General Mathematics

Question: The Expression `(1 - 1/3)(1 - 1/4)(1 -1/5)....(1 - 1/m) when simplifraction yeilds`.
A
`(1 - m)/m`

B
`2/m`

C
`2/m(m - 1)`

D
`2/(m(m + 1)`

Note: `(1 - 1/3)(1 - 1/4)(1 - 1/5)...(1 - 1/m)` `= 2/3 xx 3/4 xx 4/5xx ....xx (m - 1)/m` `= 2/m`
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Question: when simplied ,the product `(2 - 1/3)(2 - 3/5)(2 - 5/3) ....( 2 - 999/1001)` is equal to :
A
`991/1001`

B
`1001/13`

C
`1003/13`

D
None of these

Note: `(2 - 1/3)(2 - 3/5)(2 - 5/7)....(2 - 999/1001)` `= 5/3 xx 7/5 xx 9/7 xx...xx 1003/1001` `= 1003/3`.
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Question: A class starts at `10` a.m .and lasts till `1.27`p.m. Four periods are held during this interval .After every period, 5 minits are given free to the students .The exact duration of each period is .
A
`42 minutes `

B
`48 minutes `

C
`51 minutes `

D
`53 minutes `

Note: Time between `10` a.m. and `13.27` hours `= 3`hours `27` min.`= 207` min. For three period in between free time `15 min` :.Remaining time `= (207 - 15)` min`= 192` min. Duration of each of the `4` periods `= (192/4)` min.`=48`.
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Question: A light was seen at intervals of `13` seconds .It was seen for the first time at `1` hrs min `50` secs.a.m. and the last time at `3 hrs``17 hrs` min `49` secs .a.m. How many times was light seen ?
A
`378`

B
`375`

C
`360`

D
`384`

Note: Hrs min sec `3 − 17 − 4` `(-)1 − 54 − 50` _____________________ `1 − 22 − 59` _____________________ :. Toatal time `= (1 xx 60 + 22) min. + 59 sec.` `= (82 xx 60 + 59) sec. = 4979`. Number of times the light is seen `= (4979/13 + 1)` `= 384`.
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Question: A person gave Rs `2500` to eldest son,`5/12` of the whole property to the second son and to the youngest as much as to the first and second son toghether .How much did the youngest son get ?
A
`Rs 10000`

B
`Rs 15000`

C
`Rs 20000`

D
Rs 25000`

Note: Let total property be worth of Rs .x.Then `2500 + (5x)/12 + (2500 + (5x)/12) = x` or` 2 (2500 + (5x)/12) = x` or` 5000 + (5x)/6 = x` or` x - (5x)/6 = 5000` `x/6 = 5000` or `x = 30000`. :. youngest son gets = Rs `(2500 + (5 xx 30000)/12)` `= Rs. 15000`.
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Question: `1/4` of Nikhil ,s money is equal to `1/6` of yogesh ,s money .If both together have Rs `600`, the difference between thier amounts is .
A
`Rs 50`

B
`Rs 120`

C
`Rs 240`

D
`Rs 230`

Note: `1/4 N = 1/6 Y & N + y = 600` or `N = 2/3 `Y. So, `2/3 Y + Y =600` or `5/3` Y `= 600` :.Y` = (600 xx 3/5)` ` = 360` & N `= (2/3 xx 360)= 240` :.Y - N` = (360 - 240)` `= 120`.
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Question: If `x/y = 4/5`, the value of `(5/8 + (y - x)/(y + x))`is
A
`49/72`

B
`53/72`

C
`23/72`

D
None of these

Note: `(5/8 + (y - x)/(y + x))` `= (5/8 + (1 - x/y)/(1 + x/y))` `= (5/8 + (1 - 4/5)/(1 + 4/5))` `= 5/8 + ((1∕5))/((9∕5))` `= (5/8 + 1/5 xx 5/9)` `= 5/8 + 1/9)` `= 3/72`
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Question: If `a/2b = 3/2`, then the value of `(2a + b)/(a - 2b)` equals :
A
`1/7`

B
`7`

C
`7.1`

D
None of these

Note: Not available
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Question: If`a/b = 1/5`, then (5a + 2b)/(5a - 2b)` is equal to :
A
`3`

B
`- 3`

C
`- 5`

D
`-1`

Note: `(5a + 2b)/(5a - 2b)` `= 5 (a/b) + 2/5 (a/b) - 2` `= (5 xx 1/5 +2)/(5 xx 1/5 - 2)` `= 3/(1 -2)` `= -3`
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Question: If`a/3 = b/4 = c/7`, the value of (a + b + c)/c `is :
A
`7`

B
`2`

C
`1/2`

D
`1/7`

Note: Let,`a/3 = b/4 = c/7 = k`. Then,`a = 3k, b = 4k & c = 7k`. :.`(a + b + c)/c` `= (3k + 4k + 7k)/7k` `= (14k)/(7k)` `= 2`.
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Question: The Expression `(1 - 1/3)(1 - 1/4)(1 -1/5)....(1 - 1/m) when simplifraction yeilds`.

Question: when simplied ,the product `(2 - 1/3)(2 - 3/5)(2 - 5/3) ....( 2 - 999/1001)` is equal to :

Question: A class starts at `10` a.m .and lasts till `1.27`p.m. Four periods are held during this interval .After every period, 5 minits are given free to the students .The exact duration of each period is .

Question: A light was seen at intervals of `13` seconds .It was seen for the first time at `1` hrs min `50` secs.a.m. and the last time at `3 hrs``17 hrs` min `49` secs .a.m. How many times was light seen ?

Question: A person gave Rs `2500` to eldest son,`5/12` of the whole property to the second son and to the youngest as much as to the first and second son toghether .How much did the youngest son get ?

Question: `1/4` of Nikhil ,s money is equal to `1/6` of yogesh ,s money .If both together have Rs `600`, the difference between thier amounts is .

Question: If `x/y = 4/5`, the value of `(5/8 + (y - x)/(y + x))`is

Question: If `a/2b = 3/2`, then the value of `(2a + b)/(a - 2b)` equals :

Question: If`a/b = 1/5`, then (5a + 2b)/(5a - 2b)` is equal to :

Question: If`a/3 = b/4 = c/7`, the value of (a + b + c)/c `is :