Q. A boat is moving upstream at 10 km/h in a river that flows downstream at 5 km/h. What is the speed of the boat relative to the riverbank?
A.
5 km/h
B.
10 km/h
C.
15 km/h
D.
20 km/h
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Solution
Speed of boat relative to riverbank = Speed of boat - Speed of river = 10 km/h - 5 km/h = 5 km/h.
Correct Answer: A — 5 km/h
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Q. A boat is moving upstream at 10 km/h in a river that flows downstream at 5 km/h. What is the speed of the boat relative to the ground?
A.
5 km/h
B.
10 km/h
C.
15 km/h
D.
20 km/h
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Solution
Speed of boat relative to ground = Speed of boat - Speed of river = 10 km/h - 5 km/h = 5 km/h.
Correct Answer: A — 5 km/h
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Q. A boat travels 30 km downstream in 2 hours. What is the speed of the boat in still water if the speed of the current is 5 km/h?
A.
10 km/h
B.
15 km/h
C.
20 km/h
D.
25 km/h
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Solution
Speed downstream = distance/time = 30/2 = 15 km/h. Speed of boat in still water = speed downstream - speed of current = 15 - 5 = 10 km/h.
Correct Answer: B — 15 km/h
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Q. A boat travels 30 km downstream in 2 hours. What is the speed of the current if the speed of the boat in still water is 15 km/h?
A.
2.5 km/h
B.
5 km/h
C.
7.5 km/h
D.
10 km/h
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Solution
Speed downstream = distance/time = 30/2 = 15 km/h. Speed of current = speed downstream - speed of boat = 15 - 15 = 0 km/h.
Correct Answer: B — 5 km/h
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Q. A boat travels across a river with a speed of 4 m/s relative to the water. If the river flows at 3 m/s, what is the resultant speed of the boat relative to the riverbank?
A.
3 m/s
B.
4 m/s
C.
5 m/s
D.
7 m/s
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Solution
Resultant speed = √(4^2 + 3^2) = √(16 + 9) = √25 = 5 m/s.
Correct Answer: C — 5 m/s
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Q. A boat travels across a river with a speed of 8 km/h relative to the water. If the river flows at 6 km/h, what is the speed of the boat relative to the riverbank?
A.
8 km/h
B.
10 km/h
C.
14 km/h
D.
6 km/h
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Solution
Speed of boat relative to riverbank = √(8^2 + 6^2) = √(64 + 36) = √100 = 10 km/h.
Correct Answer: B — 10 km/h
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Q. A boat travels upstream at 4 km/h and downstream at 6 km/h. What is the speed of the current?
A.
1 km/h
B.
2 km/h
C.
3 km/h
D.
4 km/h
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Solution
Let the speed of the current be x. Then, 4 + x = 6 - x. Solving gives x = 2 km/h.
Correct Answer: B — 2 km/h
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Q. A body is moving in a circular path of radius 4 m with a constant speed of 8 m/s. What is the net force acting on the body if its mass is 2 kg?
A.
4 N
B.
8 N
C.
16 N
D.
32 N
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Solution
Centripetal force F = m(v²/r) = 2(8²/4) = 32 N.
Correct Answer: C — 16 N
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Q. A body is thrown vertically upwards with a speed of 20 m/s. How high will it rise before coming to rest?
A.
20 m
B.
40 m
C.
10 m
D.
30 m
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Solution
Using the formula h = v²/(2g), where g = 10 m/s², h = (20)²/(2*10) = 20 m.
Correct Answer: B — 40 m
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Q. A body is thrown vertically upwards with a speed of 20 m/s. How high will it rise? (g = 10 m/s²)
A.
20 m
B.
40 m
C.
30 m
D.
10 m
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Solution
Using v² = u² - 2gh, 0 = (20)² - 2*10*h, h = 20 m.
Correct Answer: B — 40 m
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Q. A body moves in a straight line with a uniform acceleration of 2 m/s². If its initial velocity is 5 m/s, what will be its velocity after 10 seconds?
A.
25 m/s
B.
20 m/s
C.
15 m/s
D.
10 m/s
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Solution
Final velocity = initial velocity + acceleration * time = 5 + 2 * 10 = 25 m/s.
Correct Answer: A — 25 m/s
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Q. A body moves in a straight line with an initial velocity of 10 m/s and accelerates at 2 m/s². What will be its velocity after 5 seconds?
A.
20 m/s
B.
25 m/s
C.
30 m/s
D.
35 m/s
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Solution
Final velocity (v) = u + at = 10 + 2*5 = 20 m/s.
Correct Answer: C — 30 m/s
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Q. A body moving with a uniform speed of 10 m/s covers a distance of 100 m. How much time does it take?
A.
5 s
B.
10 s
C.
15 s
D.
20 s
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Solution
Time = distance / speed = 100 m / 10 m/s = 10 s.
Correct Answer: B — 10 s
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Q. A body of mass 2 kg is moving with a velocity of 3 m/s. What is its kinetic energy?
A.
9 J
B.
6 J
C.
18 J
D.
12 J
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Solution
Kinetic Energy (KE) = 1/2 * m * v^2 = 1/2 * 2 * (3^2) = 9 J
Correct Answer: A — 9 J
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Q. A box contains 10 balls, 4 of which are red and 6 are blue. If one ball is drawn, what is the probability that it is blue?
A.
2/5
B.
3/5
C.
4/10
D.
6/10
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Solution
The probability of drawing a blue ball is 6/10 = 3/5.
Correct Answer: B — 3/5
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Q. A box contains 10 balls, 4 of which are red and 6 are blue. If one ball is drawn at random, what is the probability that it is not blue?
A.
2/5
B.
3/5
C.
4/10
D.
1/5
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Solution
The probability of not drawing a blue ball = Number of red balls / Total balls = 4/10 = 2/5.
Correct Answer: A — 2/5
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Q. A box contains 10 balls, 4 of which are white and the rest are black. If one ball is drawn at random, what is the probability that it is not black?
A.
1/5
B.
2/5
C.
3/5
D.
4/5
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Solution
Total balls = 10. Non-black balls = 4 (white). Probability = 4/10 = 2/5.
Correct Answer: D — 4/5
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Q. A box contains 10 balls, 4 of which are white and the rest are black. If one ball is drawn at random, what is the probability that it is not white?
A.
2/5
B.
3/5
C.
4/5
D.
1/5
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Solution
The total number of balls is 10. The number of non-white balls is 10 - 4 = 6. Thus, the probability of drawing a non-white ball is 6/10 = 3/5.
Correct Answer: B — 3/5
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Q. A box contains 10 balls, 4 red and 6 green. If one ball is drawn at random, what is the probability that it is green given that it is not red?
A.
1/2
B.
3/5
C.
2/5
D.
4/5
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Solution
If the ball is not red, it must be green. Therefore, P(Green | Not Red) = 1.
Correct Answer: B — 3/5
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Q. A box contains 4 red, 3 green, and 2 blue balls. If a ball is drawn and it is green, what is the probability that the next ball drawn is red?
A.
4/9
B.
2/9
C.
1/3
D.
1/4
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Solution
After drawing a green ball, there are 4 red, 2 green, and 2 blue balls left. The probability of drawing a red ball next is 4/8 = 1/2.
Correct Answer: A — 4/9
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Q. A box contains 4 red, 3 green, and 2 blue marbles. If a marble is drawn and it is green, what is the probability that the next marble drawn is red?
A.
0.4
B.
0.5
C.
0.6
D.
0.3
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Solution
After drawing a green marble, there are 4 red, 2 green, and 2 blue marbles left. The probability of drawing a red marble next is 4/(4+2+2) = 4/8 = 0.5.
Correct Answer: A — 0.4
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Q. A box contains 4 red, 3 green, and 5 blue balls. If a ball is drawn and it is blue, what is the probability that the next ball drawn is red?
A.
4/11
B.
3/11
C.
5/11
D.
1/3
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Solution
After drawing a blue ball, there are 4 red, 3 green, and 4 blue left. The probability of drawing a red ball next is 4/11.
Correct Answer: A — 4/11
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Q. A box contains 4 white and 6 black balls. If one ball is drawn and it is black, what is the probability that the next ball drawn is also black?
A.
1/2
B.
1/3
C.
1/5
D.
2/5
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Solution
After drawing one black ball, there are 5 black and 4 white balls left. The probability of drawing another black ball is 5/9.
Correct Answer: D — 2/5
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Q. A box contains 4 white and 6 black balls. If one ball is drawn at random, what is the probability that it is black given that it is not white?
A.
2/5
B.
3/5
C.
4/5
D.
1/5
Show solution
Solution
The total number of balls is 10. The number of favorable outcomes (black balls) is 6. The probability that the ball is black given that it is not white is P(Black | Not White) = 6/6 = 1.
Correct Answer: C — 4/5
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