Determinants - July Dec Revision

Determinants - July Dec Revision
12.1 Definition

Every square matrix can be associated to an expression or a number which is known as determinant.

If the matrix has only one element a11 then a11 is the determinant.

If the matrix is of order 2 that 2 by 2 matrix

|A| =

|a11 a12|
|a21 a22| =

a11*a22 – a12*a21

Determinant of a square matrix of order 3

Determinant of a square matrix of order 3 is the sum of the product of elements a1j in the first row with (-1) 1+j times the determinant of a 2×2 sub-matrix obtained by leaving the first row and column passing through the element.



(i) Only square matrices have determinants.
(ii) The determinant of a square matrix of order three can be expanded along any row or column.

Determinant of a square matrix of order 4 or more

(iii) Determinant of a square matrix of order 4 or more can be determined following the procedure of finding the determinant of a square matrix of order 3. But in this case, especially in the case of 4×4 matrix, when we omit the rows and columns containing the elements of a row, we get 3×3 sub-matrices and we have to find determinants for them.

12.2 Singular matrix

A square matrix is a singular matrix if its determinant is zero.
Otherwise it is a non-singular matrix.


12.3 Minors and cofactors

Minor: For a square matrix [aij] or order n, the minor Mij of aij, in A is the determinant of the square sub-matrix of order (n-1), obtained by leaving (or striking off) ith row and jth column of A.

Cofactor: Cofactor of an element aij in a square matrix [aij] is termed Cij.

Cij = (-1) i+j Mij

Mij is the minor of element aij in a square matrix [aij].

Minors and cofactors are defined for elements of a square matrix only. They are not defined for determinants.

12.4 Properties of determinants

1. For a square matrix, the sum of the product of elements of any row (or column) with their cofactors is always equal to determinants of the matrix.

2. For a square matrix, the sum of the product of elements of any row (or column) with the cofactors of corresponding elements of some other row (or column) is zero.

3. The value of a determinant remains unchanged if its rows and columns are interchanged.

4. If any two rows (or columns) of a determinant are interchanged, then the value of the determinant changes by minus sign only.

5. If any two rows or columns of a determinant are identical then its value is zero.

6. If each element of a row (or a column) of a determinant is multiplied by a constant k, then the value of the new determinant is ‘k’ times the value of the original determinant.

7. If each element of a row (or a column) of a determinant is expressed as a sum of two or more terms, then the determinant can be expressed as the sum of two or more determinants of the same order.

8. If each element of a row (or a column) of a determinant is multiplied by the same constant and then added to the corresponding elements of some other row (column) then the value of the determinant remains same.

9. If each element of a row (or column) in a determinant is zero, then its value is zero.

10. If the matrix is a diagonal square matrix then its determinant is the product of all the diagonal elements.

11. If A and B are square matrices of the same order, then

|AB| = |A| |B|

12. If a matrix is a triangular matrix of order n, then its determinant is the product of all the diagonal elements.

12.5 Evaluation of Determinants

To evaluate determinants or large matrices, we use the properties of determinants given in section 12.4 above, to create many zeroes in the elements of a row or column and then expand the determinant using elements and cofactors of that row or column.

12.6 Evaluation of Determinants by using Factor Theorem

If f(x) is a polynomial and f(α) = 0 the, (x- α) is a factor of f(x).

If a determinant is a polynomial in x, then (x- α) is factor of the determinant if its value is zero when we put x = α.

Using this rule we can find determinant as a product of its factors.

12.7 Product of Determinants

A definition of product of determinants is similar to the rule of multiplication of matrices.

IIT JEE 2010 Chemistry Study Plan 3 October

IIT JEE 2010 Chemistry Study Plan 3 October
3 October 2008 Chapter S-Block Elements Session 2
Based on NCERT BOOK, Class XI, Part II, Unit 10


Study Sections in the chapter

10.2 General Characteristics of the Compounds of the Alkali Metals

10.2.1 Oxides and Hydroxides
10.2.2. Halides
10.2.3 Salts of Oxo acids

10.3 Anomalous Properties of Lithium
10.3.1 Points of Difference between Lithium and other Alkali Metals
10.3.2 points of similarity between Lithium and Magnesium

Example Problem 10.3
Answer Exercise question 3,4,5,.
Revise two exercise questions from P-Block chapter

IIT JEE 2010 Chemistry Study Plan 4 October 2008

IIT JEE 2010 Chemistry Study Plan 4 October 2008
4 October 2008 Chapter S-Block Elements Session 3
Based on NCERT BOOK, Class XI, Part II, Unit 10


Study Sections in the chapter

10.4 Some Important Compounds of Sodium

Sodium Carbonate
Sodium Chloride
Sodium Hydroxide
Sodium Hydrogencarbonate

10.5 Biological Importance of Sodium and Potassium


Answer Exercise questions 7,9,10,12, 13,

Revise two exercise questions from P-Block chapter or do two questions from Past IIT JEE questions


Visit for some material on various compounds of metals given in JEE syllabus
http://iit-jee-chemistry.blogspot.com/search/label/Compounds-metals

Visit for material on non-metals
http://iit-jee-chemistry.blogspot.com/search/label/Nonmetals


Visit for compounds of non metals
http://iit-jee-chemistry.blogspot.com/search/label/Compounds-nonmetals

Andhra boasts of producing maximum IITians

Andhra boasts of producing maximum IITians

Andhra Pradesh breeds the most number of IITians in the country. At least the JEE organizing committee’s report to MHRD proves so. This year the maximum number of students qualifying for IIT from a single state - 1,697 - came from Andhra Pradesh with Uttar Pradesh following next with 1,194 students out of a total of 5,524 successful candidates.

According to the data compiled after the joint entrance examination (JEE) in 2007, Andhra had given the highest number of students to IITs - 1,384. According to IIT veterans, Andhra Pradesh has been on the top of the state-wise list of qualifying students in the last few years.

“This has been a general perception among all IITians that number of students coming to IIT from AP is more than from other state. The main reason for it is that Hyderabad is a major hub of coaching centres like Kota. And I must say, these coaching centres are doing a great job in training students for IIT JEE,” said M S Anand, director, IIT-Chennai.

According to IIT professors, many students from south India migrate to Hyderabad for coaching and manage to crack JEE. So the students coming from Andhra Pradesh may not necessarily be natives. Most of them are known to go for a seat in IIT Chennai or IIT Bombay. And, with IIT Hyderabad debuting this year under the mentorship of IIT Chennai, the number is expected to go up.

“Students in Andhra Pradesh did not have an IIT till now. But they studied really hard and usually joined Chennai or Bombay. But of late, it seems most of them are going to IIT-Bombay. They say they like the food there better!” remarked Anand. Surprisingly, only 202 out of 9,929 students qualified from Tamil Nadu itself.

According to R Chattopadhyay, JEE chairperson, IIT-Delhi, this trend has come up in the last couple of years. “Once the students join the classes, nobody knows who comes from where because they all mingle so well. But the figures in the last two years have shown that most students qualify from Andhra. Many students also travel to Hyderabad for coaching adding to the number,” he said. According to IIT officials, while IIT Delhi mostly gets students from north India in BTech, there are many students from Andhra Pradesh in the MTech course.

As for the maximum number of students appearing for JEE, UP leads the pack with 72,028 students appearing for JEE 2008 while 57,488 in 2007. Bihar also had a huge number of IIT aspirants - 30,490 this year and 14,854 in 2007 - however, unlike UPSC exams, they could not take IITs by storm. While 533 qualified this time, 146 were successful last year.

Courtesy :- Times Of India

JOINT ENTRANCE EXAMINATION 2009 (JEE – 2009)

JOINT ENTRANCE EXAMINATION 2009 (JEE – 2009)
For admission to undergraduate course at seven Indian Institutes of Technology, IT – BHU, Varanasi and Indian School of Mines University, Dhanbad.

IIT Joint Entrance Examination (JEE 2009) Schedule

April 12, 2009 (Sunday)

09.00 –12.00 hrs Paper – 1
14.00 - 17.00 hrs Paper - 2

Paper – 1 and Paper – 2 will each have three separate sections on Physics, Chemistry, Mathematics. Both the papers will be objective types, designed to test comprehension, reasoning and analytical ability of candidates.

INDIAN INSTITUTES OF TECHNOLOGY JOINT ENTRANCE EXAMINATION (JEE-2009)

INDIAN INSTITUTES OF TECHNOLOGY JOINT ENTRANCE EXAMINATION (JEE-2009)

For Admission to Undergraduate Courses at all IITs, IITs, IT-BHU, Varanasi and ISMU, Dhanbad.

Examination Schedule
April 12, 2009 (Sunday)
Paper 1: 09.00 - 12.00 hrs
Paper 2: 14.00 - 17.00 hrs


Paper 1 and Paper 2 will each have separate selections in Chemistry, Mathematics and Physics. Both Papers will be of Objective type, designed to test comprehension, reasoning and analytical ability of candidates.

Syllabus for this examination will be available on the websties of all IITs and will also be given in the information brochure of JEE-2009.
The Candidate will have the option of submitting the application form either on-line or off-line.

Important dats regarding Application Form and Brochure:
Duration of On line Application process and Sale at designated branches of Banks and IITs: November 19, 2008 - December 24, 2008
Postal request for Application Form: November 19, 2008 - December 16, 2008
Last Date for receipt of completed Application Form at IITs: December 24, 2008


Further details regarding the application process will be published in leading National Dailies and Employment News/ Rozgar Samachar on November 08, 2008.

Joint Entrance Examinations - 2009 - IIT-JEE

Joint Entrance Examinations-2009-IIT-JEE

Preparing for joint entrance exams? Then here is some information for 2009 IIT-JEE exams.
If you are studying in class 10+2 or Just have passed 10+2 with Science (physics, chemistry, mathematics) and wants to study engineering and technology then read this. You need 60% marks in 10+2 science.
I am sure you know about IIT-JEE. If you don't know much about this examination, not to worry! Why I am here?
IIT or Indian Institute Of Technology is India's one of the brilliant place to study technology.
The seven IITs are located in Kharagpur, Bombay, Madras, Kanpur, Delhi, Guwahati, and Roorkee. With the plan to setup eight more IITs in the states of Rajasthan, Bihar (Patna), Andhra Pradesh ( Hyderabad), Himachal Pradesh, Orissa (Bhubaneshwar), Madhya Pradesh (Indore), Gujarat (Gandhinagar) and Punjab, and the conversion of IT-BHU to an IIT, the total number of IITs will be increased to 16. All IITs are autonomous universities that draft their own curricula, and they are members of LAOTSE, an international network of universities in Europe and Asia. LAOTSE membership allows the IITs to exchange students and senior scholars with universities in other countries.
What are the courses and degrees IITs offer?
You can grab your B.Tech degree (almost 35 subjects available to choose) from there. Not only that, you can choose 5years integrated M.Sc degree (can choose from 11 subjects almost), 5yrs. Msc.Tech (on 2subjects), 5yrs integrated M.Tech (almost 6 subjects) and B.Tech M.Tech Dual Degree on over 70+ subjects.
When the IIT-JEE exam will be held at 2009?
12th April, Sunday, 2009 is the exam date of IIT-JEE.


From where you will get the form and prospectus?
You can get it from few bank, IITs directly and IIT-Online-Website. (See below for the list of IITs websites) Also check out employment newspaper and popular newspaper at 8th nov, 2008 to read the announcement of IIT-JEE exam.
You can collect the forms and prospectus between 19th Nov to 24 Dec , 2008.
Last date of the submission of forms (at IIT) are 24th December,2008.

IIT websites are,

www.iitkgp.ac.in - IIT Kharagpur
www.iitd.ac.in - IIT Delhi
www.iitb.ac.in - IIT Bombay (Mumbai)
www.iitm.ac.in - IIT Madras (Chennai)
www.iitk.ac.in - IIT Kanpur
www.iitr.ac.in - IIT Roorkee
www.iitg.ac.in - IIT Guwahati