All Categories MCQs
Topic Notes: All Categories
General Description
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
3031
A sphere of radius 3 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 6 cm. If the sphere is completely submerged, by how much will the water level rise?
Answer:
1 cm
The volume of the displaced water equals the volume of the sphere. Volume of sphere = (4/3)π(3³) = 36π. The volume of the displaced cylindrical water = π * R² * h = π * 6² * h = 36π * h. Equating them: 36π = 36π * h, giving h = 1 cm.
3032
If a cone, a cylinder, and a hemisphere have the same base radius and the same height, what is the ratio of their volumes?
Answer:
1:3:2
Let radius be r. Since height h = r for all shapes. Volume of cone = (1/3)πr²(r) = (1/3)πr³. Volume of cylinder = πr²(r) = πr³. Volume of hemisphere = (2/3)πr³. The ratio is (1/3) : 1 : (2/3), which scales to 1 : 3 : 2.
3033
Find the area of a circle whose radius is 10 cm. (Use π ≈ 3.14)
Answer:
314 cm²
The area formula for a circle is A = πr². Substituting the values: A = 3.14 * 10² = 3.14 * 100 = 314 cm².
3034
Which theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides?
Answer:
Pythagorean Theorem
The Pythagorean Theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that a² + b² = c².
3035
A quadrilateral with exactly one pair of parallel sides is called a:
Answer:
Trapezium
By geometric definition, a trapezium (or trapezoid) is a convex quadrilateral that has exactly one pair of parallel opposite sides.
3036
What is the equation of a straight line with slope 3 passing through the y-intercept (0, 4)?
Answer:
y = 3x + 4
The slope-intercept form of a line is y = mx + c, where m is the slope and c is the y-intercept. Here, m = 3 and c = 4. Thus, the equation is y = 3x + 4.
3037
Find the slope of a line passing through the points (2, 5) and (4, 9).
Answer:
2
The slope formula is m = (y2 - y1) / (x2 - x1). Substituting the points: m = (9 - 5) / (4 - 2) = 4 / 2 = 2.
3038
What is the distance of the point (-3, 4) from the origin?
Answer:
5 units
The distance from the origin (0,0) to any point (x,y) is given by √(x² + y²). Here, distance = √((-3)² + 4²) = √(9 + 16) = √25 = 5 units.
3039
If the sum of two adjacent angles on a straight line is 180 degrees, they are called:
Answer:
Linear pair
A linear pair consists of two adjacent angles created by intersecting lines. Because they form a straight line, their measures always add up to exactly 180 degrees.
3040
In a circle, the angle subtended by an arc at the center is double the angle subtended by it at:
Answer:
Any point on the remaining part of the circle
The Inscribed Angle Theorem states that the angle subtended by an arc at the center of a circle is exactly double the angle subtended by the same arc at any point on the remaining circumference.