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
41
Simplify: cos(A) * tan(A)
Answer:
sin(A)
Using the basic identity tan(A) = sin(A) / cos(A), we substitute this into the expression: cos(A) * (sin(A) / cos(A)). The cos(A) terms in the numerator and denominator cancel out, perfectly leaving sin(A).
42
What is the equivalent of 1 / csc(x)?
Answer:
sin(x)
The cosecant function, csc(x), is formally defined as the reciprocal of the sine function. Therefore, the reciprocal of cosecant, 1 / csc(x), brings us straight back to sin(x).
43
If sin(θ) = cos(θ) for an acute angle θ, what is the value of 2*sin(θ)?
Answer:
√2
Sine and cosine are equal at exactly 45° in the first quadrant. At 45°, sin(45°) = 1/√2. The question asks for 2*sin(θ), which is 2 * (1/√2). Rationalizing this gives √2.
44
What is the value of tan(135°)?
Answer:
-1
Wait, let's re-calculate. 135° is in Quadrant II. Reference angle is 180 - 135 = 45°. Tangent is negative in QII. So tan(135°) = -tan(45°) = -1. Let me adjust the correct option to b.
45
If an angle θ is in the second quadrant, which of the following is true?
Answer:
sin(θ) > 0, cos(θ) < 0
In the second quadrant (between 90° and 180°), the y-coordinates on the unit circle are positive while the x-coordinates are negative. This means sine is positive (>0) and cosine is negative (<0).
46
Which of the following equals cos(2A)?
Answer:
1 - 2*sin²(A)
The double-angle formula for cosine has three standard variations: cos²(A) - sin²(A), 2cos²(A) - 1, and 1 - 2sin²(A). Option B correctly matches the third variation.
47
Evaluate the expression: sin(x)cos(y) + cos(x)sin(y) when x=30° and y=60°.
Answer:
1
This expression matches the sine addition formula: sin(x + y). Substituting the given angles, we get sin(30° + 60°) = sin(90°). The sine of 90 degrees is exactly 1.
48
Find the value of csc(45°).
Answer:
√2
The cosecant function is the reciprocal of the sine function. We know sin(45°) = 1/√2. Taking the reciprocal gives csc(45°) = √2/1 = √2.
49
If the shadow of a tree is √3 times its height, what is the sun's altitude angle?
Answer:
30°
Let height be h and shadow be h√3. The tangent of the elevation angle θ is tan(θ) = opposite(height)/adjacent(shadow) = h / (h√3) = 1/√3. The angle whose tangent is 1/√3 is 30°.
50
What is the exact value of cos(210°)?
Answer:
-√3/2
An angle of 210° lies in the third quadrant, where the cosine function is negative. The reference angle is 210° - 180° = 30°. Therefore, cos(210°) = -cos(30°) = -√3/2.