CSIR NET MATHEMATICS JUNE 2015 QUESTION PAPER
...
download the csir net mathematics december 2014 question paper
CSIR NET MATHEMATICS DECEMBER 2014 QUESTION PAPER is now available at http://mathexamtips.blogspot.in .Soon we are going to provide the clear solutions of CSIR NET MATHEMATICS DECEMBER 2014 QUESTION PAPER
...
download the csir net mathematics june 2014 question paper
CSIR NET MATHEMATICS JUNE 2014 QUESTION PAPER is now available at http://mathexamtips.blogspot.in .Soon we are going to provide the clear solutions of CSIR NET MATHEMATICS JUNE 2014 QUESTION PAPER
...
100 SOLVED QUESTIONS FOR CSIR,GATE, SET AND OTHER COMPETITIVE EXAMS-PART 3
100 SOLVED QUESTIONS FOR CSIR,GATE, SET AND OTHER COMPETITIVE EXAMS-PART 3
Question 10: Let H=\{e,(12)(34)\} and K=\{e,(12)(34),(13)(24),(14)(23)\} be subgroup of S_4, where e denotes the identify element of S_4. Then
H and K are normal subgroup of S_4
H is normal in K and K are normal in A_4
H is normal in A_4 but not in S_4
H is normal in S_4 but H is n...
100 SOLVED QUESTIONS FOR CSIR,GATE, SET AND OTHER COMPETITIVE EXAMS-PART2
100 SOLVED QUESTIONS FOR CSIR,GATE, SET AND OTHER COMPETITIVE EXAMS-PART 2
Question 6: The number of elements in the set \{m:1\leq m \leq 1000, m \text{ and } 1000 \text{ are relatively prime} \} is
1.~100 \quad 2.~250 \quad 3.~300 \quad 4.~400
Answer: The question asks for \phi(1000).
And \phi(n) can be calculated using following formula.
1. \phi(p_1^{m_1}p_2^{m_2} \cdots p_r^{m_r}) = \phi(p_1^{m_1})\phi(p_2^{m_2}) \cdots \phi(p_r^{m_r}).
2. \phi(p^m) = \begin{cases}2^{m-1} &\text{ if } p= 2 \\ p^m - p^{m-1} &\text{...
100 SOLVED QUESTIONS FOR CSIR,GATE, SET AND OTHER COMPETITIVE EXAMS-PART1
100 SOLVED QUESTIONS FOR CSIR,GATE, SET AND OTHER COMPETITIVE EXAMS-PART 1
Question 1: The number of surjective maps from a set of 4 elements to a set of 3 elements is
1.~36 \quad 2.~64 \quad 3.~69 \quad 4.~81
Answer: Let A be a 4 elements set and B be a 3 elements set. Here we need to find number of surjective maps between A onto B. The idea is to partition the set A into 3 non-empty subset and assign each subset to a element of B...
ISS Examination Question Paper of 2012 Statistics-4
ISS Examination Question Paper of 2012 Statistics-4
...
ISS Examination Question Paper of 2012 Statistics-3
ISS Examination Question Paper of 2012 Statistics-3
...
ISS Examination Question Paper of 2012 Statistics-2
ISS Examination Question Paper of 2012 Statistics-2
...
ISS Examination Question Paper of 2012 Statistics-1
ISS Examination Question Paper of 2012 Statistics-1
...
Qualitative Treatment of Autonomous ODE
A differential equation is called autonomous if it has no independent term. Hence a first order general ode will look like
\dfrac{dy}{dt} = f(y) \phantom{csir net}\text{ [Independent of $t$]}.
Qualitative Treatment of Autonomous ODE
STEP I: Find the critical points y_0(solution of f(y)=0). These are horizontal solution of the given ode.
Since two solutions(called integral curve) can’t intersect, hence other solution will be in the...
Problems on Permutation Group
Question: Let H=\{e,(12)(34)\} and K=\{e,(12)(34),(13)(24),(14)(23)\} be subgroup of S_4, where e denotes the identify element of S_4. Then
H and K are normal subgroup of S_4
H is normal in K and K are normal in A_4
H is normal in A_4 but not in S_4
H is normal in S_4 but H is not
Answer: Recall
Conjugation preserve disjoint cyclic structure in permutation group, i.e., for all \sigma, \tau \in S_n, the disjoint cyclic decomposition of \tau and \sigma \tau \sigma^{-1} will be the same.
Since K contain all element with...
AP-TS SET 2014 MATHEMATICS SOLUTIONS
AP-TS SET 2014 MATHEMATICS SOLUTIONS
PAPER-2 SOLUTIONS
Q 1
$S=\left\{ 1-\frac { { \left( -1 \right) }^{ n } }{ n } \quad :\quad n=1,2,3,... \right\} \\ \quad =\left\{ 2,1-\frac { 1 }{ 2 } ,1+\frac { 1 }{ 3 } ,1-\frac { 1 }{ 4 } ,... \right\} \\ \alpha \quad =\quad inf\quad S\quad =\quad \frac { 1 }{ 2 } \\ \beta \quad =\quad sup\quad S\quad =\quad 2\\ \\ \therefore \quad \left( \alpha ,\beta \right) \quad =\left( \frac { 1 }{ 2 } ,2 \right)$
Q 2
$Let\quad { x }_{ n }\rightarrow l\\ { x }_{ n+1 }\quad...
Problems on Euler's Theorem
Question: The number of elements in the set \{m:1\leq m \leq 1000, m \text{ and } 1000 \text{ are relatively prime} \} is
1.~100 \quad 2.~250 \quad 3.~300 \quad 4.~400
Answer: The question asks for \phi(1000).
And \phi(n) can be calculated using following formula.
1. \phi(p_1^{m_1}p_2^{m_2} \cdots p_r^{m_r}) = \phi(p_1^{m_1})\phi(p_2^{m_2}) \cdots \phi(p_r^{m_r}).
2. \phi(p^m) = \begin{cases}2^{m-1} &\text{ if } p= 2 \\ p^m - p^{m-1} &\text{ if } p \neq 2\end{cases}
Or equivalently it can be calculated by...
Finding Last Digit
Question: The unit digit of 2^{100} is
1.~2 \quad 2.~4 \quad3.~6 \quad4.~8
Answer: This problem can be solved by basic idea of periodicity. Calculating few terms mod 10,
2^1
2^2
2^3
2^4
2^5
2^6
2
4
8
6
2
4
We can see that the periodicity is 4.
Hence 2^{k + 4n}= 2^k for k =\{1,2,3,4\}.
Here 2^{100} = 2^{4+ 24\cdot 4} = 2^4 = 6.
Hence 3 is correct answer.
Question: The last digit of 38^{2011} is
1.~6 \quad 2.~2 \quad 3.~4 \quad 4.~8
Answer: First note that 38 = 8 (mod 10)....
Problems on Counting
Question: The number of surjective maps from a set of 4 elements to a set of 3 elements is
1.~36 \quad 2.~64 \quad 3.~69 \quad 4.~81
Answer: Let A be a 4 elements set and B be a 3 elements set. Here we need to find number of surjective maps between A onto B. The idea is to partition the set A into 3 non-empty subset and assign each subset to a element of B.
Different partition of set A into 3 non-empty subset is equal to \binom{4}{2},...
AP-TS SET 2014 MATHEMATICAL SCIENCE OFFICIAL KEY
AP-TS SET 2014 MATHEMATICAL SCIENCE OFFICIAL KEY
...
CSIR NET MATHEMATICS DECEMBER 2014 KEY
CSIR NET MATHEMATICS DECEMBER 2014 KEY is now available at http://mathexamtips.blogspot.in .Soon we are going to provide the clear solutions of CSIR NET MATHEMATICS DECEMBER 2014 QUESTION PAPER
...