## Discrete Mathematics MCQ Set 1

1. Which of the following statement is a proposition?

a) Get me a glass of milkshake

b) God bless you!

c) What is the time now?

d) The only odd prime number is 2

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2. The truth value of given statement is

‘4+3=7 or 5 is not prime’.

a) False

b) True

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3. Which of the following option is true?

a) If the Sun is a planet, elephants will fly

b) 3 +2 = 8 if 5-2 = 7

c) 1 > 3 and 3 is a positive integer

d) -2 > 3 or 3 is a negative integer

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4. What is the value of x after this statement, assuming initial value of x is 5?

‘If x equals to one then x=x+2 else x=0’.

a) 1

b) 3

c) 0

d) 2

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5. Let P: I am in Bangalore. , Q: I love cricket. ; then q -> p(q implies p) is:

a) If I love cricket then I am in Bangalore

b) If I am in Bangalore then I love cricket

c) I am not in Bangalore

d) I love cricket

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6. Let P:If Sahil bowls, Saurabh hits a century. ,Q: If Raju bowls , Sahil gets out on first ball. Now if P is true and Q is false then which of the following can be true?

a) Raju bowled and Sahil got out on first ball

b) Raju did not bowled

c) Sahil bowled and Saurabh hits a century

d) Sahil bowled and Saurabh got out

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7. The truth value of given statement is

‘If 9 is prime then 3 is even’.

a) False

b) True

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8. Let P: I am in Delhi. , Q: Delhi is clean. ; then q ^ p(q and p) is:

a) Delhi is clean and I am in Delhi

b) Delhi is not clean or I am in Delhi

c) I am in Delhi and Delhi is not clean

d) Delhi is clean but I am in Mumbai

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9. Let P: This is a great website, Q: You should not come back here.

Then ‘This is a great website and you should come back here.’ is best represented by:

a) ~P V ~Q

b) P ∧ ~Q

c) P V Q

d) P ∧ Q

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10. Let P: We should be honest., Q: We should be dedicated .,R: We should be overconfident.

Then ‘We should be honest or dedicated but not overconfident.’ is best represented by:

a) ~P V ~Q V R

b) P ∧ ~Q ∧ R

c) P V Q ∧ R

d) P V Q ∧ ~R

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## Discrete Mathematics MCQ Set 2

1. Let set A ={1, 2} and C be {3, 4} then A X B (Cartesian product of set A and B) is

a) {1, 2, 3, 4}

b) {(1, 3) ,(2, 4)}

c) {(1, 3) , (2, 4), (1, 4) , (2, 3) }

d) {(3, 1), (4, 1)}

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2. If set A has 4 elements and B has 3 elements then set n(A X B) is

a) 12

b) 14

c) 24

d) 7

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3. If set A has 3 elements then number of elements in A X A X A are

a) 9

b) 27

c) 6

d)19

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4. Which of the following statements regarding sets is false ?

a) A X B = B X A

b) A X B ≠ B X A

c) n(A X B) = n(A) * n(B)

d) All of the mentioned

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5. If n(A X B) = n(B X A) = 36 then which of the following may hold true?

a) n(A)=2, n(B)=18

b) n(A)=9, n(B)=4

c) n(A)=6, n(b)=6

d) None of the mentioned

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6. If C = {1} then C X (C X C) = (C X C) X C the given statement is

a) True

b) False

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7. Let the sets be A, B, C, D then (A ∩ B) X (C ∩ D) is equivalent to

a) (A X C) ∩ (B X D)

b) (A X D) U (B X C)

c) (A X C) U ( B X D)

d) None of the mentioned

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8. If A ⊆ B then A X C ⊆ B X C the given statement is

a) True

b) False

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9. If set A and B have 3 and 4 elements respectively then the number of subsets of set (A X B) is

a) 1024

b) 2048

c) 512

d) 4096

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10. If set A X B=B X A then which of the following sets may satisfy

a) A={1, 2, 3} , B={1, 2, 3, 4}

b) A={1, 2} , B={2, 1}

c) A={1, 2, 3} , B={2, 3, 4}

d) None of the mentioned

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## Discrete Mathematics MCQ Set 3

1. {x: x is an integer neither positive nor negative} is

a) Empty set

b) Non- empty set

c) Finite set

d) Both b and c

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2. {x: x is a real number between 1 and 2} is an

a) Infinite set

b) Finite set

c) Empty set

d) None of the mentioned

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3. Write set {1, 5, 15, 25,…} in set-builder form :

a) {x: either x=1 or x=5n, where n is a real number}

b) {x: either x=1 or x=5n, where n is a integer}

c) {x: either x=1 or x=5n, where n is an odd natural number}

d) {x: x=5n, where n is a natural number}

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4. Express {x: x= n/ (n+1), n is a natural number less than 7} in roster form:

a) {^{1}⁄_{2}, ^{2}⁄_{3}, ^{4}⁄_{5}, ^{6}⁄_{7}}

b) {^{1}⁄_{2}, ^{2}⁄_{3}, ^{3}⁄_{4}, ^{4}⁄_{5}, ^{5}⁄_{6}, ^{6}⁄_{7}, ^{7}⁄_{8}}

c) {^{1}⁄_{2}, ^{2}⁄_{3}, ^{3}⁄_{4}, ^{4}⁄_{5}, ^{5}⁄_{6}, ^{6}⁄_{7}}

d) Infinite set

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^{1}⁄

_{2}and n>7.

5. Number of power set of {a, b}, where a and b are distinct elements.

a) 3

b) 4

c) 2

d) 5

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6. Which of the following is subset of set {1, 2, 3, 4}.

a) {1, 2}

b) {1, 2, 3}

c) {1}

d) All of the mentioned

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7. A = {∅,{∅},2,{2,∅},3} ,which of the following is true.

a) {{∅,{∅}} ∈ A

b) {2} ∈ A

c) ∅ ⊂ A

d) 3 ⊂ A

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8. Subset of the set A= { } is:

a) A

b) {}

c) ∅

d) All of the mentioned

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9. {x: x ∈ N and x is prime} then it is:

a) Infinite set

b) Finite set

c) Empty set

d) Not a set

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10. Convert set {x: x is a positive prime number which divides 72} in roster form:

a) {2, 3, 5}

b) {2, 3, 6}

c) {2, 3}

d) {∅}

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## Discrete Mathematics MCQ Set 4

1. Let the sequence be 1×2, 3×2^{2}, 5×2^{3}, 7×2^{4}, 9×2^{5}……… then this sequence is

a) An airthmetic sequence

b) A geometic progression

c) Airthmetico-geometric progression

d) None of the mentioned

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_{1}, a

_{2}……… are in AP and b

_{1}, b

_{2}………. are in GP then a

_{2}b

_{2}, a

_{2}b

_{2},……… are in AGP.

2. Let the sequence be 1×2, 3×2^{2}, 5×2^{3}, 7×2^{4}, 9×2^{5}……… then the next term of this AGP is given by:

a) 10×26

b) 10×27

c) 11×26

d) None of the mentioned

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_{1}, a

_{2}……… are in AP and b

_{1}, b

_{2}………. are in GP then a

_{2}b

_{2}, a

_{2}b

_{2},……… are in AGP thus a

_{n}= 11 and b

_{n}= 2

^{6}.

3. The sum of the first n natural numbers is given by:

a) n(n+1)/2

b) n(n-1)/2

c) n^{2}(n+1)/2

d) None of the mentioned

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4. The sum of square of the first n natural numbers is given by:

a) n(n+1)(2n+1)/6

b) n(n-1)/2(2n+1)

c) n^{2}(n+1)(2n+1)/6

d) None of the mentioned

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^{2}+ 2

^{2}+ 3

^{2}+ 4

^{2}+……n

^{2}= n(1+n)(2n+1)/6.

5. The sum of cubes of the first n natural numbers is given by:

a) {n(n+1)/2}^{2}

b) {n(n-1)/2}^{2}

c) {n2(n+1)/2}^{2}

d) None of the mentioned

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^{3}+ 2

^{3}+ 3

^{3}+ 4

^{3}+……+ n

^{3}= {n(n+1)/2}

^{2}.

6. State whether the given statement is true or false

The series 1, 1, 1, 1, 1…….. is not an AGP.

a) True

b) False

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7.If in a AGP the common ratio of GP is 1 then that sequence becomes a AP sequence.

a) True

b) False

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8. The sequence 1, 1, 1, 1, 1…. is :

a) Absolutely summable

b) Is not absolutely summable

c) Can’t say

d) None of the mentioned

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9. Which of the following is a Triangular number series :

a) 1, 3, 6, 9, 12, 15…..

b) 1, 3, 6, 10, 15, 21……

c) 1, 6, 12, 18, 24…..

d) none of the mentioned

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10.Which of the following is a fibonacci series:

a) 0, 1, 2, 3, 4…….

b) 0, 1, 1, 2, 3, 5……

c) 10, 12, 14, 16…….

d) none of the mentioned

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## Discrete Mathematics MCQ Set 5

1. The contrapositive of p → q is the proposition:

a) ¬p → ¬q

b) ¬q → ¬p

c) q → p

d) ¬q → p

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2. The inverse of p → q is the proposition:

a) ¬p → ¬q

b) ¬q → ¬p

c) q → p

d) ¬q → p

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3. The converse of p → q is the proposition:

a) ¬p → ¬q

b) ¬q → ¬p

c) q → p

d) ¬q → p

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4. What is the contrapositive of the conditional statement? “The home team misses whenever it is drizzling?”

a) If it is drizzling, then home team misses

b) If the home team misses, then it is drizzling

c) If it is not drizzling, then the home team does not misses

d) If the home team wins, then it is not drizzling

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5. What is the converse of the conditional statement “If it ices today, I will play ice hockey tomorrow.

a) “I will play ice hockey tomorrow only if it ices today.”

b) “If I do not play ice hockey tomorrow, then it will not have iced today.”

c) “If it does not ice today, then I will not play ice hockey tomorrow.”

d) “I will not play ice hockey tomorrow only if it ices today.”

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6. What are the contrapositive of the conditional statement “I come to class whenever there is going to be a test.

a) “If I come to class, then there will be a test.”

b) “If I do not come to class, then there will not be a test.”

c) “If there is not going to be a test, then I don’t come to class.”

d) “If there is going to be a test, then I don’t come to class.”

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7. What are the inverse of the conditional statement “ A positive integer is a composite only if it has divisors other than 1 and itself.”

a) “A positive integer is a composite if it has divisors other than 1 and itself.”

b) “If a positive integer has no divisors other than 1 and itself, then it is not composite.”

c) “If a positive integer is not composite, then it has no divisors other than 1 and itself.”

d) None of the mentioned

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8. What are the converse of the conditional statement “When Raj stay up late, it is necessary that Raj sleep until noon.”

a) “If Raj stay up late, then Raj sleep until noon.”

b) “If Raj does not stay up late, then Raj does not sleep until noon.”

c) “If Raj does not sleep until noon, then Raj does not stay up late.”

d) “If Raj sleep until noon, then Raj stay up late.”

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9. What are the contrapositive of the conditional statement “Medha will find a decent job when she labour hard.”?

a) “If Medha labour hard, then she will find a decent job.”

b) “If Medha will not find a decent job, then she not labour hard.”

c) “If Medha will find a decent job, then she labour hard.”

d) “If Medha not labour hard, then she will not find a decent job.”

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10. What are the inverse of the conditional statement “If you make your notes, it will be a convenient in exams.”

a) “If you make notes, then it will be a convenient in exams.”

b) “If you do not make notes, then it will not be a convenient in exams.”

c) “If it will not be a convenient in exams, then you did not make your notes.”

d) “If it will be a convenient in exams, then you make your notes