MFCS previous year question paper 2019 | HNBGU MCA First semester

MCA

HNBGU MCA Previous Question Paper 2019

UNIT I

1. 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}

2. 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

UNIT II

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

   2. Define cyclic group with example.

4. 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.

UNIT III

5. 1. Evaluate :
      
      lim (1/x-1/sinx)
      
      x->0
      

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

6. 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
                        

UNIT IV

7. 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).

8. Define the following:

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