Q. What is the discriminant of the equation x² + 6x + 9 = 0? (2020)
Solution
The discriminant is b² - 4ac = 6² - 4*1*9 = 0.
Correct Answer: A — 0
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Q. What is the distance between the center of a circle and a point on its circumference if the radius is 8 cm? (2023)
-
A.
8 cm
-
B.
16 cm
-
C.
4 cm
-
D.
0 cm
Solution
The distance from the center to a point on the circumference is the radius, which is 8 cm.
Correct Answer: A — 8 cm
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Q. What is the distance between the center of a circle and a point on its circumference if the radius is 12 cm? (2022)
-
A.
6 cm
-
B.
12 cm
-
C.
18 cm
-
D.
24 cm
Solution
The distance from the center to a point on the circumference is the radius, which is 12 cm.
Correct Answer: B — 12 cm
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Q. What is the distance between the center of a circle and a point on its circumference if the radius is 10 cm? (2022)
-
A.
5 cm
-
B.
10 cm
-
C.
15 cm
-
D.
20 cm
Solution
The distance from the center to a point on the circumference is the radius, which is 10 cm.
Correct Answer: B — 10 cm
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Q. What is the distance between the center of a circle and a point on its circumference if the radius is 15 cm? (2014)
-
A.
15 cm
-
B.
30 cm
-
C.
10 cm
-
D.
5 cm
Solution
The distance from the center to any point on the circumference is always the radius, which is 15 cm.
Correct Answer: A — 15 cm
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Q. What is the distance between the centers of two circles with equations (x - 1)² + (y - 2)² = 9 and (x + 3)² + (y + 4)² = 16?
Solution
The distance between centers (1, 2) and (-3, -4) is calculated using the distance formula.
Correct Answer: D — 6
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Q. What is the distance between the foci of the ellipse given by the equation 4x^2 + 9y^2 = 36?
Solution
The distance between the foci is 6, calculated using the formula 2c where c = √(a^2 - b^2).
Correct Answer: A — 6
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Q. What is the distance between the foci of the ellipse x^2/25 + y^2/16 = 1?
Solution
The distance between the foci is given by 2c, where c = √(a^2 - b^2) = √(25 - 16) = 3, so the total distance is 2c = 6.
Correct Answer: A — 7
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Q. What is the distance between the parallel planes 2x + 3y - z = 5 and 2x + 3y - z = 10? (2021)
-
A.
5/√14
-
B.
10/√14
-
C.
15/√14
-
D.
20/√14
Solution
Distance = |d1 - d2| / √(A² + B² + C²) = |5 - 10| / √(2² + 3² + (-1)²) = 5/√14.
Correct Answer: B — 10/√14
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Q. What is the distance between the parallel planes x + 2y + 3z = 4 and x + 2y + 3z = 10? (2023)
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)
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
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)
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)?
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)?
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)
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)?
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)?
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)?
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 (3, 4) and (7, 1)?
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
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)?
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)?
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 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)?
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 from the point (1, 1) to the line x + y = 2? (2023)
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?
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)
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)
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)
Solution
Distance = |(1*2 + 1*3 - 5)| / √(1² + 1²) = |5 - 5| / √2 = 0
Correct Answer: A — 1
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