Geometry PYQ — Page 2

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:

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 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 diagonal of a square is $4\sqrt{2}$ cm. The diagonal of another square whose area is double that of the first square, is:

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

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:

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:

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

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:

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:

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

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?

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°?

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?

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:

If area of a square is 44 cm², find the area of the circle formed by the same perimeter.

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

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:

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 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.

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.

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?

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