Q. A chord of a circle is 8 cm long and is 3 cm away from the center. What is the radius of the circle? (2021)
A.
5 cm
B.
7 cm
C.
10 cm
D.
9 cm
Show solution
Solution
Using Pythagoras theorem, r² = (3)² + (4)² = 9 + 16 = 25. Thus, r = 5 cm.
Correct Answer:
B
— 7 cm
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Q. A circle has a circumference of 31.4 cm. What is its radius? (2021)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
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Solution
Circumference = 2πr. Thus, r = Circumference/(2π) = 31.4/(2π) = 5 cm.
Correct Answer:
A
— 5 cm
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Q. A line segment is divided into two parts in the ratio 3:2. If the total length of the segment is 50 cm, what is the length of the longer part? (2023)
A.
30 cm
B.
20 cm
C.
25 cm
D.
15 cm
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Solution
The longer part is (3/5) * 50 = 30 cm, since the total ratio is 3 + 2 = 5.
Correct Answer:
A
— 30 cm
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Q. A rectangle has a length of 12 cm and a width of 5 cm. What is its perimeter? (2021)
A.
34 cm
B.
30 cm
C.
24 cm
D.
40 cm
Show solution
Solution
Perimeter = 2(length + width) = 2(12 + 5) = 2 * 17 = 34 cm
Correct Answer:
B
— 30 cm
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Q. A transversal intersects two lines such that one of the interior angles is 120 degrees. What is the measure of the exterior angle at that intersection?
A.
60 degrees
B.
120 degrees
C.
90 degrees
D.
180 degrees
Show solution
Solution
The exterior angle is supplementary to the interior angle. Therefore, the exterior angle = 180 - 120 = 60 degrees.
Correct Answer:
A
— 60 degrees
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Q. A transversal intersects two parallel lines creating a pair of corresponding angles. If one of the angles measures 60 degrees, what is the measure of the corresponding angle? (2019)
A.
60 degrees
B.
120 degrees
C.
90 degrees
D.
30 degrees
Show solution
Solution
Corresponding angles are equal when a transversal intersects parallel lines. Thus, the corresponding angle is also 60 degrees.
Correct Answer:
A
— 60 degrees
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Q. A transversal intersects two parallel lines creating a pair of corresponding angles. If one of the angles measures 120 degrees, what is the measure of the corresponding angle?
A.
60 degrees
B.
120 degrees
C.
90 degrees
D.
30 degrees
Show solution
Solution
Corresponding angles are equal when a transversal intersects two parallel lines. Therefore, the corresponding angle also measures 120 degrees.
Correct Answer:
B
— 120 degrees
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Q. A transversal intersects two parallel lines creating a pair of corresponding angles. If one of the corresponding angles measures 60 degrees, what is the measure of the other corresponding angle?
A.
60 degrees
B.
120 degrees
C.
90 degrees
D.
180 degrees
Show solution
Solution
Corresponding angles are equal when a transversal intersects two parallel lines. Therefore, the other corresponding angle is also 60 degrees.
Correct Answer:
A
— 60 degrees
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Q. If a circle has an area of 50π cm², what is its diameter? (2020)
A.
10 cm
B.
20 cm
C.
5 cm
D.
15 cm
Show solution
Solution
Area = πr², so r² = 50. Thus, r = √50 = 5√2 cm. Diameter = 2r = 10√2 cm ≈ 14.14 cm.
Correct Answer:
A
— 10 cm
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Q. If a circle's radius is doubled, how does its area change? (2020)
A.
It remains the same
B.
It doubles
C.
It triples
D.
It quadruples
Show solution
Solution
Area = πr². If radius is doubled (2r), new area = π(2r)² = 4πr², which is quadruple the original area.
Correct Answer:
D
— It quadruples
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Q. If a transversal intersects two parallel lines, how many pairs of corresponding angles are formed? (2023)
Show solution
Solution
A transversal intersecting two parallel lines forms 4 pairs of corresponding angles.
Correct Answer:
D
— 4
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Q. If a transversal intersects two parallel lines, what can be said about the same-side interior angles? (2023)
A.
They are equal
B.
They are supplementary
C.
They are complementary
D.
They are unequal
Show solution
Solution
When a transversal intersects two parallel lines, the same-side interior angles are supplementary, meaning they add up to 180 degrees.
Correct Answer:
B
— They are supplementary
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Q. If the angles of a quadrilateral are in the ratio 1:2:3:4, what is the measure of the largest angle?
A.
90 degrees
B.
120 degrees
C.
150 degrees
D.
180 degrees
Show solution
Solution
Let the angles be x, 2x, 3x, and 4x. The sum of angles in a quadrilateral is 360 degrees. Therefore, x + 2x + 3x + 4x = 360, which gives 10x = 360, so x = 36 degrees. The largest angle = 4x = 144 degrees.
Correct Answer:
C
— 150 degrees
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Q. If the angles of triangle JKL are in the ratio 2:3:4, what is the measure of the largest angle? (2023)
A.
40 degrees
B.
60 degrees
C.
80 degrees
D.
90 degrees
Show solution
Solution
Let the angles be 2x, 3x, and 4x. Then, 2x + 3x + 4x = 180 degrees. Therefore, 9x = 180, x = 20. The largest angle is 4x = 80 degrees.
Correct Answer:
C
— 80 degrees
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Q. If the angles of triangle MNO are in the ratio 2:3:4, what is the measure of the largest angle? (2023)
A.
40 degrees
B.
60 degrees
C.
80 degrees
D.
90 degrees
Show solution
Solution
Let the angles be 2x, 3x, and 4x. Then, 2x + 3x + 4x = 180 degrees. Thus, 9x = 180 degrees, x = 20 degrees. The largest angle = 4x = 80 degrees.
Correct Answer:
C
— 80 degrees
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Q. If the area of a circle is 50π cm², what is the diameter? (2022)
A.
10 cm
B.
20 cm
C.
25 cm
D.
15 cm
Show solution
Solution
Area = πr² = 50π. Thus, r² = 50, r = √50 = 5√2 cm. Diameter = 2r = 10√2 cm ≈ 20 cm.
Correct Answer:
B
— 20 cm
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Q. If the area of triangle ABC is 60 square units and the base AC is 12 units, what is the height from point B to line AC? (2019)
A.
5 units
B.
10 units
C.
15 units
D.
20 units
Show solution
Solution
Area = 1/2 * base * height. Therefore, 60 = 1/2 * 12 * height, which gives height = 10 units.
Correct Answer:
A
— 5 units
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Q. If the area of triangle ABC is 60 square units and the base is 10 units, what is the height of the triangle? (2019)
A.
6 units
B.
12 units
C.
10 units
D.
8 units
Show solution
Solution
Area = 1/2 * base * height. Therefore, 60 = 1/2 * 10 * height, which gives height = 12 units.
Correct Answer:
A
— 6 units
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Q. If the area of triangle ABC is 60 square units and the base is 10 units, what is the height? (2019)
A.
6 units
B.
12 units
C.
10 units
D.
8 units
Show solution
Solution
Area = 1/2 * base * height. Therefore, 60 = 1/2 * 10 * height, which gives height = 12 units.
Correct Answer:
A
— 6 units
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Q. If the area of triangle ABC is 60 square units and the base is 12 units, what is the height? (2019)
A.
5 units
B.
10 units
C.
15 units
D.
20 units
Show solution
Solution
Area = 1/2 * base * height. Therefore, 60 = 1/2 * 12 * height, which gives height = 10 units.
Correct Answer:
A
— 5 units
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Q. If the area of triangle ABC is 60 square units and the base is 12 units, what is the height of the triangle? (2019)
A.
5 units
B.
10 units
C.
15 units
D.
20 units
Show solution
Solution
Area = 1/2 * base * height. Therefore, 60 = 1/2 * 12 * height, which gives height = 10 units.
Correct Answer:
A
— 5 units
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Q. If the base of a triangle is 10 cm and the height is 5 cm, what is the area of the triangle? (2022)
A.
25 cm²
B.
50 cm²
C.
15 cm²
D.
30 cm²
Show solution
Solution
Area = (1/2) * base * height = (1/2) * 10 * 5 = 25 cm².
Correct Answer:
A
— 25 cm²
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Q. If the center of a circle is at (3, 4) and it passes through the point (7, 1), what is the radius? (2019)
A.
5 units
B.
4 units
C.
3 units
D.
6 units
Show solution
Solution
Radius = distance from center to point = √[(7-3)² + (1-4)²] = √[16 + 9] = √25 = 5 units.
Correct Answer:
A
— 5 units
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Q. If the diagonals of a rhombus are 8 cm and 6 cm, what is the area of the rhombus? (2023)
A.
24 cm²
B.
48 cm²
C.
36 cm²
D.
18 cm²
Show solution
Solution
Area = (d1 * d2) / 2 = (8 * 6) / 2 = 48 cm²
Correct Answer:
A
— 24 cm²
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Q. If the diameter of a circle is 10 cm, what is its area? (2019)
A.
25π cm²
B.
50π cm²
C.
100π cm²
D.
75π cm²
Show solution
Solution
Area = π * (radius)² = π * (5)² = 25π cm²
Correct Answer:
A
— 25π cm²
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Q. If the diameter of a circle is 12 cm, what is the circumference? (2019)
A.
12π cm
B.
24π cm
C.
6π cm
D.
36π cm
Show solution
Solution
Circumference = πd = π(12) = 12π cm.
Correct Answer:
B
— 24π cm
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Q. If the diameter of a circle is 20 cm, what is the circumference? (2019)
A.
20π cm
B.
40π cm
C.
10π cm
D.
30π cm
Show solution
Solution
Circumference = πd = π(20) = 20π cm.
Correct Answer:
B
— 40π cm
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Q. If the diameter of a circle is increased by 50%, what is the percentage increase in the area of the circle? (2021)
A.
50%
B.
75%
C.
100%
D.
125%
Show solution
Solution
If diameter increases by 50%, radius increases by 25%. Area increases by (new area - old area)/old area = (1.25² - 1) × 100% = 56.25%.
Correct Answer:
C
— 100%
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Q. If the length of a side of a square is doubled, what happens to the area? (2023)
A.
It remains the same
B.
It doubles
C.
It triples
D.
It quadruples
Show solution
Solution
Area of square = side². If side is doubled, new area = (2 * side)² = 4 * side², so area quadruples.
Correct Answer:
D
— It quadruples
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Q. If the lengths of the sides of a rectangle are 4 cm and 6 cm, what is its perimeter? (2022)
A.
20 cm
B.
24 cm
C.
10 cm
D.
12 cm
Show solution
Solution
Perimeter = 2 * (length + width) = 2 * (4 + 6) = 20 cm
Correct Answer:
A
— 20 cm
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