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Q. What is the distance between the parallel planes x + 2y + 3z = 4 and x + 2y + 3z = 10? (2023)

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

Solution

Distance = |d1 - d2| / √(a² + b² + c²) = |4 - 10| / √(1² + 2² + 3²) = 6 / √14.

Correct Answer: A — 2

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Q. What is the distance between the point (2, 3, 4) and the plane x + y + z = 10? (2022)

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

Solution

Distance = |(2 + 3 + 4 - 10) / √(1² + 1² + 1²)| = |(-1)/√3| = 1/√3.

Correct Answer: A — 1

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Q. What is the distance between the points (-1, -1) and (2, 3)? (2022) 2022

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

Solution

Distance = √[(2 - (-1))² + (3 - (-1))²] = √[3² + 4²] = √25 = 5.

Correct Answer: A — 5

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Q. What is the distance between the points (-1, -1) and (2, 3)? (2023)

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

Solution

Distance = √[(2 - (-1))² + (3 - (-1))²] = √[3² + 4²] = √25 = 5.

Correct Answer: A — 5

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Q. What is the distance between the points (0, 0) and (3, 4)?

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

Solution

Using the distance formula: d = √[(3 - 0)² + (4 - 0)²] = √[9 + 16] = √25 = 5.

Correct Answer: A — 5

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Q. What is the distance between the points (0, 0) and (8, 6)?

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

Solution

Using the distance formula: d = √((8 - 0)² + (6 - 0)²) = √(64 + 36) = √100 = 10.

Correct Answer: A — 10

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Q. What is the distance between the points (0, 0) and (x, y) where x = 3 and y = 4? (2022)

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

Solution

Using the distance formula: d = √[(3 - 0)² + (4 - 0)²] = √[9 + 16] = √25 = 5.

Correct Answer: A — 5

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Q. What is the distance between the points (1, 1) and (4, 5)?

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

Solution

Using the distance formula, d = √[(x2 - x1)² + (y2 - y1)²] = √[(4 - 1)² + (5 - 1)²] = √[3² + 4²] = √[9 + 16] = √25 = 5.

Correct Answer: C — 5

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Q. What is the distance between the points (1, 2) and (4, 6)?

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

Solution

Distance = √[(4-1)² + (6-2)²] = √[9 + 16] = √25 = 5.

Correct Answer: A — 5

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Q. What is the distance between the points (2, 3) and (5, 7)?

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

Solution

Using the distance formula, d = √((5 - 2)² + (7 - 3)²) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

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Q. What is the distance between the points (2, 3) and (6, 7)?

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

Solution

Using the distance formula: d = √[(6 - 2)² + (7 - 3)²] = √[16 + 16] = √32 = 4√2 ≈ 5.66.

Correct Answer: A — 5

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Q. What is the distance between the points (3, 2) and (3, -2)?

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

Solution

Using the distance formula: d = √[(3 - 3)² + (-2 - 2)²] = √[0 + 16] = √16 = 4.

Correct Answer: A — 4

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Q. What is the distance between the points (3, 4) and (7, 1)?

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

Solution

Distance = √[(7-3)² + (1-4)²] = √[16 + 9] = √25 = 5.

Correct Answer: A — 5

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Q. What is the distance between the points (3, 4) and (7, 1)? (2021) 2021

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

Solution

Distance = √[(7-3)² + (1-4)²] = √[4 + 9] = √13 ≈ 5.

Correct Answer: A — 5

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Q. What is the distance between the points (3, 7) and (3, 1)?

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

Solution

Using the distance formula: d = √[(3 - 3)² + (1 - 7)²] = √[0 + 36] = √36 = 6.

Correct Answer: A — 6

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Q. What is the distance between the points (5, 5) and (1, 1)?

A. 4√2
B. 5√2
C. 6
D. 7

Solution

Using the distance formula: d = √[(1 - 5)² + (1 - 5)²] = √[16 + 16] = √32 = 4√2.

Correct Answer: A — 4√2

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Q. What is the distance between the points (6, 8) and (6, 2)?

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

Solution

Using the distance formula: d = √[(6 - 6)² + (2 - 8)²] = √[0 + 36] = √36 = 6.

Correct Answer: A — 6

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Q. What is the distance between the points A(1, 2, 3) and B(4, 5, 6)? (2023)

A. 3√2
B. 3√3
C. 3
D. √27

Solution

Distance = √[(4-1)² + (5-2)² + (6-3)²] = √[3² + 3² + 3²] = √27 = 3√3.

Correct Answer: A — 3√2

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Q. What is the distance between the points P(1, 2, 3) and Q(4, 5, 6)?

A. 3√3
B. 3√2
C. 3
D. √3

Solution

Distance = √((4-1)² + (5-2)² + (6-3)²) = √(9 + 9 + 9) = 3√3.

Correct Answer: A — 3√3

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Q. What is the distance between the points P(3, 4) and Q(7, 1) in the coordinate plane?

A. 5
B. 6
C. 7
D. 8

Solution

Using the distance formula d = √((x2 - x1)² + (y2 - y1)²), we find d = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5.

Correct Answer: B — 6

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Q. What is the distance between the points P(3, 4) and Q(7, 1)?

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

Solution

Using the distance formula, d = √[(7-3)² + (1-4)²] = √[16 + 9] = √25 = 5.

Correct Answer: A — 5

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Q. What is the distance from the center of a circle to a tangent line if the radius is 4 cm?

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

Solution

The distance from the center to the tangent line is equal to the radius of the circle, which is 4 cm.

Correct Answer: B — 4

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Q. What is the distance from the point (1, 1) to the line x + y = 2? (2023)

A. 1
B. 2
C. 0
D. 3

Solution

Distance = |1 + 1 - 2| / √(1² + 1²) = 0 / √2 = 0.

Correct Answer: A — 1

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Q. What is the distance from the point (1, 2) to the line 3x + 4y - 10 = 0?

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

Solution

Distance = |3(1) + 4(2) - 10| / √(3² + 4²) = |3 + 8 - 10| / 5 = 1.

Correct Answer: B — 2

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Q. What is the distance from the point (1, 2) to the line x + y - 3 = 0? (2023)

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

Solution

Distance = |1 + 2 - 3| / √(1² + 1²) = |0| / √2 = 0, closest option is 1.

Correct Answer: B — 2

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Q. What is the distance from the point (1, 2) to the line x + y = 5? (2020)

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

Solution

Distance = |1 + 2 - 5| / √(1² + 1²) = | -2 | / √2 = 2/√2 = √2.

Correct Answer: A — 3

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Q. What is the distance from the point (2, 3) to the line x + y - 5 = 0? (2022)

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

Solution

Distance = |(1*2 + 1*3 - 5)| / √(1² + 1²) = |5 - 5| / √2 = 0

Correct Answer: A — 1

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Q. What is the distance from the point (2, 3) to the line x + y = 5? (2020)

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

Solution

Distance = |(1*2 + 1*3 - 5)| / √(1² + 1²) = |5 - 5| / √2 = 0/√2 = 0

Correct Answer: B — 2

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Q. What is the distance from the point (3, 4) to the line 2x + 3y - 6 = 0?

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

Solution

Distance = |2(3) + 3(4) - 6| / √(2² + 3²) = |6 + 12 - 6| / √13 = 12/√13.

Correct Answer: A — 1

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Q. What is the distance from the point (3, 4) to the line x + y = 5? (2022)

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

Solution

Distance = |3 + 4 - 5| / √(1² + 1²) = |2| / √2 = 2/√2 = √2.

Correct Answer: B — 2

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Major Competitive Exams

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