CSIR NET MATHEMATICAL SCIENCE JUNE 2012 QUESTION & ANSWER,

CSIR NET MATHS JUNE 2012 QUESTION & ANSWER,

CSIR NET MATHEMATICS JUNE 2012 QUESTION & ANSWER

Note

CSIR NET MATHS JUNE 2012 QUESTION & ANSWER,

CSIR NET MATHEMATICS JUNE 2012 QUESTION & ANSWER

__Part B__- The number of words that can be formed permuting the letters of the word 'MATHEMATICS' is ...........

Answer:

number of letters in the word 'MATHEMATICS' = 11.In the word 'MATHEMATICS' M occurs 2 times, A 2 times, T 2 times, other letters 1 time. Required number of permutations = 11!/ 2! 2! 2! = 4989600. - Number of divisors of 50,000 = ............

Answer: Factorise 50,000 as 5 x 10,000 = 5 x 10^4 = 5 x 2^4 x 5^4 = 2^4 x 5 ^ 5.

Number of divisors of 50,000 = ( 4+1) (5+1) = 30. - The radius of convergence of the series
**satisfies**- Last digit in the number (38)^ 2011 is .
**........... Ans: 2** - √2e
^{iπ }is?

1) Rational Number

2) Irrational Number

3) Imaginary Number

^{4) transcendental}

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7. The Second order PDE 4u

_{xx}– yu_{yy }+ λu = 0 is
1) Elliptic in the region y=0

2) Parabolic in the region y < 0

3) Elliptic in the region y < 0

^{4) }Hyperbolic in the region y < 0

8. Which of the following is correct?

1) Rank (A+B) = Rank A+ Rank B

2) Rank (A+B) ≤ Rank A+ Rank B

3) Rank (A+B) ≤ min{Rank A, Rank B}

4) Rank (A+B) ≤ max{Rank A, Rank B}

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**:**If you know answers write as a comment here.
Mr.Suresh Kannan,

ReplyDeleteThank you for starting this blog. It shall be a great help to all.

In Question 3 , according to me, the Radius of convergence of the series should be < square root(3). As If we include the end points, then the series is a constant series 1+1+1+.....which is divergent. I am confused so please suggest.

< is not right.

Deletethanks, can you please explain why ?

Deletei think | z-1 | < sq root (3)

DeleteI also agreed with preetimaths

DeleteYou are correct.

DeleteAns is < root 3 Only.