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Q. A circle has a radius of 7 cm. What is its circumference? (2023)

A. 44 cm
B. 40 cm
C. 38 cm
D. 42 cm

Solution

Circumference of a circle = 2πr = 2 × 3.14 × 7 cm ≈ 44 cm.

Correct Answer: A — 44 cm

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Q. A circle has a radius of 7 cm. What is the area of the circle?

A. 154 cm²
B. 144 cm²
C. 160 cm²
D. 150 cm²

Solution

Area of a circle = πr². Using π ≈ 3.14, Area = 3.14 × (7)² = 3.14 × 49 = 153.86 cm², which rounds to 154 cm².

Correct Answer: A — 154 cm²

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Q. A circle has a radius of 7 cm. What is the area of the circle? (Use π ≈ 22/7)

A. 154 cm²
B. 144 cm²
C. 160 cm²
D. 150 cm²

Solution

Area of a circle = πr² = (22/7) × (7)² = (22/7) × 49 = 154 cm².

Correct Answer: A — 154 cm²

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Q. A circle has a radius of 7 cm. What is the area of the circle? (Use π ≈ 3.14)

A. 154 cm²
B. 144 cm²
C. 160 cm²
D. 150 cm²

Solution

Area = πr² = 3.14 × (7)² = 3.14 × 49 = 153.86 cm², which rounds to 154 cm².

Correct Answer: A — 154 cm²

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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 defined by the equation x² + y² - 10x + 6y + 25 = 0. What is the radius of the circle?

A. 5
B. 6
C. 7
D. 4

Solution

Rearranging gives (x - 5)² + (y + 3)² = 9, so the radius is √9 = 3.

Correct Answer: A — 5

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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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Q. A circle is inscribed in a square of side 8 cm. What is the area of the circle? (2022)

A. 50.24 cm²
B. 64 cm²
C. 25.12 cm²
D. 32 cm²

Solution

Radius = 8/2 = 4 cm; Area = πr² = π * 4² = 50.24 cm².

Correct Answer: A — 50.24 cm²

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Q. A circle is inscribed in a triangle with sides 7, 8, and 9. What is the radius of the inscribed circle?

A. 3
B. 4
C. 5
D. 6

Solution

Using the formula for the radius of the incircle r = A/s, where A is the area and s is the semi-perimeter.

Correct Answer: B — 4

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Q. A circle is inscribed in a triangle with sides 7, 8, and 9. What is the radius of the circle?

A. 4
B. 5
C. 6
D. 3

Solution

Using the formula for the radius of the incircle r = A/s, where A is the area and s is the semi-perimeter.

Correct Answer: B — 5

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Q. A circle is tangent to the x-axis at the point (4, 0). What is the equation of the circle if its radius is 3?

A. (x - 4)² + (y - 3)² = 9
B. (x - 4)² + (y + 3)² = 9
C. (x + 4)² + (y - 3)² = 9
D. (x + 4)² + (y + 3)² = 9

Solution

The center of the circle is (4, 3) since it is 3 units above the tangent point (4, 0).

Correct Answer: B — (x - 4)² + (y + 3)² = 9

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Q. A circle passes through the points (1, 2), (3, 4), and (5, 6). What is the radius of the circle?

A. 2
B. 3
C. 4
D. 5

Solution

Using the distance formula, the radius can be calculated from the center found using the circumcircle method.

Correct Answer: B — 3

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Q. A circuit consists of a 9V battery and two resistors of 3Ω and 6Ω in series. What is the current flowing through the circuit? (2021)

A. 1A
B. 2A
C. 3A
D. 4A

Solution

Total resistance R = 3Ω + 6Ω = 9Ω. Current I = V/R = 9V / 9Ω = 1A.

Correct Answer: B — 2A

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Q. A circuit contains a 10Ω resistor and a 5Ω resistor in series with a 15V battery. What is the total current in the circuit?

A. 1A
B. 2A
C. 3A
D. 4A

Solution

Total resistance R = 10Ω + 5Ω = 15Ω. Current I = V/R = 15V/15Ω = 1A.

Correct Answer: B — 2A

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Q. A circuit contains a 10Ω resistor and a 5Ω resistor in series. What is the total resistance?

A. 5Ω
B. 10Ω
C. 15Ω
D. 50Ω

Solution

In series, total resistance R = R1 + R2 = 10Ω + 5Ω = 15Ω.

Correct Answer: C — 15Ω

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Q. A circuit contains a 12 V battery and two resistors of 4 ohms and 8 ohms in series. What is the current flowing through the circuit?

A. 0.5 A
B. 1 A
C. 1.5 A
D. 2 A

Solution

Total resistance R = 4 + 8 = 12 ohms. Current I = V/R = 12 V / 12 ohms = 1 A.

Correct Answer: B — 1 A

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Q. A circuit contains a 12V battery and two resistors of 4 ohms and 8 ohms in series. What is the total current in the circuit?

A. 1 A
B. 0.5 A
C. 2 A
D. 3 A

Solution

Total resistance R = R1 + R2 = 4 + 8 = 12 ohms. Current I = V/R = 12V / 12 ohms = 1 A.

Correct Answer: B — 0.5 A

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Q. A circuit contains a 12V battery and two resistors of 4Ω and 6Ω in parallel. What is the total current supplied by the battery? (2019)

A. 1.2 A
B. 2 A
C. 3 A
D. 4 A

Solution

First, find the equivalent resistance R_eq = 1/(1/4 + 1/6) = 2.4Ω. Then, I = V/R_eq = 12V/2.4Ω = 5 A.

Correct Answer: C — 3 A

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Q. A circuit contains a 9V battery and two resistors in series: 3Ω and 6Ω. What is the voltage across the 6Ω resistor?

A. 6V
B. 3V
C. 9V
D. 0V

Solution

The total resistance R_total = 3Ω + 6Ω = 9Ω. The current I = V/R_total = 9V / 9Ω = 1A. Voltage across 6Ω, V = I * R = 1A * 6Ω = 6V.

Correct Answer: A — 6V

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Q. A circuit contains a 9V battery and two resistors of 3 ohms and 6 ohms in series. What is the voltage drop across the 6 ohm resistor?

A. 3 V
B. 6 V
C. 9 V
D. 4.5 V

Solution

Total resistance R_total = 3 + 6 = 9 ohms. Current I = V/R_total = 9V / 9Ω = 1 A. Voltage drop across 6 ohm resistor = I * R = 1 A * 6Ω = 6 V.

Correct Answer: B — 6 V

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Q. A circuit contains a 9V battery and two resistors of 3 ohms and 6 ohms in series. What is the voltage across the 6 ohm resistor?

A. 6V
B. 3V
C. 9V
D. 4.5V

Solution

Total resistance R_total = 3 + 6 = 9 ohms. Current I = V/R_total = 9V / 9Ω = 1 A. Voltage across 6 ohm resistor = I * R = 1 A * 6Ω = 6V.

Correct Answer: A — 6V

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Q. A circuit contains a 9V battery and two resistors of 3Ω and 6Ω in series. What is the voltage across the 6Ω resistor?

A. 6V
B. 3V
C. 9V
D. 0V

Solution

The total resistance R_total = 3Ω + 6Ω = 9Ω. The current I = V/R_total = 9V / 9Ω = 1A. Voltage across 6Ω, V = I * R = 1A * 6Ω = 6V.

Correct Answer: A — 6V

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Q. A circuit has a 15V battery and a 5Ω resistor. What is the voltage drop across the resistor? (2021)

A. 3V
B. 5V
C. 15V
D. 10V

Solution

The voltage drop across the resistor is equal to the battery voltage, which is 15V.

Correct Answer: C — 15V

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Q. A circuit has a 15V battery and a total resistance of 5Ω. What is the total current flowing through the circuit? (2023)

A. 1A
B. 2A
C. 3A
D. 4A

Solution

Using Ohm's law, I = V/R = 15V/5Ω = 3A.

Correct Answer: C — 3A

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Q. A circuit has a 24V battery and a total resistance of 12Ω. What is the current flowing through the circuit? (2020)

A. 2A
B. 4A
C. 6A
D. 8A

Solution

Using Ohm's law, I = V/R = 24V / 12Ω = 2A.

Correct Answer: B — 4A

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Q. A circuit has a 24V battery and a total resistance of 6Ω. What is the current flowing through the circuit? (2020)

A. 4A
B. 6A
C. 8A
D. 2A

Solution

Using Ohm's law, I = V/R = 24V / 6Ω = 4A.

Correct Answer: A — 4A

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Major Competitive Exams

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