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
71
Which of the following is the quadratic equation with roots 0 and 5?
Answer:
x^2 - 5x = 0
The roots are 0 and 5, so the factors are (x - 0) and (x - 5). Multiplying these gives x(x - 5) = x^2 - 5x = 0.
72
Form a quadratic equation whose roots have a sum of -2 and a product of -15.
Answer:
x^2 + 2x - 15 = 0
Using x^2 - Sx + P = 0, where S = -2 and P = -15. Substitute these values to get x^2 - (-2)x + (-15) = 0, which simplifies to x^2 + 2x - 15 = 0.
73
What is the quadratic equation if the sum of its roots is 4 and the product is 4?
Answer:
x^2 - 4x + 4 = 0
The standard form of an equation from its sum (S) and product (P) of roots is x^2 - Sx + P = 0. Substituting S=4 and P=4, we get x^2 - 4x + 4 = 0.
74
Find the quadratic equation whose roots are 4 and 5.
Answer:
x^2 - 9x + 20 = 0
The sum of the roots is 4+5=9, and the product is 4*5=20. Using the format x^2 - (sum)x + (product) = 0, the equation is x^2 - 9x + 20 = 0.
75
Which equation has roots -1 and 1?
Answer:
x^2 - 1 = 0
If the roots are -1 and 1, the factors are (x+1) and (x-1). Multiplying these gives (x+1)(x-1) = x^2 - 1 = 0.
76
Which quadratic equation has roots 2 and 3?
Answer:
x^2 - 5x + 6 = 0
An equation with roots alpha and beta is given by x^2 - (alpha + beta)x + (alpha*beta) = 0. Here, sum = 2+3=5 and product = 2*3=6. Therefore, the equation is x^2 - 5x + 6 = 0.
77
Solve the quadratic equation 2x^2 + 5x - 3 = 0.
Answer:
1/2 and -3
Multiply a and c (2*-3 = -6). Find factors of -6 that add to 5, which are 6 and -1. Rewrite: 2x^2 + 6x - x - 3 = 0. Factor by grouping: 2x(x+3) - 1(x+3) = 0. (2x-1)(x+3) = 0. Roots are 1/2 and -3.
78
Solve the equation x^2 + 4x - 21 = 0.
Answer:
-7 and 3
The factors of -21 that add up to 4 are 7 and -3. Factoring gives (x+7)(x-3)=0, which yields the roots x=-7 and x=3.
79
The roots of x^2 - 11x + 30 = 0 are:
Answer:
5 and 6
Factors of 30 that sum to -11 are -5 and -6. Thus, the equation can be written as (x-5)(x-6)=0, giving the roots 5 and 6.
80
Solve the equation x^2 + 2x - 8 = 0.
Answer:
-4 and 2
We need numbers that multiply to -8 and add to 2. These are 4 and -2. The factored equation is (x+4)(x-2)=0, leading to roots x=-4 and x=2.