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## 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

Answer: a [Reason:] 5, it is number of elements in the sets.

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

Answer: a [Reason:] Two equal sets should have same number of elements.

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

Answer: b [Reason:] B contains all the elements of A, as well as other elements.

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

Answer: c [Reason:] If there is bijection then two sets A and B will be equinumerous and thus will have same cardinality.

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

Answer: c [Reason:] There is bijection then two sets E and O and they will be equinumerous and thus will have same cardinality.

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

Answer: a [Reason:] From a, b, c…z there will be 26 elements.

7. Cardinality of the set of even prime number under 10 is 4.
a) True
b) False

Answer: b [Reason:] Since 2 is only even prime thus cardinality should be 1.

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

Answer: b [Reason:] If there doesnot exist a bijective function from A to B that means there are some elements in B whose preimage is not in A, thus cardinality of B is strictly greater than A.

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

Answer: c [Reason:] Thus if cardinality of (A U B) = cardinality of A+ cardinality of B ,it means they don’t have any element in common, n(A∩B) = 0.

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

Answer: a [Reason:] A U B U C = C, since a, b are subsets to C.

## 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

Answer: a [Reason:] The difference in any term with previous term is same.

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

Answer: d [Reason:] nth 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.

Answer: a [Reason:] nth term = a + (n – 1)d, nth 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.

Answer: c [Reason:] Let nth 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.

Answer: a [Reason:] Let nth 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. Nth 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

Answer: b [Reason:] 1, 1, 1, 1, 1…….. is AP, GP and HP series.

7. In the given Airthmetic progression, ’25’ would be a term in it.
5, 8, 11, 14, 17, 20………50.
a) True
b) False

Answer: b [Reason:] nth 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) an = 2n2 + 3n
b) an = 2n2 + 3
c) an = 3n2 + 3n
d) an = 5 + 3n

Answer: d [Reason:] an = 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

Answer: c [Reason:] The term b should be the airthmetic mean of of term a and c.

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

Answer: a [Reason:] Let a1, b1, c1 be three terms ,then a1 + b1 + c1 = 180, a1 + c1 = 2b1(A M property), 3b1 = 180, b1=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

Answer: c [Reason:] Binary numbers are formed with combination of 0 & 1 only.

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

Answer: c [Reason:] Octal numbers are formed with combination of 0 to 7 only.

3. Hexadecimal number equivalent of decimal 10 is:
a) 10
b) A
c) F
d) None of the mentioned.

Answer: b [Reason:] In hexadecimal representation A is represented as decimal 10.

4. Decimal equivalent of binary number 1010 is:
a) 11
b) A
c) 10
d) None of the mentioned.

Answer: c [Reason:] 0X1 + 1X2 + 0X4 + 1X8 = 10 in decimal.

5. Decimal 13 in base 8 can be represented as :
a) 15
b) 12
c) 22
d) None of the mentioned

Answer: a [Reason:] 1X8 + 5X1 = 12, 15 is the octal representaion of 13.

6. State whether the given statement is true or false
F in hexadecimal representaion is equivalent to 9 in decimal.
a) True
b) False

Answer: b [Reason:] F in hexadecimal representaion is equivalent to 15 in decimal.

7. Octal number may contains digits from 1 to 8.
a) True
b) False

Answer: b [Reason:] Octal number contain digits from 0 to 7, * is not allowed.

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

Answer: b [Reason:] A base r number may contain digits from 0 to r-1.

9. The binary number 100110 in octal is reprsented by
a) 45
b) 10012
c) 46
d) 58

Answer: c [Reason:] Pairing 3 numbers from right hand side we get 110 as 6 and 100 as 4 in octal so number is 46.

10. A number greater than 32 would require minimum of how may bits in binary representation:
a) 5
b) 6
c) 4
d) 10

Answer: b [Reason:] Since through 5 bits we can only represent numbers till 31 , since 25 = 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

Answer: b [Reason:] Defination of HCF(a, b)-greatest integer divisor of both a and b.

2. The HCF of two number 1, b(integer) are
a) b + 2
b) 1
c) b
d) None of the mentioned

Answer: b [Reason:] Since 1 is the greatest integer divisor of both 1 and b.

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

Answer: b [Reason:] Hcf of number is either equal to smallest number or is least among all.

4. HCF of 6, 10 is:
a) 60
b) 30
c) 10
d) 2

Answer: d [Reason:] Since 2 is the greatest integer divisor of both 6 and 10.

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

Answer: b [Reason:] The hcf of two number a and b is given by (hcf(a, b)) = ab/ lcm(a, b).

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

Answer: b [Reason:] The lcm of two number a and b is given by lcm(a,b) = ab/(GCD(a, b)), this implies ab = lcm(a, b) * gcd(a, b).

7. If a number is 22 x 31 x 50 and b is 22 x 31 x 51 then hcf of a, b is:
a) 22 x 31 x 51
b) 22 x 32 x 52
c) 21 x 31 x 50
d) 22 x 32 x 50

Answer: c [Reason:] Hcf is the product of sets having least exponent value among a and b.

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

Answer: a [Reason:] HCF function can be reursively defined.

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

Answer: a [Reason:] ab = lcm(a, b)*hcf(a, b), which implies HCF(a,b) = ab/(LCM(a, b)).

10. The HCF of two prime numbers a and b is:
a) ab
b) ab
c) a + b
d) 1

Answer: d [Reason:] Since they doesnot have any factor in common other than 1.

## 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

Answer: b [Reason:] One-One functions are also known as injection.

2. A mapping f : X -> Y is one one if :
a) f(x1) ≠ f(x2) for all x1, x2 in X.
b) If f(x1) = f(x2) then x1 = x2 for all x1, x2 in X.
c) f(x1) = f(x2) for all x1, x2 in X.
d) None of the mentioned

Answer: b [Reason:] In one one function every element in A should have unique image in B,thus if two image are equal this means there preimages are same.

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) nCm x m!
b) nCm x n!
c) 0
d) none of the mentioned

Answer: a [Reason:] From n elements in B we need to select m elements and then arrange them in all ways, thus answer=nCm 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) nCm x m!
b) nCm x n!
c) 0
d) none of the mentioned

Answer: c [Reason:] Since for function to be defined every element should have a image , since m > n atleast one element need to have same image, thus we can’t form any unique images and hence the number of one one function are zero.

5. State whether the given statement is true or false
For an onto function range is equivalent to codomain.
a) True
b) False

Answer: a [Reason:] Since in onto function every image should have preimage thus all the elements in codomain should have preimages.

6. State whether the given statement is true or false
Onto function are known as injection.
a) True
b) False

Answer: b [Reason:] Onto functions are known as surjection.

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

Answer: b [Reason:]Injections will be 4C3 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=1r=n nCr (-1)n-r rm
b) r=1r=n nCr (-1)n-r rn
c) r=1r=n nCr (-1)m-r rn
d) None of the mentioned

Answer: a [Reason:] The number of onto function is equal tpo the coffecient of xm in m!(ex – 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) nCm x m!
b) nCm x n!
c) 0
d) none of the mentioned