Q. If a wire carrying current I is bent into a semicircular arc of radius R, what is the magnetic field at the center of the arc?
A.
μ₀I/(4R)
B.
μ₀I/(2R)
C.
μ₀I/(8R)
D.
μ₀I/(πR)
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Solution
The magnetic field at the center of a semicircular arc of radius R carrying current I is given by B = μ₀I/(4R).
Correct Answer:
A
— μ₀I/(4R)
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Q. If a wire is bent into a semicircular shape, what is the magnetic field at the center of the semicircle due to current I?
A.
μ₀I/(4R)
B.
μ₀I/(2R)
C.
μ₀I/(πR)
D.
μ₀I/(8R)
Show solution
Solution
The magnetic field at the center of a semicircular wire carrying current I is given by B = μ₀I/(4R) for the semicircle, which is half of the full circular loop.
Correct Answer:
C
— μ₀I/(πR)
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Q. If a wire is bent into a semicircular shape, what is the magnetic field at the center of the semicircle due to the current I?
A.
μ₀I/(4R)
B.
μ₀I/(2R)
C.
μ₀I/(8R)
D.
μ₀I/(6R)
Show solution
Solution
The magnetic field at the center of a semicircular wire carrying current I is given by B = μ₀I/(4R).
Correct Answer:
A
— μ₀I/(4R)
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Q. If a wire is stretched and its length increases by 2%, what is the strain?
A.
0.02
B.
0.2
C.
2
D.
200
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Solution
Strain is defined as the change in length divided by the original length, so 2% = 0.02.
Correct Answer:
A
— 0.02
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Q. If a wire of length L and cross-sectional area A is stretched by a force F, what is the expression for the elongation?
A.
F * L / (A * E)
B.
A * F / (L * E)
C.
E * F / (A * L)
D.
L * E / (A * F)
Show solution
Solution
The elongation (ΔL) can be expressed as ΔL = F * L / (A * E).
Correct Answer:
A
— F * L / (A * E)
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Q. If a wire's length is doubled while keeping its cross-sectional area constant, how does its resistance change?
A.
Remains the same
B.
Doubles
C.
Halves
D.
Quadruples
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Solution
Resistance is directly proportional to length; doubling the length doubles the resistance.
Correct Answer:
B
— Doubles
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Q. If a woman with blood type A (genotype AO) has a child with a man with blood type B (genotype BO), what are the possible blood types of their child?
A.
A, B, AB, O
B.
A, B, AB
C.
A, O
D.
B, O
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Solution
The possible blood types from AO x BO are A, B, AB, and O.
Correct Answer:
A
— A, B, AB, O
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Q. If a worker completes a task in 4 hours, how long will it take 3 workers to complete the same task working together?
A.
1 hour
B.
2 hours
C.
3 hours
D.
4 hours
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Solution
3 workers can complete the task in 4/3 hours, which is 1 hour and 20 minutes, approximately 2 hours.
Correct Answer:
B
— 2 hours
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Q. If a worker completes a task in 4 hours, how many tasks can he complete in a 40-hour work week?
A.
8 tasks
B.
10 tasks
C.
12 tasks
D.
6 tasks
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Solution
In a 40-hour week, he can complete 10 tasks (40 hours / 4 hours per task).
Correct Answer:
B
— 10 tasks
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Q. If a worker has a shift from 2 PM to 10 PM, what is the duration of the shift?
A.
6 hours
B.
7 hours
C.
8 hours
D.
9 hours
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Solution
The shift lasts for 8 hours.
Correct Answer:
C
— 8 hours
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Q. If a ≡ 2 (mod 3) and b ≡ 1 (mod 3), what is the value of (a * b) mod 3?
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Solution
a * b ≡ 2 * 1 ≡ 2 (mod 3).
Correct Answer:
B
— 1
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Q. If a ≡ 2 (mod 5) and b ≡ 3 (mod 5), what is the value of (a * b) mod 5?
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Solution
a * b ≡ 2 * 3 ≡ 6 (mod 5), which is equivalent to 1.
Correct Answer:
B
— 1
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Q. If a ≡ 3 (mod 7) and b ≡ 5 (mod 7), what is a + b (mod 7)?
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Solution
a + b ≡ 3 + 5 ≡ 8 ≡ 1 (mod 7).
Correct Answer:
A
— 1
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Q. If a ≡ b (mod m) and c ≡ d (mod m), which of the following is necessarily true?
A.
a + c ≡ b + d (mod m)
B.
a * c ≡ b * d (mod m)
C.
a - c ≡ b - d (mod m)
D.
All of the above
Show solution
Solution
All operations (addition, multiplication, and subtraction) preserve congruence in modular arithmetic.
Correct Answer:
D
— All of the above
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Q. If a ≡ b (mod m) and c ≡ d (mod m), which of the following is true?
A.
a + c ≡ b + d (mod m)
B.
a - c ≡ b - d (mod m)
C.
a * c ≡ b * d (mod m)
D.
All of the above
Show solution
Solution
All operations (addition, subtraction, multiplication) maintain congruence under modular arithmetic.
Correct Answer:
D
— All of the above
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Q. If A ≤ B and B < C, which of the following is true?
A.
A < C
B.
C < A
C.
B = A
D.
C < B
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Solution
From A ≤ B and B < C, we can conclude A < C.
Correct Answer:
A
— A < C
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Q. If A(1, 2, 3) and B(4, 5, 6) are two points in space, what is the vector AB?
A.
(3, 3, 3)
B.
(2, 3, 4)
C.
(1, 1, 1)
D.
(0, 0, 0)
Show solution
Solution
Vector AB = B - A = (4-1, 5-2, 6-3) = (3, 3, 3).
Correct Answer:
A
— (3, 3, 3)
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Q. If A(1, 2, 3) and B(4, 5, 6) are two points, what is the vector AB?
A.
(3, 3, 3)
B.
(3, 3, 0)
C.
(0, 0, 0)
D.
(1, 1, 1)
Show solution
Solution
Vector AB = B - A = (4-1, 5-2, 6-3) = (3, 3, 3).
Correct Answer:
A
— (3, 3, 3)
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Q. If A(2, 3, 4) and B(1, 0, -1) are two points in space, find the vector AB.
A.
(1, 3, 5)
B.
(1, -3, -5)
C.
(1, 3, -5)
D.
(1, -3, 5)
Show solution
Solution
AB = B - A = (1 - 2, 0 - 3, -1 - 4) = (-1, -3, -5) = (1, 3, 5) in the opposite direction.
Correct Answer:
A
— (1, 3, 5)
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Q. If A, B, and C invest in a business in the ratio of 2:3:5 and the total profit is $50,000, how much does A receive?
A.
$10,000
B.
$15,000
C.
$20,000
D.
$25,000
Show solution
Solution
Total parts = 2 + 3 + 5 = 10. A's share = (2/10) * 50000 = $10,000.
Correct Answer:
B
— $15,000
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Q. If A, B, C, D, and E are seated in a circle and A is between B and C, who is sitting opposite D?
Show solution
Solution
If A is between B and C, then E must be opposite D.
Correct Answer:
C
— E
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Q. If A, B, C, D, and E are seated in a circle and A is not next to B, which of the following statements must be true?
A.
C is next to D
B.
E is next to A
C.
B is next to D
D.
C is not next to E
Show solution
Solution
Since A is not next to B, it is possible for B to be next to D, making this statement true in some arrangements.
Correct Answer:
C
— B is next to D
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Q. If A, B, C, D, and E are sitting in a circle and A is to the right of B, who is sitting to the left of D if C is opposite A?
Show solution
Solution
Arranging A, B, C, D, and E, we find that E is to the left of D.
Correct Answer:
B
— E
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Q. If A, B, C, D, E, and F are seated in a circle and A is between B and C, who is sitting directly opposite D?
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Solution
By arranging A, B, and C, we can find the positions of D, E, and F. The person opposite D will be F.
Correct Answer:
B
— F
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Q. If all birds can fly and a penguin is a bird, what can we conclude?
A.
Penguins can fly
B.
Penguins cannot fly
C.
All birds are penguins
D.
Some birds cannot fly
Show solution
Solution
Although penguins are birds, they are an exception and cannot fly.
Correct Answer:
B
— Penguins cannot fly
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Q. If all birds can fly and some animals cannot fly, which of the following must be true?
A.
Some animals are not birds.
B.
All animals are birds.
C.
All birds are animals.
D.
Some birds cannot fly.
Show solution
Solution
Since not all animals can fly, it must be true that some animals are not birds, as all birds can fly.
Correct Answer:
A
— Some animals are not birds.
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Q. If all birds can fly and some birds are penguins, which of the following statements is true?
A.
Penguins can fly.
B.
Not all birds can fly.
C.
All penguins are birds.
D.
Some birds cannot fly.
Show solution
Solution
The premise contradicts itself, as it states that all birds can fly while also stating that some birds are penguins, which cannot fly.
Correct Answer:
B
— Not all birds can fly.
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Q. If all Bloops are Razzies and all Razzies are Lazzies, which of the following statements is true? (2021)
A.
All Bloops are Lazzies.
B.
Some Lazzies are Bloops.
C.
No Razzies are Bloops.
D.
All Lazzies are Razzies.
Show solution
Solution
Since all Bloops are Razzies and all Razzies are Lazzies, it follows that all Bloops are also Lazzies.
Correct Answer:
A
— All Bloops are Lazzies.
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Q. If all cats are animals and some animals are not dogs, which of the following statements is true?
A.
All cats are dogs.
B.
Some cats are not animals.
C.
Some animals are cats.
D.
No cats are animals.
Show solution
Solution
The statement 'Some animals are cats' is true based on the premises given.
Correct Answer:
C
— Some animals are cats.
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Q. If all cats are animals and some animals are not pets, which of the following statements is true?
A.
All cats are pets
B.
Some cats are not pets
C.
No cats are animals
D.
Some pets are not animals
Show solution
Solution
Since some animals are not pets, it follows that some cats, being animals, may also not be pets.
Correct Answer:
B
— Some cats are not pets
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