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Q. A card is drawn from a standard deck of 52 cards. What is the probability of drawing a heart?

A. 1/4
B. 1/13
C. 1/2
D. 1/52

Solution

Number of hearts = 13. Probability = 13/52 = 1/4.

Correct Answer: A — 1/4

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Q. A changing magnetic field induces an electric field. This phenomenon is described by which of the following laws?

A. Faraday's law of induction
B. Ampere's law
C. Gauss's law
D. Ohm's law

Solution

The phenomenon of a changing magnetic field inducing an electric field is described by Faraday's law of induction.

Correct Answer: A — Faraday's law of induction

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Q. A charge of +1 μC is placed in an electric field of strength 1000 N/C. What is the force experienced by the charge? (2023)

A. 0.001 N
B. 0.01 N
C. 1 N
D. 10 N

Solution

Force F = qE = (1 × 10^-6 C)(1000 N/C) = 0.001 N.

Correct Answer: B — 0.01 N

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Q. A charge of +10 μC is placed in an electric field of 2000 N/C. What is the force experienced by the charge? (2023)

A. 20 N
B. 200 N
C. 2 N
D. 0.2 N

Solution

Force F = qE = (10 × 10^-6 C) * (2000 N/C) = 0.02 N = 20 N.

Correct Answer: A — 20 N

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Q. A charge of +10 µC is placed in an electric field of strength 2000 N/C. What is the force acting on the charge? (2023)

A. 20 N
B. 200 N
C. 2 N
D. 0.2 N

Solution

Force F = qE = (10 × 10^-6 C) * (2000 N/C) = 0.02 N = 20 N.

Correct Answer: A — 20 N

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Q. A charge of +4 µC is placed in a uniform electric field of strength 500 N/C. What is the work done in moving the charge 0.2 m in the direction of the field?

A. 400 J
B. 200 J
C. 100 J
D. 50 J

Solution

W = F * d = (E * q) * d = (500 N/C * 4 × 10^-6 C) * 0.2 m = 0.4 J.

Correct Answer: B — 200 J

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Q. A charge of +5 μC is placed in an electric field of 1000 N/C. What is the work done in moving the charge 0.2 m in the direction of the field? (2022)

A. 1 J
B. 0.1 J
C. 0.5 J
D. 2 J

Solution

Work done W = F * d = (E * q) * d = (1000 N/C * 5 × 10^-6 C) * 0.2 m = 0.1 J.

Correct Answer: B — 0.1 J

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Q. A charge of +5 µC is placed in an electric field of 300 N/C. What is the work done in moving the charge 0.2 m in the direction of the field? (2019)

A. 30 J
B. 12 J
C. 6 J
D. 3 J

Solution

Work done W = F * d = (E * q) * d = (300 N/C * 5 × 10^-6 C) * 0.2 m = 0.3 J.

Correct Answer: C — 6 J

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Q. A charge of -2 µC is placed in an electric field of 500 N/C. What is the direction of the force acting on the charge? (2023)

A. Towards the positive charge
B. Away from the positive charge
C. No force
D. Depends on the field strength

Solution

The force on a negative charge is in the direction opposite to the electric field, hence towards the positive charge.

Correct Answer: A — Towards the positive charge

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Q. A charged particle moves in a magnetic field. What is the path of the particle if it enters the field perpendicular to the lines of force? (2019)

A. Straight line
B. Circular path
C. Elliptical path
D. Parabolic path

Solution

A charged particle moving perpendicular to the magnetic field will follow a circular path due to the magnetic force acting as a centripetal force.

Correct Answer: B — Circular path

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Q. A charged particle moves in a magnetic field. What is the path of the particle if it enters the field perpendicularly? (2023)

A. Straight line
B. Circular path
C. Elliptical path
D. Parabolic path

Solution

A charged particle moving perpendicularly to a magnetic field experiences a magnetic force that acts as a centripetal force, causing it to move in a circular path.

Correct Answer: B — Circular path

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Q. A charged particle moves in a magnetic field. What is the path of the particle? (2019)

A. Straight line
B. Circular
C. Elliptical
D. Parabolic

Solution

A charged particle moving in a magnetic field experiences a force that is perpendicular to its velocity, resulting in circular motion.

Correct Answer: B — Circular

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Q. A charged particle moves perpendicular to a uniform magnetic field. What is the path of the particle? (2021)

A. Straight line
B. Circle
C. Ellipse
D. Parabola

Solution

A charged particle moving perpendicular to a uniform magnetic field will move in a circular path due to the magnetic force acting as a centripetal force.

Correct Answer: B — Circle

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Q. A chord of a circle is 10 cm long and is 6 cm away from the center. What is the radius of the circle? (2023)

A. 8 cm
B. 10 cm
C. 12 cm
D. 14 cm

Solution

Using Pythagoras theorem: r² = (10/2)² + 6²; r² = 25 + 36 = 61; r = √61 ≈ 10 cm.

Correct Answer: B — 10 cm

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Q. A chord of a circle is 12 cm long and is 5 cm away from the center. What is the radius of the circle? (2020)

A. 10 cm
B. 13 cm
C. 15 cm
D. 12 cm

Solution

Using Pythagoras theorem: r² = (5)² + (6)² = 25 + 36 = 61; r = √61 ≈ 7.81 cm.

Correct Answer: B — 13 cm

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Q. A circle has a diameter of 10 cm. What is its circumference? (2022)

A. 31.4 cm
B. 20 cm
C. 15.7 cm
D. 25 cm

Solution

Circumference = πd = π * 10 = 31.4 cm.

Correct Answer: A — 31.4 cm

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Q. A circle has a diameter of 20 cm. What is its circumference? (2022)

A. 62.8 cm
B. 40 cm
C. 31.4 cm
D. 20 cm

Solution

Circumference = πd = π * 20 = 62.8 cm.

Correct Answer: A — 62.8 cm

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Q. A circle has a radius of 10 cm. What is the diameter? (2020)

A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm

Solution

Diameter = 2 * radius = 2 * 10 cm = 20 cm.

Correct Answer: D — 20 cm

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Q. A circle has a radius of 12 cm. What is the diameter? (2020)

A. 6 cm
B. 12 cm
C. 24 cm
D. 18 cm

Solution

Diameter = 2 * radius = 2 * 12 = 24 cm.

Correct Answer: C — 24 cm

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Q. A circle has a radius of 3 cm. What is the diameter in millimeters? (2023)

A. 30 mm
B. 60 mm
C. 90 mm
D. 120 mm

Solution

Diameter = 2 * radius = 2 * 3 cm = 6 cm = 60 mm.

Correct Answer: A — 30 mm

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Q. A circle has a radius of 3 m. What is the diameter? (2022)

A. 3 m
B. 6 m
C. 9 m
D. 12 m

Solution

Diameter = 2 * radius = 2 * 3 m = 6 m.

Correct Answer: B — 6 m

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Q. A circle has a radius of 5 cm. What is the length of an arc that subtends a central angle of 60 degrees? (2021)

A. 5.24 cm
B. 10.47 cm
C. 3.14 cm
D. 6.28 cm

Solution

Arc length = (θ/360) * 2πr; = (60/360) * 2π * 5 = 10.47 cm.

Correct Answer: B — 10.47 cm

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Q. A circle has a radius of 5 cm. What is the length of an arc that subtends an angle of 60 degrees? (2023)

A. 5.24 cm
B. 3.14 cm
C. 5.00 cm
D. 10.47 cm

Solution

Arc length = (θ/360) × 2πr; = (60/360) × 2π × 5 ≈ 5.24 cm.

Correct Answer: A — 5.24 cm

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Q. A circle has a radius of 5 cm. What is the length of an arc that subtends an angle of 60 degrees at the center? (2020)

A. 5.24 cm
B. 3.14 cm
C. 5.00 cm
D. 10.47 cm

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. A circle has an area of 154 cm². What is the radius? (2019)

A. 7 cm
B. 14 cm
C. 21 cm
D. 28 cm

Solution

Area = πr². Therefore, r = √(Area/π) = √(154/3.14) ≈ 7 cm.

Correct Answer: B — 14 cm

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Q. A circle has an area of 154 cm². What is the radius? (2019) 2019

A. 7 cm
B. 14 cm
C. 21 cm
D. 28 cm

Solution

Area = πr². Therefore, r = √(Area/π) = √(154/3.14) ≈ 7 cm.

Correct Answer: B — 14 cm

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Q. A circle has an area of 78.5 cm². What is its radius? (Use π = 3.14) (2019)

A. 5 cm
B. 7 cm
C. 10 cm
D. 12 cm

Solution

Area = πr². Therefore, r² = Area / π = 78.5 cm² / 3.14 = 25. r = √25 = 5 cm.

Correct Answer: B — 7 cm

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Q. A circle has an area of 78.5 cm². What is the radius? (Use π = 3.14) (2022)

A. 5 cm
B. 7 cm
C. 10 cm
D. 12 cm

Solution

Area = πr². Therefore, r² = Area / π = 78.5 cm² / 3.14 = 25. r = √25 = 5 cm.

Correct Answer: B — 7 cm

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Q. A circle is inscribed in a square of side 10 cm. What is the area of the circle? (2019)

A. 78.5 cm²
B. 100 cm²
C. 50 cm²
D. 25 cm²

Solution

Radius = 10/2 = 5 cm; Area = πr² = π * 5² = 78.5 cm².

Correct Answer: A — 78.5 cm²

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Q. A circle is inscribed in a square of side 10 cm. What is the area of the circle? (Use π = 3.14) (2020)

A. 78.5 cm²
B. 50 cm²
C. 100 cm²
D. 25 cm²

Solution

Radius of the circle = side/2 = 10 cm / 2 = 5 cm. Area = πr² = 3.14 * 5² = 78.5 cm².

Correct Answer: A — 78.5 cm²

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