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
101
The point of intersection of the altitudes of a triangle is called the:
Answer:
Orthocenter
In geometry, the point where all three altitudes of a triangle intersect is specifically known as the orthocenter.
102
Which set of side lengths can form a valid triangle?
Answer:
5, 6, 10
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides must be strictly greater than the length of the third side. In option C: 5+6>10, 6+10>5, and 5+10>6. All conditions are satisfied.
103
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.
104
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.
105
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.
106
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).
107
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.
108
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.
109
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.
110
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.