question_answer 1)
A parallelogram and a rhombus are equal in area. The diagonals of the rhombus measure 60 m 22 m. If side of a parallelogram is \[\frac{\mathbf{3}}{\mathbf{4}}\] of longer diagonals of the rhombus then altitude from the given base of the parallelogram is _________
A)
15 m done
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B)
13 m done
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C)
1233 m done
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D)
14.67 m done
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E)
None of these done
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question_answer 2)
The length of the longest pole that can be put in a room of dimensions \[(\mathbf{12}\text{ }\mathbf{ft}\text{ }\times \text{ }\mathbf{9}\text{ }\mathbf{ft}\text{ }\times \text{ }\mathbf{8}\text{ }\mathbf{ft})\]is
A)
18 ft done
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B)
9 ft done
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C)
15 ft done
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D)
17 ft done
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E)
None of these done
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question_answer 3)
Which among the following statements is not true?
A)
The volume of a sphere of radius V is equal to one third of the volume of a cylinder of radius V whose height is equal to double the diameter of the sphere. done
clear
B)
If A solid sphere of side 'a' is converted into a cone having its radius equals to the side of the cube, then the height of the cone is twice to its diameter. done
clear
C)
If diagonal of a cube is 9 m then volume of the cube will be \[81{{m}^{3}}\]. done
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D)
All the above done
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E)
None of these done
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question_answer 4)
If side of the cube is increased by 300 % then its surface area will increase by ___________
A)
12 times done
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B)
13 times done
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C)
14 times done
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D)
15 times done
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E)
None of these done
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question_answer 5)
A right angled triangle whose base is 21 cm and height is 20 cm, is made to turn round on the longer side. If the volume of the solid, thus generated V and the curved surface area is S, then __________
A)
\[V=9240\text{ }c{{m}^{3}},\text{ }S=1914\text{ }c{{m}^{2}}\] done
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B)
\[V=8820\text{ }c{{m}^{3}},\text{ }S=1885\text{ }c{{m}^{2}}\] done
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C)
\[V=3820\text{ }c{{m}^{3}},\text{ }S=1685\text{ }c{{m}^{2}}\] done
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D)
\[V=8240\text{ }c{{m}^{3}},\text{ }S=1734c{{m}^{2}}\] done
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E)
None of these done
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question_answer 6)
Two cones have their heights in the ratio 2 : 3 and the radii of their bases are in the ratio 3 : 2, then the ratio of their volumes is _________
A)
3 : 2 done
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B)
1 : 2 done
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C)
1 : 3 done
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D)
4 : 1 done
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E)
None of these done
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question_answer 7)
The volume of the largest right circular cone which can be fitted in a cube whose side is '3a' equals to _________
A)
\[\frac{1}{8}\] of volume of a hemisphere of radius 'a' done
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B)
\[\frac{27}{8}\]of volume of sphere of radius 'a'. done
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C)
\[\frac{27}{16}\]of volume of sphere of radius '2a'. done
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D)
\[\frac{27}{8}\]of volume of hemisphere of radius 'a' done
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E)
None of these done
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question_answer 8)
Which one among the following statements is true?
A)
A cylinder, A hemisphere and a cone stand on equal and the same height. The ratio of their volumes is 3 : 1 : 2 respectively. done
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B)
If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of cube is 6 : n. done
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C)
If the radius of a cylinder is tripled and height is doubled then, the volume will be 18 times of the previous. done
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D)
All the above done
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E)
None of these done
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question_answer 9)
The circumradius of the triangle having its sides 11 cm, 60 cm and 61 cm is R. Find the Area of this circle, \[\left( Use\text{ }\pi \frac{22}{7} \right)\text{ }\]
A)
\[11694.57\,c{{m}^{2}}\] done
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B)
\[12384.85\,c{{m}^{2}}\] done
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C)
\[9694.57\,c{{m}^{2}}\] done
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D)
\[13964.29\,c{{m}^{2}}\] done
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E)
None of these done
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question_answer 10)
Two circles touch each other externally. The sum of there areas is \[274\text{ }\pi \text{c}{{\text{m}}^{\text{2}}}\]. The distance between their centres is 22 cm. Find the difference in their radii.
A)
8 cm done
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B)
10 cm done
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C)
15 cm done
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D)
7 cm done
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E)
None of these done
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question_answer 11)
Find the area of the shaded region where each circle is of radius 7 cm as shown in the figure.
A)
\[126\,c{{m}^{2}}\] done
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B)
\[252\,c{{m}^{2}}\] done
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C)
\[342\,c{{m}^{2}}\] done
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D)
\[378\,c{{m}^{2}}\] done
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E)
None of these done
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question_answer 12)
The length of an hour hand clock is 9 cm. The area covered by it from 9 : 20 am to 10 : 00 am is _________
A)
\[14.143\,c{{m}^{2}}\] done
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B)
\[12.362\,c{{m}^{2}}\] done
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C)
\[13.263\,c{{m}^{2}}\] done
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D)
\[10.285\,c{{m}^{2}}\] done
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E)
None of these done
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question_answer 13)
The external length, breadth and height of a closed rectangular wooder box are 20 cm, 16 cm and 8 cm respectively. The weight of the box, when is empty, is 13 kg and when it is filled with sand, is 72 kg. If it is given that thickness of the wood is - cm, then the weights of one cubic cm of wood and cubic cm of sand are respectively ________
A)
\[\frac{13}{265}kg\text{ and }\frac{59}{995}kg\] done
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B)
\[\frac{13}{565}kg\text{ and }\frac{59}{1995}kg\] done
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C)
\[\frac{13}{365}kg\text{ and }\frac{419}{1495}kg\] done
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D)
\[\frac{13}{1565}kg\text{ and }\frac{72}{1995}kg\] done
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E)
None of these done
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question_answer 14)
A solid cylinder has total surface area of 1848 square cm. Its curved surface area is one third of its total surface area. If a hemisphere is formed from this cylinder, then the radius (in cm) of this hemisphere is __________
A)
5 done
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B)
\[{{7}^{3}}\sqrt{6}\] done
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C)
\[{{14}^{3}}\sqrt{6}\] done
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D)
\[17\sqrt{6}\] done
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E)
None of these done
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question_answer 15)
The curved surface area of a hemisphere of radius 6 cm is equal to \[\frac{2}{5}\] of the curved surface area of a cone of radius 12 cm. Find the volume of the cone.
A)
\[1357\text{ }71\,c{{m}^{3}}\] done
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B)
\[102238\,c{{m}^{3}}\] done
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C)
\[1252.61\,c{{m}^{3}}\] done
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D)
\[2039.68\,c{{m}^{3}}\] done
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E)
None of these done
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question_answer 16)
If the radius of a sphere is increased by 40 %, then its volume will be increased by _________
A)
74% done
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B)
74.4% done
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C)
174.4% done
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D)
80% done
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E)
None of these done
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question_answer 17)
If the length of a cuboid is increased by 30%, breadth is increased by 40% and height is increased by 50% then its volume will be increased by ___________
A)
173% done
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B)
273% done
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C)
163% done
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D)
263% done
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E)
None of these done
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question_answer 18)
In an event, laddoos of same size were distributed among 400 students in which each student got 1 laddoo. If the size of each laddoos was decreased by 50 % then to how many students they distributed?
A)
400 done
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B)
800 done
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C)
1600 done
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D)
3200 done
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E)
None of these done
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question_answer 19)
Three solid cubes of type A and three solid cubes of type B are melted to form a cube. If the lengths of diagonals of cubes of type A and Type B are \[\mathbf{4}\sqrt{\mathbf{3}}\text{ }\]cm and \[\mathbf{8}\sqrt{\mathbf{3}}\text{ }\]cm respectively, then find the lateral surface area of the cube so formed.
A)
\[625\,c{{m}^{2}}\] done
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B)
\[529\,c{{m}^{2}}\] done
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C)
\[576\,c{{m}^{2}}\] done
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D)
\[784\,c{{m}^{2}}\] done
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E)
None of these done
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question_answer 20)
In a right prism, the base is an equilateral triangle, Its is \[\mathbf{135}\sqrt{\mathbf{3}}\mathbf{c}{{\mathbf{m}}^{\mathbf{3}}}\] and lateral surface area is\[\mathbf{270}\,\mathbf{c}{{\mathbf{m}}^{\mathbf{2}}}\]. If height of the prism is increased by 60%, then its new volume will be ___________
A)
\[140\sqrt{3}\text{ c}{{\text{m}}^{3}}\] done
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B)
\[216\sqrt{3}\text{ c}{{\text{m}}^{3}}\] done
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C)
\[236\sqrt{3}\text{ c}{{\text{m}}^{3}}\] done
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D)
\[306\sqrt{3}\text{ c}{{\text{m}}^{3}}\] done
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E)
None of these done
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question_answer 21)
Two cubes each of volume \[\mathbf{1331}\text{ }\mathbf{c}{{\mathbf{m}}^{\mathbf{3}}}\]are joined end to end. Find the difference between total surface area and lateral surface area of the cuboid so form.
A)
\[576c{{m}^{2}}\] done
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B)
\[484c{{m}^{2}}\] done
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C)
\[376c{{m}^{2}}\] done
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D)
\[242c{{m}^{2}}\] done
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E)
None of these done
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question_answer 22)
0.25 cubic metre of aluminium-sheet is extended by hammering so as to cover an area of 1 hectare. The thickness of the Aluminium sheet is ____
A)
2.35 cm done
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B)
3.25 cm done
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C)
0.0025 cm done
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D)
0.0035 cm done
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E)
None of these done
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question_answer 23)
A room is 10 m long, 6 m wide and 3 m high. It has four windows, each measuring \[\mathbf{2 m\times ~1 m}\]and a door of dimensions\[\mathbf{3}\text{ }\mathbf{m\times 1}.\mathbf{5}\text{ }\mathbf{m}\]. If the interior walls are to be coloured and a painter charges Rs. 3.25 per sq m, then the cost of colouring is Rs._________
A)
251.375 done
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B)
261.375 done
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C)
271.375 done
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D)
270.375 done
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E)
None of these done
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question_answer 24)
The difference between the areas of outside and inside surface of a cylindrical metallic pipe 14 cm long is \[\mathbf{132c}{{\mathbf{m}}^{\mathbf{2}}}\]. If the pipe is made of \[\mathbf{495c}{{\mathbf{m}}^{\mathbf{3}}}\] of metal, find the outer and inner radii of the pipe.
A)
4.5 cm and 3 cm done
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B)
3.5 cm and 2.0 cm done
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C)
5.0 cm and 3.5 cm done
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D)
4.0 cm and 2.5 cm done
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E)
None of these done
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question_answer 25)
The minute hand of a clock is \[\frac{\mathbf{x}}{\mathbf{2}}\] cm long. The area covered by the minute hand of the clock in 35 minutes is _________
A)
\[\frac{10{{x}^{2}}}{21}uni{{t}^{2}}\] done
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B)
\[\frac{11{{x}^{2}}}{24}uni{{t}^{2}}\] done
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C)
\[\frac{7{{x}^{2}}}{5}uni{{t}^{2}}\] done
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D)
\[\frac{13{{x}^{2}}}{5}uni{{t}^{2}}\] done
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E)
None of these done
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question_answer 26)
A closed rectangular shed has dimensions \[\mathbf{28 m\times 14m}\]. It is inside a field. A cow is tied outside the shed at one of its corners with a 28 m rope. The area over which the cow can graze is ________
A)
\[2002{{m}^{2}}\] done
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B)
\[1004{{m}^{2}}\] done
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C)
\[728{{m}^{2}}\] done
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D)
\[1992{{m}^{2}}\] done
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E)
None of these done
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question_answer 27)
The volumes of two spheres are in the 125 : 64. If the radius is increased by 30 % in first sphere and 50 % in second sphere, then the ratio between their surface areas is __________
A)
144 : 121 done
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B)
125 : 64 done
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C)
1 : 1 done
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D)
169 : 144 done
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E)
None of these done
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question_answer 28)
A cylindrical container of radius 8 cm and height 35 cm is filled with ice-cream. The whole ice-cream is distributed among 15 children in equal cones with hemispherical tops« If the height of the conical portion is five times the radius of its base, then the radius of the ice-cream cone is _________
A)
3 cm done
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B)
4 cm done
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C)
5 cm done
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D)
6 cm done
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E)
None of these done
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question_answer 29)
The difference in radii of two spheres is 2 cm and ratios of their volumes on decreasing the radius of the larger sphere by \[69\frac{3}{13}%\] and the smaller 13 sphere by \[33\frac{1}{3}%\] is 8:27. Find the difference of surface areas of two spheres.
A)
\[276.57c{{m}^{2}}\] done
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B)
\[168.39c{{m}^{2}}\] done
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C)
\[302.87c{{m}^{2}}\] done
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D)
\[29439c{{m}^{2}}\] done
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E)
None of these done
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question_answer 30)
The internal and external diameters of a hallow hemispherical vessel are 22 cm and 24 cm respectively. The cost to paint 1 cm2 of the surface is Rs. 0.50. Find the total cost to paint the vessel all over.
A)
Rs. 669 done
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B)
Rs. 869 done
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C)
Rs. 325 done
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D)
Rs. 485 done
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E)
None of these done
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question_answer 31)
A storage tank consists of a circular a cylinder with a hemisphere adjoined on either end. If the external diameter of the cylinder be 2.8 m and the cost of painting it on the outside at the rate of Rs. 20 per \[{{m}^{2}}\] is Rs. 765.60, then find the height of the circular cylinder.
A)
8.7 m done
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B)
2.95 m done
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C)
435 m done
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D)
5.65 m done
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E)
None of these done
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question_answer 32)
If a solid sphere of radius 10 cm is melted to stretch into a wire of 1000 cm, then curved surface area of the wire is ________
A)
\[7005\,c{{m}^{2}}\] done
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B)
\[7266.72\,c{{m}^{2}}\] done
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C)
\[3268.66c{{m}^{2}}\] done
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D)
\[8645.55c{{m}^{2}}\] done
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E)
None of these done
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question_answer 33)
Water flows in a tank \[\mathbf{110 m\times 100 m}\]at the base, through a pipe whose cross-section is 2 cm by 2.5 cm at the speed of 12 km per hour. In how many hours, the water will be 6 m deep in the tank?
A)
70 hours done
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B)
90 hours done
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C)
110 hours done
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D)
130 hours done
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E)
None of these done
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question_answer 34)
The diameters of the top and bottom portions of a milk can are 30 cm and 8 cm respectively. If the height of the can is 60 cm, then _________ \[\left( Use\text{ }\pi \text{ = }\frac{22}{7} \right)\]
A)
area of metal sheet required to make the can (without lid) is \[3692.86\,c{{m}^{2}}\] done
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B)
Amount of milk which container can hold is \[18220c{{m}^{3}}\]. done
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C)
area of metal sheet required = curved surface area of bottom base. done
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D)
both B and C done
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E)
None of these done
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question_answer 35)
Which among the following is true about a regular tetrahedron?
A)
All the faces of a regular tetrahedron are of right angled triangle. done
clear
B)
The lateral surface area of a regular tetrahedron is \[\frac{2\sqrt{3}}{4}{{a}^{2}}\] when 'a' is the done
clear
C)
The total surface area of a regular tetrahedron = 3a2 (when 'a' is the edge) done
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D)
Volume of regular tetrahedron is \[\frac{{{a}^{3}}}{3\sqrt{2}}\] done
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E)
None of these done
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question_answer 36)
If in a triangle the sum of any two sides exceeds the third side by 8 cm, then its area _______
A)
is \[16\sqrt{3}\text{ }c{{m}^{2}}\] done
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B)
is \[10\sqrt{3}\text{ c}{{\text{m}}^{\text{2}}}\] done
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C)
is \[9\sqrt{3}\text{ }c{{m}^{2}}\] done
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D)
Cannot be determined done
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E)
None of these done
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question_answer 37)
A cylinder is within the cube touching all the vertical faces. A is the cylinder If their heights are same with the same base, then the ratio of their volumes is ___________
A)
21 : 33 : 11 done
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B)
42 : 23 : 11 done
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C)
42 : 33 : 22 done
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D)
42 : 33 : 11 done
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E)
None of these done
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question_answer 38)
A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder If the radius of the sphere is 7 cm, then the volume of the cylinder is _________
A)
\[308c{{m}^{3}}\] done
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B)
\[1156\,c{{m}^{3}}\] done
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C)
\[2156\,c{{m}^{3}}\] done
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D)
\[368\,c{{m}^{3}}\] done
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E)
None of these done
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question_answer 39)
A square of side ?a? cm is cut from each corner of a square sheet of side 12 cm. The remaining sheet is folded to form a cuboid. If the minimum possible volume of the cuboid is M cubic cm and a is an integer, then M is _________
A)
20 done
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B)
64 done
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C)
32 done
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D)
16 done
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E)
None of these done
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question_answer 40)
In a triangle, the average of any two sides is 18 cm more than half of the third side. The area of the triangle (in sq. cm) is _________
A)
\[162\sqrt{3}\text{ }\] done
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B)
\[324\sqrt{3}\text{ }\] done
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C)
\[218\sqrt{3}\text{ }\] done
clear
D)
\[420\sqrt{3}\text{ }\] done
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E)
None of these done
clear
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