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

1. Given a $n\times n$ matrix $B$ defined by $e^B$ by  $$e^B=\sum_{j=0}^\infty \frac{B^j}{j!}$$ Let p be the characteristic polynomial of $B$ Then the matrix $e^{P(B)}$ is $I_{n\times n}$ $0_{n\times n}$ $e \times I_{n\times n}$ $\pi \times I_{n\times n}$ Solution: Since every characteristic...

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CSIR-NET Mathematical science Paper : June 2016

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Some Solved problems on zeros and poles.

Few Useful results regaring the poles and zeros in terms of quotients and product of two functions, Let $f(z)=h(z)/g(z)$, where $h$ and $g$ are analytic in some open disk about $z_0$, then $f$ has a pole of order $n$ at $z_0$. Let $f(z)=h(z)/g(z)$ and suppose $h$ and $g$ are...

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

Short Answer Type NCERT Exemplar Problems and Solution Question – 1 Let$A = (a, b, c)$ and the relation $R$  be defined on $A$  as follows: $R = ((a, a), (b, c), (a, b)).$ Then, write minimum number of ordered pairs to be added in $R$ to make $R$ reflexive and transitive. Solution: In...

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Long Answer Type NCERT Exemplar Problems and Solution Part 1

Question – 16: If $A = (1, 2, 3, 4)$, define relations on $A$ 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 $R_1$= { $(1,1),(2,2),(1,2)$} Thus,...

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CSIR Part A: Solved: December 2015 (Mathematics)

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)                    ...

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

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...

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

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...

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

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...

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