## Discrete Mathematics MCQ Set 1

1. The cardianlity of the set A = {1, 2, 3, 4, 6} is:

a) 5

b) 6

c) Integer

d) None of the mentioned

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2. For two equal sets there:

a) Cardinality is same

b) Cardinality is different

c) May be same or different

d) None of the mentioned

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3. If A is a subset of B:

a) Cardinality of A is greater than B

b) Cardinality of B is greater than A

c) Can’t say

d) None of the mentioned

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4. If there is bijection between two sets A and B then :

a) Cardinality of A is greater than B

b) Cardinality of B is greater than A

c) Cardinality of B is equal to A

d) None of the mentioned

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5. Let a set E ={0,2,4,6,8….} of non-negative even numbers and O = {1, 3, 5, 7, 9,…..} of non-negative odd numbers then :

a) Cardinality of set E is greater thanthat of O

b) Cardinality of set O is greater than that of E

c) Cardinality of set E is equal to that of O

d) None of the mentioned

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6. State whether the given statement is true or false

Cardinality of the set of lower letter english alphabets is 26.

a) True

b) False

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7. Cardinality of the set of even prime number under 10 is 4.

a) True

b) False

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8. If for sets A and B there exists a injective function but not bijective function from A to B then:

a) Cardinality of A is stricly greater than B

b) Cardinality of B is strictly greater than A

c) Cardinality of B is equal to A

d) None of the mentioned

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9. If cardinality of (A U B) = cardinality of A+ cardinality of B. This means:

a) A is a subset of B

b) B is a subset of A

c) A and B are disjoint

d) None of the mentioned

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10. If A is a subset of B and B is a subset of C,then cardinaity of A U B U C is equal to :

a) Cardinality of C

b) Cardinality of B

c) Cardinality of A

d) None of the mentioned

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## Discrete Mathematics MCQ Set 2

1. Let the sequence be 1, 3, 5, 7, 9……… then this sequence is

a) An airthmetic sequence

b) A geometic progression

c) A harmonic sequence

d) None of the mentioned

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2. In the given AP series find the number of terms

5, 8, 11, 14, 17, 20………50.

a) 11

b) 13

c) 15

d) None of the mentioned

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^{th}term = first_term + (number_of_terms – 1)common_differnce., 50 = 5 + (n-1)3, n=16.

3. In the given AP series the term at position 11 would be

5, 8, 11, 14, 17, 20………50.

a) 35

b) 45

c) 25

d) None of the mentioned.

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^{th}term = a + (n – 1)d, n

^{th}term = 5+(11-1)3 = 35.

4. For the given Airthmetic progression find the position of first negative term?

50, 47, 44, 41,…………

a) 17

b) 20

c) 18

4) None of the mentioned.

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^{th}term=0 ,the next term would be first negative term. 0 = 50 + (n-1) – 3, n = 17.66.. therfore at n = 18 the first negative term would occur.

5. For the given Airthmetic progression find the first negative term?

50, 47, 44, 41,…………

a) -1

b) -2

c) -3

4) None of the mentioned.

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^{th}term = 0, the next term would be first negative term. 0 = 50 +(n-1)- 3, n = 17.66.. therfore at n=18 the first negative term would occur. N

^{th}term = 50 + (18-1) – 3 = -1.

6. State whether the given statement is true or false

A series can either be AP only or GP only or HP only but not all at the same time.

a) True

b) False

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7. In the given Airthmetic progression, ’25’ would be a term in it.

5, 8, 11, 14, 17, 20………50.

a) True

b) False

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^{th}term = a + (n-1)d, 25 = 5 + (n-1)3, n = 23/3, n = 7.666 not an integer. Thus 25 is not a term in this series.

8. Which of the following sequeces in AP will have common difference 3,where n is an Integer?

a) a_{n} = 2n^{2} + 3n

b) a_{n} = 2n^{2} + 3

c) a_{n} = 3n^{2} + 3n

d) a_{n} = 5 + 3n

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_{n}= 5 + 3n it is a linear expression with coefficient of as 3. So it is AP with common difference 3.

9. If a, b, c are in AP then relation between a, b, c can be

a) 2b = 2a + 3c

b) 2a = b + c

c) 2b = a + c

d) 2c = a + c

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10. Let the sum of the 3 consecutive terms in AP be 180 then midlle of those 3 terms would be:

a) 60

b) 80

c) 90

d) 179

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_{1}, b

_{1}, c

_{1}be three terms ,then a

_{1}+ b

_{1}+ c

_{1}= 180, a

_{1}+ c

_{1}= 2b

_{1}(A M property), 3b

_{1}= 180, b

_{1}=60.

## Discrete Mathematics MCQ Set 3

1. Which of the number is not allowed in Binary representation of a number:

a) 0

b) 1

c) 2

d) None of the mentioned

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2. Which of the number is not allowed in Octal representation of a number:

a) 0

b) 4

c) 8

d) None of the mentioned

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3. Hexadecimal number equivalent of decimal 10 is:

a) 10

b) A

c) F

d) None of the mentioned.

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4. Decimal equivalent of binary number 1010 is:

a) 11

b) A

c) 10

d) None of the mentioned.

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5. Decimal 13 in base 8 can be represented as :

a) 15

b) 12

c) 22

d) None of the mentioned

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6. State whether the given statement is true or false

F in hexadecimal representaion is equivalent to 9 in decimal.

a) True

b) False

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7. Octal number may contains digits from 1 to 8.

a) True

b) False

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8. For some base r, the digits which are allowed in its representaion are?

a) Digits from 1 to r

b) Digits from 0 to r-1

c) Digits from 1 to r-1

d) None of the mentioned

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9. The binary number 100110 in octal is reprsented by

a) 45

b) 10012

c) 46

d) 58

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10. A number greater than 32 would require minimum of how may bits in binary representation:

a) 5

b) 6

c) 4

d) 10

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^{5}= 32 we need greater than 5 bits, so minimum would be 6.

## Discrete Mathematics MCQ Set 4

1. A Highest Common Factor of a, b is defined as:

a) It is the smallest integer divisible by both a and b

b) It is the greatest integer divisor of both a and b

c) It is the sum of the number a and b

d) None of the mentioned

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2. The HCF of two number 1, b(integer) are

a) b + 2

b) 1

c) b

d) None of the mentioned

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3. If a,b are integers such that a > b then hcf(a, b) lies in

a) a> hcf(a, b)>b

b) a>b> = hcf(a, b)

c) hcf(a, b)> = a>b

d) None of the mentioned

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4. HCF of 6, 10 is:

a) 60

b) 30

c) 10

d) 2

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5. The product of two numbers are 12 and there LCM is 6 then HCF is :

a) 12

b) 2

c) 6

4) None of the mentioned

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6. If LCM of two number is 10 and GCD is 5 then the product of two numbers is :

a) 45

b) 50

c) 7

d) 49

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7. If a number is 2^{2} x 3^{1} x 5^{0} and b is 2^{2} x 3^{1} x 5^{1} then hcf of a, b is:

a) 2^{2} x 3^{1} x 5^{1}

b) 2^{2} x 3^{2} x 5^{2}

c) 2^{1} x 3^{1} x 5^{0}

d) 2^{2} x 3^{2} x 5^{0}

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8. State whether the given statement is True or False.

HCF (a, b, c, d) = HCF(a,(HCF(b,(HCF(c, d)))).

a) True

b) False

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9. HCF(a, b) is equals to :

a) ab/(LCM(a, b))

b) (a + b)/(LCM(a, b))

c) (LCM(a, b))/ab

d) None of the mentioned

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10. The HCF of two prime numbers a and b is:

a) ^{a}⁄_{b}

b) ab

c) a + b

d) 1

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## Discrete Mathematics MCQ Set 5

1. An injection is a function which is :

a) many-one

b) one-one

c) onto

d) none of the mentioned

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2. A mapping f : X -> Y is one one if :

a) f(x_{1}) ≠ f(x_{2}) for all x_{1}, x_{2} in X.

b) If f(x_{1}) = f(x_{2}) then x_{1} = x_{2} for all x_{1}, x_{2} in X.

c) f(x_{1}) = f(x_{2}) for all x_{1}, x_{2} in X.

d) None of the mentioned

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3. A function is defined by mapping f : A -> B such that A contains m elements and B contains n elements and m ≤ n then number of one one functions are :

a) ^{n}C_{m} x m!

b) ^{n}C_{m} x n!

c) 0

d) none of the mentioned

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^{n}C

_{m}x m!.

4. A function is defined by mapping f : A -> B such that A contains m elements and B contains n elements and m>n then number of one one functions are :

a) ^{n}C_{m} x m!

b) ^{n}C_{m} x n!

c) 0

d) none of the mentioned

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5. State whether the given statement is true or false

For an onto function range is equivalent to codomain.

a) True

b) False

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6. State whether the given statement is true or false

Onto function are known as injection.

a) True

b) False

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7. Set A has 3 elements and set B has 4 elements then number of injections defined from A to B are?

a) 12

b) 24

c) 36

d) 48

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^{4}C

_{3}x 3!=24.

8. A function is defined by mapping f : A -> B such that A contains m elements and B contains n elements and 1≤n≤m then number of onto functions are:

a) _{r=1}∑^{r=n} ^{n}C_{r} (-1)^{n-r} r^{m}

b) _{r=1}∑^{r=n} ^{n}C_{r} (-1)^{n-r} r^{n}

c) _{r=1}∑^{r=n} ^{n}C_{r} (-1)^{m-r} r^{n}

d) None of the mentioned

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^{m}in m!(e

^{x}– 1)n.

9. A function is defined by mapping f:A->B such that A contains m elements and B contains n elements and m > n then number of bijections are :

a) ^{n}C_{m} x m!

b) ^{n}C_{m} x n!

c) 0

d) none of the mentioned

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10. State True or False.

A bijection is a function which is many-one and onto.

a) True

b) False