1 .
The circumference of two circles is 88 m and 220 m respectively. What is the difference between the area of the larger circle and the smaller circle ?
A.  3422 sq m
B.  3242 sq m
C.  3244 sq m
D.  3424 sq m
E.  None of these
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2 .
The length of a rectangle is twice the diameter of a circle. The circumference of the circle is equal to the area of a square of side 22 cm. What is the breadth of the rectangle if its perimeter is 668 cm ?
A.  24 cm
B.  26 cm
C.  52 cm
D.  Cannot be determined
E.  None of these
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3 .
The area of a square is 196 sq. cm. whose side is half the radius of a circle. The circumference of the circle is equal to breadth of a rectangle, if perimeter of the rectangle is 712 cm. What is the length of the rectangle ?
A.  196 cm
B.  186 cm
C.  180 cm
D.  190 cm
E.  None of these
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4 .
A tank 30 m long, 20 m wide and 12 m deep is dug in a field 500 m long and 30 m wide. By how much will the level of the field rise, if the earth dug out of the tank is evenly spread over the field?
A.  0.33 m
B.  0.5 m
C.  0.25 m
D.  0.4 m
E.  None of these
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5 .
The circumference of two circles is 132 m, and 176 m respectively. What is the difference between the area of the larger circle and the smaller circle ?
A.  1048 sq m
B.  1076 sq m
C.  1078 sq m
D.  1090 sq m
E.  None of these
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6 .
If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. The perimeter of the original rectangle (in centimetres) is :
A.  44
B.  46
C.  48
D.  50
E.  None of these
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7 .
What will be the area (in square metre) of 1.5 m wide garden developed around all the four sides of a rectangular field having area equal to 300 sq. m and breadth equal to threefourth of the length ?
A.  96
B.  105
C.  114
D.  Cannot be determined
E.  None of these
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8 .
A cylinder is circumscribed about a hemisphere and a cone is inscribed in the cylinder so as to have its vertex at the centre of one end, and the other end as its base. The volume of the cylinder, hemisphere and the cone are, respectively in the ratio :
A.  2 : 3 : 2
B.  3 : 2 : 1
C.  3 : 1 : 2
D.  1 : 2 : 3
E.  None of these
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9 .
Three cubes of a metal are of edges 3 cm, 4 cm and 5 cm. These are melted together and from the melted material, another cube is formed. The edge of this cube is :
A.  8 cm
B.  10 cm
C.  9 cm
D.  6 cm
E.  None of these
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10 .
A solid cylinder and a solid cone have equal base and equal height. If the radius and the height be in the ratio of 4 : 3, the total surface area of the cylinder to that of the cone are in the ratio of :
A.  10 : 9
B.  11 : 9
C.  12 : 9
D.  14 : 9
E.  None of these
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11 .
The length, breadth and height of a cuboid are in the ratio 1 : 2 : 3. The length, breadth and height of the cuboid are increased by 100%, 200% and 200%, respectively. Then, the increase in the volume of the cuboid will be :
A.  5 times
B.  6 times
C.  12 times
D.  17 times
E.  None of these
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12 .
A sphere of radius 3 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 6 cm. If the sphere is submerged completely, then the surface of the water is raised by :
A.  $1 \over 4$ cm
B.  $1 \over 2$ cm
C.  1 cm
D.  2 cm
E.  None of these
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13 .
Four equal circles are described about the four corners of a square so that each touches two of the others. If a side of the square is 14 cm, then the area enclosed between the circumferences of the circles is :
A.  24 $cm^2$
B.  42$cm^2$
C.  154$cm^2$
D.  196$cm^2$
E.  None of these
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14 .
The largest triangle is inscribed in a semi-circle of radius 14 cm. Find the area inside the semi-circle which is not occupied by the triangle.
A.  100$cm^2$
B.  112$cm^2$
C.  115$cm^2$
D.  113$cm^2$
E.  None of these
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15 .
In a quadrilateral, the length of one of its diagonal is 23 cm and the perpendiculars drawn on this diagonal from other two vertices measure 17 cm and 7 cm respectively. Find the area of the quadrilateral.
A.  250$cm^2$
B.  276$cm^2$
C.  300$cm^2$
D.  325$cm^2$
E.  None of these
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16 .
A cube of maximum volume (each corner touching the surface from inside) is cut from a sphere. Find the ratio of the volumes of the cube and the sphere.
A.  2 : $\sqrt {3}$p
B.  3 : 2P
C.  5 : 4P
D.  3 : $\sqrt {2}$p
E.  None of these
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17 .
A large cube is formed from the material obtained by melting three smaller cubes of dimensions 3, 4 and 5 cm. What is the ratio of the total surface areas of the smaller cubes and the large cube ?
A.  2 : 1
B.  3 : 2
C.  27 : 20
D.  25 : 18
E.  None of these
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18 .
A circular wire of radius 42 cm is cut and bent in the form of a rectangle whose sides are in the ratio of 6 : 5. Find the smaller side of the rectangle.
A.  50 cm
B.  60 cm
C.  70 cm
D.  80 cm
E.  None of these
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19 .
A right circular cone is exactly fitted inside a cube in such a way that the edges of the base of the cone are touching the edges of one of the faces of the cube and the vertex is on the opposite face of the cube. If the volume of the cube is 343 cc, what, approximately, is the volume of the cone?
A.  80 cc
B.  90 cc
C.  110 cc
D.  105 cc
E.  None of these
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20 .
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 4.5 cm :
A.  430
B.  440
C.  450
D.  460
E.  None of these
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21 .
A rectangular lawn 80 metres by 60 metres has two roads 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 ` 30 per square metre :
A.  Rs.39000
B.  Rs.3900
C.  Rs.3600
D.  Rs.36000
E.  None of these
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22 .
A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are transferred into a cylindrical vessel whose radius is 50% more than its height. If the diameter is same for both bowl and cylinder, then the volume of the beverage in the cylindrical vessel will be
A.  66$2 \over 3$%
B.  78.5%
C.  100%
D.  More than 100% (that is, some liquid will still be left in the bowl)
E.  None of these
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23 .
If the angle of triangle are in the ratio of 4 : 3 : 2, then the traingle
A.  is obtuse angled triangle
B.  has one angle greater than 80 °
C.  is a right triangle
D.  is acute angled triangle
E.  None of these
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24 .
The length of a room is double its 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.
A.  4.5 m
B.  4 m
C.  3.5 m
D.  5 m
E.  None of these
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25 .
A rectangular piece of iron sheet measuring 50 cm by 100 cm is rolled into cylinder of height 50 cm. If the cost of painting the cylinder is Rs. 50 per square metre, then what will be the cost of painting the outer surface of the cylinder?
A.  Rs.25.00
B.  Rs.37.50
C.  Rs.75.00
D.  Rs.87.50
E.  None of these
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26 .
A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6 cm and 8 cm, then find the edge of the third smaller cube.
A.  10 cm
B.  14 cm
C.  12 cm
D.  16 cm
E.  None of these
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27 .
Four horses are tied on the four corners of a square field of 14 m length so that each horse can just touch the other two horses. They were able to graze in the area accessible to them for 11 days. For how many days is the ungrazed area sufficient for them ?
A.  3 days
B.  4 days
C.  5 days
D.  2 days
E.  None of these
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28 .
The radius of a cylindrical cistern is 10 metres and its height is 15 metres. Initially the cistern is empty, we start filling the cistern with water through a pipe whose diameter is 50 cm, water is coming out of the pipe with a velocity of 5 m/s. How many minutes will it take in filling the cistern with water?
A.  20
B.  40
C.  60
D.  80
E.  None of these
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29 .
A garden is 24 m long and 14 m wide. There is a path 1 m wide outside the garden along its sides. If the path is to be constructed with square marble tiles 20 cm $\times$ 20 cm, the number of tiles required to cover the path is
A.  1800
B.  200
C.  2000
D.  2150
E.  None of these
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30 .
An order was placed for supply of carpet of breadth 3 metres. The length of carpet was 1.44 times of breadth. Subsequently the breadth and length were increased by 25 and 40 percent respectively. At the rate of Rs. 45 per square metre, what would be the increase in the cost of the carpet?
A.  1020.6
B.  398.8
C.  437.4
D.  583.2
E.  None of these
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Hcf and lcm Number system


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