General Test Geometry questions from CUET UG 2025.
A 2 m tall boy is 30 m away from a tower. The angle of elevation of the top of the tower from his eye is 45°. What is the height of the tower?
A boy was playing with a rectangular cardboard of dimensions 13 cm x 6 cm. While playing, he sliced off identical triangles from the corners of the cardboard in such a manner that a figure having all its sides equal was generated (as shown in the adjoining figure). The area of this six-sided figure is: 
A cylindrical jar having a base of radius 15 cm, is filled with water up to a height of 20 cm. If a solid iron spherical ball of radius 10 cm is dropped in the jar to submerge completely in the water, then the increase in the level of water is:
A drainage tile is a cylindrical shell 21cm long. The inside and outside diameters are 4.5 cm and 5.1 cm, respectively. What is the volume of clay required for making a tile?
A flask in the shape of a right circular cone of height 36 cm is completely filled with tea. The tea is then poured into another right circular cylindrical flask whose radius is two-third of the radius of base of the circular cone. Then, the height of the tea in the cylindrical flask is
A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 60° with the man's eye when at a distance of 60 metres from the tower. After 9 seconds, the angle of depression becomes 30°. The speed of the boat, assuming that it is running in still water, will be:
A right circular metal cone (solid) is 42 cm high and its radius is $\frac{21}{2}$ cm. It is melted and recast into a sphere. Then the radius of the sphere will be:
A solid, metallic right circular cone of radius 7 cm and height 3 cm is melted into three cubes. If the sides of two cubes are 3 cm and 5 cm, then the side of the third cube will be how much?
A solid sphere of radius 15 cm is melted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 9 cm and its height is 100 cm, find the uniform thickness of the cylinder.
A sphere of maximum volume is 'cut out' from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut-out sphere is:
(A). The angles of depression of two ships from the top of a lighthouse are $60^\circ$ and $45^\circ$ towards the east. If the ships are $300$ meter apart, the height of the lighthouse is $150(3+\sqrt{3})$ $$\newline$ (B). If the surface area of a cube is $726 \text{ m}^2$, then its volume shall be $1331 \text{ m}^3$ $$\newline$ (C) If the ratio of diameters of two spheres is $3:5$, then the ratio of their surface area shall be $9:25$ $$\newline$$ Determine as to which of the statements given above are correct :
A wheel makes 2000 rounds when it covers a distance of 88 km. Find the radius of the wheel?
A wire is looped in the form of a circle of diameter 70 cm. It is bent again into a square form. What will be the approximate length of the diagonal of the largest possible square? (Assume $\pi = 22/7$)
An observer, 1.5 m tall, is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. Determine the height of the chimney?
An observer 2 m tall is 24$\sqrt{3}$ m away from a building. The angle of elevation of the top of the building as seen by him is 30°. What is the height of the building?
$V_1, V_2, V_3$ and $V_4$ are the volumes of four cubes of side lengths x cm, 2x cm, 3x cm and 4x cm respectively. The following statements regarding these volumes are given below. (A) $V_1 + V_2 + 2V_3 < V_4$ (B) $V_1 + 3V_2 > V_3 + V_4$ (C) $2(V_1 + V_3) + V_2 = V_4$ (D) $V_1 + 4V_2 + V_3 < V_4$ Which of these statements is/are correct? Choose the correct answer from the options given below:
At the foot of a mountain, the elevation of the summit is 45°. After ascending 2 kilometers towards the mountain, at an incline of 30°, the elevation changes to 60°. Determine the height of the mountain?
Consider the following statements: I. If the height of a cylinder is doubled, the area of the curved surface is doubled. II. If the radius of a hemispherical solid is doubled, its total surface area becomes fourfold. Which of the above statement(s) is / are true:
Consider the following statements: I. If the height of a cylinder is doubled, the area of the curved surface is doubled. II. If the radius of a hemispherical solid is doubled, its total surface area becomes fourfold. Which of the above statement(s) is / are true:
Consider the surface area of the following: (A) A cube having each side as 6 cm. (B) A cylinder with a diameter of base 14 cm and length 80 cm. (C) A cone of diameter 14 cm and a slant height of 10 cm. (D) A sphere of radius 10.5 cm. The surface area of these in decreasing order are: Choose the correct answer from the options given below:
Consider the volumes of the following: (A) A cylinder with a radius of base 7 cm and height 10 cm. (B) A cone of radius 7 cm and height 9 cm. (C) A sphere of radius 6 cm. The volumes of these figures in decreasing order shall be: Choose the correct answer from the options given below:
Find the coordinates of the point which divides the line segment joining the points (4, -3) and (8,5) in the ratio 3:1 internally?
Find the value of k for which the points A (-1,3), B (2, k) and C (5, -1) are collinear.
Find the value of x in the adjoining figure, if it is given that PR and QS are diameters of the circle. 
Find the values and arrange in increasing order: (A) If each edge of a cube is increased by 20%, then the percentage increase in its volume is: (B) If the radius of a cylinder is increased by 20%, while height increase 10%, then the percentage increase in the volume of the cylinder (C) If each edge of a cube is increased by 20%, then the percentage increase in its surface area is: (D) If the radius of a sphere is increased by 10%, then the percentage increase in its volume is: Choose the correct order:
Four circles of equal radius are drawn with centers, A, B, C and D such that ABCD is a square of side 14 cm and the circles touch externally as in the figure. The area of the shaded region bounded by the 4 circles is: (Take $\pi = \frac{22}{7}$) 
From a point exactly midway between the foot of two towers P and Q, the angle of elevation of their tops are 30° and 60°, respectively. The ratio of the heights of tower P to that of Q is:
From A point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45°, respectively. If the bridge is at a height of 9 m from the surface of the river, then find the width of the river.
From the top of a building 78 m high, the angles of depression of the bottom and the top of a tower are observed to be 45° and 30° respectively. Determine the approximate height of the tower so observed?
From the top of a tower, the angles of depression of two objects A and B (situated on the ground on the same side of the tower) are observed to be 30° and 60°, respectively. If the distance between the objects is 200√3 m, then the height of the tower is?
How many meters of cloth 6 metre wide will be required to make a conical tent, the radius of whose base is 21m and height is 20m?
If a cone and sphere have equal radii and volumes, then determine the ratio of the diameter of the sphere to the height of the cone?
If a metallic rod of 10 cm length and 2 cm radius is stretched into a wire of 40 m length having uniform thickness, then find the radius of the stretched wire.
If a point (x, y) in a plane is equidistant from the points (-1,1) and (4,3), then:
If area of a square is 44 cm², find the area of the circle formed by the same perimeter.
If the area of an equilateral triangle is $36\sqrt{3}$ cm², then the length of the side is:
If the areas of adjacent faces of a cuboid (rectangular prism) are in the ratio of 2: 3: 5 and its volume is 900 cm³, then the length of the longest side is
If the distance between the points (2, -2) and (5, k) is 5 units, then one of the possible values of k shall be which of the following?
If the height of a pole is $8\sqrt{3}$ meters and the length of its shadow is 8 meters, then the angle of elevation of the sun is:
If the length of a cuboid is increased by 20% and its breadth is decreased by 20%, then the volume of cuboid
If the points (1, 7), (4, 2), (-1, -1) and (-4, 4) are the vertices of a square then what is the length of the diagonal of square?
If the points A(11, y), B(13, 5), C(14, 7) and D(12, 6) are the vertices of a parallelogram, taken in order, find the value of y:
If the points A(3, 0), B(x, 5), C(-1, 4) and D(-2, -1) are the vertices of a rhombus, taken in order, find the value of x.
If the points P(8,5), Q(4,8), R(0,5) and S(4,k) are the vertices of a rhombus, taken in order, then the value of k is
If the points X(2, -1), Y(3, k), Z(1, 4) are colinear, then the value of k is
If the radius of a sphere is increased by 50%, find the percent increase in surface area.
If the ratio of the radii of the sphere and hemisphere is √3:2, then determine the ratio of their total surface area?
If the slant height of a cone is decreased by 15 percent and the radius of its base is increased by 20 percent, then by what percent will its curved surface area change?
If the slope of a line passing through the points A (2, 1) and B (3, y) is 4, then the value of y will be:
If the two vertices of a triangle are (5,4), and (-2,4) and the centroid is (5,6), then the third vertex is:
If two tangents inclined at an angle 60° are drawn to a circle of radius 5 cm, then what is the length of each tangent?
If two vertices of a triangle are (5, 4) and (-2, 4) and centroid is (5,6), then third vertex is:
In the adjoining figure, a rectangle has dimensions of 18 cm x 12 cm. The area of the parallelogram (shaded portion) is 
In what ratio are the volumes of a cylinder, a cone and a sphere, if each has the same diameter and the same height?
Match List-I with List-II | List-I | List-II | |---|---| | (Figures, etc.) | (Area/Volume/Diagonal etc.) | | (A) Surface area of Cube | (I) $\pi(R^2 - r^2)$ | | (B) Volume of Right pyramid | (II) $a\sqrt{2}$ | | (C) Area of Circular Ring | (III) $6a^2$ | | (D) Diagonal of Square | (IV) $\frac{1}{3}$(area of base) × height | Choose the correct answer from the options given below:
Match List-I with List-II | List-I | List-II | |---|---| | (Shapes) | (Area/Perimeter/Diagonal/slant height) | | (A) Trapezium | (I) √(l² + b² + h²) | | (B) Sector of a circle | (II) √(R² + (R - r)²) | | (C) Cuboid | (III) 1/2 h(a + b) | | (D) Frustum of cone | (IV) (θ/360°) × 2πr | Choose the correct answer from the options given below:
Match the given areas of various solid objects with their respective formulae: | List I | List II | |---|---| | Area of solid object | Formula | | (A) Lateral surface area of a cylinder | (I) $\pi r\sqrt{r^2 + h^2}$ | | (B) Total surface area of a hemisphere | (II) $4\pi r^2$ | | (C) Lateral surface area of a cone | (III) $2\pi rh$ | | (D) Surface area of a sphere | (IV) $3\pi r^2$ | (Where, r = radius of the solid shape (or base) and h = height of the solid shape.) Choose the correct answer from the options given below:
Point A (4, 2) divides segment BC in the ratio 2:5. Coordinates of B and C are (2,6), (9,y) respectively. Find the value of y.
Read the information given carefully and answer the question that follows: $$\newline$ (A) 72 kmph = 20 m/s $\newline$ (B) 25 m/s = 80 kmph $\newline$ (C) Total Surface area of a Cube of edge length $a$ is \$6a^2$ $\newline$ (D) Volume of a Cube of edge length $a$ is $a^3$ $$\newline$$ Choose the correct answer from the options given below:
The angle of elevation of the sun, when the length of the shadow of a tower is 1/√3 times the height of the tower, is
The angle of elevation of the top of an unfinished tower at a distance of 75m from its base is 30°. How much higher must the tower be raised so that the angle of elevation of its top at the same point may be 60°?
The angle of elevation of the top of a tower from a certain point is 60°. If the observer moves 10 m away from the tower, the angle of elevation of the top of the tower decreases by 15°. The height of the tower is:
The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower when seen from the foot of the building is 60°. If the tower is 60 m high, then the height of the building is:
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.
The angles of elevation of the top of a tower from two points at a distance of 5 meters and 20 meters along the same straight line from the base of the tower, are complementary. Find the height of the tower.
The area of a rectangle whose length is 5 more than twice its width is 75 square unit. What is the perimeter of the rectangle?
The area of a right-angled triangle with hypotenuse 17 cm and one side being 8 cm shall be:
The area of a sector of a circle of radius 36 cm is $72\pi$ cm². Find the length of the corresponding arc of the sector.
The area of the right-angled isosceles triangle having hypotenuse A cm is:
The areas of three adjacent faces of a cuboidal box are 96 cm², 48 cm² and 72 cm², respectively. The volume of the box is
The base diameter of a cylinder is 21 cm and the height is 28 cm, then: (A) Radius of cylinder = 10.5 cm (B) Volume = 12936 cm³ (C) Curved Surface Area = 1848 cm² (D) Total surface area = 2541 cm² Which of the following is/ are correct? Choose the correct answer from the options given below:
The base radius of a cone is 21 cm and the height is 28cm, then which of the following is/are correct? (A) Slant height = 35 cm (B) Slant height = 33 cm (C) Volume = 12936 cm³ (D) Curved Surface Area = 2310 cm² Choose the correct answer from the options given below:
The diagonal of a square is $4\sqrt{2}$ cm. The diagonal of another square whose area is double that of the first square, is:
The distance between points A (-5, 7) and B (-1, 3) is:
The equation of the line which makes equal intercepts on the axis and passes through the point (2,5) shall be:
The height of an equilateral triangle is $5\sqrt{3}$ cm, then its area is:
The number of diagonals in a Hexagon is:
The perimeter of an isosceles triangle is 32 cm while its equal sides together measure 18 cm. Find the length of the other side
The ratio of radii of two right circular cylinders (A and B) is 2:3. The ratio of volumes of the cylinders A and B is 9:7, then what is the ratio of the heights of the cylinders A and B?
The ratio of the diameter and height of the right circular cylinder is 4 : 3. If the diameter of the cylinder is reduced 25 %, then its total surface area is reduced to 318.5π m². What is the circumference of the base of the cylinder?
The ratio of the radius and height of a cone is 3:4. Its volume is $37\frac{5}{7}$ cm³. The slant height of the cone is
The reflection of the point (6, - 3) on the line y = 2 is:
The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude is 30° than when it is 60°. Find the height of the tower.
The shadow of the pole standing on a level surface is found to be 5 m shorter when the sun's elevation is 60° than when it is 45°. What is the height of the pole?
The sides of a triangle are in the ratio of $\frac{1}{4}:\frac{1}{5}:\frac{1}{6}$. If the perimeter of the triangle is 37 cm, then find the length of the greatest side of the triangle?
The tops of two poles of height 22 m and 31 m are connected by a wire. If the wire makes an angle of 60° with the horizontal, then the length of the wire (in m) is:
The tops of two poles of height 25 m and 16 m are connected by a wire. If the wire makes an angle 30° with the vertical, then the distance between the two poles is
The tops of two poles of height 38 m and 56 m are connected by a cable. If the cable makes an angle of 30° with the horizontal, then the distance between the bases of the poles is:
Three spherical balls of radius 2 cm, 4 cm, and 6 cm are melted to form a new spherical ball. In this process, there is a loss of 25% of the material. What is the radius (in cm) of the new ball?
Two men are on opposite side of tower. They measure the angles of elevation of the top of the tower as 30° and 45° respectively. If the height of the tower is 50 meters, find the distance between the two men.
Two perpendicular cross roads of equal width run through the middle of a rectangular field of length 80 m and breadth 60 m. If the area of the cross roads is 675 square meters, then the width of each road is:
What is the slope of x - axis?
What is the value of x for which the points A (-1, 3), B (2, x) and C (5, -1) are collinear?
What will be the reflection of point (2, 3) in the second quadrant?
When a particular wire is bent into the shape of a square, then the area of the square turns out to be $81cm^2$. When the same wire is bent into a circle, then the radius of the circle (correct to two decimal places) is
Which of the following statements are true? (A) If the diagonal of a cube is $6\sqrt{3}$ cm, then its volume and surface area are equal. (B) If a rectangular block having dimensions 6 cm x 12 cm x 15 cm is cut into an exact number of equal cubes, then the least possible number of such cubes is 27. Choose the correct answer from the options given below: