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Download SGBAU BCA 2019 Summer 1st Sem Discrete Mathematics Question Paper

Download SGBAU (Sant Gadge Baba Amravati university) BCA 2019 Summer (Bachelor of Computer Applications) 1st Sem Discrete Mathematics Previous Question Paper

This post was last modified on 10 February 2020

This download link is referred from the post: SGBAU BSc Last 10 Years 2010-2020 Question Papers || Sant Gadge Baba Amravati university


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B.C.A. (Part-I) Semester-I Examination

DISCRETE MATHEMATICS

Paper-1ST5S

Time : Three Hours] [Maximum Marks : 60

Note :— Attempt one question from each unit.

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UNIT-I

  1. (a) Among the integers 1 to 1000, how many are not divisible by 5 and 7 but divisible by 3? 6
  2. (b) State and prove principle of inclusion exclusion for three sets. 6
  1. (p) Define : (i) one-one function (ii) onto function (iii) composite function. Give one example of each. 6
  2. (q) Define Countability and prove that if A and B are Countable then A*B is also countable. 6
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UNIT-II

  1. (a) Define ordinary generating function and exponential generating function. Determine the sequence for the generating function : (1) e (2) (1! 6
  2. (b) Define Ferrer's and Conjugate Ferrer's diagram and Draw both 7+5+3+2+1 of 18. 6
  1. (p) Find the coefficient of x'® in the series (x*+x*+x*+.....)% 6
  2. (q) Define probability generating function and prove that E(x) = P'x(1). 6
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UNIT-III

  1. (a) Define Recussive formula and find recurrence relation for the infinite sequence : 1) 3:7,11515;19,23..... (i) 4,6,8,10,12,..... 6
  2. (b) Find particular solution of a — 7a_ + 10a_, = 8r+ 6 6
  1. (p) Find Homogeneous solution of a — 8a_, + 16a_, = 0 with initial conditions a, = 16, a, = 48. 6
  2. (q) Find Total solution of a_— 10a_, + 25a , = 2 6
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UNIT-IV

  1. (a) Find the truth values of the following statements : (1) 2+5=7 and 4+2=6 (i) 10+2=7 or 11+2=14 (iii) 1+3=9 and 2+5=7 (iv) 4+2=7 and 3+7-10 (v) 13+2=15 or 10+3=13 (vi) 1+1=2 and 2+4=6 6
  2. (b) Prove that both join and meet operations are associative. 6

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l irBtoankes'soehnjce and mcet operations are distributive. . 6

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  1. Find the duals of the followingz : (i) an(avb)=a (i) an(bac)=(anrb) (iv) (av b)1 (vi) a< 0 6

UNIT-V

  1. (a) Prove that in a distributive lattice if an element has complement then this complement 1s unique. 6
  2. (b) If B is the sets of statements from closed under A, v and ~. Show that B Ko .t > is Boolean algebra where C is contradiction and t is tautology. 6
  1. (p) If a distributive lattice if zero and unit element is complemented then prove that for any X, the inverse x' is unique. 6
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  3. (q) Find disjuction normal form of (xvy)Aa(x'vy"). 6


This download link is referred from the post: SGBAU BSc Last 10 Years 2010-2020 Question Papers || Sant Gadge Baba Amravati university

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