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
211
What is the sum of the exterior angles of a decagon?
Answer:
360 degrees
The sum of the exterior angles (one per vertex) of any simple convex polygon, regardless of the number of sides, is always 360 degrees.
212
If an interior angle of a regular polygon is 150 degrees, how many sides does it have?
Answer:
12
If the interior angle is 150 degrees, the corresponding exterior angle is 180 - 150 = 30 degrees. The number of sides n = 360 / exterior angle. Thus, n = 360 / 30 = 12 sides.
213
A polygon has 20 diagonals. How many sides does it have?
Answer:
8
The formula for the number of diagonals is n(n - 3) / 2 = 20. Multiplying by 2 gives n(n - 3) = 40. The factors of 40 that differ by 3 are 8 and 5 (so n=8 and n-3=5). Thus, the polygon has 8 sides (an octagon).
214
What is the measure of each exterior angle of a regular hexagon?
Answer:
60 degrees
The sum of the exterior angles of any polygon is 360 degrees. A regular hexagon has 6 equal exterior angles. Each exterior angle = 360 / 6 = 60 degrees.
215
The sum of the interior angles of a polygon is 1260 degrees. How many sides does it have?
Answer:
9
Using the formula for the sum of interior angles: (n - 2) * 180 = 1260. Dividing by 180 gives (n - 2) = 7. Adding 2 gives n = 9. The polygon is a nonagon (9 sides).
216
If the exterior angle of a regular polygon is 40 degrees, how many sides does the polygon have?
Answer:
9
The sum of the exterior angles of any convex polygon is 360 degrees. For a regular polygon, all exterior angles are equal. Number of sides = 360 / (exterior angle measure) = 360 / 40 = 9 sides.
217
What is the measure of each interior angle in a regular octagon?
Answer:
135 degrees
First, find the sum of the interior angles of an octagon (n = 8): (8 - 2) * 180 = 6 * 180 = 1080 degrees. Since it is regular, all 8 angles are equal. Each interior angle = 1080 / 8 = 135 degrees.
218
How many diagonals does a regular hexagon have?
Answer:
9
The number of diagonals in a polygon with n sides is given by the formula n(n - 3) / 2. For a hexagon, n = 6. Number of diagonals = 6(6 - 3) / 2 = 6(3) / 2 = 18 / 2 = 9.
219
What is the sum of the interior angles of a pentagon?
Answer:
540 degrees
The formula for the sum of interior angles of an n-sided polygon is (n - 2) * 180 degrees. For a pentagon, n = 5. So, Sum = (5 - 2) * 180 = 3 * 180 = 540 degrees.
220
The area of a parallelogram is 64 cm². If the base is 4 times its height, what is the height?
Answer:
4 cm
Let the height be h. Then the base is 4h. Area = base * height = (4h) * h = 4h². Given Area = 64, so 4h² = 64, meaning h² = 16. Therefore, the height h = 4 cm.