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The length of a room is double the breadth. The cost of colouring the ceiling at Rs. 25 per sq. m is Rs. 5,000 and the cost of painting the four walls at Rs. 240 per sq. m is Rs. 64,800. Find the height of the room.

4.5 m

4 m

3.5 m

5 m

A rectangular lawn 80 metres by 60 metres has two rods each 10 metres wide running in the middle of it, one parallel to the length and the other parallel to the breadth. Find the cost of gravelling them at rs. 30 per square metre :

Rs. 39,000

Rs. 3,900

Rs. 3,600

Rs. 36,000

The water in a rectangular reservoir having a base 80 metres by 660 metres is 6.5 metres deep. In what time can the water be emptied by a pipe of which the cross- section is a square of side 20 cm, if the water runs through the pipe at the rate of 15 km per hour?

52 hrs

26 hrs

65 hrs

42 hrs

A hemispherical bowl is made up o steel 0.5cm thick. The inside radius of bowl is 4cm. The volume of the steel used in making the bowl is :

56.83 cm2

55.83cm2

57.83 cm2

58.83 cm2

It is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 440 cubic metres in 10 minutes. The inner radius of the pipe should be :

m

2 m

½ m

1/m

A conical cavity is drilled in a circular cylinder of 15cm height and 16cm base diameter. The height and the base diameter of the cone are same as those of the cylinder. Determine the total surface area of the remaining solid ;

440 p cm2

215 p cm2

542p cm2

376p cm2

If 5 p/6 is the measure of each interior angle of a regular convex polygon, then it must be a :

Octagon

Hexagon

Dodecagon

Decagon

/

108 m

110 m

112 m

115 m

Find the number of coins, 1.5 cm in diameter and 0.2 cm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5cm :

430

440

450

460

A rectangular tank measuring 5m x 4.5m x 2.1m is dug in the center of the field measuring 13.5m x 2.5m. The earth dug out is spread evenly over the remaining portion of the field. How much is the level of the field raised?

4.0 m

4.1 m

4.2 m

4.3 m

A circular grassy plot of land 42m in diameter has a path of 3.5m wide running round, it out side. Find the cost of gravelling the path at Rs. 4 per square meter :

Rs. 2002

Rs. 2002

Rs. 2003

Rs. 2000

A wire is looped is in the form of circle of radius 28cm. It is re-bent into a square form. Determine the length of the side of square :

44 cm

45 cm

46 cm

48 cm

The area of a square increases by …………. if its sides increase by 30%.

71%

60%

69%

30%

If the height, curved surface area and the volume of a cone are h, c and v respectively, then 3pvh3 – c2h2 + 9v2 will be equal to :

0

1

chv

v2h

The areas of three adjacent faces have the same surface area. The ratio of the volume of the cuboid is V, then V2 is equal to :

abc

(ab + bc + ac)

c/ab

Nine of these

A sphere and a cube have a same surface area. The ratio of the volume of the sphere to that of the cube is :

1 : 2

:

6 : p

3 : 1

Three cubes with sides in the ratio 3: 4: 5 are melted to form a single cube whose diagonal is 12cm. The sides of the cubes are :

6cm, 8cm, 10 cm

3cm, 4cm, 5cm

9cm, 12cm, 15cm

None of these

Five equal, cubes each of side 5 cm, are placed adjacent to each other. The volume of the new solid formed will be :

15525 cm3

625 cm3

125 cm3

None of these

By what percent the volume of a cube increases, if the length of each edge was increases by 50% :

237.5%

273.5%

125%

50%

Four equal circles are described about the four corners of a square so that each touches two of the others. If each side of the square is 14cm, then the area enclosed between the circumferences of the circles is :

24 cm2

42 cm2

154 cm2

196cm2

If the perimeter of an isosceles right triangle is (6 + 3)m, then the area of the triangle is

4.5 m2

5.4 m2

9 m2

81 m2

The cost of painting the wall of a room at the rate of Rs. 1.35 per square metre is Rs.340.20 and the cost of matting the floor t the rate of Rs. 0.85 per m2 is rs.91.80. If the length of the room is 12m, then the height of the room is :

6 m

12 m

1.2 m

12.6 m

The sum of length, breadth and the height of a room is 19m. the length of the diagonal is 11m. The cost of painting the total surface area of the room at the rate of rs. 10 per m2 is :

Rs. 240

Rs. 2400

Rs.420

Rs.4200

A metallic sheet is of rectangular shape with dimensions 28m * 36m. From each corners, a square is cut off so as to make an open box. The volume of the box is X m3, when the length of the square is 8m. the value of X is :

5120

8960

4830

5130

A storage tank consists of a circular cylinder with a hemisphere adjoined on either side. If the external diameter of the cylinder be 14m and its length be 50m, then what will be the cost of painting it @ Rs.10 per sq. m?

Rs. 38160

Rs. 28160

Rs. 39160

None of these

A horse is placed for grazing inside a rectangular field of 70m by 52m and is tethered to one corner by a rope 21m long. On how much area can it graze?

386.5 m2

325.5 m2

346.5 m2

246.5 m2

A cylindrical bucket of height 36cm and radius 21cm is filled with sand. The bucket is emptied on the ground and conical heap of sand is formed the height of the conical is 12cm. The radius of the hap at the base is :

63 cm

53 cm

56 cm

66 cm

How many squares are there in a 5 inch by 5 inch square grid, if the grid is made up of one inch by one inch squares?

50

150

55

25

A hemispherical bowl is made up of steel 0.5cm thick. The inside radius of bowl is 4cm. The volume of the steel used in making the bowl is :

55.83 cm2

56.83cm2

57.83 cm2

58.83 cm2

If the radius of the circle is increased by 100%, then the area of the circle increases by :

100%

200%

300%

400%

The length of the longest rod that can be placed in a room which is 12 m long, 9 m broad and 8 m high is :

27 m

19 m

17 m

13 m

A pond 100m in diameter is surrounded by a circular grass walk2m wide. How many square metres of grass is there on the walk?

98p

100p

204p

202p

The sides of the triangle are in the ratio of ::. If the perimeter is 52 cm, then the length of the smallest side is :

9 cm

10 cm

11 cm

12 cm

A largest cube is formed from the material obtained by melting three cubes of 3, 4, 5cm side. What is the ratio of the total surface area of the smaller cubes to the large cube?

2 : 1

3 : 2

27 : 20

25 : 18

The perimeter of a rectangular field is 52m. If the length of the field is 2m more than the breadth, then what is the breadth of the field?

6.5 m

6.25 m

13 m

6 m

The area of four walls of the room is 1220 m2 and the length is twice the breadth. If the height of the room is 4 m, then find the area of the floor :

48 m2

49 m2

50 m2

52 m2

A cone, a hemisphere and a cylinder have equal bases and have same heights. Their volumes will be in the ratio :

1 : 2 : 3

3 : 4 : 1

3 : 2 : 1

None of these

The curved surface of a right circular cone of height 15cm and base diameter 16cm is :

120p cm2

60p cm2

136p cm2

68p cm2

The number of revolutions made by a wheel of diameter 56cm in covering a distance 1.1 km is :

31.25

56.25

625

62.5

In the accompanying figure, AB is one of the diameter in the circle and OC is perpendicular to it through the center O. If AC is 7cm, then what is the area of the circle in sq. cm?

24. 5

49

98

154

A circular well is dug to a depth of 14 metres with a diameter of 2 metres. What is the volume of earth dug out? ( Use p = 22/7)

32 m3

36 m3

40 m3

44 m3

The dimensions of the rectangular box are in the ratio 1 : 2 : 4 and the difference between the costs of covering in with the cloth and sheet at the rate of Rs.20 and Rs.20.5 per square metre respectively is Rs. 126. Find the dimensions of the box :

3m, 6m, 12m

6m, 12m, 24m

1m, 2m, 4m

Nine of these.

The volume of the largest right circular cone that can be cut out of a cube of edge 7 cm is :

89.8 cm3

147.68 cm3

13.6 cm3

121 cm3

A steel wire bent in the form of a square of area 121cm2. If the same wire is bent in the form of a circle, then the area of the circle is :

130 cm2

136 cm2

145 cm2

None of these

The height of a bucket is 45 cm. the radii of the two circular edges are 28 cm and 7 cm respectively. The volume of the bucket is :

38610 cm3

48600 cm3

48510 cm3

None of these

Let A be the area of a square inscribed in a circle of radius ‘r’ and let B the area of a hexagon inscribed in the same circle. Then B/A equals :

2

3/4

2/4

None of these

The weight of a solid cone having diameter 14cm and vertical height 51 cm is ………….. if the material of solid cone weights 10 grams per cube cm :

16.18 kg

17.25 kg

26.18 kg

71.40 kg

If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball is :

60p cm2

50p cm2

75p cm2

100p cm2

A track is in the form of a ring whose inner circumference is 352 m and the outer circumference is 396 m. The width of the track is :

44m

14m

22m

7m

A person wishes to make a 100 sq m rectangular garden. Since he has only 30 m barbed wire for fencing, he fences only three sides letting the house wall act as the fourth side. The width of the garden is :

10m

5m

50m

500m

4.5 m

4 m

3.5 m

5 m

A rectangular lawn 80 metres by 60 metres has two rods each 10 metres wide running in the middle of it, one parallel to the length and the other parallel to the breadth. Find the cost of gravelling them at rs. 30 per square metre :

Rs. 39,000

Rs. 3,900

Rs. 3,600

Rs. 36,000

The water in a rectangular reservoir having a base 80 metres by 660 metres is 6.5 metres deep. In what time can the water be emptied by a pipe of which the cross- section is a square of side 20 cm, if the water runs through the pipe at the rate of 15 km per hour?

52 hrs

26 hrs

65 hrs

42 hrs

A hemispherical bowl is made up o steel 0.5cm thick. The inside radius of bowl is 4cm. The volume of the steel used in making the bowl is :

56.83 cm2

55.83cm2

57.83 cm2

58.83 cm2

It is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 440 cubic metres in 10 minutes. The inner radius of the pipe should be :

m

2 m

½ m

1/m

A conical cavity is drilled in a circular cylinder of 15cm height and 16cm base diameter. The height and the base diameter of the cone are same as those of the cylinder. Determine the total surface area of the remaining solid ;

440 p cm2

215 p cm2

542p cm2

376p cm2

If 5 p/6 is the measure of each interior angle of a regular convex polygon, then it must be a :

Octagon

Hexagon

Dodecagon

Decagon

/

108 m

110 m

112 m

115 m

Find the number of coins, 1.5 cm in diameter and 0.2 cm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5cm :

430

440

450

460

A rectangular tank measuring 5m x 4.5m x 2.1m is dug in the center of the field measuring 13.5m x 2.5m. The earth dug out is spread evenly over the remaining portion of the field. How much is the level of the field raised?

4.0 m

4.1 m

4.2 m

4.3 m

A circular grassy plot of land 42m in diameter has a path of 3.5m wide running round, it out side. Find the cost of gravelling the path at Rs. 4 per square meter :

Rs. 2002

Rs. 2002

Rs. 2003

Rs. 2000

A wire is looped is in the form of circle of radius 28cm. It is re-bent into a square form. Determine the length of the side of square :

44 cm

45 cm

46 cm

48 cm

The area of a square increases by …………. if its sides increase by 30%.

71%

60%

69%

30%

If the height, curved surface area and the volume of a cone are h, c and v respectively, then 3pvh3 – c2h2 + 9v2 will be equal to :

0

1

chv

v2h

The areas of three adjacent faces have the same surface area. The ratio of the volume of the cuboid is V, then V2 is equal to :

abc

(ab + bc + ac)

c/ab

Nine of these

A sphere and a cube have a same surface area. The ratio of the volume of the sphere to that of the cube is :

1 : 2

:

6 : p

3 : 1

Three cubes with sides in the ratio 3: 4: 5 are melted to form a single cube whose diagonal is 12cm. The sides of the cubes are :

6cm, 8cm, 10 cm

3cm, 4cm, 5cm

9cm, 12cm, 15cm

None of these

Five equal, cubes each of side 5 cm, are placed adjacent to each other. The volume of the new solid formed will be :

15525 cm3

625 cm3

125 cm3

None of these

By what percent the volume of a cube increases, if the length of each edge was increases by 50% :

237.5%

273.5%

125%

50%

Four equal circles are described about the four corners of a square so that each touches two of the others. If each side of the square is 14cm, then the area enclosed between the circumferences of the circles is :

24 cm2

42 cm2

154 cm2

196cm2

If the perimeter of an isosceles right triangle is (6 + 3)m, then the area of the triangle is

4.5 m2

5.4 m2

9 m2

81 m2

The cost of painting the wall of a room at the rate of Rs. 1.35 per square metre is Rs.340.20 and the cost of matting the floor t the rate of Rs. 0.85 per m2 is rs.91.80. If the length of the room is 12m, then the height of the room is :

6 m

12 m

1.2 m

12.6 m

The sum of length, breadth and the height of a room is 19m. the length of the diagonal is 11m. The cost of painting the total surface area of the room at the rate of rs. 10 per m2 is :

Rs. 240

Rs. 2400

Rs.420

Rs.4200

A metallic sheet is of rectangular shape with dimensions 28m * 36m. From each corners, a square is cut off so as to make an open box. The volume of the box is X m3, when the length of the square is 8m. the value of X is :

5120

8960

4830

5130

A storage tank consists of a circular cylinder with a hemisphere adjoined on either side. If the external diameter of the cylinder be 14m and its length be 50m, then what will be the cost of painting it @ Rs.10 per sq. m?

Rs. 38160

Rs. 28160

Rs. 39160

None of these

A horse is placed for grazing inside a rectangular field of 70m by 52m and is tethered to one corner by a rope 21m long. On how much area can it graze?

386.5 m2

325.5 m2

346.5 m2

246.5 m2

A cylindrical bucket of height 36cm and radius 21cm is filled with sand. The bucket is emptied on the ground and conical heap of sand is formed the height of the conical is 12cm. The radius of the hap at the base is :

63 cm

53 cm

56 cm

66 cm

How many squares are there in a 5 inch by 5 inch square grid, if the grid is made up of one inch by one inch squares?

50

150

55

25

A hemispherical bowl is made up of steel 0.5cm thick. The inside radius of bowl is 4cm. The volume of the steel used in making the bowl is :

55.83 cm2

56.83cm2

57.83 cm2

58.83 cm2

If the radius of the circle is increased by 100%, then the area of the circle increases by :

100%

200%

300%

400%

The length of the longest rod that can be placed in a room which is 12 m long, 9 m broad and 8 m high is :

27 m

19 m

17 m

13 m

A pond 100m in diameter is surrounded by a circular grass walk2m wide. How many square metres of grass is there on the walk?

98p

100p

204p

202p

The sides of the triangle are in the ratio of ::. If the perimeter is 52 cm, then the length of the smallest side is :

9 cm

10 cm

11 cm

12 cm

A largest cube is formed from the material obtained by melting three cubes of 3, 4, 5cm side. What is the ratio of the total surface area of the smaller cubes to the large cube?

2 : 1

3 : 2

27 : 20

25 : 18

The perimeter of a rectangular field is 52m. If the length of the field is 2m more than the breadth, then what is the breadth of the field?

6.5 m

6.25 m

13 m

6 m

The area of four walls of the room is 1220 m2 and the length is twice the breadth. If the height of the room is 4 m, then find the area of the floor :

48 m2

49 m2

50 m2

52 m2

A cone, a hemisphere and a cylinder have equal bases and have same heights. Their volumes will be in the ratio :

1 : 2 : 3

3 : 4 : 1

3 : 2 : 1

None of these

The curved surface of a right circular cone of height 15cm and base diameter 16cm is :

120p cm2

60p cm2

136p cm2

68p cm2

The number of revolutions made by a wheel of diameter 56cm in covering a distance 1.1 km is :

31.25

56.25

625

62.5

In the accompanying figure, AB is one of the diameter in the circle and OC is perpendicular to it through the center O. If AC is 7cm, then what is the area of the circle in sq. cm?

24. 5

49

98

154

A circular well is dug to a depth of 14 metres with a diameter of 2 metres. What is the volume of earth dug out? ( Use p = 22/7)

32 m3

36 m3

40 m3

44 m3

The dimensions of the rectangular box are in the ratio 1 : 2 : 4 and the difference between the costs of covering in with the cloth and sheet at the rate of Rs.20 and Rs.20.5 per square metre respectively is Rs. 126. Find the dimensions of the box :

3m, 6m, 12m

6m, 12m, 24m

1m, 2m, 4m

Nine of these.

The volume of the largest right circular cone that can be cut out of a cube of edge 7 cm is :

89.8 cm3

147.68 cm3

13.6 cm3

121 cm3

A steel wire bent in the form of a square of area 121cm2. If the same wire is bent in the form of a circle, then the area of the circle is :

130 cm2

136 cm2

145 cm2

None of these

The height of a bucket is 45 cm. the radii of the two circular edges are 28 cm and 7 cm respectively. The volume of the bucket is :

38610 cm3

48600 cm3

48510 cm3

None of these

Let A be the area of a square inscribed in a circle of radius ‘r’ and let B the area of a hexagon inscribed in the same circle. Then B/A equals :

2

3/4

2/4

None of these

The weight of a solid cone having diameter 14cm and vertical height 51 cm is ………….. if the material of solid cone weights 10 grams per cube cm :

16.18 kg

17.25 kg

26.18 kg

71.40 kg

If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball is :

60p cm2

50p cm2

75p cm2

100p cm2

A track is in the form of a ring whose inner circumference is 352 m and the outer circumference is 396 m. The width of the track is :

44m

14m

22m

7m

A person wishes to make a 100 sq m rectangular garden. Since he has only 30 m barbed wire for fencing, he fences only three sides letting the house wall act as the fourth side. The width of the garden is :

10m

5m

50m

500m

This question paper consists of 50 questions which are required to be finished in an hours time.

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