Publish your solutions!!

Thanks for following my blog.
I am quite busy these days that's why I need your contributions.

Please provide the typed solutions of the questions of today's exam - CSIR Net/Jrf Dec-2018, Mathematical Sciences.
I will upload that solutions in this blog followed by your name.
Thank you.

All the best for the result.

Best wishes

ALL THE BEST everyone for  CSIR  -NET/JRF  DEC - 2018 EXAM.

CSIR NET-JRF June 2018 Result declared !!

Click on the given link.

CSIR NET-JRF June 2018 Result

Csir Net/Jrf Mathematics -solutions 2018 June - Part- B

The numbers of the solutions are according to the booklet C.

For the question paper of CSIR Net/Jrf Mathematics - June 2018 Click here

21

22 

23                          

25 

26

27

28

29

30

32   

33

34

36

39 

Csir Net/Jrf Mathematics - 2018- Part A- General Aptitude - Solutions

 Part - A 

Q.1  The area of the triangle formed by joining the points (2017, 2017), (2027, 2027) and (2037,  2017) is

Solution -

Q.2  A stick of length L is broken into two pieces at random . what is the average length of the smaller piece ?

Solution - The average length is L/2.

Q.3 Number of times a research paper is viewed and cited is shown in the plot. In which month was the percentage increase in citation more than double  of the percentage increase in view?

Solution - 

Q.4 Four males M1,M2,M3,M4 and four females F1, F2, F3 and F4 are sitting around a round table facing away from the table. If each one moves three positions to his/her right and then one position to the left,  then in which directions does F4 face ?

Solution-

Q.5 In the diagram , what is the ratio of the total shaded area ( of the circle and semi-circle) to the total area of the square and the rectangle?

Solution-

Q.6 Which of the following options is the best choice for the missing number?

Solution- 

Q.7 Fourteen of the students in a class are girls. Eight students in the class wear blue shirts. Two are neither girls nor wear blue shirts. Five students who wear blue shirts are girls. How many students are there in the class?

Solution-

 

Q.8 Prof Murthy likes to let her students to choose who their partners will be; however , no pair of students may work together for more than seven class periods in a row. Alice and bob Have worked together for seven class periods in a row. Calvin and Denny worked together for three class periods in a row. Calvin does not want to work with Alice. Who should be assigned to work with Bob?

Solution -

Q.9 Three semi circles are drawn inside a big circle as shown in the figure. If the radius of the two identical smaller semi circles is 1/4 th of that of the big circle and the radius of the bigger semicircle is twice that of the small semi circle,what proportion of the big circle's area is shaded?

Solution-

 

Q.11 Consider a number 54 expressed in a base different from ten. What is the base of this number system if its equivalent value in the decimal system is 49?

Solution-

Q.12 A fuel station sold diesel costing Rs 15000 to 150 persons on a day. If the lower limit of sale to a person is Rs 50.what is the maximum amount in rupees for which one person could have purchased diesel on that day?

Solution-

Q.13 which of  the options is appropriate for the blank space?

Solution-

Q.14 If sangeeta's daughter is my daughter's mother , then how am I related to sangeeta?

Solution-

  

Q.15 In a group of 44 players, 26 play hockey, 24 play football and 24 play cricket. Eight of them play both hockey and football, 12 play both football and cricket, and 5 play all the three games. How many play both hockey and cricket ?

Solution- 15

Q.16 It is given that (a)* = a if a>0 and (a)* =0 if a<=0 for any real number a.suppose for any two real numbers x and y (xy)* = (x)*(y)*. Then which of the following is necessarily true?

1) x>0 ans y>0 

2) {x<0 and y<0} or { x>0 ans y>0} 

3) {x<=0 and y<=0} or { x>=0 and y>=0}  

4) {x>=0} or {y>=0} or { x>=0 and y>=0}

Solution-

Q.17 A long distance runner find a water station after completing 1/7 th of the total distance. After covering another another 1/6 th of the total distance he gets medical- aid. another runner joins him 4km after the medical-aid station. The second runner stops 4km before the completion of run, covering 1/2 of the total distance. what is the total distance?

Solution-

Q.18 A and B move clockwise around a circle, starting from a common point o. A takes 9 minutes to complete a round but restarts after a delay of 1 minute. b takes 13 minutes to complete the round but restarts after a delay of two minutes. How many minutes after they began would they meet again at O?

Solution - 28 minutes

Q.19 Two students are solving the same problem independently. if the probability that the first one solves the problem is 3/5 and the probability that the second solves the problem is 4/5, what is the probability that at least one of them solves the problem?

Solution -

Csir Net/jrf June -2018 mathematics question paper solutions.

Difference equations- Numerical analysis.

Here we have to solve the given difference equations to know whether it's solutions are bounded or unbounded.

For that we convert the delta operator into shift operator.

Here is the problem and solution.

Next problem 

Calculus of variations- 

Here I have provide the method to solve this problem quickly.

You find that only the quadratic polynomial is the possible answer and there is only one option 1 is quadratic polynomial.

Next question- 

Calculus of variations

Next question

Integral equations- 

For getting more solutions follow the blog.

Best wishes !! Share your experience

Hello, all my dear Csir net/Jrf exam aspirants.
My good wishes are with you.
Please after exam write about your experience in comment section.
If possible  mail me the question paper ( scanned PDF form ). I will soon upload the solutions .
All the best.

Things to do in Csir net mathematics.

1) Don't fall in love with any question in examination hall, if you are not able to solve it just leave it and go further.
2) Try to solve the easier questions first, don't leave them for last hour
3) Fill the OMR with  precision and simultaneously with each part.
4) Take a water bottle with you.
5) Attempt atleast 130-150 marks of  questions to reach the cutoff.
All the best to all of you guys.

DIPS ONLINE TEST REVIEW- CSIR-UGC Net/JRF Mathematics

Hello,
I am writing here about the online line tests I have purchased from dips academy before one week of the exam.
Here are some talks about the tests-
1)The tests were 4 in total and they were full length tests which costed Rs 1500.
2)The pattern is same as per the question paper of the exam.
3) The tests will be  provided one by one.
4) You can give the test only one time after that they will remove the link.
5) You will get the instant result of your test.
I found the tests expensive but helpful if you have prepared well and have not go through any type of test or mock test than it is better to try this one and any other one if you can.
You will have the experience of how you can manage the time in examination hall, which portion you should attempt first, which section give you more marks etc.

Download - BOOKS OF MATHEMATICS

Some Reference Books helpful for preparation of  CSIR NET/JRF MATHEMATICS.
You can download them in PDF format from the given links, for each book link is given below the name of the book.

Real Analysis-

1) Mathematical analysis - TOM M. APOSTOL                                       

    Click to download

2) Principle of Mathematical analysis- Walter Rudin                               
    Click to download

3) Foundations of Mathematical Analysis - S. ponnusamy                       
    Click to download

4) Real Analysis - Gerald B. Folland                                                         
    Click to download

5) Methods of Real Analyis - Richard R. Goldberg                                   
    Click to download

Linear Algebra-

1) Linear Algebra and its applications - Gilbert Strang                             
    Click to download
2) Linear Algebra - Hoffman- Kunze                                                         
    Click to download
3) Elementary Linear Algebra                                                                   
    Click to download

Abstract Algebra-

1) Abstract Algebra - Schaum series                                                           
    Click to download
2) Contemporary Abstract Algebra - Joseph A. Gallian                             
    Click to download
3) Topics in Algebra - I.N Herstein                                                           
    Click to download

Partial Differential Equations-

1) Elements of Partial differential Equations- Sneddon                             
    Click to download
2) Partial differential equations and boundary value problems-  Mark A. pinsky
    Click to download

Numerical analysis-

1) Numerical methods -Iyenger & Jain                   
    Click to download

 Complex Analysis -

1)Complex Variables - Schaum series
   Click to download

Differential Equations-

1) Differential Equations- Schaum series
    Click to download
2) An introduction to ordinary differential equations
    Click to download
3) Elementary Differential equations and boundary value problems
    Click to download

Csir net mathematics science question solution Dec 2017

Question- A new tyre can be used for at most 90 km. What is the maximum distance (in km) that can be covered by a three wheeled vehicle carrying one spare heel, all four tyres being new ?
Solution:

CSIR Net Mathematics Exam june 2018- practice test

Test for CSIR Net Mathematics Exam- 
Real analysis Topic - Countability 

1. A  set S is said to be countable if
Options:
a) there exists an injection from S to N
b) there exists a surjection from  N to S
c) it is a subset of a countable set
d) all the these

2. which of the followings set is not countable?
Options:
a) subset of an uncountable set
b) countable union of countable set
c) finite product of countable sets
d) countably infinite product of countable sets

3. The power set of a finite set is
Options:
a) finite
b) infinite
c) uncountable
d) none of these

4. The set of all binary sequence is
Options:
a) countable
b) uncountable
c) countably infinite
d) denumberable

5. The cardinality of set of algebraic numbers is equal to that of
Options:
a) Natural numbers
b) Real numbers
c) set of all binary sequences
d) b,c

6. which of the following sets are uncountable?
a) set of all functions f such that f :R->R
b) set of all functions f such that f: N-> Z2
c) set of all functions f such that f: Z2 -> N
d) set of all polynomials P : R->R

Options:
a) c
b) a,b
c) a,b,d
d) b,d

7. The collections of all isolated points of any set is
Options:
a) countable
b) uncountable
c) not enough information
d) finite

8. cantor set is ?

Options:
a) countable
b) finite
c) uncountable
d) countably finite

9. The cardinality of all disjoint intervals is not equals to
Options:
a) natural numbers
b) real numbers
c) algebraic numbers
d) rational numbers

10. set of all subsets of N are
Options:
a) countable
b) uncountable
c) finite
d) countably finite

Dowload CSIR Net/Jrf Mathematics Previous year question papers / answer keys

Hello all, as per the demand and need of all the students i am providing the link to get the previous years papers with answer keys. I have tried my best to make you available all the related papers but still one or two papers or answer keys are left. If anyone has that then please send  me the link i will add it here.
Thank you all.
wish you all the best for the preparation.
Question Papers
2012 June
2013 June 
2014 June
2015 June
2016 June
2017 June
2012 Dec
2014 Dec
2015 Dec
2016 Dec
2017 Dec
2018 June
Answer keys
2012 June
2013 June
2014 June
2015 June
2016 June
2017 June
2013 Dec
2014 Dec
2015 Dec
2016 Dec
2017 Dec

Question of the day

Subject- Abstract algebra
Question:  Do permutations cycles form a group ? 

An algebraic structure

What is operation in mathematics languages?

An operation is like a function which when act on an element of a set changes its value or some thing like because to operate means to change, right !

Now, what is binary operation ?

Binary means which involves two.

So it is clear from the name that this operation involves two elements of a set.

I think you can now digest the below definition.

Binary operation is a function that assigns to each ordered pairs of elements of set, an element of that set .

Notation - *

operation between a and b is denoted by a*b, where a and b are elements of set.

Here ordered pairs talks about two elements of set, as you know pairs means two elements together but why there is “ ordered “ here.

Ordered pairs and not just pairs because here order matters, because a*b is different from b*a , it can be equal but not generally.

Duality -important results

Useful for both NET and GATE exam

1. If the primal problem has finite optimal feasible solution then it's dual has also optimal feasible solution and conversely.
2. If the primal problem has an unbounded objective function, then it's dual has no feasible solution and conversely.
3. The problem has finite optimal solution iff there is a feasible solution to it's dual problem.

Review of book - Csir - Net General Aptitude - A New outlook

Book Name
CSIR - NET GENERAL APTITUDE - A NEW OUTLOOK
Author- Christy Varghese a
Publisher- Lilly publishing house
This book has two sections-
Section 1.
Theory and questions of following topics
1. Numerical ability ( numbers, probability and arrangements, distance and directions)
2. daily life problems ( finding the X , average, monetary problems)
3. Geometry type problem's
( Geometry, mensuration and quantitative comparison)
4. Logical reasoning ( Data interpretation, observational ability, logical puzzles)
5. Typical problems ( calendar problem, clock problem, moving locomotive problem, series formation)
6. General science
Section 2
Previous year's exam question papers
From June 2012 to Dec 2017
( Mathematical sciences, chemical sciences, earth sciences, physical sciences, life sciences).
Each and every solution is properly solved in this book
Model question papers
Total 7 model question papers are given in the book ( along with answers ).
Review- If your part-A is very weak, you take much time in solving questions then you can purchase this book. It has full explanation of previous year papers
You can get guidance  and trick  to solve them.
Including both previous years papers and model papers there are enough papers to practice through.
Although I found this book somewhat expensive.
It's approximate price is Rs 330 ( may vary)
It is available in Amazon, Flipkart, Paytm, ebay .

IMPORTANT TOPICS WHICH COVER MAJOR PORTION OF QUESTION PAPER

UNIT – 1,2 and 3

Analysis-

Topics- countability, supremum ,infimum, convergence of sequences and series , limsup, liminf,

Bw Theorem, continuity , uniform continuity, differentiability , mean value theorem ,

sequence and series of functions, uniform convergence , monotonocity , function of bounded variation ,

directional derivative , metric space – compactness and connectedness.

Linear Algebra

vector space and its subspace, L.D , L.I , Basis and dimension , Linear Transformation and its matrix transformation , Matrices, Rank of determinant of matrices, system of linear equations, eigen values and eigen vectors, Diagonalisation, triangularization, Jordan canonical form, orthogonality , Quadratic forms.

Complex Analysis

Power series, Analyticity, Cauchy Riemann equations, Cauchy integral formula, Maximum modulus principle, open mapping theorem, Taylor and Laurent series , residues, conformal mappings ,Mobius Transformation.

Algebra

Solution of Congruence equations, Euler phi function, primitive roots, groups , subgroups- Normal , Quotient. Homomorphisms , Isomorphisms, cyclic , permutations and dihedral groups, class equations, sylow theorems, Maximal and prime ideals , finite fields , field extension , polynomial and Quotients rings, irreducibility, Euclidean domain , PID , UFD.

ODEs and PDEs

All topics

Numerical Analysis -

Newton Raphson method, Rate of convergence, Lagrange interpolation, Numerical differentiation, Picard method , Euler and modified Euler, RK methods.

Calculus of variations

Euler Lagrange equation , Necessary and sufficient conditions for extrema.

Linear Integral Equations

All topics