Geometry PYQ

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

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 area of a rectangle whose length is 5 more than twice its width is 75 square unit. What is the perimeter of the rectangle?

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?

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:

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?

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:

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:

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:

(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 :

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:

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 $\pi = 22/7$)

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:

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?

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.

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:

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

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

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

$V_1, V_2, V_3$ 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:

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.

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: