Saturday, January 25, 2020
03:13 AM (GMT +5)

Go Back   CSS Forums > CSS Optional subjects > Group II > Pure Mathematics

Reply Share Thread: Submit Thread to Facebook Facebook     Submit Thread to Twitter Twitter     Submit Thread to Google+ Google+    
 
LinkBack Thread Tools Search this Thread
  #31  
Old Saturday, October 30, 2010
j87ibz's Avatar
39th CTP (PAAS)
CSP Medal: Awarded to those Members of the forum who are serving CSP Officers - Issue reason: CE 2010 - Merit 92
 
Join Date: May 2010
Location: Wah Cantt + Charsadda.
Posts: 71
Thanks: 60
Thanked 97 Times in 45 Posts
j87ibz is on a distinguished road
Default

||@sibgakhan :

Salam, but let me try to solve it, though i dont know much about pure maths.


f(x)= x^2 -x-1
g(x)= 3/x


now fog(x)= f { g(x) } = f ( 3/x )
replace x by 3/x in f(x)

fog(x) = (3/x)^2 - (3/x) - 1

= (9/x^2) -3/x -1

The above expression can be simplified easily , taking LCM as x^2,

= 9 -3x - x^2
------------
x^2


Domain of f (x) = { all real numbers }
Domain of g (x) = { all real numbers except 0 }
Domain of fog(x) = { all real numbers except 0}






Lim x^3 -5x^2 + 6x / ( x^2 -9)
x--->3

Solution :

Applying limit to every factor, we get

Lim x^3 - Lim 5x^2 + Lim 6x / ( x^2 -9)
x-->3 x-->3 x-->3


The limit Lim 6x / ( x^2 -9) is in (c /0) form, so requires L hospital rule
x-->3


so taking d/dx to 6x / ( x^2 -9) in denominator and nominator separately, we get,

6/ (2x-9)

now putting value an applying limit, we get

Lim x^3 - Lim 5x^2 + Lim 6/ (2x-9)
x-->3 x-->3 x-->3


= 3^3 - 5(3)^2 + 6 /( 2*3 -9)

= 27 - 45 -2
= -20



03.

7< ( 1-2x) ≤ 10

can be broken to two in equalities

=> 7< 1-2x ||||||||| 1- 2x ≤ 10

=> 7-1 < -2x ||||||||| => -2x ≤ 10-1

=> 6< -2x ||||||||| => -2x ≤ 9

=> -6 > 2x ||||||||| => 2x > -9

=> -3 > x ||||||||| => x > -4.5
which means between -∞ , -3 ||||||||| which means between -4.5 , ∞



when plotted together.

__-9/2------4-------3_____-2_____-1_____0____ 1_____2_____3______4___
__________________
Influentials of history have made me realized that they always had flexible principles to others and strict to themselves.
Reply With Quote
The Following 2 Users Say Thank You to j87ibz For This Useful Post:
sahibakhushik89 (Sunday, May 29, 2016), sibgakhan (Saturday, October 30, 2010)
  #32  
Old Saturday, October 30, 2010
tanolig's Avatar
Senior Member
 
Join Date: Aug 2010
Posts: 105
Thanks: 33
Thanked 83 Times in 46 Posts
tanolig is on a distinguished road
Default

Q#01
Solve the two sided inequality and show the solution on real line
7 < 1-2x ≤ 10

Solution:
=> 7 < 1-2x ≤ 10
multiply through out by (-)
=> -10 ≤ 2x-1 <-7
=> -9 ≤ 2x < -7
Divide through out by 2
=> -9/2 ≤ x < -7/2
Hence the resultant solution is semi close semi open interval [-9/2 , -7/2) on real line.

Q#03
Simplify, then apply the rules of limit to evaluate
lim x->3 x3(power3)-5x2(power2)+6x/x2(power2)-9

Solution:
lim x->3 {x3(power3)-5x2(power2)+6x/x2(power2)-9} --------> {c/0 form}
(Applying Lop-ital)
Differentiating both denominator and nominator w.r.t 'x'
=> lim x->3 {3x2(power2)-10x+6/2x}
Now applying limt
=> {3*(3^2)-10*3+6}/2*3
=> {27-30+6}/6
=> 3/6
=> 1/2 Ans
__________________
He who asks is a fool for five minutes, but he who does not ask remains a fool forever!
GOOD LUCK!
Reply With Quote
The Following User Says Thank You to tanolig For This Useful Post:
sibgakhan (Monday, November 01, 2010)
  #33  
Old Saturday, October 30, 2010
tanolig's Avatar
Senior Member
 
Join Date: Aug 2010
Posts: 105
Thanks: 33
Thanked 83 Times in 46 Posts
tanolig is on a distinguished road
Lightbulb Maths!

@ Sibgakhan

Q#01
Solve the two sided inequality and show the solution on real line
7 < 1-2x ≤ 10


Solution:
=> 7 < 1-2x ≤ 10
multiply through out by (-)
=> -10 ≤ 2x-1 <-7
=> -9 ≤ 2x < -7
Divide through out by 2
=> -9/2 ≤ x < -7/2
Hence the resultant solution is semi close semi open interval [-9/2 , -7/2) on real line.

Q#03
Simplify, then apply the rules of limit to evaluate
lim x->3 x3(power3)-5x2(power2)+6x/x2(power2)-9


Solution:
lim x->3 {x3(power3)-5x2(power2)+6x/x2(power2)-9} -------->(A) {c/0 form}
L' Hospital Rule is applied only if function has the form either {0/0} or {∞/∞}.
Now we proceed as follows
=> lim {x->3 x^3-5x^2+6x}/x^2 - 9
Nominator can be expanded as
x^3-5x^2+6x = x^3-3x^2-2x^2+6x = x^2*(x-3)-2x*(x-3) = (x^2-2x)*(x-3) ---->(i)
Also
x^2 - 9 = (x+3)*(x-3) ------>(ii)
Now using (i) and (ii) in (A)
=> lim x->3 {(x^2-2x)*(x-3)}/(x+3)*(x-3)
=> lim x->3 {(x^2-2x)}/(x+3)
Applying limit
=> {3^2 -2*3}/3+3
=> {9-6}/6
=> 3/6
=> 1/2 Ans

Best Regards!
__________________
He who asks is a fool for five minutes, but he who does not ask remains a fool forever!
GOOD LUCK!
Reply With Quote
  #34  
Old Saturday, November 06, 2010
SIBGA-TUL-JANAT
Medal of Appreciation: Awarded to appreciate member's contribution on forum. (Academic and professional achievements do not make you eligible for this medal) - Issue reason: Appreciation
 
Join Date: Jul 2005
Posts: 1,222
Thanks: 349
Thanked 427 Times in 261 Posts
sibgakhan is a jewel in the roughsibgakhan is a jewel in the roughsibgakhan is a jewel in the roughsibgakhan is a jewel in the rough
Default

how we can convert fraction part of a question into hours and min?
i mean 5 5/7 and 10 2/70 comtains how many hours and min and what the formula??

thanks
__________________
Aalam-e-soz o saz main, wasl se barh ker hai firaaq
Hijr me lazt-e-talb, wasl main marg-e-arzoo...!!!
Reply With Quote
  #35  
Old Sunday, November 07, 2010
Ayesha Mahmood's Avatar
Senior Member
 
Join Date: Jan 2010
Location: DGKhan & Isb
Posts: 323
Thanks: 376
Thanked 264 Times in 178 Posts
Ayesha Mahmood will become famous soon enoughAyesha Mahmood will become famous soon enough
Default

Quote:
Originally Posted by sibgakhan View Post
how we can convert fraction part of a question into hours and min?
i mean 5 5/7 and 10 2/70 comtains how many hours and min and what the formula??
you can't convert fractions to minutes or hours. Only units are inter converted.


suppose you have to convert 5 5/7 seconds to minutes and hours then you may proceed as follows:

1 min = 60 sec
=>60 sec = 1 min
=>1 sec = 1/60 min
=>5 5/7 sec= 5 5/7 * 1/60 min = 40/7 *1/60 min = 2/21 min




1 hour = 60 min = 60 * 60 sec = 3600 sec
=>3600 sec = 1 hour
=>1 sec = 1/3600 hr
=>5 5/7 sec = 5 5/7 * 1/3600 hr = 40/7 * 1/3600 hr = 1/630 hr



and if 5 5/7 is not in sec but days then it will be converted to min and hours as follows:

1 day = 24 hrs
=>5 5/7 days = 5 5/7 * 24 hrs = 40/7 * 24 hrs = 137 1/7 hrs


also

1 day = 24 hrs = 24 * 60 min = 1440 min
=> 5 5/7 days = 40/7 * 1440 min = 8228 4/7 min.
Reply With Quote
The Following User Says Thank You to Ayesha Mahmood For This Useful Post:
sibgakhan (Sunday, November 07, 2010)
  #36  
Old Wednesday, February 16, 2011
SIBGA-TUL-JANAT
Medal of Appreciation: Awarded to appreciate member's contribution on forum. (Academic and professional achievements do not make you eligible for this medal) - Issue reason: Appreciation
 
Join Date: Jul 2005
Posts: 1,222
Thanks: 349
Thanked 427 Times in 261 Posts
sibgakhan is a jewel in the roughsibgakhan is a jewel in the roughsibgakhan is a jewel in the roughsibgakhan is a jewel in the rough
Default can anyone solve these questions...

1. If the area of rectangle increased by 69%, the length of arm of the rectangle should increase:

2. If the length of arms of rectangle increased by 5% and 7% respectively, then the area of rectangle should increase by:

3. Jack’s salary is 150% of Tom’s salary; Tom’s salary is 80% of Adam’s salary.
If Adam’s salary is S, then what is the ratio of Jack’s salary to Adam’s salary:

5. The cost price of a toy is $50, but its offer price is 108%. After one week it is sold on 10% discount. What will be the cost of toy?

6. The cost of first 500 prints is $10, while after it, cost for each is (10-x/50). What will be X, if the total cost is $75

7. 45% of people of a town have brown hair, while 20% of people have brown eyes. Meanwhile 10% have both brown hair and brown eyes. How much people have neither brown hair nor brown eyes?

8. In a town an appeal for fund raising is made. People of the town respond to that in this way: 45% people contributed $40, 30% contributed $20 while rest contributes $2. If the total amount of people who contribute $2 is $300, then what will be the total?

9. if the mean of 10 items is -10 and sum of 6 items is 100. what is the mean of remaining items?

10. In 2009, Ali read 10 English and 7 French books. In 2010, his ratio of English buks is 3times french buks and he read 60% of
french books in 2010 then how many books he read in 2010?

11. Ahmed buys a merchandise on commission of 25 paisa. if the cost price is Rs.20 what percentage of commission he received?

12. if the price of tea increases by 20%. suppose a consumer expenditure on tea is Rs.200. then by what percentage he should cut his consumption of tea so that 20% increase in price of tea does'nt effect on his original expenditure on tea?

13. The growth rate is increased by 25% from 2000 to 2010. if the growth in 2010 is "W". what was the growth on 2000?

14. A can do a piece of work in 20 days which A and B together can do in 12 days. B alone can do it in hw many days?

15. In an election one of the 2 candidates gets 40% of the total votes but he losses by 160 votes . what is the total number of votes?

16. Salma spent 1/10 of her income on clothes, 1/10 of the remaining on food, and 1/3 of the remaining on rental. if she left with Rs. 648 what is her total income?

17. The total no. of students in a class are 335250. if they are adjusted in a square class with equal rows and columns, only 9 are left behind. what is the no. of rows?
__________________
Aalam-e-soz o saz main, wasl se barh ker hai firaaq
Hijr me lazt-e-talb, wasl main marg-e-arzoo...!!!

Last edited by sibgakhan; Wednesday, February 16, 2011 at 12:51 AM.
Reply With Quote
  #37  
Old Saturday, February 19, 2011
SIBGA-TUL-JANAT
Medal of Appreciation: Awarded to appreciate member's contribution on forum. (Academic and professional achievements do not make you eligible for this medal) - Issue reason: Appreciation
 
Join Date: Jul 2005
Posts: 1,222
Thanks: 349
Thanked 427 Times in 261 Posts
sibgakhan is a jewel in the roughsibgakhan is a jewel in the roughsibgakhan is a jewel in the roughsibgakhan is a jewel in the rough
Default

1. If the area of rectangle increased by 69%, the length of arm of the rectangle should increase:

2. If the length of arms of rectangle increased by 5% and 7% respectively, then the area of rectangle should increase by:

plz solve these questions urgently.
__________________
Aalam-e-soz o saz main, wasl se barh ker hai firaaq
Hijr me lazt-e-talb, wasl main marg-e-arzoo...!!!
Reply With Quote
  #38  
Old Tuesday, February 22, 2011
bear's Avatar
Senior Member
 
Join Date: Jun 2010
Location: لاہور
Posts: 109
Thanks: 54
Thanked 93 Times in 50 Posts
bear is on a distinguished road
Default

question 1
area = 100 ( 50 x 2)
new area = 169 (increased by 69 percent )

169 = 84.2 x2

84.5 - 50 = 34.5
34.5 /50 = 69 %

this means arm length will also increase by same amount if other arm's length doesn't change .

question 2

area = a x b = ab
new area = 1.05a x 1.07b = 1.1235ab

new area - old area = 1.1235-1 = .1235 = 12.35 %
Reply With Quote
  #39  
Old Thursday, February 24, 2011
Malik Asfand Yar's Avatar
Junior Member
 
Join Date: Nov 2010
Location: Dera Ismail Khan
Posts: 8
Thanks: 5
Thanked 0 Times in 0 Posts
Malik Asfand Yar is on a distinguished road
Default

Q9 100+X/10=-10
X=-200 and the average of remaining items is -50
Reply With Quote
  #40  
Old Wednesday, October 21, 2015
Aamish Bhatti's Avatar
Senior Member
 
Join Date: Jan 2012
Location: Atlantis
Posts: 268
Thanks: 609
Thanked 105 Times in 78 Posts
Aamish Bhatti is on a distinguished road
Default

Quote:
Originally Posted by ATIF FAUN View Post
6) A shopkeeper sold an electric iron at 10% profit. Had he sold an iron at 20% profit, he would have gain rs.%) more. The cost price of the fan was:
A)400 B)450 C)550 D)500

I think problem has been mis-typed. Please mention the amount.
__________________
Khushboo Hai Mere Khoon Mein Kafoor Ki Manind,
Bikhrunga Fizaun Mein Ek Noor Ki Manind . . .
Reply With Quote
Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Solve the MCQ`s of Past Five Years theelegant444 Geography 16 Sunday, July 03, 2011 09:50 PM
Please Solve These Questions s_m_u_yousaf Pure Mathematics 10 Saturday, November 14, 2009 06:57 PM
Solve the subjective portion of current affair 2009 paper.. Noor_2009 Current Affairs 3 Sunday, November 01, 2009 12:44 AM
Solve Palestinian Issue Now, Says Sarkozy Princess Royal News & Articles 0 Tuesday, January 15, 2008 11:10 PM


CSS Forum on Facebook Follow CSS Forum on Twitter

Disclaimer: All messages made available as part of this discussion group (including any bulletin boards and chat rooms) and any opinions, advice, statements or other information contained in any messages posted or transmitted by any third party are the responsibility of the author of that message and not of CSSForum.com.pk (unless CSSForum.com.pk is specifically identified as the author of the message). The fact that a particular message is posted on or transmitted using this web site does not mean that CSSForum has endorsed that message in any way or verified the accuracy, completeness or usefulness of any message. We encourage visitors to the forum to report any objectionable message in site feedback. This forum is not monitored 24/7.

Sponsors: ArgusVision   vBulletin, Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.