446 questions asked across 4 exam years, newest first
The angle subtended by an arc at the center is , and its length is . Find the radius of the circle.
Answer: A
If a prism's height is tripled while the base area remains constant, what happens to the volume?
Answer: B
A cone is melted and recast into another cone with half the radius. Find the new height if the original height was .
Answer: A
The Incenter of a triangle is located at . The length of the altitude from the Incenter to side AB is . What is the radius of the triangle's incircle?
Answer: A
What is the area of the segment formed by a chord in a circle of radius , if the angle subtended at the center is ?
Answer: A
The volume of a sphere is . If the radius is doubled, what is the new volume?
Answer: B
A prism has a base perimeter of 30 cm and height 7 cm. If its total surface area is , what is the area of both bases combined?
Answer: D
If two circles of radius 6 cm and 2 cm have their centers 10 cm apart, what is the length of the direct common tangent?
Answer: C
A chord separates a circle into two segments. If the angle formed by the chord at the center is , what is the angle formed at a point located in the major segment?
Answer: A
In a circle, the chords AB and CD are equal. The angle subtended by AB at the circumference is . What is the angle subtended by CD at the circumference?
Answer: B
A chord AB is drawn in a circle with center O. The tangent at A and the tangent at B meet at a point P. If , measure the angle subtended by the chord AB at the circumference of the circle?
Answer: C
A line is tangent to a circle at point A. If a chord AB has a length of 8 cm and makes an angle of with the tangent, what is the radius of the circle?
Answer: B
A building has 4 square pyramidal turrets, each of base 4 m and height 6 m. If each need 1.25 times volume for structural fill, find total fill needed.
Answer: A
The radii of three concentric circles are in arithmetic progression. If the innermost radius is 7 cm and the outermost is 21 cm, what is the radius of the middle circle?
Answer: D
If the height of a cylinder is equal to its diameter and radius is 5 cm, find its volume.
Answer: B
A right triangular prism has a base area of 24 cm and height 10 cm. What is its volume?
Answer: B
What is the area of the segment formed by a chord in a circle of radius 6 cm, if the angle subtended at the center is ?
Answer: A
A square and a rectangle have equal areas. The square's side is 20 cm, and the rectangle's length is 25 cm. Find its breadth.
Answer: B
A composite wall consists of a rectangle 12 m by 9 m with a triangular window of base 4 m and height 3 m cut out. If the wall needs to be painted at Rs. 120 per sq m, find the painting cost after deducting the window area.
Answer: C
A circle with a radius of 10 cm, and a chord makes a 60° angle at the center. What is the length of that chord?
Answer: B
Three points P, Q, R, and S are located on the circumference of a circle. If ∠RPS = 30° and ∠PQS = 40°, what is the measure of ∠PRS?
Answer: B
In a circle, points P, Q, R, and S lie on the circumference such that chords PR and QS intersect at the center, and both ∠RPQ and ∠RSQ are subtended by the same arc RQ. If ∠RPQ = 50°, what is the measure of ∠RSQ?
Answer: B
A man walks around a square plot of area 121 m². If he walks once around its boundary, how far does he walk?
Answer: A
A tangent is drawn from a point 17 cm from the center of a circle of radius 8 cm. Find the length of the tangent.
Answer: B
A spherical shell has an outer diameter of 20 cm and is 1 cm thick. What is the volume of the material in the shell? (Use ).
Answer: A
