MFCS previous year question paper 2019 | HNBGU MCA First semester


HNBGU MCA Previous Question Paper 2019

    1. Define reflexive, antisymmetric and transitive relations with example.

    2. Define generating function and also find the generating function for the finite sequence {1,1,1,1,1}

    1. Determine whether the sequence {an} where an=3n for ever non-negative integer n, is a solution of the recurrence relation an = an-1-an-2 for n=2,3,4

    2. By mathematical induction , prove that:

      12+22+32+....+n2=1/6*n(n+1)(2n+1)for the positive integer

    1. Prove that the inverse of each element of a group in unique.

    2. Define cyclic group with example.

    1. Prove that (ab)^-1=b^-1a^-1 for every a,b,e=EG where G is a group.

    2. Define permutation group with an example.

    1. Evaluate :

      lim (1/x-1/sinx)


    2. Solve the differential equation:
      (x2-y2)dx+2x.y dy =0

    1. Find the inverse of the matrix: A=

      1 2
      3 4
    2. Prove that:

      (a) a^2 b+c
      (b) b^2 c+a = (a-b)(b-c)(c-a)(a+b+c)
      (c) c^2 a+b
    1. Show that the set S ={(1,2,1)(2,1,0)(1,-1,2)} forms a basis of R3(R).

    2. Prove that {(x,y,z):x+y = 0} is the subspace of the vector space R3(R).

  1. Define the following:

    (a) Normal form
    (b) Inference Theory
    (c) Hasse Diagram