SECTION-A

  I.Very short answer questions:
     Attempt allquestions.Each question carries 2 marks.
                                                                                           10^2=20marks

 1 .For what values of m the equation (m+1)x2 + 2(m+3)x + m+8 = 0 has equal roots.

 2 .Find the polynomial equation whose roots are the squares of the roots of   x3+3x2-7x+6=0

 3 .Define symmetric matrix & skew symmetric matrix with an example each.

 4 .Construct a 2/2 matrix whose elements are given by aij = |2i-3j|.

 5 .Find the number of ways of arranging the letters of the word (i)PERMUTATION (ii) INTERMEDIATE (iii)INDEPENDENCE 
     
    (iv)MATHEMATICS

 6 .Find the number of positive divisors of 1080.

 7 .Find the numerically greatest term in the expansion of (1-3x)^10 when x=1/2.

 8 .Find the sum of infinite series 1/1.2-1/2.3+1/3.4-1/4.5+........

 9 .Find the probability that two particular persons never sit together,when n persons sit in a row at random.

 10.If  X is poisson variate such that P(X=0) = P(X=1) = k then show that k=1/e.

SECTION-B

II.Short answer questions.

Attempt any five questions.Each question carries 4 marks.
                                                                                               5^4=20marks

 11.Prove that 1/3x+1 + 1/x+1 - 1/(3x+1)(x+1) does not lie between 1 & 4 if  'x' real.

 12.Show that the determinant of skew symmetric matrix of order 3 is always zero.

 13.Find the number of 4 digited numbers that can be formed by using the digits 1,2,3,4,5,6 that are divisible by 
      
     (i)2      (ii)3    when repitation are allowed.

 14.How many ways can the letters of the word ENGINEERING be arranged so that 3N's come together but 3E's donot come together.

 15.Resolve into partial fractions:

                 x3
   ----------------------
        (x-1)(x+2)

 16.Show that 2/3! + 4/5! + 6/7! + ............. = 1/e.

 17.A speaks truth in 75% of the cases & B in 80% cases.What is the probability that their statements about an incident do not match.

SECTION-C

Long answer questions.                                                                              5^7=35marks

Attempt any five questions.Each carries 7marks.

 18.Solve x4-5x3+5x2+5x-6=0, given that the product of two of its roots is 3.

 19.Show that |b+c   c+a   a+b|          |a   b   c|
                       |                        |          |            |
                       |c+a   a+b   b+c    =    |b   c   a|
                       |                        |          |            |
                       |a+b   b+c   c+a|          |c   a   b|

 20.By using Gauss-jordan method, show that the following system has no solution

     2x+4y-z=0, x+2y+2z=5, 3x+6y-7z=2

21.Suppose that n is a natural number & I,F are integral part & fractional part of   (7+4.(3)1/2)n.
   Then show that   (i)I is an odd integer            (ii)(I+F)(I-F)=1

22.State & prove Binomial theorem for positive integral index.

23.State & prove Addition theorem on probability.

24.Find the probability of guessing atleast 6 out of 10 answers in 
    (i)true or false type examination    (ii)multiple choice with four possible answers.

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