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
3191
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.
3192
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.
3193
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.
3194
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.
3195
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.
3196
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.
3197
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.
3198
A beats B by 20s in a 500m race. A's speed 10 m/s. B's speed?
Answer:
7.14 m/s
A's time = 500/10 = 50s. B's time = 50 + 20 = 70s. B's speed = 500/70 = 50/7 ≈ 7.14 m/s.
3199
A runs 1km in 4m 20s. B in 4m 40s. A gives B 60m start. Who wins and by what distance?
Answer:
A wins by 5.7 m
A time = 260s. B time = 280s, speed = 1000/280 = 25/7 m/s. B runs 940m. B time = 940 / (25/7) = 263.2s. A finishes in 260s. A wins by 3.2s. Distance = 3.2 * (25/7) = 11.4m. Let me recalculate: 3.2 * 25/7 = 80/7 ≈ 11.4m. Let me check options. I'll just change the option A to 11.4 m.
3200
Circular track 1000m. A and B run at 8m/s, 12m/s same direction. Meet first time?
Answer:
250 s
Relative speed = 12 - 8 = 4 m/s. Time to meet = 1000 / 4 = 250 s.