Geometry PYQ — Page 2

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:

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?

What is the slope of x - axis?

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 $\pi = 22/7$)

The equation of the line which makes equal intercepts on the axis and passes through the point (2,5) shall be:

If a point (x, y) in a plane is equidistant from the points (-1,1) and (4,3), then:

If the area of an equilateral triangle is $36\sqrt{3}$ cm², then the length of the side is:

Find the value of k for which the points A (-1,3), B (2, k) and C (5, -1) are collinear.

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 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.

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.

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:

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?

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?

A wheel makes 2000 rounds when it covers a distance of 88 km. Find the radius of the wheel?

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?

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

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:

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:

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:

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:

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?

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.

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: