MCA
HNBGU MCA Previous Question Paper 2019


Define reflexive, antisymmetric and transitive relations with example.

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



Determine whether the sequence {an} where an=3n for ever nonnegative integer n, is a solution of the recurrence relation an = an1an2 for n=2,3,4

By mathematical induction , prove that:
1^{2}+2^{2}+3^{2}+....+n^{2}=1/6*n(n+1)(2n+1)for the positive integer



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

Define cyclic group with example.



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

Define permutation group with an example.



Evaluate :
lim (1/x1/sinx)
x>0

Solve the differential equation:
(x^{2}y^{2})dx+2x.y dy =0



Find the inverse of the matrix: A=
1 2 3 4

Prove that:
(a) a^2 b+c (b) b^2 c+a = (ab)(bc)(ca)(a+b+c) (c) c^2 a+b



Show that the set S ={(1,2,1)(2,1,0)(1,1,2)} forms a basis of R^{3}(R).

Prove that {(x,y,z):x+y = 0} is the subspace of the vector space R^{3}(R).


Define the following:
(a) Normal form (b) Inference Theory (c) Hasse Diagram
UNIT I
UNIT II
UNIT III
UNIT IV