Q. A rectangle has a length that is twice its width. If the perimeter is 48 cm, what is the area of the rectangle?
A.
96 cm²
B.
144 cm²
C.
192 cm²
D.
256 cm²
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Solution
Let width = w, then length = 2w. Perimeter = 2(l + w) = 48. Solving gives w = 8, l = 16. Area = l * w = 16 * 8 = 128 cm².
Correct Answer: B — 144 cm²
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Q. A rectangle has a length that is twice its width. If the perimeter of the rectangle is 48 cm, what is the width?
A.
8 cm
B.
12 cm
C.
10 cm
D.
6 cm
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Solution
Let the width be w. Then the length is 2w. The perimeter P = 2(length + width) = 2(2w + w) = 6w. Setting this equal to 48 gives 6w = 48, so w = 8 cm.
Correct Answer: B — 12 cm
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Q. A rectangle has a perimeter of 40 cm. What dimensions maximize the area? (2022)
A.
10 cm by 10 cm
B.
8 cm by 12 cm
C.
5 cm by 15 cm
D.
6 cm by 14 cm
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Solution
For maximum area, the rectangle should be a square. Thus, each side = 40/4 = 10 cm.
Correct Answer: A — 10 cm by 10 cm
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Q. A rectangle has a perimeter of 40 cm. What dimensions will maximize the area? (2022)
A.
10 cm by 10 cm
B.
15 cm by 5 cm
C.
20 cm by 0 cm
D.
12 cm by 8 cm
Show solution
Solution
For maximum area, the rectangle should be a square. Thus, each side = 40/4 = 10 cm.
Correct Answer: A — 10 cm by 10 cm
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Q. A rectangle has a perimeter of 40 units. What dimensions maximize the area? (2022) 2022
A.
10, 10
B.
5, 15
C.
8, 12
D.
6, 14
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Solution
For maximum area, the rectangle should be a square. Thus, each side = 40/4 = 10.
Correct Answer: A — 10, 10
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Q. A rectangle has a perimeter of 40 units. What dimensions maximize the area? (2022)
A.
10, 10
B.
8, 12
C.
6, 14
D.
5, 15
Show solution
Solution
For a fixed perimeter, the area is maximized when the rectangle is a square. Thus, side = 10 units.
Correct Answer: A — 10, 10
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Q. A rectangle has an area of 48 square meters and a length of 12 meters. What is the width?
A.
4 meters
B.
6 meters
C.
8 meters
D.
10 meters
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Solution
Area = length × width. Thus, 48 = 12 × width, giving width = 48/12 = 4 meters.
Correct Answer: B — 6 meters
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Q. A rectangle has an area of 60 square meters and a length of 12 meters. What is the width?
A.
5 meters
B.
6 meters
C.
7 meters
D.
8 meters
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Solution
Area = length × width. Thus, 60 = 12 × width, giving width = 60/12 = 5 meters.
Correct Answer: B — 6 meters
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Q. A rectangular field is 50 meters long and 30 meters wide. If a fence is built around it, what is the total length of the fence?
A.
160 m
B.
140 m
C.
120 m
D.
180 m
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Solution
Perimeter = 2(length + width) = 2(50 + 30) = 2 × 80 = 160 m.
Correct Answer: A — 160 m
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Q. A rectangular garden is 10 m long and 6 m wide. If a path of width 1 m is built around it, what is the area of the path? (2023)
A.
32 m²
B.
36 m²
C.
40 m²
D.
44 m²
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Solution
Area of the garden = 10 * 6 = 60 m². Area including the path = (10 + 2) * (6 + 2) = 12 * 8 = 96 m². Area of the path = 96 - 60 = 36 m².
Correct Answer: B — 36 m²
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Q. A rectangular garden is 30 meters long and 20 meters wide. If a path of 1 meter width is built around it, what is the area of the path?
A.
80 m²
B.
100 m²
C.
120 m²
D.
140 m²
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Solution
Area of the garden = 30 × 20 = 600 m². Area including the path = (30 + 2) × (20 + 2) = 32 × 22 = 704 m². Area of the path = 704 - 600 = 104 m².
Correct Answer: B — 100 m²
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Q. A rectangular plate of mass M and dimensions a x b is rotated about an axis along one of its edges. What is its moment of inertia?
A.
1/3 Ma^2
B.
1/12 Ma^2 + 1/3 Mb^2
C.
1/2 Ma^2
D.
1/4 Ma^2 + 1/3 Mb^2
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Solution
The moment of inertia of a rectangular plate about an edge is I = 1/12 Ma^2 + 1/3 Mb^2.
Correct Answer: B — 1/12 Ma^2 + 1/3 Mb^2
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Q. A rectangular prism has dimensions 3 cm, 4 cm, and 5 cm. What is its volume?
A.
60 cm³
B.
12 cm³
C.
15 cm³
D.
20 cm³
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Solution
Volume of a rectangular prism = length × width × height = 3 × 4 × 5 = 60 cm³.
Correct Answer: A — 60 cm³
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Q. A rectangular prism has dimensions 3 m, 4 m, and 5 m. What is its surface area?
A.
47 m²
B.
60 m²
C.
70 m²
D.
80 m²
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Solution
The surface area of a rectangular prism is given by SA = 2(lw + lh + wh). Here, SA = 2(3*4 + 3*5 + 4*5) = 2(12 + 15 + 20) = 2(47) = 94 m².
Correct Answer: B — 60 m²
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Q. A rectangular prism has dimensions 4 m, 3 m, and 5 m. What is its surface area?
A.
47 m²
B.
60 m²
C.
70 m²
D.
80 m²
Show solution
Solution
The surface area of a rectangular prism is given by SA = 2(lw + lh + wh). Here, SA = 2(4*3 + 4*5 + 3*5) = 2(12 + 20 + 15) = 2(47) = 94 m².
Correct Answer: B — 60 m²
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Q. A refrigerator operates between 250 K and 300 K. What is its coefficient of performance (COP)? (2022)
A.
1.2
B.
2.0
C.
3.0
D.
4.0
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Solution
COP = T_cold / (T_hot - T_cold) = 250 K / (300 K - 250 K) = 250 / 50 = 5.0.
Correct Answer: C — 3.0
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Q. A refrigerator removes heat from the inside at a rate of 200 J/s and expels it to the surroundings at a rate of 250 J/s. What is the coefficient of performance (COP) of the refrigerator? (2023)
A.
0.8
B.
1.25
C.
1.5
D.
2.0
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Solution
COP = Q_in / W = 200 J/s / (250 J/s - 200 J/s) = 200 / 50 = 4.
Correct Answer: B — 1.25
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Q. A refrigerator removes heat from the inside at a rate of 200 J/s and expels it to the outside at a rate of 250 J/s. What is the coefficient of performance (COP) of the refrigerator? (2022)
A.
0.8
B.
1.25
C.
1.5
D.
2.0
Show solution
Solution
COP = Q_c / W = 200 J/s / (250 J/s - 200 J/s) = 200 / 50 = 4.
Correct Answer: B — 1.25
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Q. A refrigerator removes heat from the interior at a rate of 200 W. If the coefficient of performance (COP) is 4, what is the power consumed by the refrigerator?
A.
50 W
B.
100 W
C.
200 W
D.
800 W
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Solution
COP = Qc/W, thus W = Qc/COP = 200 W / 4 = 50 W.
Correct Answer: B — 100 W
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Q. A report states that companies with flexible work hours have higher employee satisfaction. What can be inferred from this report?
A.
Flexible work hours guarantee employee satisfaction.
B.
All companies should adopt flexible work hours.
C.
There is a positive relationship between work hours flexibility and employee satisfaction.
D.
Employee satisfaction is unrelated to work hours.
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Solution
The report indicates a positive relationship between flexible work hours and employee satisfaction, but it does not guarantee satisfaction or suggest that all companies should adopt this policy.
Correct Answer: C — There is a positive relationship between work hours flexibility and employee satisfaction.
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Q. A report states that increased screen time is linked to higher rates of anxiety among teenagers. What can be inferred from this report?
A.
All teenagers with high screen time experience anxiety.
B.
Screen time is the only factor contributing to teenage anxiety.
C.
There is a potential relationship between screen time and anxiety.
D.
Teenagers should reduce screen time to avoid anxiety.
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Solution
The report indicates a link but does not claim that screen time is the sole cause of anxiety.
Correct Answer: C — There is a potential relationship between screen time and anxiety.
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Q. A resistor of 10 ohms is connected to a 20V battery. What is the current flowing through the resistor?
A.
0.5 A
B.
1 A
C.
2 A
D.
5 A
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Solution
Using Ohm's Law, I = V/R = 20V / 10Ω = 2 A.
Correct Answer: C — 2 A
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Q. A resistor of 10 Ω and a capacitor of 100 μF are connected in series to an AC source of frequency 50 Hz. What is the capacitive reactance? (2020)
A.
3.18 Ω
B.
31.8 Ω
C.
0.318 Ω
D.
318 Ω
Show solution
Solution
Capacitive reactance Xc = 1/(2πfC) = 1/(2π(50)(100 × 10^-6)) ≈ 3.18 Ω.
Correct Answer: A — 3.18 Ω
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Q. A resistor of 10Ω is connected across a 20V battery. What is the power consumed by the resistor? (2021)
A.
40W
B.
20W
C.
10W
D.
5W
Show solution
Solution
Power (P) is given by P = V^2/R = 20V^2 / 10Ω = 400W / 10 = 40W.
Correct Answer: A — 40W
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Q. A resistor of 10Ω is connected to a 20V battery. What is the power consumed by the resistor? (2021)
A.
40W
B.
20W
C.
10W
D.
2W
Show solution
Solution
Power (P) is given by P = V^2/R = (20V)^2 / 10Ω = 400/10 = 40W.
Correct Answer: A — 40W
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Q. A resistor of 10Ω is connected to a 20V power supply. What is the power consumed by the resistor? (2021)
A.
40W
B.
20W
C.
10W
D.
2W
Show solution
Solution
Power (P) is given by P = V^2/R = (20V)^2 / 10Ω = 400/10 = 40W.
Correct Answer: A — 40W
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Q. A retailer bought a bicycle for $300 and sold it for $360. What is the profit percentage?
A.
15%
B.
20%
C.
25%
D.
30%
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Solution
Profit = Selling Price - Cost Price = $360 - $300 = $60. Profit Percentage = (Profit / Cost Price) * 100 = ($60 / $300) * 100 = 20%.
Correct Answer: B — 20%
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Q. A retailer buys a bicycle for $300 and sells it for $360. What is the profit percentage? (2023)
A.
15%
B.
20%
C.
25%
D.
30%
Show solution
Solution
Profit = Selling Price - Cost Price = 360 - 300 = 60. Profit Percentage = (Profit/Cost Price) * 100 = (60/300) * 100 = 20%.
Correct Answer: B — 20%
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Q. A retailer buys a watch for $120 and sells it at a profit of 15%. What is the selling price?
A.
$138
B.
$140
C.
$144
D.
$150
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Solution
The selling price is calculated as $120 + (15% of $120) = $120 + $18 = $138.
Correct Answer: C — $144
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Q. A retailer buys a watch for $150 and sells it at a profit of 25%. What is the selling price? (2023)
A.
$175
B.
$180
C.
$187.5
D.
$200
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Solution
Selling Price = Cost Price + Profit = 150 + (25% of 150) = 150 + 37.5 = $187.5.
Correct Answer: C — $187.5
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