446 questions asked across 4 exam years, newest first
A rectangular sheet has an area equal to a square plot. If the sheet measures 72 m in length and 50 m in breadth, and the square plot has an area equal to the sheet, find the perimeter of the square plot.
Answer: C
A chord of length 24 cm lies 7 cm away from the center of a circle. What is the approximate radius of the circle?
Answer: B
A chord AB of a circle has a length of 10 cm. The angle subtended by the chord at a point C on the major arc is 30°. Find the radius of the circle.
Answer: B
A pyramid is inscribed inside a cube with edge 12 cm, sharing the base and apex at center of top. Find volume of pyramid.
Answer: B
A rectangular field has an area of 600 square meters. If its length were increased by 10 meters and its width decreased by 2 meters, the area of the field would remain the same. Find the original dimensions (length and width) of the field.
Answer: C
Consider a right trapezoidal field. Its two parallel sides are 30 meters and 50 meters long. One of its non-parallel sides, which acts as the height, measures 20 meters. What is the area of this field?
Answer: B
A hexagon is drawn inside a circle with a radius of 21 cm. Determine the approximate area of the hexagon.
Answer: A
A triangle has sides 8 cm and 10 cm, and the angle between them is 120°. What is its area?
Answer: B
A right prism has a base in the shape of a trapezium with parallel sides 10 cm and 6 cm, and height 4 cm. If the prism height is 15 cm, what is the volume?
Answer: A
If the numerical value of the volume of a sphere is equal to the numerical value of its surface area, find the radius of the sphere.
Answer: D
The line segment from the center of a circle to the midpoint of a chord is 10 cm long. If the radius is 26 cm, what is the length of the chord?
Answer: D
A chord of a circle subtends an angle of 60° at the center. What is the angle subtended at a point on the circle in the same segment?
Answer: B
A pyramid with an equilateral triangular base of side 10 cm and height 14 cm is placed on top of a cube with side length 10 cm. Find the total volume of the composite solid.
Answer: B
A regular hexagon is inscribed inside a circle of radius 14 cm. Find the area of the hexagon.
Answer: B
Answer: A
Three metallic spheres with radii 3 cm,4 cm, and 5 cm respectively are melted together and recast into a single solid sphere. What is the radius of the new sphere?
Answer: C
A prism with a square base of side length 5 cm is constructed in layers. Its height follows an arithmetic progression, increasing from 4 cm in the first layer to 16 cm in the fourth layer. What is the total volume of the prism?
Answer: C
A circle of radius of 12 cm, two radii are drawn such that the length of the chord connecting their endpoints is 12 cm. What is the area of the minor segment formed?
Answer: B
A hemisphere is inscribed in a cube of side 6 cm. What is the volume of the hemisphere?
Answer: A
By an external point P, two tangents are drawn to a circle, touching the circle at points A and B. The chord of contact AB subtends an angle θ at the center of the circle O. What is the angle ∠APB between the tangents in terms of θ?
Answer: C
A hemisphere of radius 5 cm is carved from a sphere. What is the volume of the hemisphere?
Answer: C
A right-angled triangle has a hypotenuse of 13 cm and one leg of 5 cm. A second right-angled triangle is similar to the first, and its hypotenuse is 39 cm. What is the area of the second triangle?
Answer: D
A circle is inscribed in a right triangle with legs of length 5 and 12. What is the radius of the circle?
Answer: A
If the curved surface area of a hemisphere is 154 cm², find its diameter.
Answer: A
A cone has height h and radius r. The cone is melted and recast into a smaller cone whose height is and radius is . What fraction of the original volume is unused?
Answer: A
