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
111
What is the slope of the line joining the points (-1, -1) and (2, 2)?
Answer:
1
Step 1: Apply the slope formula m = (y2 - y1) / (x2 - x1). Step 2: Substitute: m = (2 - (-1)) / (2 - (-1)). Step 3: Simplify: m = (2 + 1) / (2 + 1) = 3 / 3 = 1.
112
Find the slope of the line passing through the points (1, 2) and (3, 6).
Answer:
2
Step 1: Use the slope formula m = (y2 - y1) / (x2 - x1). Step 2: Substitute the given values: m = (6 - 2) / (3 - 1). Step 3: Compute the result: m = 4 / 2 = 2.
113
What is the slope of the line passing through the points (0, 0) and (3, 3)?
Answer:
1
Step 1: Use the slope formula m = (y2 - y1) / (x2 - x1). Step 2: Substitute the coordinates: m = (3 - 0) / (3 - 0). Step 3: Simplify: m = 3 / 3 = 1.
114
What is the center of a circle if the endpoints of its diameter are (-4, 2) and (4, -2)?
Answer:
(0, 0)
Step 1: The center of a circle is the midpoint of its diameter. Step 2: Use the midpoint formula for (-4, 2) and (4, -2). Step 3: x = (-4 + 4)/2 = 0; y = (2 + (-2))/2 = 0. The center is the origin (0, 0).
115
For the points A(-2, 4) and B(4, -2), what is the midpoint of segment AB?
Answer:
(1, 1)
Step 1: Use the midpoint formula. Step 2: x-coordinate = (-2 + 4)/2 = 2/2 = 1. Step 3: y-coordinate = (4 + (-2))/2 = 2/2 = 1. The midpoint is (1, 1).
116
The midpoint of the line segment joining the origin (0, 0) and the point (10, 10) is:
Answer:
(5, 5)
Step 1: Apply the midpoint formula to points (0,0) and (10,10). Step 2: x = (0 + 10)/2 = 5. Step 3: y = (0 + 10)/2 = 5. The midpoint is (5, 5).
117
If (x, y) is the midpoint of the line segment joining (2, 3) and (4, 7), what is the value of x + y?
Answer:
8
Step 1: Find the midpoint coordinates. x = (2 + 4)/2 = 3. y = (3 + 7)/2 = 5. Step 2: The midpoint is (3, 5). Step 3: Calculate the sum: x + y = 3 + 5 = 8.
118
Find the coordinates of the point that divides the line segment joining (1, 2) and (3, 6) internally in the ratio 1:1.
Answer:
(2, 4)
Step 1: Dividing a segment in a 1:1 ratio is the same as finding the midpoint. Step 2: x = (1 + 3)/2 = 4/2 = 2. Step 3: y = (2 + 6)/2 = 8/2 = 4. The point is (2, 4).
119
What is the midpoint of the line segment connecting (-5, 7) and (3, -1)?
Answer:
(-1, 3)
Step 1: Use the midpoint formula. Step 2: x = (-5 + 3)/2 = -2/2 = -1. Step 3: y = (7 + (-1))/2 = 6/2 = 3. The midpoint is (-1, 3).
120
One endpoint of a circle's diameter is (1, 2) and its center is (3, 4). What is the other endpoint?
Answer:
(5, 6)
Step 1: Let the other endpoint be (x, y). The center is the midpoint of the diameter. Step 2: Set up equations: (1 + x)/2 = 3 and (2 + y)/2 = 4. Step 3: Solve for x and y: 1 + x = 6 => x = 5; 2 + y = 8 => y = 6. The point is (5, 6).