Download DBATU B.Tech 2019 March 4th Semester Discrete Structures and Applications Question Paper

DR. BABASAHEB AMBEDKAR TECHNOLOGICAL UNIVERSITY, LONERE

Mid Semester Examination - March 2019

Course: B. Tech in Information Technology

--- Content provided by​ FirstRanker.com ---

Subject Name: Discrete Structures and Applications

Sem: IV

Date: 13/03/2019

Max Marks: 20

Subject Code: BTITC403

--- Content provided by‌ FirstRanker.com ---

Duration: 1 Hr.

Instructions to the Students:

1. Assume suitable data wherever necessary.

Q.1 Select any one option from the following questions.

1. The cardinality of A = {5, 6, 3, 2, 3, 2} is (CO1)
   

   --- Content provided by‍ FirstRanker.com ---

   a) 6 b) 5 c) 4 d) 3
2. In a conditional statement, the first part is the antecedent and the second part is the... (CO1)
   a) Predicate b) Consequent c) Subject d) Disjunct
3. A function is said to be _______ if and only if f(a) = f(b) implies that a = b for all a and b in the domain of f. (CO2)
   a) One-to-many b) One-to-one c) Many-to-many d) Many-to-one

--- Content provided by⁠ FirstRanker.com ---

4. Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) = 3x + 4. Then the composition of f and g is (CO2)
   a) 6x + 9 b) 6x + 7 c) 6x + 6 d) 6x + 8
5. A coin is tossed 3 times. Find out the number of possible outcomes. (CO2)
   a) None of these b) 8 c) 2 d) 1
6. Letters of SAP taken all at a time can be written in (CO2)
   

   --- Content provided by​ FirstRanker.com ---

   a) 2 ways b) 6 ways c) 24 ways d) 120 ways

Q.2 Solve Any Two of the following. (3X2)

1. Give reasons for each step needed to show that the following argument is valid. (CO1)
   [p ? (p?q) ? (s?r) ? (r?¬q)] ? (s?t)
   Steps                           Reasons
   

   --- Content provided by‌ FirstRanker.com ---

   1) p
   2) p?q
   3) q
   4) r? ¬q
   5) q?¬r
   

   --- Content provided by‍ FirstRanker.com ---

   6) ¬r
   7) s?r
   8) s
   9) s?t
2. Prove following for all n>=1 by the principle of mathematical induction. (CO2)
   

   --- Content provided by​ FirstRanker.com ---

   1² + 3² + 5² + .......... + (2n-1)² = n (2n-1) (2n+1)/3
3. List all the combinations of size 3 that result for the letters m, r, a, f and t. (CO2)

Q.3 Solve Any One of the following. (8)

1. In how many ways can 12 different books be distributed among 4 children so that (CO2)
   a) each child gets three books? b) the two oldest children get four books each and the two youngest get two books each?

--- Content provided by⁠ FirstRanker.com ---

2. Let p(x), q(x) and r(x) be the following open statements. (CO1)
   p(x): x²-7x+10=0
   q(x): x²-2x-3=0
   r(x): x<0
   a) determine the truth or falsity of the following statements, where the universe is all integers. If a statement is false, provide a counterexample or explanation.
   

   --- Content provided by​ FirstRanker.com ---

   1) ?x [p(x) ? ¬r(x)] 2) ?x [q(x) ?r(x)]
   b) find the answers to part a) when the universe consists of all positive integers.

*** End ***

For more previous year question papers visit: FirstRanker.com

--- Content provided by‌ FirstRanker.com ---