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
Determine the discriminant of the equation 2x^2 - 5x + 3 = 0.
Answer:
1
Here, a=2, b=-5, and c=3. The discriminant D = b^2 - 4ac = (-5)^2 - 4(2)(3) = 25 - 24 = 1. Since D > 0, the equation has two distinct real roots.
112
If the discriminant of a quadratic equation is greater than zero, what is the nature of its roots?
Answer:
Real and distinct
A positive discriminant (D > 0) indicates that the quadratic equation has two distinct real roots. Geometrically, this means the parabola intersects the x-axis at two separate points.
113
If the discriminant of a quadratic equation is exactly zero, what can be said about its roots?
Answer:
They are real and equal
When the discriminant (b^2 - 4ac) equals zero, the quadratic equation has two real and identical roots. This means the parabola touches the x-axis at exactly one point.
114
Which of the following is the correct formula for the discriminant of a quadratic equation?
Answer:
b^2 - 4ac
The discriminant of a quadratic equation ax^2 + bx + c = 0 is represented by the formula D = b^2 - 4ac. It is used to determine the nature of the roots of the equation.
115
What is the geometric shape of the graph of a quadratic function y = ax^2 + bx + c?
Answer:
Parabola
The graph of a quadratic function always forms a U-shaped curve known as a parabola. Depending on the sign of 'a', it either opens upwards (a > 0) or downwards (a < 0).
116
If a = 0 in the equation ax^2 + bx + c = 0, what type of equation does it become?
Answer:
Linear equation
If a = 0, the x^2 term is eliminated, and the equation reduces to bx + c = 0. Since the highest degree of x is now 1, it becomes a linear equation.
117
What is the coefficient of x^2 in the equation 4x^2 - 7x + 3 = 0?
Answer:
4
In the standard form ax^2 + bx + c = 0, 'a' represents the coefficient of x^2. In the given equation 4x^2 - 7x + 3 = 0, the coefficient of x^2 is 4.
118
What is the maximum number of real roots a quadratic equation can have?
Answer:
2
According to the fundamental theorem of algebra, a polynomial of degree n has exactly n roots. Therefore, a quadratic equation (degree 2) can have a maximum of 2 real roots.
119
Which of the following is a quadratic equation?
Answer:
x^2 - 5x + 6 = 0
The equation x^2 - 5x + 6 = 0 is a quadratic equation because the highest power of the variable x is 2. The others are cubic, linear, and quartic equations, respectively.
120
What is the degree of a quadratic equation?
Answer:
2
A quadratic equation is a polynomial equation of the second degree, which means the highest exponent of the variable x is always 2.