General Mathematics

Question: The radius of a cylinders is the same as that of a sphere. Their volumes are equal. The height of the cylinder is how many times its radius ?
A
`4/3 `

B
`2/3`

C
`1`

D
`2`

Note: `4/3 π R^3` `= πR^2h ⇒ h` `= 4/3 R.`
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Question: The material of a cone is converted into the shape of a cylinder of equal radius. If the height of the cylinder is `6` cm, the height of the cone is :
A
`2 cm`

B
`6 cm`

C
`18 cm`

D
`36 cm`

Note: `1/3 π R^2h` `= πR^2 xx 6 or h` `= 18 cm.`
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Question: A powder tin has a square base with side `8` cm and height `14`cm. Another tin has a circular base with diameter `8` cm and height`14`cm. The difference in their capacities is :
A
`0`

B
`132 cm^3`

C
`192 cm^3`

D
`137.1 cm^3`

Note: Difference in capacities `= (8 xx 8 xx 14 - 22/7 xx 4 xx 4 xx 14) cm^3` `= 192 cm^3`
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Question: The value of log``343`` 7 is :
A
`1/3`

B
`- 3`

C
`- 1/3`

D
`3`

Note: Let `long_343 7 = m.` Then, `(343)^m` `= 7 ⇒ (7^3)^m` `= 7 ⇔ 7^3m` `= 7^1 ⇔ 3m` `= 1 ⇔ m` `= 1/3`. `:. long_343 7 = 1/3.`
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Question: The value of log`5` (1/125) is :
A
`3`

B
`- 3`

C
`1/3`

D
`- 1/3`

Note: Let log`5 (1/125) = m` Then,`5m = 1/125 ⇔ 5^m` `= 1/5^3 ⇔ 5^m` `= 5-3` `:. m = - 3` and log`5(1/125)` `= -3`
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Question: The value of log`√2^32` is :
A
`5/2`

B
`5`

C
`10`

D
`1/10`

Note: Let log`√2 ^32` = m. Then,`(√2)^m = 32 ⇔ 2^m/2` `= 2^5 ⇔ m/2` `= 5 ⇔ m` `= 10` :.` log√2 ^32` `= 10`
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Question: The value of `log_10 (.0001)` is :
A
`1/4`

B
`-1/4`

C
`-4`

D
`4`

Note: Let `log_10 (.0001) = m`.Then, `10^m = .0001 ⇔ 10^m` `= 1/10000 ⇔ 10^m` `= 1/10^4 ⇔ 10^m` `= 10 ^-4 ⇔ m` `- 4`
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Question: The value of log`_(.01) (1000) is :`
A
`1/3`

B
`-1/3`

C
`3/2`

D
`- 3/2`

Note: Let log`_(.01) (1000) =m.` Then,`(.01)^m = 100 ⇔ (1/100)^m` `= 100` `⇔ (1/10^2)^m` `= 10^3 ⇔ (10 ^-2)^m` `= 10^3 ⇔ 10^-2m` `= 10^3.` `:. - 2m = 3 or m` `= - 3/2`
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Question: If `log_3 x = -2,` then x is equal to :
A
`- 9`

B
`- 6`

C
`- 8`

D
`1/9`

Note: `log_3 x = - 2 ⇔ x` `= 3 _2` `= 1/3^2` `= 1/9.`
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Question: If `log_x (9/16) = - 1/2,` then x is equal to :
A
`3/4`

B
`- 3/4`

C
`81/256`

D
`256/81`

Note: `log_x (9/16)` `= - 1/2 ⇔ x^- 1/2` `= 9/16 ⇔ 1/√x` `= 9/16 ⇔ √x` `= 16/9` :. x`= (16/9 xx 16/9)` `= 256/81.`
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Question: The radius of a cylinders is the same as that of a sphere. Their volumes are equal. The height of the cylinder is how many times its radius ?

Question: The material of a cone is converted into the shape of a cylinder of equal radius. If the height of the cylinder is `6` cm, the height of the cone is :

Question: A powder tin has a square base with side `8` cm and height `14`cm. Another tin has a circular base with diameter `8` cm and height`14`cm. The difference in their capacities is :

Question: The value of log``343`` 7 is :

Question: The value of log`5` (1/125) is :

Question: The value of log`√2^32` is :

Question: The value of `log_10 (.0001)` is :

Question: The value of log`_(.01) (1000) is :`

Question: If `log_3 x = -2,` then x is equal to :

Question: If `log_x (9/16) = - 1/2,` then x is equal to :