In a right-angled triangle, if the hypotenuse is 13 cm and one leg is 5 cm, what is the length of the other leg?
Options: A: 12 cm, B: 10 cm, C: 8 cm, D: 14 cm
Correct Answer: A
Explanation: Using the Pythagorean theorem: a² + b² = c², where c is the hypotenuse. Here, 5² + b² = 13² → 25 + b² = 169 → b² = 144 → b = 12 cm. Thus, the other leg is 12 cm.
What is the area of a circle with a diameter of 14 cm? (Use π = 22/7)
Options: A: 154 cm², B: 77 cm², C: 44 cm², D: 256 cm²
Correct Answer: A
Explanation: The radius (r) is half the diameter, so r = 7 cm. The area of a circle is πr². Substituting values: (22/7) * 7² = (22/7) * 49 = 154 cm².
If two angles of a triangle are 45° and 65°, what is the measure of the third angle?
Options: A: 70°, B: 80°, C: 60°, D: 50°
Correct Answer: A
Explanation: The sum of angles in a triangle is always 180°. So, the third angle = 180° - (45° + 65°) = 180° - 110° = 70°.
A rectangle has a length of 8 cm and a diagonal of 10 cm. What is its width?
Options: A: 6 cm, B: 4 cm, C: 5 cm, D: 7 cm
Correct Answer: A
Explanation: Using the Pythagorean theorem for the rectangle's diagonal: length² + width² = diagonal² → 8² + w² = 10² → 64 + w² = 100 → w² = 36 → w = 6 cm.
What is the perimeter of a square whose area is 144 cm²?
Options: A: 48 cm, B: 36 cm, C: 24 cm, D: 60 cm
Correct Answer: A
Explanation: The area of a square is side². So, side = √144 = 12 cm. The perimeter is 4 * side = 4 * 12 = 48 cm.
If the radius of a sphere is 7 cm, what is its volume? (Use π = 22/7)
Options: A: 1436.67 cm³, B: 1078.67 cm³, C: 179.33 cm³, D: 4312 cm³
Correct Answer: A
Explanation: The volume of a sphere is (4/3)πr³. Substituting values: (4/3) * (22/7) * 7³ = (4/3) * (22/7) * 343 = (4/3) * 22 * 49 = 1436.67 cm³.
In a parallelogram, adjacent angles are:
Options: A: Supplementary, B: Complementary, C: Equal, D: Right angles
Correct Answer: A
Explanation: In a parallelogram, adjacent angles are supplementary, meaning their sum is 180°. This is a fundamental property of parallelograms.
What is the length of the arc of a sector with a central angle of 60° and a radius of 14 cm? (Use π = 22/7)
Options: A: 14.67 cm, B: 28 cm, C: 44 cm, D: 9.33 cm
Correct Answer: A
Explanation: The length of an arc is given by (θ/360) * 2πr, where θ is the central angle. Substituting values: (60/360) * 2 * (22/7) * 14 = (1/6) * 88 = 14.67 cm.
If the height of a cylinder is 10 cm and the radius is 3 cm, what is its total surface area? (Use π = 3.14)
Options: A: 282.6 cm², B: 188.4 cm², C: 200 cm², D: 150.8 cm²
Correct Answer: A
Explanation: The total surface area of a cylinder is 2πr(r + h). Substituting values: 2 * 3.14 * 3 * (3 + 10) = 2 * 3.14 * 3 * 13 = 282.6 cm².
A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. What type of triangle is it?
Options: A: Right-angled triangle, B: Equilateral triangle, C: Isosceles triangle, D: Scalene triangle
Correct Answer: A
Explanation: Check using the Pythagorean theorem: 7² + 24² = 49 + 576 = 625, and 25² = 625. Since 7² + 24² = 25², the triangle is right-angled.