APRAJITA'S BLOG

Tuesday, July 05, 2016

CSIR -NET Linear algebra Solved question : part B : June 2016

by Aprajita / in linear algebra , PART B&C / with 12 comments /

1. Given a

n \times n

$n\times n$ matrix

B

$B$ defined by

e^{B}

$e^B$ by

e^{B} = \infty \sum j = 0 \frac{B^{j}}{j!}

$e^B=\sum_{j=0}^\infty \frac{B^j}{j!}$ Let p be the characteristic polynomial of

B

$B$ Then the matrix

e^{P (B)}

$e^{P(B)}$ is

I_{n \times n}

$I_{n\times n}$

0_{n \times n}

$0_{n\times n}$

e \times I_{n \times n}

$e \times I_{n\times n}$

π \times I_{n \times n}

$\pi \times I_{n\times n}$ Solution: Since every characteristic...

Friday, July 01, 2016

CSIR-NET Mathematical science Paper : June 2016

by Aprajita / in CSIR PART A , PART B&C / with 11 comments /

...

Wednesday, April 20, 2016

Some Solved problems on zeros and poles.

by Aprajita / in complex analysis , PART B&C / with 3 comments /

Few Useful results regaring the poles and zeros in terms of quotients and product of two functions, Let

f (z) = h (z) / g (z)

$f(z)=h(z)/g(z)$ , where

h

$h$ and

g

$g$ are analytic in some open disk about

z_{0}

$z_0$ , then

f

$f$ has a pole of order

n

$n$ at

z_{0}

$z_0$ . Let

f (z) = h (z) / g (z)

$f(z)=h(z)/g(z)$ and suppose

h

$h$ and

g

$g$ are...

Saturday, April 16, 2016

Relation and Function - NCERT Exemplar Problems and Solution (Short Answer Type)

by Aprajita / in 12th class / with 2 comments /

Short Answer Type NCERT Exemplar Problems and Solution Question – 1 Let

A = (a, b, c)

$A = (a, b, c)$ and the relation

R

$R$ be defined on

A

$A$ as follows:

R = ((a, a), (b, c), (a, b)) .

$R = ((a, a), (b, c), (a, b)).$ Then, write minimum number of ordered pairs to be added in

R

$R$ to make

R

$R$ reflexive and transitive. Solution: In...

Long Answer Type NCERT Exemplar Problems and Solution Part 1

by Aprajita / in 12th class / with No comments /

Question – 16: If

A = (1, 2, 3, 4)

$A = (1, 2, 3, 4)$ , define relations on

A

$A$ which have properties of being (a) Reflexive, transitive but not symmetric (b) Symmetric but neither reflexive nor transitive. (c) Reflexive, symmetric and transitive. Solution: Let

R_{1}

$R_1$ = {

(1, 1), (2, 2), (1, 2)

$(1,1),(2,2),(1,2)$ } Thus,...

CSIR Part A: Solved: December 2015 (Mathematics)

by Aprajita / in CSIR PART A / with 19 comments /

Question 1: A circle drawn in the

$x-y$ coordinate plane passes through the origin and has chords of lengths

$8$ units and

$7$ units on the

$x$ and

$y$ axes, respectively. The coordinates of its centre are 1. (8, 7) ...

CSIR-NET Mathematical Science and Life Science (Part A Solved):2015 June

by Aprajita / in CSIR PART A / with 4 comments /

1. A pyramid shaped toy is made by tightly placing cubic blocks of

$1\times 1 \times 1$

$cm^3$ . The base of the toy is a square

$4\times 4$

$Cm^2$ . The width of each step is 0.5 Cm . how many blocks are required to make the toy? Solution...

2015 (December) CSIR Part A (Solution): Engineering Science, Chemical Science and physical Science.

by Aprajita / in CSIR PART A / with 4 comments /

1.Each of the following pairs of words hides a number, based on which you can arrange them in ascending order. Pick the correct answer: I. Cloth reel J. Silent Wonder K. Good tone L . Bronze rod...

Part A: CSIR - NET Solution (Bio Group):Dec 2015

by Aprajita / in CSIR PART A / with 8 comments /

1. A shopkeeper purchased a product for Rs.

$100$ and sells it making a profit of

$10$ %. The customer resells it to the same shopkeeper incurring a loss of

$10$ %. In these dealings the shopkeeper makes 1. no profit, no los...

Tuesday, July 05, 2016

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