Undergraduate
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
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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
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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 radius 5 cm and angle 60 degrees? (2020)
A.
5.24 cm
B.
3.14 cm
C.
5.00 cm
D.
6.00 cm
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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
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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)
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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)
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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)
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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 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
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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
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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
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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
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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
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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
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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
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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)
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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 main advantage of sexual reproduction? (2023)
A.
Faster reproduction
B.
Genetic variation
C.
Less energy required
D.
No need for a mate
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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
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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 transgenic animals in research? (2021)
A.
Increased lifespan
B.
Disease modeling
C.
Higher reproduction rate
D.
Better growth rate
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Solution
Transgenic animals are primarily used in research for disease modeling, helping scientists understand human diseases.
Correct Answer: B — Disease modeling
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Q. What is the main assumption of the quantum mechanical model of the atom? (2023)
A.
Electrons are in fixed orbits
B.
Electrons have wave-like properties
C.
Electrons are stationary
D.
Electrons have no mass
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Solution
The quantum mechanical model assumes that electrons exhibit both particle and wave-like properties.
Correct Answer: B — Electrons have wave-like properties
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Q. What is the main characteristic of a molecular solid? (2021)
A.
High melting point
B.
Low melting point
C.
Good electrical conductivity
D.
High density
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Solution
Molecular solids generally have low melting points due to weak intermolecular forces.
Correct Answer: B — Low melting point
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Q. What is the main characteristic of amorphous solids? (2023)
A.
Long-range order
B.
Short-range order
C.
Definite melting point
D.
Anisotropic
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Solution
Amorphous solids lack long-range order, which distinguishes them from crystalline solids.
Correct Answer: B — Short-range order
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Q. What is the main characteristic of elastomers?
A.
Brittle
B.
Elastic
C.
Rigid
D.
Transparent
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Solution
Elastomers are characterized by their elastic properties, allowing them to stretch and return to their original shape.
Correct Answer: B — Elastic
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Q. What is the main characteristic of mammals? (2021)
A.
Cold-blooded
B.
Feathers
C.
Hair or fur
D.
Scales
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Solution
Mammals are characterized by the presence of hair or fur and mammary glands that produce milk.
Correct Answer: C — Hair or fur
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Q. What is the main characteristic of the phylum Mollusca? (2021)
A.
Jointed legs
B.
Soft-bodied with a hard shell
C.
Radial symmetry
D.
Exoskeleton made of chitin
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Solution
Mollusca are primarily soft-bodied animals, many of which have a hard shell for protection.
Correct Answer: B — Soft-bodied with a hard shell
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Q. What is the main characteristic of the phylum Porifera? (2021)
A.
Presence of a true coelom
B.
Body symmetry
C.
Presence of pores
D.
Presence of a notochord
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Solution
Porifera, or sponges, are characterized by the presence of numerous pores (ostia) in their body.
Correct Answer: C — Presence of pores
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Q. What is the main component of natural rubber?
A.
Polyisoprene
B.
Polystyrene
C.
Polyethylene
D.
Polyvinyl acetate
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Solution
Natural rubber is primarily composed of polyisoprene, which is derived from latex.
Correct Answer: A — Polyisoprene
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