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
1
Find sin 60°.
Answer:
0.866
Step-by-step solution: 1. Recall standard trigonometric values. 2. For angle 60°, sin value is 0.866. 3. Convert to radians if needed: 60° = 1.047 rad.
2
Find sin 75°.
Answer:
0.966
Step-by-step solution: 1. Recall standard trigonometric values. 2. For angle 75°, sin value is 0.966. 3. Convert to radians if needed: 75° = 1.309 rad.
3
Find sin 30°.
Answer:
0.5
Step-by-step solution: 1. Recall standard trigonometric values. 2. For angle 30°, sin value is 0.5. 3. Convert to radians if needed: 30° = 0.524 rad.
4
Find sin 45°.
Answer:
0.707
Step-by-step solution: 1. Recall standard trigonometric values. 2. For angle 45°, sin value is 0.707. 3. Convert to radians if needed: 45° = 0.785 rad.
5
Evaluate the expression: sin²(θ) + sin²(90° - θ)
Answer:
1
Using complementary angles, we know that sin(90° - θ) is identical to cos(θ). Therefore, sin²(90° - θ) equals cos²(θ). The expression simplifies to sin²(θ) + cos²(θ), which is the fundamental Pythagorean identity that always equals 1.
6
Which of these functions is completely positive in the 4th quadrant?
Answer:
Cosine
In Cartesian coordinates, the fourth quadrant has positive x-values and negative y-values. Since cosine represents the x-coordinate on the unit circle, the cosine function (and its reciprocal secant) is the only primary trigonometric function that remains positive there.
7
The angle of elevation of a tower is 45° from a point 50m away from its base. What is the height of the tower?
Answer:
50 m
Using the tangent function: tan(45°) = height / adjacent_distance. Because tan(45°) = 1, the ratio height/50 must equal 1. Thus, the height of the tower perfectly equals the distance, which is 50m.
8
Find the value of sin(15°) / cos(15°).
Answer:
tan(15°)
By definition, the ratio of the sine of any angle to the cosine of that same angle is identically the tangent of that angle. Therefore, sin(15°) / cos(15°) rigorously simplifies to tan(15°).
9
If tan(θ) = undefined in the interval [0, 2π], what are the values of θ?
Answer:
π/2, 3π/2
Tangent is defined as sin(θ) / cos(θ). The function becomes undefined exactly where the denominator, cos(θ), is zero. Within a single circle [0, 2π], cosine is zero at the angles 90° (π/2) and 270° (3π/2).
10
What is the equivalent of cos(-x)?
Answer:
cos(x)
The cosine function is fundamentally an even function, which mathematically means that f(-x) must equal f(x) for all values in its domain. Consequently, cos(-x) = cos(x).