General Mathematics

Question: A rectangular box is `2` m long and `3.5` m wide. How many cubic metres of sand are needed to fill the box upto a depth of `12` cm ?
A
`84`

B
`8.4`

C
`0.84`

D
`0.084`

Note: Volume` = (2 xx 7/2 xx 12/100) ` `= 0.84 cu.m.`
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Question: A beam `9` m long, `40` cm wide and `20` cm high is made up of iron which weighs `50` kg per cubic metre. The wight of the beam is :
A
`56 kg`

B
`48 kg`

C
`36 kg`

D
`27 kg`

Note: Volume `= (9 xx 40/100 xx 20/100) cu.m` `= 18/25 cu.m`. :. Wight` = (18/25 xx 50) kg` `= 36 kg`.
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Question: The length of the longest rod that can be placed in a room `30` m long,`24` m broad and `18` m high, is :
A
`30 m`

B
`15√2 m`

C
`30√2 m`

D
`60 m`

Note: Length of longest rod = Length of diagonal `= √1^2 + b^2 + h^2` `= √(30)^2 + (24)^2 + (18)^2` `= √1800` `= 30√2 m`.
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Question: The maximum length of a pencil that can be kept is a rectangular box of dimension `8 cm xx 6 cm xx 2 cm, `is :
A
`2√13 cm`

B
`2√14 cm`

C
`2√26 m`

D
`10√2 cm`

Note: Not available
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Question: A wooden box of dimension `8 m xx 7 m xx 6 m` is to carry rectangular boxes of dimensions `8 cm xx 7 cm xx 6 cm`. The maximum number of boxes that can be carried in the wooden box, is :
A
`9800000`

B
`7500000`

C
`1000000`

D
`1200000`

Note: Number of boxes `= ((800 xx 700 xx 600)/(8 xx 7 xx 6))` `= 1000000`
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Question: A will `8` m long, `6` m high and `22.5` cm thick is made up of bricks, each measuring `(25 cm xx 11.25 cm xx 6 cm)`. The number of bricks required is :
A
`6000`

B
`5600`

C
`6400`

D
`7200`

Note: Number of bricks `= ((800 xx 600 xx 22.5)/(25 xx 11.25 xx 6))` `= 6400`.
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Question: The dimension of bricks are `24 cm xx 12 cm xx 8 cm`. How many bricks will be required to build a wall `24` m long, `8` m high and `60` cm thick, if `10%` of the wall is filled with mortar ?
A
`40000`

B
`20000`

C
`50000`

D
`45000`

Note: Volume of wall `= (2400 xx 800 xx 60) cu. cm`. Volume of wall (apart from mortar) `= (/100 xx 2400 xx 800 xx 60) cu.m`. Volume of `1` bricks `= (24 xx 12 xx 8) cu. cm.` :. Number of bricks required `= (90/10 xx 2400 xx 800 xx 60 xx 1/(24 xx 12 xx 8)` `= 45000`.
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Question: A rectangular block `6` cm by `12` cm by `15` cm is cut up into exact number of equal cubes. The least possible number of cubes will be :
A
`6`

B
`11`

C
`33`

D
`40`

Note: Volume of block `= (6 xx 12 xx 15) cu. cm` `= 1080 cu. cm`. The side of largest cube = H.C.F.of `6 cm, 12 cm, 15 cm = 3 cm`. Volume of this cube `= (3 xx 3 xx 3) cm^3 = 27 cm^3` Number of cubes `= (1080/27)` `= 40`.
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Question: The breadth of a room is twice its height and half its length. The volume of the room is `512 cu.m. The length of the room is :
A
`12 m`

B
`16 m`

C
`32 m`

D
`20 m`

Note: Suppose height = x metres . Then, breadth = 2x metres and length = 4x metres. `:. x xx 2x xx 4x = 512` `or x^3 = 64` `or x = 4`. `:. Length = 4x = 16 m.
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Question: Three cubes of iron whose edges are `6`cm, `8 cm` and `10` cm respectively are melted and formed into a single cube. The edge of the new cube formed is :
A
`12 cm`

B
`14 cm`

C
`16 cm`

D
`18 cm`

Note: Volume of new cube `= [6^3 + 8^3 + (10)^3] cu. cm` `= 1728 cu. cm`. Let the edge of new cube be a cm. Then,` a^3 = 1728` `= (4 xx 4 xx 4 xx 3 xx 3 xx 3)` `or a = 12 cm`.
1. Report

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Question: A rectangular box is `2` m long and `3.5` m wide. How many cubic metres of sand are needed to fill the box upto a depth of `12` cm ?

Question: A beam `9` m long, `40` cm wide and `20` cm high is made up of iron which weighs `50` kg per cubic metre. The wight of the beam is :

Question: The length of the longest rod that can be placed in a room `30` m long,`24` m broad and `18` m high, is :

Question: The maximum length of a pencil that can be kept is a rectangular box of dimension `8 cm xx 6 cm xx 2 cm, `is :

Question: A wooden box of dimension `8 m xx 7 m xx 6 m` is to carry rectangular boxes of dimensions `8 cm xx 7 cm xx 6 cm`. The maximum number of boxes that can be carried in the wooden box, is :

Question: A will `8` m long, `6` m high and `22.5` cm thick is made up of bricks, each measuring `(25 cm xx 11.25 cm xx 6 cm)`. The number of bricks required is :

Question: The dimension of bricks are `24 cm xx 12 cm xx 8 cm`. How many bricks will be required to build a wall `24` m long, `8` m high and `60` cm thick, if `10%` of the wall is filled with mortar ?

Question: A rectangular block `6` cm by `12` cm by `15` cm is cut up into exact number of equal cubes. The least possible number of cubes will be :

Question: The breadth of a room is twice its height and half its length. The volume of the room is `512 cu.m. The length of the room is :

Question: Three cubes of iron whose edges are `6`cm, `8 cm` and `10` cm respectively are melted and formed into a single cube. The edge of the new cube formed is :