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
If x^2 - 10x + 21 = 0, what are the possible values for x?
Answer:
3 and 7
Find factors of 21 that add up to -10. The numbers are -3 and -7. The equation factors as (x-3)(x-7) = 0, which means x=3 or x=7.
82
Find the roots of 4x^2 - 9 = 0.
Answer:
3/2 and -3/2
This is a difference of squares. It factors to (2x - 3)(2x + 3) = 0. Setting each factor to zero yields 2x=3 (or x=3/2) and 2x=-3 (or x=-3/2).
83
Solve the quadratic equation x^2 - 2x - 15 = 0.
Answer:
5 and -3
Find two numbers that multiply to -15 and add to -2. These numbers are -5 and 3. The factored form is (x-5)(x+3)=0. The roots are x=5 and x=-3.
84
What is the positive root of x^2 - 64 = 0?
Answer:
8
Rearrange the equation to x^2 = 64. The roots are x = 8 and x = -8. The question asks specifically for the positive root, which is 8.
85
The roots of the equation x^2 - 3x = 0 are:
Answer:
0 and 3
Factor out the common x to get x(x - 3) = 0. By the zero product property, the roots are x = 0 and x = 3.
86
What are the roots of the equation 3x^2 - 12 = 0?
Answer:
2 and -2
Add 12 to both sides to get 3x^2 = 12. Divide by 3 to get x^2 = 4. Taking the square root gives x = 2 and x = -2.
87
Find the roots of x^2 + 8x + 16 = 0.
Answer:
-4 and -4
This is a perfect square trinomial. It factors into (x+4)^2 = 0. Therefore, the equation has two equal real roots, both being x = -4.
88
What are the roots of the equation x(x - 5) = 0?
Answer:
0 and 5
By the Zero Product Property, if a*b = 0, then a=0 or b=0. Setting each factor to zero: x = 0 or x - 5 = 0. Therefore, the roots are x = 0 and x = 5.
89
Solve the equation (x - 2)^2 = 0.
Answer:
2 only
Taking the square root of both sides gives x - 2 = 0. Adding 2 to both sides results in x = 2. This is a repeated (or double) root of the quadratic equation.
90
The solution set of x^2 = 16 is:
Answer:
{4, -4}
Taking the square root of both sides of x^2 = 16 yields two possible solutions, because both 4^2 and (-4)^2 equal 16. Thus, the solution set is {4, -4}.