Engineering Mathematics, Question Paper of MCA Semester 1, Download Question Paper 6

Roll No………

Total No. of Questions: 9

Paper ID [B0104]

MCA (Sem.-1^st)

COMPUTER MATHEMATICAL FOUNDATION

 SUBJECT CODE: (MCA-104)(N2)

Time: 3 Hrs.                                                                           Max. Marks: 60

Instruction to Candidates:

1. Attempt any One question from each Section-A, B, C, & D.

2. Section-E is Compulsory.

3. Use of non-programmable scientific calculator is allowed.

SECTION-A

Q1.    With usual notations, prove that  (A^C= A^CB^C.

Q2.    Let R be an equivalence relation in A, then show that,

(a)  a for every aA

(b) [a] = [b] if and if a Rb

(c) If [a][b], then [a] and [b] are disjoint.

SECTION-B

Q3.    If p-q and q=r then show that p=r where p, q are logical statements.

Q4.    Use laws of logic to show that, ~ (p v q) V ( ~ P ^ q) = ~p.

SECTION-C

Q5.    Apply Gauss- Jordan method to solve the equations,

          x+y+z=9, 2x-3y+4z=13,  3x+4y+5z=40.

Q6.    Solve by matrix inversion method.

          X+y+2z=4, 2x-y+3z=9, 3x-y-z=12.

SECTION-D

Q7.    Give an example of a connected graph that has

(a) Neither an Euler circuit nor a Hamilton cycle.

(b) An Euler circuit but no Hamilton cycle.

(c) A Hamilton cycle but no Euler circuit.

(d) Both a Hamilton cycle and an Euler circuit.

Q8     Find the chromatic number of the following graphs.

SECTION-E

Q9.    (a) Show that A=b iff B^C=A^C/

(b) Define an equivalence relation and give an example for the same.

(c) Give an example of a tautology.

(d) Determine the contrapositive of the statement, “If Kamal is a poet, then he is poor.”

(e) Define the product of two matrices.

(f) Find the inverse of

(g) Define a graph. When it is said to be connected?

(h) Differentiate between a Hamiltonian graph and  a Eluerian graph.

(i) State any one property of equivalence relations.

(j) Find the rank of