Saturday, 23 June 2012

CSIR NET –JUNE 2012


Part-A
1.      1) Find the area of the shaded region in the given fig.

Solution:
          Radius of  the circle = 2cm
          Sides of  the square =2√2
          Area of  the shaded region=(Area of  the circle-Area of  the square)/4
                                                            =  (πr2 - a2)/4
                                                =  (4π - 8)/4
                                                = π-2

2.      2) The angles of  a  right angle triangular garden are in arithmetic progression. The smallest side of  the garden is 10m. Then Howmany meters  is needed to fence the garden ?
1)      10       2) 47       3) 60      4)
  1. From  the following semicircle, AQ=2AP then which of  the following is correct?

1)      ∟AQP=2∟APB
2)      ∟AQB=∟APB
3)      ∟AQB > ∟APB
4)      ∟AQB < 2∟APB
  1. Two types of rabbit community are A&B. Type A’s population is increasing 25% per year. Type B’s population is increasing 50% per year. In the present year both are equal. Then after two years  ratio of  the  population  of B and  A is ,
1)      1      
2)      1.72
3)      1.94
4)      1.47  
  1. From the fig which of the following is correct?


1)      a + ab + ab2 +………..= a/(1-b),  │b│<1
2)      a > b then a3 > b3
3)      (a+b)2  = a 2 + 2ab + b2
4)      a > b then  -a < -b

Tuesday, 19 June 2012

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 (Memory Based)

Part C

  1. If f is an entire function and Im f > 0 then
    1) Re f is constant   2) f is constant    3) f = 0     4) f' is a non-zero constant
  2.  Let C be an n x n matrix. Let V be a vector space spanned by {I, C, C^2, ... C^2n}. Then dim V is
    1) n^2     2) 2n       3) at most n^2             4) at most 2n
  3. Let N be a 3x3 non-zero matrix with the property that N^2 = 0. Then
    1) N is not similar to a diagonal matrix    2) N is  similar to a diagonal matrix 
    3) N has one non-zero eigen vector    4) N has three linearly independent  eigen vectors

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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  is?
1)      Rational Number
2)      Irrational Number
3)      Imaginary Number
4)       transcendental

7. The Second order PDE 4uxx – yuyy  + 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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Monday, 4 June 2012

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