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)

3. 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

4. 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  

5. 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

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^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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