For proving the questions on Groups many students commits mistakes on the following questions.
1. If Q1 is the set of rationall numbers other than 1 with binary operation * defined by a*b=a+bab for all a,b εQ1, Show that (Q1,*) is an abelian group and solve 5*x=3 in Q1.
2.If Q1 is the set of all rational numbers except 1 and * is a binary operation defined on Q1 by a*b= a+b+ab, Prove that Q1 is an abelian group.
For verifying closure law for the above the problems, many students simply do in the following way
Wrong approach:
Closure law: a*b=a+bab is again a rational number and hence closure law is true.
However Here student did not verified a*b is a rational number except 1. Hence it is very necessary to show that a*b is a rational numbr other than 1 . Other wise 1Mark will be reduced in the valuation. In april 2002, the 1 Mark is reduced for the students who did not verified the closure law correctly.
The correct approach is as follows:
For question number 1:
Let a, b Q1 such that a #1, b#1 a+bab is also a rational number and it cannot be equal to 1
Because If a+bab=1, then a+bab1=0
then (a1)(b1)=0
thereofore a=1 or b=1 which is not true as a#1 and b#1. a*b belongs to Q1
therefore Q1 is closed w.r.t * (GIVING REASONS IS IMP)
Similarly for verfying closure for 2 question
Closure law: or Q1 a*b=a+bab is again a rational number and hence closure law is true.
Let a, b Q1such that a # 1 b#1 a+b+ab is also a rational number and it cannot be equal to 1
Because If a+b+ab=1, then a+b+ab+1=0
therefore (a+1)(b+1)=0
Hence a= 1 or b= 1 which is not true as a# 1 and b# 1. a*b belongs to Q1
Q1 is closed w.r.t * (GIVING REASONS IS IMP)

Pages
 model papermaths
 MODEL QUESTION PAPERBIOLOGY
 MODEL QUESTION PAPERBIOLOGY
 QUESTION PAPERBIOLOGYMARCH 2008
 MODEL QUESTION PAPER2BIOLOGY
 MODEL CHEMISTRY QUESTION PAPER
 TIME TABLE OF II PUC MARCH 2009 EXAMINATION
 CHEMISTRY II PUC QUESTION PAPERJULY2006
 CHEMISTRY II PUC QUESTION PAPER APRIL2006
 CHEMISTRY II PUC QUESTION PAPER APRIL2007
 CHEMISTRY II PUC QUESTION PAPER JULY2007
 CHEMISTRY II PUC QUESTION PAPER MARCH2008
 CHEMISTRY II PUC QUESTION PAPER JUNE2008
 PREVIOUS YEARS II PU QUESTION PAPERS
 notes periodic properties
 NOTES THEORY OF DILUTE SOLUTIONS

Categories

Archives
Blogroll

RSS Feeds

Meta
Comments
You are doing good thing.I felt happy.
very nice
thank u
a very important approach which will surely save our precious one mark.
thank you
thank you……! its flit happy