Geometry PYQ — Page 4

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:

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:

What will be the reflection of point (2, 3) in the second quadrant?

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:

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.

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.

If the points X(2, -1), Y(3, k), Z(1, 4) are colinear, then the value of k is

The height of an equilateral triangle is $5\sqrt{3}$ cm, then its area is:

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

The area of a right-angled triangle with hypotenuse 17 cm and one side being 8 cm shall be:

If the radius of a sphere is increased by 50%, find the percent increase in surface area.

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 number of diagonals in a Hexagon is:

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 distance between points A (-5, 7) and B (-1, 3) is:

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.

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?

If the ratio of the radii of the sphere and hemisphere is √3:2, then determine the ratio of their total surface area?

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:

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 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: 

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 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:

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 $\pi = \frac{22}{7}$)