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

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Roll No………
Total No. of Questions: 9

Paper ID [B0104]
MCA (Sem.-1st)
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= AC BC.
Q2.    Let R be an equivalence relation in A, then show that,
(a)  a for every a A
(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 BC=AC/
(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 