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
111
If the length of a rectangle is halved and its width is tripled, the area of the new rectangle compared to the original is:
Answer:
Increased by 50%
Original Area = L * W. New Area = (L / 2) * (3W) = (3/2) * LW = 1.5 * LW. The area is 1.5 times the original, which represents an increase of 50%.
112
What is the area of the largest triangle that can be inscribed in a semicircle of radius 'r'?
Answer:
r²
The base of the largest inscribed triangle will be the diameter of the semicircle (2r), and its maximum height will be the radius (r). Area = (1/2) * base * height = (1/2) * 2r * r = r².
113
A conical tent is 10 m high and the radius of its base is 24 m. What is the slant height of the tent?
Answer:
26 m
Using the Pythagorean theorem: l² = r² + h². l² = 24² + 10² = 576 + 100 = 676. Taking the square root, the slant height l = √676 = 26 m.
114
What is the maximum number of points of intersection between a circle and a straight line?
Answer:
2
A straight line can intersect a circle in at most two points, creating a secant line. It can also intersect at exactly one point (tangent) or zero points.
115
A point P divides the line segment joining A(2, 4) and B(6, 8) internally in the ratio 1:3. What are the coordinates of P?
Answer:
(3, 5)
Using the section formula: x = (m1*x2 + m2*x1) / (m1 + m2) and y = (m1*y2 + m2*y1) / (m1 + m2). Here m1=1, m2=3. x = (1*6 + 3*2) / 4 = 12/4 = 3. y = (1*8 + 3*4) / 4 = 20/4 = 5. The point is (3, 5).
116
Two corresponding sides of two similar polygons are 3 cm and 4 cm. If the area of the larger polygon is 80 cm², what is the area of the smaller polygon?
Answer:
45 cm²
The ratio of the areas of similar polygons is the square of the ratio of their corresponding sides. Ratio of areas = (3/4)² = 9/16. Let the smaller area be A. A / 80 = 9 / 16. A = 80 * (9 / 16) = 5 * 9 = 45 cm².
117
What is the volume of a regular tetrahedron with edge length 'a'?
Answer:
a³√2 / 12
A regular tetrahedron is a triangular pyramid where all four faces are equilateral triangles. Its volume is given by the standard formula V = (a³√2) / 12.
118
If a right triangle has legs of length a and b, what is the area of the square drawn on its hypotenuse?
Answer:
a² + b²
According to the Pythagorean theorem, the square of the hypotenuse (c²) equals the sum of the squares of the legs (a² + b²). The area of a square drawn on the hypotenuse is exactly c², which equals a² + b².
119
Which of the following transformations changes the size of a geometric figure?
Answer:
Dilation
Translation, rotation, and reflection are rigid transformations (isometries) that preserve both the shape and size of a figure. Dilation (scaling) changes the size of the figure while maintaining its shape.
120
The internal and external radii of a hollow spherical shell are 3 cm and 5 cm respectively. What is the volume of the material in the shell?
Answer:
392π/3 cm³
Volume of a hollow sphere = (4/3)π(R³ - r³). Substituting R = 5 and r = 3: V = (4/3)π(5³ - 3³) = (4/3)π(125 - 27) = (4/3)π(98) = 392π/3 cm³.