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This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on Discrete Mathematics Set 5
Q1 | Which of the arguments is not valid in proving sum of two odd number is not odd.
- 3 + 3 = 6, hence true for all
- 2n +1 + 2m +1 = 2(n+m+1) hence true for all
- all of the mentioned
- none of the mentioned
Q2 | A proof broken into distinct cases, where these cases cover all prospects, such proofs are known as
- direct proof
- contrapositive proofs
- vacuous proof
- proof by cases
Q3 | A proof that p → q is true based on the fact that q is true, such proofs are known as
- direct proof
- contrapositive proofs
- trivial proof
- proof by cases
Q4 | In the principle of mathematical induction, which of the following steps is mandatory?
- induction hypothesis
- inductive reference
- induction set assumption
- minimal set representation
Q5 | For m = 1, 2, …, 4m+2 is a multiple ofis known as
- lemma
- corollary
- conjecture
- none of the mentioned
Q6 | For any integer m>=3, the series 2+4+6+…+(4m) can be equivalent to
- m2+3
- m+1
- mm
- 3m2+4
Q7 | For every natural number k, which of the following is true?
- (mn)k = mknk
- m*k = n + 1
- (m+n)k = k + 1
- mkn = mnk
Q8 | For any positive integer m is divisible by 4.
- 5m2 + 2
- 3m + 1
- m2 + 3
- m3 + 3m
Q9 | What is the induction hypothesis assumption for the inequality m ! > 2m where m>=4?
- for m=k, k+1!>2k holds
- for m=k, k!>2k holds
- for m=k, k!>3k holds
- for m=k, k!>2k+1 holds
Q10 | A polygon with 7 sides can be triangulated into
- 7
- 14
- 5
- 10
Q11 | A polygon with 12 sides can be triangulated into
- 7
- 10
- 5
- 12
Q12 | Which amount of postage can be formed using just 4-cent and 11-cent stamps?
- 2
- 5
- 30
- 10
Q13 | Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n+2) is true.
- p(3)
- p(2)
- p(4)
- p(6)
Q14 | Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) and P(2) is true; for all positive integers n, if P(n) and P(n+1) is true then P(n+2) is true.
- p(1)
- p(2)
- p(4)
- p(n)
Q15 | A polygon with 25 sides can be triangulated into
- 23
- 20
- 22
- 21
Q16 | How many even 4 digit whole numbers are there?
- 1358
- 7250
- 4500
- 3600
Q17 | In a multiple-choice question paper of 15 questions, the answers can be A, B, C or D. The number of different ways of answering the question paper are
- 65536 x 47
- 194536 x 45
- 23650 x 49
- 11287435
Q18 | Neela has twelve different skirts, ten different tops, eight different pairs of shoes, three different necklaces and five different bracelets. In how many ways can Neela dress up?
- 50057
- 14400
- 34870
- 56732
Q19 | For her English literature course, Ruchika has to choose one novel to study from a list of ten, one poem from a list of fifteen and one short story from a list of seven. How many different choices does Rachel have?
- 34900
- 26500
- 12000
- 10500
Q20 | The code for a safe is of the form PPPQQQQ where P is any number from 0 to 9 and Q represents the letters of the alphabet. How many codes are possible for each of the following cases? Note that the digits and letters of the alphabet can be repeated.
- 874261140
- 537856330
- 549872700
- 456976000
Q21 | Amit must choose a seven-digit PIN number and each digit can be chosen from 0 to 9. How many different possible PIN numbers can Amit choose?
- 10000000
- 9900000
- 67285000
- 39654900
Q22 | A head boy, two deputy head boys, a head girl and 3 deputy head girls must be chosen out of a student council consisting of 14 girls and 16 boys. In how many ways can they are chosen?
- 98072
- 27384
- 36428
- 44389
Q23 | A drawer contains 12 red and 12 blue socks, all unmatched. A person takes socks out at random in the dark. How many socks must he take out to be sure that he has at least two blue socks?
- 18
- 35
- 28
- 14
Q24 | When four coins are tossed simultaneously, in number of the outcomes at most two of the coins will turn up as heads.
- 17
- 28
- 11
- 43
Q25 | How many numbers must be selected from the set {1, 2, 3, 4} to guarantee that at least one pair of these numbers add up to 7?
- 14
- 5
- 9
- 24