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
81
What is the sum of the x-intercept and the y-intercept of the line x + y = 5?
Answer:
10
Step 1: Find the x-intercept by setting y = 0: x + 0 = 5, so x-intercept = 5. Step 2: Find the y-intercept by setting x = 0: 0 + y = 5, so y-intercept = 5. Step 3: Add the two intercepts together: 5 + 5 = 10.
82
In the intercept form of a linear equation x/a + y/b = 1, what do 'a' and 'b' represent respectively?
Answer:
X-intercept and y-intercept
Step 1: If we set y=0, we get x/a = 1, which means x=a. Thus, 'a' is the x-intercept. Step 2: If we set x=0, we get y/b = 1, which means y=b. Thus, 'b' is the y-intercept. Step 3: Therefore, 'a' and 'b' are the x-intercept and y-intercept.
83
What is the y-intercept of the line given by 4x - 5y = 20?
Answer:
-4
Step 1: The y-intercept occurs where the line crosses the y-axis, meaning the x-coordinate is 0. Step 2: Substitute x = 0 into the equation: 4(0) - 5y = 20. Step 3: Solve for y: -5y = 20, yielding y = -4.
84
What is the x-intercept of the line given by 2x + 3y = 12?
Answer:
6
Step 1: The x-intercept occurs where the line crosses the x-axis, which means the y-coordinate is 0. Step 2: Substitute y = 0 into the equation: 2x + 3(0) = 12. Step 3: Solve for x: 2x = 12, yielding x = 6.
85
What is the slope of a line parallel to the line 5x + 5y = 1?
Answer:
-1
Step 1: Convert to slope-intercept form to find the slope. Step 2: 5y = -5x + 1, which implies y = -1x + 1/5. Step 3: The slope of this line is -1. Parallel lines have equal slopes, so the required slope is also -1.
86
The lines represented by y = x and y = -x are:
Answer:
Perpendicular
Step 1: Find the slope of the first line (y = x). The slope m1 is 1. Step 2: Find the slope of the second line (y = -x). The slope m2 is -1. Step 3: Multiply the slopes: 1 * (-1) = -1. Since the product is -1, the lines are perpendicular.
87
The equations 3x + 4y = 5 and 6x + 8y = 10 represent lines that are:
Answer:
Coincident
Step 1: Check the ratio of coefficients. a1/a2 = 3/6 = 1/2. b1/b2 = 4/8 = 1/2. c1/c2 = 5/10 = 1/2. Step 2: Since a1/a2 = b1/b2 = c1/c2, the equations represent the exact same line. Step 3: Lines that are exactly the same are called coincident.
88
Find the slope of a line that is perpendicular to the line 3x - y = 8.
Answer:
-1/3
Step 1: Rewrite the given equation in slope-intercept form: y = 3x - 8. The slope is 3. Step 2: A perpendicular line will have a slope that is the negative reciprocal of 3. Step 3: The negative reciprocal of 3 is -1/3.
89
What is the equation of the line perpendicular to x - y = 0 passing through the origin?
Answer:
x + y = 0
Step 1: Find the slope of x - y = 0. Rewrite as y = x. The slope is 1. Step 2: The perpendicular slope is the negative reciprocal: -1/1 = -1. Step 3: Using y = mx + c with m = -1 and passing through (0,0), we get y = -1x + 0, which is x + y = 0.
90
What is the equation of the line parallel to 2x + 3y = 6 passing through the origin (0,0)?
Answer:
2x + 3y = 0
Step 1: Lines parallel to ax + by = c have the form ax + by = k. Step 2: The parallel line must be 2x + 3y = k. Step 3: Since it passes through (0,0), substitute x=0, y=0 to find k. 2(0) + 3(0) = k, so k = 0. The equation is 2x + 3y = 0.