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
221
What is the side length of a rhombus if its diagonals are 10 cm and 24 cm?
Answer:
13 cm
The diagonals of a rhombus bisect each other at right angles (90 degrees). This forms four right-angled triangles. The legs of each triangle are half the diagonals: 5 cm and 12 cm. The side of the rhombus is the hypotenuse: √(5² + 12²) = √(25 + 144) = √169 = 13 cm.
222
What is the perimeter of a kite if its two distinct adjacent side lengths are 8 cm and 12 cm?
Answer:
40 cm
A kite has two pairs of equal-length adjacent sides. Thus, the perimeter is the sum of all four sides: 2 * (side1) + 2 * (side2). Perimeter = 2(8) + 2(12) = 16 + 24 = 40 cm.
223
In a parallelogram, if adjacent angles are (2x - 10) degrees and (3x + 40) degrees, what is the value of x?
Answer:
30
Adjacent angles in a parallelogram are supplementary (they add up to 180 degrees). So, (2x - 10) + (3x + 40) = 180. Simplifying: 5x + 30 = 180, which means 5x = 150. Dividing by 5 gives x = 30.
224
A trapezium has an area of 105 cm² and a height of 7 cm. If one of its parallel sides is 12 cm, find the length of the other parallel side.
Answer:
18 cm
Area = (1/2) * (a + b) * h. Here, 105 = (1/2) * (12 + b) * 7. Multiplying by 2/7 gives (105 * 2) / 7 = 12 + b, which simplifies to 210 / 7 = 12 + b. Therefore, 30 = 12 + b, meaning b = 18 cm.
225
The perimeter of a rhombus is 52 cm. What is the length of its side?
Answer:
13 cm
A rhombus has four equal sides, similar to a square. The perimeter is 4 * side. Therefore, the length of one side is Perimeter / 4 = 52 / 4 = 13 cm.
226
What is the area of a trapezium with parallel sides of 10 cm and 14 cm, and a height of 6 cm?
Answer:
72 cm²
The area of a trapezium is calculated as: Area = (1/2) * (Sum of parallel sides) * height. Area = (1/2) * (10 + 14) * 6 = (1/2) * 24 * 6 = 12 * 6 = 72 cm².
227
If the area of a rhombus is 150 cm² and one of its diagonals is 15 cm, what is the length of the other diagonal?
Answer:
20 cm
Using the area formula for a rhombus: Area = (1/2) * d1 * d2. We have 150 = (1/2) * 15 * d2. Multiplying both sides by 2 gives 300 = 15 * d2. Dividing by 15 gives d2 = 20 cm.
228
Find the area of a rhombus whose diagonals measure 16 cm and 12 cm.
Answer:
96 cm²
The area of a rhombus can be calculated using its diagonals (d1 and d2). Formula: Area = (1/2) * d1 * d2. Substituting the given values: Area = (1/2) * 16 * 12 = 8 * 12 = 96 cm².
229
What is the area of a parallelogram with a base of 15 cm and a corresponding height of 8 cm?
Answer:
120 cm²
The area of a parallelogram is calculated by multiplying the base by its corresponding vertical height. Formula: Area = base * height. Substituting the values: Area = 15 cm * 8 cm = 120 cm².
230
If the length of a rectangle is increased by 10% and its breadth is decreased by 10%, what is the net change in its area?
Answer:
1% decrease
Let the original length and breadth be L and B. Original Area = LB. New length = 1.1L, new breadth = 0.9B. New Area = 1.1L * 0.9B = 0.99LB. This represents a 1% decrease from the original area (1LB - 0.99LB = 0.01LB).