Reg No.:

B7401

Total Pages: 2

Name:

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FIRST SEMESTER MCA DEGREE EXAMINATION, DECEMBER 2017

Course Code: RLMCA103
Course Name: DISCRETE MATHEMATICS

Max. Marks: 60 Duration: 3 Hours

10

11
12

13

14

PART A
Answer all questions, each carries 3 marks. Marks

Show that(AUB)*=A‘OB‘ (3)

Find GCD(12378,3054) (3)
Find the number of arrangements of letters of the word MISSISSIPPI in which (3) the 4
I’s come together

Finda when a = 58 witha=2 (3)

Define Regular graph and Connected graph with example (3)

A connected planar graph has 9 vertices having degrees 2,2,2,3,3,3,4,4,5.Find the
(3) number of edges and faces

Define Tautology and show that (pOq)®p is a tautology (3)

Show that p®q and [7०१ are logically equivalent (3)

PART 8
Answer six questions, one full question from each module and carries6 marks. Module I
a) Define equivalence relation (1) b) Prove that for x, y€Z the relation defined
by R = {(x, y): 5 divides x - y}is an (5)
equivalence relation

OR

a) Let f: R®R defined by f(x)=x+2 and g(x)= .Find gof and fog (2) b) Let f:
R-{3} © R-{1} defined by f(x)= —_ .Check whether f is bijective (4)

Module 11

Solve the linear Diophantine equation 172x+20y=1000 (6) OR

Solve the set of simultaneous congruences x02(mod3), 2113൩005), x02(mod7) (6)

Module III
a) Determine all integer solutions 10 the equation x1+X2+x3+Xx4=7 (2) b) A committee
of 10 people is to be formed from 12 men and 8 women. In how (4)
many ways can the committee be formed if
i) There should be an even number of men
ii) There should be at least 8 men

OR

a) Find the coefficient of x y z in the expansion of (x + y + z) (2)

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