1. If the length, breadth and height of a rectangular parallelepiped are in the ratio 6 : 5 : 4 and if the total surface area is 33300 sq. cm, then the length, breadth and the height of the parallelepiped (in cm) respectively are:
(a) 90, 85, 60
(b) 85, 75, 60
(c) 90, 75, 70
(d) 90, 75, 60
(e) None of these
Sol 1. (d); Let Length, breadth & height of a pipe=6x, 5x & 4x
2(6x*5x+5x*4x+6x*4x)=33300
x=15
so, l=90, b=75, h=60
2. A wooden box of dimensions 8 m X 7 m X 6 m is to carry rectangular boxes of dimensions 8 cm X 7 cm X 6 cm. The maximum number of boxes that can be carried in the wooden box, is:
(a) 9800000
(b) 7500000
(c) 1000000
(d) 1200000
(e) None of these
Sol 2. (c); Number of boxes=(800X700X600)/(8X7X6)=1000000
3. The length of longest pole that can be placed on the floor of a room is 10 m and the length of longest pole that can be placed in the room is 10(2)^(1/2)m. The height of the room is:
(a) 6 m
(b) 7.5 m
(c) 8 m
(d) 10 m
(e) None of these
Sol 3. (d); l^2+b^2=(10)^2 ..............(i)
Sol 3. (d); l^2+b^2=(10)^2 ..............(i)
& l^2+b^2+h^2=[10(2)^(1/2)]^2 .............(ii)
from eq. (i) & (ii)
h=10
4. 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 is:
(a) 5 times
(b) 6 times
(c) 12 times
(d) 17 times
(e) None of these
Sol 4. (d); Let initial l=x, b=2x, h=3x
after increase l=2x, b=6x, h=9x
original volume=x*2x*3x=6x^3
New volume=2x*6x*9x=108x^3
increase in volume=(102x^3)/(6x^3)=17 time
5. How many bags of grain can be stored in a cuboid granary 8 m X 6 m X 3 m, if each bag occupies a space of 0.64 m^3?
(a) 8256
(b) 90
(c) 212
(d) 225
(e) None of these
Sol 5. (d); Number of boys=(8X6X3)/0.64=225
6. If three equal cubes are placed adjacently in a row, the ratio of the total surface area of the new cuboid to that of the sum of the surface areas of the three cubes is:
(a) 4 : 3
(b) 5 : 2
(c) 7 : 9
(d) 7 : 16
(e) None of these
Sol 6. (c); Let edge of each cube = a cm
total surface area of these cubes=3X6a^2=18 a^2
length of new Cuboid=3a
breath=a, height=a
S.A of this Cuboid=2(3a^2+a^2+3a^2)=14a^2
Required ratio=14a^2/18a^2=7 : 9
7. Half cubic metre of gold sheet is extended by hammering so as to cover an area of one hectare. The thickness of the sheet is:
(a) 0.5 cm
(b) 0.05 cm
(c) 0.005 cm
(d) 0.0005 cm
(e) None of these
Sol 7. (c); Thickness=volume/Area=0.5/10000 m=0.005 cm
8. A tank 3 m long, 2 m wide and 1.5 m deep is dug in a field 22 m long and 14 m wide. If the earth dug out is evenly spread over the field, the rise in level of the field will be:
(a) .299 cm
(b) .29 cm
(c) 2.98 cm
(d) 4.15 cm
(e) None of these
Sol 8. (c); Area of Field=(22X14)=308 m^2
Area of tank= 3X2=6 m^2
Rise in level=Volume/ Area= [(3X2X1.5)X100]/(308-6)cm=2.98 cm
9. A rectangular water tank is open at the top. Its capacity is 24 m^3. Its length and breadth are 4 m and 3 m respectively. Ignoring the thickness of the material used for building the tank, the total cost of painting the inner and outer surfaces of the tank at the rate of Rs. 10 per m^2 is:
(a) Rs. 400
(b) Rs. 500
(c) Rs. 600
(d) Rs. 800
(e) None of these
Sol 9(d). Height=Volume/Area=24/(4X2)= 2 m
Area to be painted=2(l+b)h+lb
=2(4+3)X2+X4X3
=28+12= 40
since painting has to be done on both side
so,total area = 2*40 = 80
hence total cose = 80*10= 800
10. The length of a hall is 15 m and width 12 m. The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls. The volume of the hall is :
(a) 1800 m^3
(b) 1200 m^3
(c) 900 m^3
(d) 720 m^3
(e) None of these
Sol 10, (b); 2X15X12=2(15+12)Xh
h=(2X15X12)/(2X27)=20/3 m
Volume =15X12X(20/3)=1200 m^3
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