MFCS Previous Year Question Paper 2018 | HNBGU BCA First semester

Admin - October 15, 2021

MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE PYQ

Section A

Draw a directed graph representation of relation R={(1,1),(2,2),(2,3),(3,2),(4,2),(4,4)} on set {1,2,3,4}. Also find R2 = RoR
Prove that the following function defined on the set of ordered pairs of real numbers is one to one and onto f (x,y) = (x+y,2x-y)s
Find the generating function f,,or the sequence 1,0,1,0,1,0,1,0.....
How many generators are there of the cyclic group of order 8?
Let f and g be the two functions defined on the set of real numbers, given by: f(x) =2x+3 and g(x) = x2=1 respectively. Find the composition function gof(x) and fog(x).
Let G = {1,-1,-i, i} with the binary operation multiplication be an algebraic structure, where i= √-1. Prove that the set G forms an abelian group under multiplication.
Solve the following recurrence relation: an-5an-1+6an-2=0 where a0=2 and a1=5

Section B

1. Determine the numeric function corresponding to the following generating function: G(x) = 2/1-4x2
2. Write down the recurrence relation for Fibonacci sequence (0,1,1,2,3,5,......) Also find thee generating function for this sequence.
1. Prove that the identity element in a group G is unique.
2. Find the order of each element of the multiplicative group G= {1,-1,I,-i}, where i=√-1
1. Let D36 = {1,2,3,4,6,9,12,18,36} denotes the set of divisors of 36 ordered of divisibility. Draw the Hasse diagram of D36.
2. Define the partially order relation with suitable example.
1. Use the Mathematical induction to prove that 12 + 22 + 32 +......+ n2 = n(n+1)(2n+1)/6 ɏn≥1.
2. Show that the functions f(x) = x3+1 and g(x) = (x-1)1/3 are converse to each other.
1. Check the validity of the following arguments: “If there was a ball game, then travelling was difficult. If they arrived on time then travelling was not difficult. They arrived on time. Therefore there was no ball game.”
2. Verify that the proposition p v ɿ (p ^ q) is a tautology.
1. Prove that p <-> Q and (P->Q) ^ (Q->P) are equivalent
2. Let R5 be the relation on the set of integers Z defined by x = y(mod5) which reads “x is congruent to y modulo 5” and which means that the difference x-y is divisible by 5. Prove that R5 is an equivalence relation.