446 questions asked across 4 exam years, newest first
A rectangular aquarium (100 cm L × 50 cm W × 60 cm H) contains water with an initial level of 20 cm. 10 identical metal spheres, each with a diameter of 10 cm, are gently lowered into the aquarium. Assuming the spheres are fully submerged, what is the rise in the water level?
Answer: B
A store sign is a 5 m × 4 m rectangle with a 2 m × 1 m rectangle cut out. Painting cost is ₹180/m. How much will the painting cost for the exposed area?
Answer: A
A regular hexagonal nut has outer side 6 cm and inner hollow side 3 cm. What is the material approximate area in the cross-section?
Answer: A
A sector of a circle having a radius of 10 cm and has a central angle of radians. What is the area of the sector?
Answer: B
The radii of two circles are 6 cm and 2 cm. The centers of the two circles are 10 cm apart. What is the length of a transverse common tangent?
Answer: A
In a circle, a chord PQ subtends an angle of at point R on the circumference. What is the angle it subtends at point S on the circumference, on the same side as R?
Answer: B
In a circle, chord AB subtends an angle of at the center. What is the angle subtended by the same chord AB at any point C on the major arc (opposite side of the center)?
Answer: A
A line is drawn from a point P located 13 cm away from the center O of a circle with radius 5 cm. If the line is tangent to the circle, what is the length of the tangent from point P to the point of contact with the circle?
Answer: C
A square tile of area 225 cm² is cut into two equal rectangular tiles. What will be the perimeter of each new tile?
Answer: D
A circle has a diameter of 10 centimeters. A line is tangent to the circle. What is the angle between the tangent and the diameter at the point of contact?
Answer: C
A sphere is inscribed inside a cube. The volume of the cube is . What is the total surface area of the sphere?
Answer: A
A regular hexagon has a perimeter of 72 cm. What is its area?
Answer: A
A triangular prism has a base with area 45 cm and height 14 cm. If 10% of the prism is hollowed out for wiring, what is the volume of the solid part?
Answer: A
In a circle, angle subtended by chord AB at the center is . What is the measure of angle , where C lies on the circle?
Answer: A
If the angle subtended by a chord at the center is , what is the angle subtended at a point on the circle in the same segment?
Answer: A
A triangle ABC has a circle inscribed within it with sides a, b, c. The area of the triangle is A. What is the radius of the inscribed circle?
Answer: B
A square field has a diagonal of m. What is its area?
Answer: B
A square has a perimeter of 100 cm. What is the area of the square?
Answer: C
A perfect cube with a side length of 8 cm has the largest possible sphere fitted inside it. What is the volume of the empty space within the cube?
Answer: A
A prism with a parallelogram base has base area 80 cm^2 and height 12 cm. If its lateral surface area is 384 cm^2, what is the perimeter of the base?
Answer: B
The angle of a sector is π/4 radians, and the radius of the circle is 8 cm. What is the area of the sector?
Answer: D
A line from the center of a circle bisects a chord. What is the angle between this line and the chord?
Answer: C
A chord divides a circle into two arcs. The angle subtended by the major arc at the circumference is 110°. What is the central angle subtended by the major arc?
Answer: C
In a circle, chord AB subtends an angle of 50° at a point C on the circle. What is the angle subtended by the same chord AB at another point D on the same arc as C?
Answer: B
From an outside point P, two tangents, PA and PB, are drawn to a circle. A third tangent to the circle at a point Q intersects PA and PB at R and S respectively. If PA=10 cm, what is the perimeter of △PRS?
Answer: C
