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
A belt runs over two pulleys of radii 10 cm and 20 cm. If the smaller pulley turns through 4 radians, through what angle does the larger pulley turn?
Answer:
2 rad
Since the belt connects both pulleys, the linear distance (arc length) traveled by the rim of both pulleys must be completely equal. Let this distance be l. l = r1*θ1 = r2*θ2. Substituting values: 10 * 4 = 20 * θ2, which implies 40 = 20 * θ2. Therefore, θ2 = 2 radians.
42
What is the equivalent of 10π/9 radians in degrees?
Answer:
200°
To convert to degrees, we can simply substitute 180° for the π symbol. The calculation becomes 10 * 180° / 9 = 10 * 20° = exactly 200°.
43
If a regular polygon has 12 sides, what is the measure of its exterior angle in radians?
Answer:
π/6
The sum of the exterior angles of any convex polygon is precisely 2π radians. For a regular dodecagon (12 sides), each exterior angle is exactly 2π / 12 = π/6 radians.
44
A satellite moves along a circular orbit of radius 6000 km. It sweeps an angle of 0.5 radians. Find the distance traveled by the satellite.
Answer:
3000 km
The distance traveled corresponds strictly to the arc length. Using the formula l = rθ: l = 6000 km * 0.5 rad = 3000 km.
45
A circle is divided into 5 equal sectors. What is the central angle of each sector in radians?
Answer:
2π/5
A complete circle consists of exactly 2π radians. Dividing this equally into 5 separate sectors gives an angle of 2π/5 radians for each individual sector.
46
The angle of a sector is 2 radians and its perimeter is 24 cm. Find the radius of the circle.
Answer:
6 cm
The perimeter of a sector is P = 2r + l, where l is the arc length. Since l = rθ and θ = 2, we have l = 2r. The perimeter becomes P = 2r + 2r = 4r. Given P = 24, we solve 4r = 24, yielding r = 6 cm.
47
What is the equivalent of 30 minutes (30') in radians?
Answer:
π/360
30 minutes is precisely half of a degree (0.5°). To convert 0.5° to radians, multiply by π/180. Thus, 0.5 * (π/180) = π/360 radians.
48
Find the length of the shadow cast by a 1m stick if the sun is at an angle of elevation of π/3 radians.
Answer:
1/√3 m
Let shadow length be x. Using the tangent function: tan(π/3) = height / shadow = 1 / x. Since tan(π/3) = √3, we have √3 = 1 / x, which directly gives x = 1/√3 meters.
49
A central angle subtends an arc of length 3π m in a circle of area 36π m². What is the angle in radians?
Answer:
π/2
From the area A = πr², we get 36π = πr², so r² = 36, giving r = 6 m. Now, using θ = l/r, we find θ = 3π / 6 = π/2 radians.
50
Convert the angle -2π/3 radians to a positive coterminal angle in degrees.
Answer:
240°
First, convert -2π/3 to degrees: -2(180°)/3 = -120°. To find the positive coterminal angle, add a full circle (360°): -120° + 360° = 240°.