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
241
A triangle has sides 7 cm, 24 cm, and 25 cm. What type of triangle is it?
Answer:
Right-angled triangle
Check if the sides satisfy the Pythagorean theorem (a² + b² = c²). Here, 7² + 24² = 49 + 576 = 625. Since 25² is also 625, the square of the longest side equals the sum of the squares of the other two sides, making it a right-angled triangle.
242
Using Heron's formula, calculate the semi-perimeter (s) of a triangle with sides 8 cm, 15 cm, and 17 cm.
Answer:
20 cm
The semi-perimeter (s) of a triangle is half of its total perimeter. Formula: s = (a + b + c) / 2. Substituting the sides: s = (8 + 15 + 17) / 2 = 40 / 2 = 20 cm.
243
If two angles of a triangle are 45 degrees and 65 degrees, what is the measure of the third angle?
Answer:
70 degrees
The sum of all interior angles in a triangle is 180 degrees. To find the third angle, subtract the sum of the given angles from 180: 180 - (45 + 65) = 180 - 110 = 70 degrees.
244
What is the sum of the interior angles of a triangle?
Answer:
180 degrees
A fundamental geometric rule states that the sum of the interior angles of any planar triangle always equals exactly 180 degrees, regardless of the triangle's shape or size.
245
In a right-angled triangle, if the hypotenuse is 13 cm and one leg is 5 cm, find the length of the other leg.
Answer:
12 cm
According to the Pythagorean theorem, a² + b² = c², where c is the hypotenuse. We have 5² + b² = 13², which simplifies to 25 + b² = 169. Subtracting 25 gives b² = 144, so b = √144 = 12 cm.
246
Find the area of an equilateral triangle with a side length of 6 cm.
Answer:
9√3 cm²
The formula for the area of an equilateral triangle is (√3 / 4) * side². Substituting the side length of 6 cm: Area = (√3 / 4) * 6² = (√3 / 4) * 36 = 9√3 cm².
247
What is the perimeter of an equilateral triangle with a side length of 7 cm?
Answer:
21 cm
An equilateral triangle has all three sides of equal length. The perimeter is the sum of all sides. Therefore, Perimeter = 3 * side length = 3 * 7 cm = 21 cm.
248
If the sides of a triangle are 3 cm, 4 cm, and 5 cm, what is its area?
Answer:
6 cm²
The given sides 3 cm, 4 cm, and 5 cm form a Pythagorean triplet (3² + 4² = 5²), which means it is a right-angled triangle. The area is (1/2) * base * height = (1/2) * 3 * 4 = 6 cm².
249
What is the area of a triangle with a base of 12 cm and a height of 8 cm?
Answer:
48 cm²
The area of a triangle is calculated using the formula: Area = (1/2) * base * height. By substituting the given values into the formula, we get: Area = (1/2) * 12 cm * 8 cm = 6 cm * 8 cm = 48 cm².