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Tuesday, December 31

Inverse of a Function

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Inverse of a Function

In this Post I will discuss the method for finding the inverse of a given function from the 4 options as given in the Entrance tests of Engineering Universities.

The very first step before finding the inverse is to make a check whether the function is One-to-One or not. 

By One-to-One function we mean that function for example f(x) should not have the same value at two different values of x. In other words for each element of the Domain there should be a distinct element in the range.


Check for One-to-One:
A function which passes the horizontal line test is a One-to-One function. This means if a horizontal line is drawn it should not cross the function curve at more than one point.
Another way to check if a function is One-to-One or not is shown below:

If ,
f(a) = f(b) , implies that a=b , the given function is One-to-One.
Consider the following examples:
f(x) = 5x + 10
f(a) = 5a + 10
f(b) = 5b + 10
Taking f(a) = f(b) gives,
5a + 10 = 5a - 10
this means
a=b
Thus the given function is One-to-One.

Now consider f(x) = x^2 + 1
f(a) = a^2 + 1
f(b) = b^2 + 1
Taking f(a) = f(b) gives,
a^2 + 1= b^2 + 1
this means
a^2 = b^2 
Now here are two possibilities ,
i.e
a=b or a=-b
Hence the given function is not One-to-One. 

I hope its clear. 

So first step before finding the inverse is to make the check for One-to-One function. If the given function is not One-to-One its inverse won't exist. In such cases there will be an option like "does not exist", "none of the above" etc. So it will be the correct answer.


In case the function is One-to-One follow the steps below to find the inverse.

The composition of a function and its inverse function is always equal to x. So take the composition of the given function with the options provided to you. The option which will give you the x will be the answer. Remember that answer of composition must be x, some people confuse it with 1 in the exams. 

This process is useful when the function to be dealt with is somewhat complex. In case of simple functions you can follow the traditional method as per mentioned in your text books. In case you forget the method to find the inverse, this process will come in handy. I'll suggest you to use this method in exams as it decrease the chances of mistakes.

In case of any confusion feel free to ask. 



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Sunday, December 29

Respiratory System In Birds

By With 4 comments:
Respiratory System In Birds

Respiratory system of birds is relatively different in mechanism and structure from mammals. They have most efficient respiratory system as they need continuous supply of oxygen due to high metabolic rate required for flight. Efficiency of birds respiratory system is because all the time fresh air is supplied to “Parabronchi” , the site for exchange of gasses(birds don’t have alveoli in their lungs as in mammals rather have these tiny passages opened at both end, connected to air sacs on both sides ).
 Anatomy of avian show unique respiratory system adaptations. Avian lungs are small as compared to mammals. Most of volume is occupied by air sacs and parabronchi are the sites for gaseous exchange. Avian have larynx yet it does not have any role in voice production instead “Syrinx” in birds does the job and is called the voice box.
 Air sacs (that are just extensions of lungs) have very thin walls with few blood vessels. So, they do not play a direct role in gas exchange. Rather, they act as a 'bellows' to ventilate the lungs. Mostly birds have 9 air sacs (depending upon the species)

  • Thoracic(two posterior thoracic and two anterior thoracic)
  • Two abdominal
  • Two cervical(not present in some species)
  • One interclavicular

Now the thing that baffles most of us is “working of air sacs and parabronchi and how parabronchi are said to be open at both ends?” Well the situation of air sacs can be made clear by above diagram showing all the air sacs. The grey area is lungs and have very thin walled parabronchi instead of alveoli. Birds have an incomplete diaphragm and the arrangements of the chest musculature and the sternum do not lend themselves to expand in the same way that the chest of mammals does. Consequently birds can’t inflate and deflate lungs in the same way as mammals do. Air is moved in and out of the respiratory system through pressure changes in the air sacs. Muscles in the chest cause sternum to move upward and outward , decreasing pressure inside and air passively enters into the lungs (here too partial pressure difference aids the movement). Although expiration is not passive, but requires certain muscles to put pressure on air sacs to expel air out through nostrils or mouth. Trachea divides into two primary bronchi after syrinx.


The above diagram shows why parabronchi are said to be open at both ends and why no stale of air remains in them because all the time fresh air is ventilated. Above diagram also depicts the pathway taken by air throughout respiration cycle.  The key to the avian respiratory system is that distention and compression of the air sacs, not the lungs, moves air in and out. 

Respiratory cycle:

Hope these diagrams do clear the pathway air takes during inspiration and expiration. 


The air sacs permit a unidirectional flow of air through the lungs, (i.e. from trachea to caudal sacs, parabronchi to cranial sacs and out) air moving through bird lungs has a higher oxygen content. In contrast, air flow is 'bidirectional' in mammals, moving back and forth into and out of the lungs. As a result, air coming into a mammal's lungs is mixed with 'old' air (air that has been in the lungs for a while) & this 'mixed air' has less oxygen. Also in birds “counter current exchange occurs” i.e. blood in parabronchi flows in opposite direction than the direction of flow of air. Rate of respiration in avian in slower than in mammals. 



Entry # 1

Written By Midhat Fatima 
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LUMS Entry Test Preparation

By With 2 comments:




Now the time has come when most of you are more worried about getting admission in medical or engineering colleges than your F.Sc. exams, and in a way I find it a good thing, after all these marks don’t matter once you are in a good university. In entrance test, one’s knowledge, concepts, ability to grasp a concept in least given time are tested. More importantly, concepts and open mindedness are at the top of the priority lists in any test. Questions are always easy, but they are twirled and twisted in such a way that you miss the true sense of the question and fail to understand it. So writing in general for all the entrance tests, I would say that going through the books all night, especially before the exam and stuffing your head with helping books won’t get you anywhere as compared to reading the text books carefully and thoroughly, solving some good questions on each topic and a good sleep before the test.

Talking about the LUMS entrance test, most of you must have applied for both, LCAT and SSE entrance test. LCAT is much like SAT. There are two sections in LCAT, math and English. If you are good at maths, you can easily do the math as it is not that difficult, not difficult yet very tricky. Calculation is always simple, you are given problems mostly from topics like percentage, simple geometry etc. When attempting the test, always read the statement twice and slowly, if you rush through a question, you will probably get it wrong. There will be almost 35 questions in each section, if you have seen the sample test, and half an hour for that section. English section is comparatively difficult. First thing to do is increase your vocabulary. Vocabulary is not tested like that in a medical test, but the language of the questions is very difficult and a large variety of words will come across you in the test. There is vocabulary list in SAT, try that. But here is a thing, no matter how much you work on vocabulary, it never enough. So when you face a difficult word, always try to figure its meaning out from the context. Second thing, start reading, read a lot, read English articles and novels. Because in paraphrase type questions, you will be given long paragraphs to read and answer the questions from the paragraph. But it is not as easy as it looks. If you are not used to reading long articles, then you will  forget most of the concepts after you have finished the paragraph, well that was the case with me. And the questions will not be in arranged order, first question might be asking something from the end of the paragraph. You will be asked to give a title to the passage or will be questioned about the idea of the author. There won’t be enough time in the examination hall to read the passage twice so its better to go there prepared. Another thing that will leave you on the horns of dilemma is that for a question, for example asking the appropriate title for the passage, you will be given 4 options that all qualify for the title, or two or three options looks correct, don’t stop there, you have to choose the best of them. Get a SAT preparation book and practice as much as you can from the math and English section. This will be a good preparation. Also attempt full length SAT tests at the end of the book. You will get a good idea of the test.

For SSE test, just read the text book for knowledge. Nothing will come out of the scope of text books. And important, as I said before, are your concepts. For that you will have to practice a lot of questions. Not from the text books. I personally solved questions from the A-level past papers from a book named Redstone. You will also find a lot of SAT-2 tests on the net you can always practice questions from them. But the thing I am trying to say here is that practice a lot of questions especially for SSE test. Its better to stay at home and solve questions than to join an academy. Last and most important thing is the time limit. You will get very short time for both test. So manage your time accordingly. Don’t spend more time on a single question. If you can not understand a question leave it and move ahead. You can always get back at it at the end if you have spare time. For a month before the test, try not to use calculator and do as many calculations as you can by yourself. Even when practicing questions, try to put a time limit upon yourself. And guys, last thing I would like to say is that prepare for the test with your full energy, and then leave the result upon Allah. Luck is very important factor that you can not control. So Do your best, and whatever the result is, never lose your heart. Don’t make a fuss out of the test before the exam. Stop studying the evening before the test, freshen up your mind, and have an at least 8 hour sleep. Never forget the negative marking, if you can’t attempt a question then its better to leave it then to give it a risky shot. I hope to cover pretty much of everything yet if you need any help you can always ask.
 Wish you GUYS best of luck.


            Contributor:                                                                         Email ID:
Ali shaan (students at LUMS)                                           Absoluteali123@gmail.com
Ahmad sher zaman dogar                                          ahmadsherzaman@gmail.com



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Thursday, December 26

Showcase Your Concepts

By With No comments:





Entry Test Preparation brings you a first competition of its kind " Showcase Your Concepts ". Your task is to select any topic from the books of Fsc, any science subject, and write an explanatory article on it. 


Some Important points about your articles:

  1.  It shouldn't include the book lines. Everyone can read from the books. 
  2. Try to make it somewhat funny, you can add images , ofcourse related to the topic. Videos should be made by you. 
  3. Try to write in such a way that would not make your readers feel bored.
  4. It should be try free. Recheck after writing it down. 
  5. You can take help from the web, but do not copy anything from the web. You can get the idea and write that in your own words.

Selection of topics Depend on you people. Here is a list of topics selected till now. Students who did not submit their topics to us send us the topic name via message to our facebook page https://www.facebook.com/Etest.Prep .

  1. Amino Acids ( Chemistry Part 2)
    Article Submitted, Read Here: Amino Acids
  2. Periodic table ( Chemistry )
    Article Submitted, Read Here: Periodic table
  3. Immunity ( Biology )
    Article Submitted, Read Here: Immunity
  4. Cell structure ( Biology )
    Article Submitted, Read Here: Cell Structure
  5. Reactions of Organic Chemistry ( Chemistry Part 2)
    Article Submitted: Read Here: Organic Reactions
  6. Nephron ( Biology Part 2)
    Article Submitted, Read Here: Nephron
  7. Respiration in birds ( Biology )
    Article Submitted, Read Here: Respiration in Birds
  8. Muscles ( Biology Part 2)
    Article Submitted, Read Here: Muscles
  9. Macro molecules ( Chemistry Part 2 )
  10. Half Life ( Chemistry )
    Article Submitted, Read Here: Half Life
  11. Resistors ( Physics )
    Article Submitted, Read Here: Resistors
  12. Series Resonance Circuit ( Physics )
    Article Submitted, Read Here: Series Resonance
  13. Human Reproductive System (Biology)
    Article Submitted, Read here: Reproductive system
  14. Ampere's Law (Physics)
    Article Submitted, Read here: Ampere's Law
Deadline:


The last date to submit your entry is 12th January, 2014.

How to submit the articles?
Send your article via email to the following ID: maathsmaster@gmail.com
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Monday, December 23

Admission in Doctor of Physical Therapy (DPT) in RMC

By With 7 comments:

Admission in Doctor of Physical Therapy (DPT) in RMC 


Admission open in RMC Allied Health Science Institute, Rawalpindi in the following courses:
  1. Doctor of Physical Therapy.
  2. Medical Imaging Technology.
  3. Medical Laboratory Technology.
  4. Optometry & Orthoptics.
  5. Orthotics & Prosthetics.
The Duration of the DPT course is 5 years while for the rest of the courses it is 4 years.



What is the Eligibility criteria?

                                                     Make sure the you meet the following conditions before applying for RMC:

  • FSc Marks: You must have atleast 60% marks in Fsc/A level.
  • Age Limit: Your age must be between 17 and 30 years.
When are the admission starting?

                                                            The admission forms will be available in the admission office from December 28, 2013.



What is the last date to submit the form?
                                                                   The last date of submission of forms is January 11, 2014. Interviews will be held on January 25, 2014 at 9.30 am in the office of Coordinator BSc Allied Health Sciences.



What is the distribution of seats and Selection criteria?

                                                                                                       There are total 100 seats, 20 seats for each discipline. Admissions are given on basis of Fsc marks only. There is no quota for any area/province. Seats are allotted on Open merit. 


When will the classes start?
                                                     The classes will start in March, 2014.

Is there any hostel facility? 
                                                      No hostel facility will be provided to the students.

When the merit list will be displayed?
                                                                          The merit list of RMC for DPT and BSc programs will be displayed on 20th or 21st of January. Those who will be selected have to appear in the interview on January 25.

What were the closing merits of Last year?
                                                                                Merit is totally based on marks of Fsc, so the list below lists the marks of Fsc .Following are the closing merits of DPT and BSc courses at RMC last year:

  1. Doctor of Physical Therapy . 945 marks
  2. Medical Imaging Technology. 893 marks
  3. Medical Laboratory Technology. 907 marks
  4. Optometry & Orthoptics. 908 marks
  5. Orthotics & Prosthetics. 895 marks
This was the first list of selected candidates, a few left the seats and merit decreased a bit in next lists. 




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Monday, December 9

FMDC Merit List 2013

By With 60 comments:

The admission test for Federal Medical and Dental College was conducted on November 10, 2013. The result of the test was announced on December 9, 2013.

The distribution of seats in FMDC is as below:

  • Open Merit  6
  • Punjab   40
  • Sindh R  9
  • Sindh U  6
  • KPK   9
  • Balochistan  5
  • Gilgit Baltistan  2
  • FATA   2
  • AJK   2
  • Federal Capital Territory   10
  • Federal Government Employees   9

The Closing Merits of the first list are given below:

  • Open Merit 84.25%
  • Punjab 80.57%
  • Sindh R 74.24%
  • Sindh U 73.9% 
  • KPK 77.65%
  • Baluchistan 77.95%
  • Gilgit Baltistan 73.99%
  • FATA 76.85%
  • AJK 81.32%
  • Federal Capital Territory 79.119%
  • Federal Government employes 79.71%
The Closing Merits of the second list are given below:

  • Open Merit 84.25%
  • Punjab 79.76%
  • Sindh R 73.38%
  • Sindh U 73.74% 
  • KPK 77.53%
  • Baluchistan 76.02%
  • Gilgit Baltistan 71.8%
  • FATA 75.73%
  • AJK 81.04%
  • Federal Capital Territory 78.75%
  • Federal Government employes 79.29%


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Sunday, December 8

Analogy

By With 6 comments:

Analogy


When you face verbal analogies, here are few things to ponder over or think.

Analogy means (in general) is a way of describing relation between two things or more by comparing with another set of objects.

e.g. Water flows through a pipe pushed by a motor and its flow can be controlled through a valve

Now consider the following statement:

Current
flow through a wire pushed by a battery and its flow can be controlled through a resistor.

Do you see something intriguing here? I just replaced some words and the sentence is still meaning full, describing a relationship between different components. So we say that in this case water flow is same is current flow, motor is analogous to battery, and valve is analogous to resistor.

Now you understand this, we will exploit this definition to do verbal analogies, our master trick will be:

“Make a sentence of given analogy which accurately expresses their relation and replace the given set of analogy by all the option one by one, the best fitting will be your answer!”

That’s it, now you know all the magic behind, now you need to practice this spell a lot to master it and win the war against the Verbal Analogy Army!!

Now one thing more, You may want to stick to past papers, but what is actually needed is practice, The more you practice and try to understand how to solve analogies, The more you will become better it. You don’t need to just do a whole paper and then match your answers in the key at the end, What you actually need to do is that do an analogy problem, see the answer at the back, if you were right pat yourself!, and if you were wrong, ask yourself, why the right answer given here is the right answer!

A Good resource to work out your skill can be found here:

Stay Blessed, and Excel! And Show the world our strength.




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Wednesday, December 4

Guideline for preparation of Computer Science of NET

By With 1 comment:

Guideline for preparation of Computer Science
NUST Entrance Test

AoA, dear members. Hope you all are well and started the preparation for NET. Let me tell you about the subject of computer science, that how to prepare it and which part of it should be prepared. 

 When we talk about computer science, I think it is the easiest subject for NET and other entrance tests of different universities because you have no formulas in it or something like numerical which are tricky and confusing. Many MCQs are from NET series (Past Papers) or the tests of other universities for CS or Software Engineering, I’ve seen that mostly only theoretical part is included, the practical part like C language is not yet there. So I think, this year the situation will also be same. The theoretical part like book of 1st year and theory of C language and database will be included but it does not mean that you should completely ignore the other, I’ll say that you should have a full command on the entire subject. They can ask you the questions about internet, computers, languages, history of computers, networking etc, so you should prepare all the stuff related to it.

One important thing that this year there will be three sessions of NET so they have to make more and more mcqs because all tests will be different, for such a huge collection of mcqs, I think they will include each and every topic of the book, same situation is for other subjects. The test can be very simple or it can be a difficult one, so you should be well prepared.
 For any type of queries regarding preparation you can contact us any time on http://www.facebook.com/etest.prep

Stay blessed !   
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Sunday, December 1

Should the students of Second year appear in NET-1 or not?

By With 1 comment:


About 10,000 students would be applying for NET-1, according to a rough idea. About 50% of them will be the college students who are still in FSC Part 2 and others are repeaters. 

For repeaters there is no issue if they want to appear in NET-1. They can easily appear in the test. Now the question arises should students of Second year appear in NET?

Many of the students of Second year will be having their exams in the last ten days of December and all the tests of NET-1 will be held during this time span. You have to appear either in your college exam or NET-1. Now according to me students of second year should be focusing on the their Fsc right now instead of NET. Let me be straight. Each and everyone of you wont be able to get admission in NUST. We all know this. This year (2013 session) about 70,000 students appeared in NET and how many were selected? About 2500 in all the fields i.e Medical, Engineering, Arts, Business, BS Maths. Same will be the case this year. In-fact this year applicants will be more. These might be about 90,000. If you will not be selected for Nust you would be opting for other options and in other institutes the weighatge of FSc marks is more than is Nust. Consider the example of UET. In UET 70% marks of FSC are counted. If unfortunately you are unable to score well in NET instead of giving all your time to it you might loose your chance of UET as well because you shifted your attention from Fsc to NET. I would say that those of you who are willing to join UET, they must not appear in NET-1. Now consider the students of medical. Only some of you would be getting admission in MBBS, others would be opting for other fields like DPT, D pharm etc. For these fields you are not tested. You are given admission on basis of Fsc marks only. So if you loose marks in Fsc in your desire of getting admission in Nust you might loose this chance.


I hope all of you are getting my point. This is what I think. If you think that you are capable of not loosing your momentum of FSC preparation because of NET then you can appear in NET, but yeah second year students wont be able to score much in NET-1 due to lack of preparation. Some of you might get disheart at their results and decide not to appear in NET-2 and NET-3. This happened last time as well. 

So what should the students of Fsc be doing in these days?
You people should learn your books properly, understand the things and prepare for your College exams. You can keep an eye on all our activity of NET so that you wont face any issue while applying for NET-2 and NET-3. 

For all the updates regarding NET and NUST join us on facebook: 
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