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
121
What is the value of tan(30°)?
Answer:
1/√3
The tangent of 30 degrees is calculated by dividing sin(30°) by cos(30°). Since sin(30°) = 1/2 and cos(30°) = √3/2, the ratio is (1/2) / (√3/2) = 1/√3.
122
From a point 20m away from the foot of a tower, the angle of elevation of the top is 60°. What is the height of the tower?
Answer:
20√3 m
Let the height of the tower be h. The horizontal distance is 20m. Using the tangent function: tan(60°) = opposite/adjacent = h / 20. We know tan(60°) = √3. Therefore, √3 = h / 20, which gives h = 20√3 meters.
123
What is the value of sin²(45°) + cos²(45°)?
Answer:
1
According to the fundamental Pythagorean identity, sin²(θ) + cos²(θ) = 1 for any angle θ. Therefore, regardless of the specific angle being 45°, the sum of their squares is always exactly 1.
124
If sec(θ) = 13/5, find the value of cos(θ).
Answer:
5/13
The secant function, sec(θ), is defined as the reciprocal of the cosine function. Therefore, cos(θ) = 1 / sec(θ). Given sec(θ) = 13/5, taking the reciprocal gives cos(θ) = 5/13.
125
Find the value of cos(60°).
Answer:
1/2
In a right triangle, cos(60°) is equivalent to sin(30°) due to complementary angles. Since sin(30°) = 1/2, it strictly follows that cos(60°) is also exactly 1/2.
126
What is the maximum value of the function y = sin(x)?
Answer:
1
The sine function represents the y-coordinate of a point on the unit circle. The maximum y-coordinate on a unit circle (radius 1) is exactly 1, occurring at 90°, 450°, etc. Therefore, the maximum value of sin(x) is 1.
127
If sin(θ) = 4/5 and θ is in the first quadrant, what is cos(θ)?
Answer:
3/5
Using the Pythagorean identity sin²(θ) + cos²(θ) = 1, we get (4/5)² + cos²(θ) = 1. This gives 16/25 + cos²(θ) = 1, so cos²(θ) = 1 - 16/25 = 9/25. Since θ is in the first quadrant, cosine is positive, so cos(θ) = 3/5.
128
Which of the following is equivalent to cot(θ)?
Answer:
1/tan(θ)
The cotangent function, cot(θ), is defined as the ratio of the adjacent side to the opposite side. This is the exact reciprocal of the tangent function (opposite/adjacent). Therefore, cot(θ) = 1 / tan(θ) or cos(θ)/sin(θ).
129
Convert π/3 radians into degrees.
Answer:
60°
To convert radians to degrees, we multiply by (180 / π). Therefore, (π / 3) * (180 / π) = 180 / 3 = 60°.
130
The shadow of a vertical tower is equal to its height. What is the angle of elevation of the sun?
Answer:
45°
Let the height of the tower be 'h' and the length of the shadow be 'x'. We are given h = x. The tangent of the angle of elevation θ is tan(θ) = opposite/adjacent = h/x. Since h = x, tan(θ) = 1. The angle whose tangent is 1 is 45°.