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
61
Evaluate the product: sin(30°) * cos(60°) * tan(45°)
Answer:
1/4
Substitute the standard values for each term: sin(30°) = 1/2, cos(60°) = 1/2, and tan(45°) = 1. Multiplying these together yields (1/2) * (1/2) * 1 = 1/4.
62
If tan(A) = √3 and A is acute, find the value of sin(A).
Answer:
√3/2
We know from standard trigonometric values that the acute angle whose tangent is √3 is 60°. Evaluating the sine for this angle gives sin(60°) = √3/2.
63
Which expression represents the Law of Sines for a triangle?
Answer:
a/sin(A) = b/sin(B) = c/sin(C)
The Law of Sines states that the ratio of a side length to the sine of its opposite angle is identically equal for all three sides of a given triangle. This is expressed as a/sin(A) = b/sin(B) = c/sin(C).
64
What is the equivalent of sin(-θ)?
Answer:
-sin(θ)
The sine function is an odd mathematical function, which means it exhibits origin symmetry. For any odd function f(x), f(-x) must equal -f(x). Thus, sin(-θ) = -sin(θ).
65
If sin(x) = 1, what is the value of x in the range [0, 2π]?
Answer:
π/2
The sine function equals 1 at exactly the peak of its wave. On the unit circle, the y-coordinate is 1 at the top of the circle, which corresponds to an angle of 90 degrees or π/2 radians.
66
Calculate the value of sec²(45°) - tan²(45°).
Answer:
1
According to the Pythagorean identity sec²(θ) - tan²(θ) = 1, this relationship holds true for all values of θ where the functions are defined. Therefore, for 45°, the expression evaluates exactly to 1.
67
What is the sign of tan(200°)?
Answer:
Positive
An angle of 200° falls into the third quadrant (between 180° and 270°). In the third quadrant, both sine and cosine are negative, which makes their ratio (tangent) strictly positive.
68
Evaluate: sin(0°) + cos(0°) + tan(0°)
Answer:
1
We evaluate each standard term: sin(0°) = 0, cos(0°) = 1, and tan(0°) = 0. Adding these values together yields exactly 0 + 1 + 0 = 1.
69
Which trigonometric ratio corresponds to 'adjacent / hypotenuse'?
Answer:
Cosine
Using the mnemonic SOH CAH TOA, 'CAH' stands for Cosine equals Adjacent over Hypotenuse. This is the foundational definition of the cosine function in a right-angled triangle.
70
What is the value of arcsin(sin(150°))?
Answer:
30°
First, find sin(150°), which is sin(180°-30°) = sin(30°) = 1/2. The arcsin function returns the principal angle in the range [-90°, 90°] whose sine is 1/2. Therefore, arcsin(1/2) = 30°.