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
121
What is the midpoint of the line segment joining (a, b) and (a, -b)?
Answer:
(a, 0)
Step 1: Use the midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2). Step 2: Calculate x: (a + a)/2 = 2a/2 = a. Step 3: Calculate y: (b + (-b))/2 = 0/2 = 0. The midpoint is (a, 0).
122
Find the midpoint of the line segment connecting (-3, -3) and (3, 3).
Answer:
(0, 0)
Step 1: Apply the midpoint formula. Step 2: x-coordinate = (-3 + 3)/2 = 0/2 = 0. Step 3: y-coordinate = (-3 + 3)/2 = 0/2 = 0. The midpoint is the origin (0, 0).
123
What is the midpoint of the line segment joining (2, 4) and (6, 8)?
Answer:
(4, 6)
Step 1: Use the midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2). Step 2: Substitute the given coordinates: x = (2 + 6)/2 = 8/2 = 4; y = (4 + 8)/2 = 12/2 = 6. Step 3: The midpoint is (4, 6).
124
What is the perimeter of the triangle with vertices (0, 0), (3, 0), and (0, 4)?
Answer:
12
Step 1: Calculate the lengths of the three sides using the distance formula. Step 2: Side 1 (0,0 to 3,0) = 3. Side 2 (0,0 to 0,4) = 4. Side 3 (3,0 to 0,4) = √[3² + 4²] = 5. Step 3: Perimeter = sum of sides = 3 + 4 + 5 = 12.
125
Which point on the x-axis is equidistant from the points (2, -5) and (-2, 9)?
Answer:
(-7, 0)
Step 1: Let the point on the x-axis be P(x, 0). Step 2: Set distances equal: √[(x - 2)² + (0 + 5)²] = √[(x + 2)² + (0 - 9)²]. Step 3: Square both sides: x² - 4x + 4 + 25 = x² + 4x + 4 + 81. Step 4: Simplify to -8x = 56, yielding x = -7. Point is (-7, 0).
126
What is the distance between the points (-3, 4) and (3, -4)?
Answer:
10
Step 1: Use the distance formula d = √[(x2 - x1)² + (y2 - y1)²]. Step 2: Substitute coordinates: d = √[(3 - (-3))² + (-4 - 4)²]. Step 3: Simplify: d = √[6² + (-8)²] = √[36 + 64] = √100 = 10.
127
Find the distance between the points (1, 1) and (13, 6).
Answer:
13
Step 1: Use the distance formula. Step 2: d = √[(13 - 1)² + (6 - 1)²]. Step 3: Simplify to d = √[12² + 5²] = √[144 + 25] = √169 = 13.
128
What is the distance between the points (a, 0) and (0, b)?
Answer:
√(a² + b²)
Step 1: Apply the distance formula d = √[(x2 - x1)² + (y2 - y1)²]. Step 2: Substitute the given points: d = √[(0 - a)² + (b - 0)²]. Step 3: Simplify the expression to get d = √(a² + b²).
129
What is the distance between the origin and the point (-8, 6)?
Answer:
10
Step 1: The distance from the origin (0,0) to a point (x,y) is given by d = √(x² + y²). Step 2: Substitute the values: d = √((-8)² + 6²). Step 3: Simplify to d = √[64 + 36] = √100 = 10.
130
Calculate the distance between the points (-1, -1) and (2, 3).
Answer:
5
Step 1: Use d = √[(x2 - x1)² + (y2 - y1)²]. Step 2: Substitute points: d = √[(2 - (-1))² + (3 - (-1))²]. Step 3: Simplify: d = √[3² + 4²] = √[9 + 16] = √25 = 5.