Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
71
What is the volume of a right prism whose base is an equilateral triangle of side 4 cm and whose height is 10 cm?
Answer:
40√3 cm³
Volume of prism = Base Area × Height. Base is an equilateral triangle, so Area = (√3/4)a² = (√3/4) × 4² = 4√3 cm². Volume = 4√3 × 10 = 40√3 cm³.
72
The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to roll once over a playground. What is the area of the playground in m²? (Use π = 22/7)
Answer:
1584 m²
Diameter = 84 cm = 0.84 m, so r = 0.42 m. Length (h) = 120 cm = 1.2 m. Area of 1 revolution = CSA = 2πrh = 2 × (22/7) × 0.42 × 1.2 = 3.168 m². Area of playground = 500 × 3.168 = 1584 m².
73
How many spherical bullets of radius 1 cm can be made out of a solid cube of lead whose edge measures 44 cm? (Use π = 22/7)
Answer:
20328
Volume of cube = 44³ = 85184 cm³. Volume of one bullet = (4/3)πr³ = (4/3) × (22/7) × 1³ = 88/21 cm³. Number of bullets = 85184 / (88/21) = (85184 × 21) / 88 = 968 × 21 = 20328.
74
A solid cylinder is melted and cast into a sphere of the same radius. What is the ratio of the height to the radius of the original cylinder?
Answer:
4:3
Volume of cylinder = Volume of sphere. πr²h = (4/3)πr³. Dividing both sides by πr² gives h = (4/3)r. Thus, the ratio of height to radius (h/r) is 4/3 or 4:3.
75
The areas of three adjacent faces of a cuboid are 15 cm², 20 cm², and 12 cm². What is the volume of the cuboid?
Answer:
60 cm³
Let dimensions be l, w, h. The areas are lw=15, wh=20, lh=12. Volume V = lwh. V² = (lw)(wh)(lh) = 15 × 20 × 12 = 3600. Therefore, V = √3600 = 60 cm³.
76
What is the surface area of a rectangular prism with length 5 cm, width 4 cm, and height 2 cm?
Answer:
76 cm²
Surface Area = 2(lw + wh + lh) = 2(5×4 + 4×2 + 5×2) = 2(20 + 8 + 10) = 2(38) = 76 cm².
77
A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.
Answer:
2.5 m
Volume of earth dug out = Volume of well (cylinder) = πr²h = (22/7) × (3.5)² × 20 = (22/7) × 12.25 × 20 = 770 m³. Volume of platform = length × width × height = 22 × 14 × h. So, 308h = 770, giving h = 770 / 308 = 2.5 m.
78
If the perimeters of the base of two cylinders are in the ratio 3:4 and their heights are in the ratio 4:5, what is the ratio of their lateral surface areas?
Answer:
3:5
Lateral surface area = Perimeter of base × height. Let the perimeters be 3P and 4P, and heights be 4H and 5H. Area ratio = (3P × 4H) : (4P × 5H) = 12 : 20 = 3 : 5.
79
A right triangle with sides 3 cm, 4 cm, and 5 cm is revolved about the 4 cm side to form a cone. What is the volume of the cone generated?
Answer:
12π cm³
When revolved about the 4 cm side, the height of the cone becomes 4 cm, and the base radius becomes 3 cm. Volume = (1/3)πr²h = (1/3)π(3)²(4) = (1/3)π(9)(4) = 12π cm³.
80
A cone of height 24 cm and base radius 6 cm is made up of modeling clay. A child reshapes it into a sphere. Find the radius of the sphere.
Answer:
6 cm
Volume of cone = (1/3)π(6)²(24) = 288π. Volume of sphere = (4/3)πr³. Since volumes are equal, (4/3)πr³ = 288π. r³ = (288 × 3) / 4 = 72 × 3 = 216. Therefore, r = 6 cm.