CSIR NET MATHEMATICAL SCIENCE JUNE 2012 QUESTION & ANSWER

CSIR NET MATHEMATICAL SCIENCE JUNE 2012 QUESTION & ANSWER,
CSIR NET MATHS JUNE 2012 QUESTION & ANSWER,
 CSIR NET MATHEMATICS JUNE 2012 QUESTION & ANSWER

Part B 

1. 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.
2. 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.
3. The radius of convergence of the series
4. satisfies  |z-1| < root 3
5. Last digit in the number (38)^ 2011 is ............ Ans: 2
6. √2e^iπ   is?

1)      Rational Number

2)      Irrational Number

3)      Imaginary Number

^{4)       transcendental}

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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