Geometry PYQ — Page 3

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

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?

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 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

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?

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?

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:

The reflection of the point (6, - 3) on the line y = 2 is:

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?

What is the value of x for which the points A (-1, 3), B (2, x) and C (5, -1) are collinear?

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:

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:

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?

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?

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 the two vertices of a triangle are (5,4), and (-2,4) and the centroid is (5,6), then the third vertex is:

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 length of a cuboid is increased by 20% and its breadth is decreased by 20%, then the volume of cuboid

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?

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?

$V_1, V_2, V_3$ 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:

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

The perimeter of an isosceles triangle is 32 cm while its equal sides together measure 18 cm. Find the length of the other side

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: