## 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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CSIR NET Mathematical Sciences previous year questions answers, study materials, Solved papers, GATE Mathematics previous year questions answers, study materials, Solved papers, IAS Maths previous year questions answers, study materials, Solved papers, IISc Maths previous year questions answers, study materials, Solved papers, Answer keys