General Mathematics

Question: An alloy is to contain copper and zinc in the ratio `9 : 4`. The zinc required (in kg) to be melted with `24` kg of copper, is ?
A
`10 2/3`

B
`10 1/3`

C
`9 2/3`

D
`9`

Note: `9 : 4 :: 24 : x` `iff 9x = 4 xx 24` `iff x = (4 xx 24)/9` `= 10 2/3` kg.
1. Report
Question: The ratio of income of `A` to that of `B` is `5 : 4` and the expenditure of `A` to that of `B` is `3 : 2`. If at the end of the year, each saves Rs. `800`, the income of `A` is :
A
Rs. `1600`

B
Rs. `1800`

C
Rs. `2000`

D
Rs. `2200`

Note: Let the income of `A` and `B` be ` 5x & 4x` and the expenditures of `A`and`B` be`3y` and `2y`. Then, `5x - 3y = 800` and `4x - 2y = 800`. On solving we get `: x = 400`. `:. A's` income `= 5x` `= Rs. 2000`.
1. Report
Question: A dog takes `3` leaps for every `5` leaps of a hare. If one leap of the dog is equal to `3` leaps of the hare, the ratio of the speed of the dog to that of the hare is :
A
`8 : 5`

B
`9 : 5`

C
`8 : 7`

D
`9 : 7`

Note: Dog : Hare `= (3 xx 3)` leaps of hare `: 5` leaps of hare `= 9 : 5`.
1. Report
Question: Two cubes have their volumes in the ratio `8 : 27.` The ratio of the volume of the sphere to that of the cube is :
A
`2 : 3`

B
`3 : 2`

C
`4 : 9`

D
`64 : 729`

Note: Let their edges be a. Then, `a^3/b^3 = 8/27 ⇔ (a/b)^3` `= (2/3)^3 ⇔ a/b = 2/3` `⇔ a^2/b^2 ⇔ 6a^2/6b^2 = 4/9.`
1. Report
Question: A sphere and a cube have equal surface areas. The ratio of the volume of the sphere to that of the cube is :
A
`√π : √6`

B
`√2 : √π`

C
`√ π: √3`

D
`√6 : √π`

Note: `4π R^2 = 6a^2 ⇒ R^2/a^2` `= 3/(2π) ⇒ R/a` `=(√3)/(√2π).` `Volume of sphere/Volume of cube` `= (4/3 πR^3)/a^3` `= (4)/(3) π.(R/a)^3` `= 4/3π . (3√3)/(2π√2π)` `= (2√3)/(√2π)` `= √12/√2π` `= (√6)/(√π).`
1. Report
Question: The ratio of the volume of a cube to that of a sphere which will fit inside the cube is :
A
`4 : R`

B
`4 : 3r`

C
`6 : r`

D
`2 : r`

Note: Let the edge of the cube be a. Then,volume of the cube `= a^3.` Radius of the sphere `= (a/2).` Volume of the sphere `= 4/3 r (a/2)^3` `= (ra^3)/6.` :. Requied Ratio `= a^3 : (ra^3/6` `= 6 : r.`
1. Report
Question: Two cube each with`6` cm edge are joined end to end. The surface area of the resulting cuboid is :
A
`864 cm^2`

B
`360 cm^2`

C
`576 cm^2`

D
`432 cm^2`

Note: New cuboid has length`= 12 cm,` breadth`= 6 cm` & height `= 6 cm` :. Its surface area`= 2(12 xx 6 xx 6 xx 6 + 12 xx 6) cm^2` ` = 360 cm^2.`
1. Report
Question: If the areas of three adjacent faces of a cuboid are x, y, z, respectively, then the volume of the cuboid is :
A
`xyz`

B
`2xyz`

C
`√xyz`

D
`3√xyz`

Note: Let length` = 1`breadth`= 6 cm` & height`= h.` Then, lb`= x, bh`= y, and lh`= z.` On multiplying, we get `(lbh)^2 = xyz` `or lbh =√xyz.` :. Volume`= √xyz.`
1. Report
Question: If v be the volume and S be the surface area of a cuboid of dimensions a, b, c, then `1/v` is equal to :
A
`s/2 (a + b + c)`

B
`2/s (1/a + 1/b + 1/c)`

C
`(2s)/(a + b + c)`

D
`2s (a + b + c)`

Note: `1/v = 1/s xx s/v` `= (2 (ab + bc + ca))/(s xx abc)` `= 2/s (1/a + 1/b + 1/c)`
1. Report
Question: A cube of side `6 cm` is cut into a number of cubes, each of side `2 cm.` The number of cubes will be :
A
`6`

B
`9`

C
`12`

D
`27`

Note: Number of cubes `= (Volume of bigger cube)/(Volume of smaller cube)` `= ((6 xx 6 xx 6)/(2 xx 2 xx 2))` `= 27.`
1. Report

First Prev 70 71 72 73 74 Next Last

Question: An alloy is to contain copper and zinc in the ratio `9 : 4`. The zinc required (in kg) to be melted with `24` kg of copper, is ?

Question: The ratio of income of `A` to that of `B` is `5 : 4` and the expenditure of `A` to that of `B` is `3 : 2`. If at the end of the year, each saves Rs. `800`, the income of `A` is :

Question: A dog takes `3` leaps for every `5` leaps of a hare. If one leap of the dog is equal to `3` leaps of the hare, the ratio of the speed of the dog to that of the hare is :

Question: Two cubes have their volumes in the ratio `8 : 27.` The ratio of the volume of the sphere to that of the cube is :

Question: A sphere and a cube have equal surface areas. The ratio of the volume of the sphere to that of the cube is :

Question: The ratio of the volume of a cube to that of a sphere which will fit inside the cube is :

Question: Two cube each with`6` cm edge are joined end to end. The surface area of the resulting cuboid is :

Question: If the areas of three adjacent faces of a cuboid are x, y, z, respectively, then the volume of the cuboid is :

Question: If v be the volume and S be the surface area of a cuboid of dimensions a, b, c, then `1/v` is equal to :

Question: A cube of side `6 cm` is cut into a number of cubes, each of side `2 cm.` The number of cubes will be :