Q. What is the length of an arc of a circle with a radius of 10 cm and a central angle of 60 degrees? (2021) 2021
A.
10.47 cm
B.
15.71 cm
C.
20.94 cm
D.
25.13 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 10 = 10.47 cm.
Correct Answer:
A
— 10.47 cm
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Q. What is the length of an arc of a circle with a radius of 10 cm and a central angle of 60 degrees? (2021)
A.
10.47 cm
B.
12.57 cm
C.
15.71 cm
D.
20.94 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 10 = 10.47 cm.
Correct Answer:
B
— 12.57 cm
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Q. What is the length of an arc of a circle with a radius of 4 cm and a central angle of 90 degrees? (2021)
A.
2π cm
B.
4π cm
C.
π cm
D.
8 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (90/360) * 2π * 4 = 2π cm.
Correct Answer:
A
— 2π cm
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Q. What is the length of an arc of a circle with a radius of 5 cm and a central angle of 60 degrees? (2020)
A.
5.24 cm
B.
3.14 cm
C.
5.00 cm
D.
10.47 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2π(5) = (1/6) * 10π ≈ 5.24 cm.
Correct Answer:
A
— 5.24 cm
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Q. What is the length of an arc of a circle with a radius of 6 cm and a central angle of 60 degrees? (Use π = 3.14) (2020)
A.
6.28 cm
B.
3.14 cm
C.
12.56 cm
D.
9.42 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 6 cm = 6.28 cm.
Correct Answer:
A
— 6.28 cm
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Q. What is the length of an arc of a circle with radius 5 cm and angle 60 degrees? (2020)
A.
5.24 cm
B.
3.14 cm
C.
5.00 cm
D.
6.00 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2 * π * 5 = 5.24 cm.
Correct Answer:
A
— 5.24 cm
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Q. What is the length of the diagonal of a cuboid with dimensions 2, 3, and 6? (2022)
A.
√49
B.
√45
C.
√36
D.
√50
Show solution
Solution
Diagonal = √(2² + 3² + 6²) = √(4 + 9 + 36) = √49 = 7.
Correct Answer:
A
— √49
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Q. What is the length of the diagonal of a rectangle with vertices at (0, 0), (0, 3), (4, 0), and (4, 3)? (2022)
Show solution
Solution
Diagonal = √[(4-0)² + (3-0)²] = √[16 + 9] = √25 = 5.
Correct Answer:
A
— 5
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Q. What is the length of the diagonal of a rectangle with vertices at (0, 0), (4, 0), (4, 3), and (0, 3)? (2021)
Show solution
Solution
Length of diagonal = √[(4-0)² + (3-0)²] = √[16 + 9] = √25 = 5.
Correct Answer:
A
— 5
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Q. What is the length of the diagonal of a rectangle with vertices at (1, 1), (1, 4), (5, 1), and (5, 4)? (2021)
Show solution
Solution
Diagonal length = √[(5-1)² + (4-1)²] = √[16 + 9] = √25 = 5.
Correct Answer:
B
— 5
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Q. What is the magnetic field at a distance r from a long straight wire carrying current I? (2020)
A.
μ₀I/(2πr)
B.
μ₀I/(4πr)
C.
μ₀I/(πr)
D.
μ₀I/(8πr)
Show solution
Solution
The magnetic field around a long straight wire is given by B = (μ₀I)/(2πr).
Correct Answer:
A
— μ₀I/(2πr)
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Q. What is the magnetic field at the center of a circular loop carrying current? (2022)
A.
Zero
B.
Directly proportional to current
C.
Inversely proportional to radius
D.
Both A and B
Show solution
Solution
The magnetic field at the center of a circular loop carrying current is directly proportional to the current and inversely proportional to the radius.
Correct Answer:
B
— Directly proportional to current
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Q. What is the magnetic field due to a straight current-carrying conductor at a distance 'r' from it? (2020)
A.
μ₀I/2πr
B.
μ₀I/4πr²
C.
μ₀I/2r
D.
μ₀I/πr
Show solution
Solution
The magnetic field due to a straight current-carrying conductor is given by B = μ₀I/2πr.
Correct Answer:
A
— μ₀I/2πr
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Q. What is the magnetic field inside a long solenoid when it carries a current? (2023)
A.
Zero
B.
Uniform and directed along the axis
C.
Varies with distance
D.
Depends on the temperature
Show solution
Solution
The magnetic field inside a long solenoid is uniform and directed along the axis of the solenoid when it carries a current.
Correct Answer:
B
— Uniform and directed along the axis
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Q. What is the magnetic field inside a long solenoid when the current is flowing through it? (2023)
A.
Zero
B.
Uniform and parallel
C.
Concentric circles
D.
Radial
Show solution
Solution
The magnetic field inside a long solenoid is uniform and parallel to the axis of the solenoid.
Correct Answer:
B
— Uniform and parallel
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Q. What is the magnetic field inside a long solenoid when the current is steady? (2023)
A.
Zero
B.
Uniform and parallel to the axis
C.
Varies with distance
D.
Depends on the temperature
Show solution
Solution
The magnetic field inside a long solenoid is uniform and parallel to the axis of the solenoid when the current is steady.
Correct Answer:
B
— Uniform and parallel to the axis
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Q. What is the magnetic field inside a long solenoid? (2023)
A.
Zero
B.
Uniform and parallel
C.
Concentric circles
D.
Decreasing
Show solution
Solution
The magnetic field inside a long solenoid is uniform and parallel to the axis of the solenoid.
Correct Answer:
B
— Uniform and parallel
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Q. What is the magnetic field inside a toroidal solenoid? (2023)
A.
Zero
B.
Uniform and non-zero
C.
Varies with position
D.
Depends on the current only
Show solution
Solution
The magnetic field inside a toroidal solenoid is uniform and non-zero, and it is given by B = (μ₀NI)/(2πr), where N is the number of turns, I is the current, and r is the distance from the center.
Correct Answer:
B
— Uniform and non-zero
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Q. What is the magnetic field strength at a distance 'r' from a long straight conductor carrying current 'I'? (2020)
A.
μ₀I/2πr
B.
μ₀I/4πr
C.
2μ₀I/πr
D.
μ₀I/πr
Show solution
Solution
The magnetic field strength (B) at a distance 'r' from a long straight conductor is given by the formula B = μ₀I/2πr.
Correct Answer:
A
— μ₀I/2πr
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Q. What is the magnetic moment of a circular loop of radius r carrying a current I? (2021)
A.
πr²I
B.
2πrI
C.
Ir²
D.
πrI
Show solution
Solution
The magnetic moment (μ) of a circular loop is given by μ = I × A, where A is the area of the loop. For a circular loop, A = πr², thus μ = I × πr² = πr²I.
Correct Answer:
A
— πr²I
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Q. What is the magnification produced by a concave mirror if the object distance is 10 cm and the image distance is 5 cm? (2019)
Show solution
Solution
Magnification (m) = -v/u. Here, v = -5 cm and u = -10 cm, so m = -(-5)/(-10) = 2.
Correct Answer:
C
— 2
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Q. What is the magnification produced by a concave mirror when the object is placed at the focus? (2019)
A.
1
B.
0
C.
Infinity
D.
Less than 1
Show solution
Solution
When the object is placed at the focus of a concave mirror, the image is formed at infinity, leading to infinite magnification.
Correct Answer:
C
— Infinity
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Q. What is the main advantage of asexual reproduction? (2023)
A.
Genetic diversity
B.
Faster population growth
C.
Requires two parents
D.
Involves gametes
Show solution
Solution
Asexual reproduction allows for faster population growth since it does not require finding a mate.
Correct Answer:
B
— Faster population growth
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Q. What is the main advantage of sexual reproduction? (2023)
A.
Faster reproduction
B.
Genetic variation
C.
Less energy required
D.
No need for a mate
Show solution
Solution
Sexual reproduction promotes genetic variation, which is beneficial for adaptation and evolution.
Correct Answer:
B
— Genetic variation
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Q. What is the main advantage of using biopesticides? (2022)
A.
They are more effective than chemical pesticides
B.
They are environmentally friendly
C.
They are cheaper to produce
D.
They have a longer shelf life
Show solution
Solution
Biopesticides are derived from natural materials and are considered environmentally friendly compared to chemical pesticides.
Correct Answer:
B
— They are environmentally friendly
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Q. What is the main advantage of using CRISPR technology in genetic engineering? (2021)
A.
High precision
B.
Low cost
C.
Speed of modification
D.
All of the above
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Solution
CRISPR technology offers high precision, low cost, and speed of modification, making it a powerful tool in genetic engineering.
Correct Answer:
D
— All of the above
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Q. What is the main advantage of using genetically modified organisms (GMOs) in agriculture? (2021)
A.
Higher nutritional value
B.
Increased resistance to diseases
C.
Lower production costs
D.
All of the above
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Solution
GMOs can provide higher nutritional value, increased resistance to diseases, and lower production costs.
Correct Answer:
D
— All of the above
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Q. What is the main advantage of using genetically modified organisms (GMOs) in food production? (2020)
A.
Higher prices
B.
Longer shelf life
C.
Increased labor costs
D.
More complex farming techniques
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Solution
GMOs can be engineered to have longer shelf lives, reducing food waste and improving food security.
Correct Answer:
B
— Longer shelf life
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Q. What is the main advantage of using genetically modified organisms in food production? (2021)
A.
Longer shelf life
B.
Higher nutritional value
C.
Resistance to pests and diseases
D.
All of the above
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Solution
Genetically modified organisms can provide multiple advantages including longer shelf life, higher nutritional value, and resistance to pests and diseases.
Correct Answer:
D
— All of the above
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Q. What is the main advantage of using hormonal contraceptives? (2023)
A.
They are 100% effective
B.
They can regulate menstrual cycles
C.
They are inexpensive
D.
They require no medical consultation
Show solution
Solution
Hormonal contraceptives can help regulate menstrual cycles in addition to preventing pregnancy.
Correct Answer:
B
— They can regulate menstrual cycles
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