General Mathematics

Question: If `1/3 A = 1/4 B = 1/5 C`, then `A : B : C` is :
A
`4 : 3 : 5`

B
`5 : 4 : 3`

C
`3 : 4 : 5`

D
`20 : 15 : 12`

Note: Not available
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Question: If `A = 1/3 B` and `B = 1/2 C` then `A : B : C` is :
A
`1 : 3 : 6`

B
`3 : 1 : 2`

C
`2 : 3 : 6`

D
`3 : 2 : 6`

Note: `A/B = 1/3` and `B/C = 1/2`. `:. A : B = 1 : 3` and `B : C = 1 : 2 = 3 : 6`. `A : B : C = 1 : 3 : 6`.
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Question: If `2A = 3B` and `4B = 5C`, then `A : C` is :
A
`4 : 3`

B
`8 : 15`

C
`15 : 8`

D
`3 : 4`

Note: `A/B = 3/2` and `B/C = 5/4`. `:. A/C = A/B xx B/C` `= 3/2 xx 5/4` `= 15/8`. so, `A : C = 15 : 8`
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Question: If `x : y = 5 : 2`, then the value of `(8x + 9y) : (8x + 2y)` is :
A
`26 : 61`

B
`61 : 26`

C
`29 : 22`

D
`22 : 29`

Note: Given : `x/y = 5/2`. `:. (8x + 9y)/(8x + 2y)` `= (8 ( x/y) + 9)/(8 (x/y) + 2)` `=(8 xx 5/2 + 9)/(8 xx 5/2 + 2)` `= 29/22`.
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Question: If `x : y = 2 : 1`, then `(x^2 - y^2) : (x^2 + y^2)` is :
A
`3 : 5`

B
`5 : 3`

C
`1 : 3`

D
`3 : 1`

Note: `x/y = 2/1 => x^2/y^2 = 4/1`. `:. (x^2 - y^2)/(x^2 + y^2)` `=(4 - 1)/(4 + 1)` `= 3/5`
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Question: If `(4x^2 - 3y^2) : (2x^2 + 5y^2) = 12 : 19`, then `x : y` is :
A
`2 : 3`

B
`1 : 2`

C
`3 : 2`

D
`2 : 1`

Note: `(4x^2 - 3y^2)/(2x^2 + 5y^2) = 12/19` `iff``19(4x^2 - 3y^2) = 12(2x^2 + 5y^2)` `iff``(76x^2 - 24x^2) = (60y^2 + 57y^2)` `iff``52x^2 = 117y^2` `iff``4x^2 = 9y^2` `iff``x^2/y^2 = 9/4` `iff``x/y = 3/2`.
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Question: The fourth proportional of `0.2`, `0.12` and `0.3` is :
A
`0.13`

B
`0.15`

C
`0.18`

D
`0.8`

Note: Let `0.2 : 0.12 = 0.3 : x`. Then, `0.2x = 0.12 xx 0.3` or, `x = (0.12 xx 0.3)/0.2` `= 0.18`.
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Question: The third proportional to `0.36` and `0.48` is :
A
`0.64`

B
`0.1728`

C
`24sqrt(.0003)`

D
None of these

Note: Let `0.36 : 0.48 = 0.48 : x`. Then, `0.36x = 0.48 xx 0.48` or, `x = (0.48 xx 0.48)/0.36` `= 0.64`
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Question: The mean of `1^2,2^2,3^2,4^2,5^2,6^2,7^2` is:
A
`40`

B
`20`

C
`30`

D
`10`

Note: `1^2 + 2^2 + 3^2 +....+n^2` `= (n(n + 1)(2n + 1))/(6)` `:. 1^2 + 2^2 +3^2 +......+7^2` `= ((7 xx 8 xx 15)/6)` `= 140`. :. Required average `= (140/7)` `= 20`
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Question: The average of all odd numbers upto `100`is:
A
`51`

B
`50`

C
`49.5`

D
`49`

Note: Sum of odd numbers upto `100` `= 1 + 3 + 5 + 7 +......+ 95 + 97 + 99` `= (1 + 99) + (3 + 97) + (5 + 95) +...upto `25`pairs. `= 100 + 100 + 100+....(25 times)` `= 2500` :. Average `= (2500/50)` `= 50`
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Question: If `1/3 A = 1/4 B = 1/5 C`, then `A : B : C` is :

Question: If `A = 1/3 B` and `B = 1/2 C` then `A : B : C` is :

Question: If `2A = 3B` and `4B = 5C`, then `A : C` is :

Question: If `x : y = 5 : 2`, then the value of `(8x + 9y) : (8x + 2y)` is :

Question: If `x : y = 2 : 1`, then `(x^2 - y^2) : (x^2 + y^2)` is :

Question: If `(4x^2 - 3y^2) : (2x^2 + 5y^2) = 12 : 19`, then `x : y` is :

Question: The fourth proportional of `0.2`, `0.12` and `0.3` is :

Question: The third proportional to `0.36` and `0.48` is :

Question: The mean of `1^2,2^2,3^2,4^2,5^2,6^2,7^2` is:

Question: The average of all odd numbers upto `100`is: