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
3051
If two lines are perpendicular, the product of their slopes is:
Answer:
-1
For any two non-vertical perpendicular lines, their slopes m1 and m2 are negative reciprocals of each other (m1 = -1/m2). Therefore, their product m1 * m2 is always -1.
3052
What is the slope of a line parallel to the y-axis?
Answer:
Undefined
A line parallel to the y-axis is perfectly vertical. It has zero horizontal change (run) between any two points. Since division by zero is mathematically undefined, the slope is undefined.
3053
A regular polygon has an exterior angle of 72 degrees. What is the name of this polygon?
Answer:
Pentagon
The number of sides n = 360 / exterior angle. Thus, n = 360 / 72 = 5 sides. A 5-sided polygon is a pentagon.
3054
What is the locus of all points in a plane that are equidistant from a fixed point?
Answer:
A circle
A circle is defined as the locus of all points in a two-dimensional plane that are at a constant, fixed distance (the radius) from a single fixed point (the center).
3055
A diagonal of a polygon connects which of the following?
Answer:
Two non-adjacent vertices
By geometric definition, a diagonal is a line segment that connects two non-adjacent vertices (corners) of a polygon.
3056
What is the total surface area of a cube if its volume is 64 cm³?
Answer:
96 cm²
Volume = side³ = 64, meaning the side length is 4 cm. Total Surface Area = 6 * side² = 6 * (4²) = 6 * 16 = 96 cm².
3057
A circle and a square have the same perimeter. Which has the larger area?
Answer:
The circle
According to the isoperimetric inequality in 2D geometry, for any given perimeter, the circle always encloses the maximum possible area compared to any other shape, including a square.
3058
Find the volume of a prism whose base is a right triangle with legs 3 cm and 4 cm, and whose length is 10 cm.
Answer:
60 cm³
Volume = Base Area * length. The base is a right triangle, so Base Area = (1/2) * 3 * 4 = 6 cm². Volume = 6 cm² * 10 cm = 60 cm³.
3059
If the length of a rectangle is halved and its width is tripled, the area of the new rectangle compared to the original is:
Answer:
Increased by 50%
Original Area = L * W. New Area = (L / 2) * (3W) = (3/2) * LW = 1.5 * LW. The area is 1.5 times the original, which represents an increase of 50%.
3060
What is the area of the largest triangle that can be inscribed in a semicircle of radius 'r'?
Answer:
r²
The base of the largest inscribed triangle will be the diameter of the semicircle (2r), and its maximum height will be the radius (r). Area = (1/2) * base * height = (1/2) * 2r * r = r².