## Discrete Mathematics MCQ Set 1

1. Which of the following bits is the negation of the bits “010110”?

a) 111001

b) 001001

c) 101001

d) 111111

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2. Which of the following option is suitable, if A is “10110110”, B is”11100000”and C is”10100000”?

a) C=A or B

b) C=~A

c) C=~B

d) C=A and B

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3. How many bits string of length 4 are possible such that they contains 2 ones and 2 zeroes?

a) 4

b) 2

c) 5

d) 6

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4. If a bit string contains {0, 1} only, having length 5 has no more than 2 ones in it. Then how many such bit strings are possible?

a) 14

b) 12

c) 15

d) 16

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5. If A is “001100” and B is “010101” then A (Ex-or) B is

a) 000000

b) 111111

c) 001101

d) 011001

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6. The Ex-nor of this string “01010101”with “11111111” is

a) 10101010

b) 00110100

c) 01010101

d) 10101001

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7. The one’s complement of this string “01010100” is

a) 10101010

b) 00110101

c) 10101011

d) 10101001

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8. The 2’s complement of this string “01010100” is

a) 10101010

b) 00110100

c) 10101100

d) 10101001

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9. If in a bits string of {0,1} ,of length 4,such that no two ones are together. Then total number of such possible strings are?

a) 1

b) 5

c) 7

d) 4

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10. Let A : “010101” ,B=? ,If { A (Ex-or) B } is a resultant string of all ones then which of the following statement regarding B is correct

a) B is negation of A

b) B is 101010

c) {A (and) B} is a resultant string having all zeroes

d) All of the mentioned

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## Discrete Mathematics MCQ Set 2

1. If there are ‘M’ switches in series numbered from 1, 2, …, M. For circuit to be complete and bulb to glow which of the following is necessary

a) 1∧ 2∧ 3 ∧ … ∧M should be on

b) 1∧ 2∧ 3 ∧ … ∧M should be off

c) 1 v 2 v 3 v … v M should be on

d) None of the mentioned

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2. If there are ‘M’ switches in parallel numbered from 1, 2, …, M. For circuit to be complete and bulb to glow which of the following is necessary

a) 1∧ 2∧ 3 ∧ … ∧M should be on

b) 1∧ 2∧ 3 ∧ … ∧M should be off

c) 1 v 2 v 3 v … v M should be on

d) None of the mentioned

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3. In the circuit shown the lamp will be glowing if

a) P: True ,Q: False

b) P: True, Q: True

c) P: False, Q: False

d) None of the mentioned

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4. In this circuit shown the lamp will be glowing if

a) P: True ,Q: True, R: False

b) P: True, Q: True, R: True

c) P: False, Q: False, R: True

d) None of the mentioned

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5. Which statement should be true in order for lamp to glow ?

a) (R ∧ (~(P ∧ Q))

b) P∧R∧Q

c) P ∧ (Q ∧ ~R)

d) None of the mentioned

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6. If it is given that switch R is closed and Q is closed then lamp will glow if

a) P: Open , S: Closed

b) P: Open , S: Open

c) P: Closed , S: Closed

d) None of the mentioned

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7. The circuit depend on which switch/switches state to be complete?

a) P

b) Q

c) Both P and Q

d) None of the mentioned

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8. The ten switches A,B,C,D,E,F,G,H,N,M are placed in the given circuit (all are open at given time).If you close one switch you need to pay 1 unit cost?

What is the cost you need to pay to glow this Lamp?

a) 1 units

b) 2 units

c) 3 units

d) 4 units

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9. If in a for it to be complete it is necessary for switch A to be closed and either of switch B or C to be closed, then which can be true?

a) Switch A should in parallel with B and C is series to them

b) Switch A should be in series with parallel circuit of B and C

c) All of the mentioned

d) None of the mentioned

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10. The given circuit can work if the switches P and Q be

a) P: True ,Q: False

b) P: True, Q: True

c) P: False, Q: False

d) None of the mentioned

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## Discrete Mathematics MCQ Set 3

1. The compound propositions p and q are called logically equivalent if ________ is a tautology.

a) p ↔ q

b) p → q

c) ¬ (p ∨ q)

d) ¬p ∨ ¬q

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2. p → q is logically equivalent to:

a) ¬p ∨ ¬q

b) p ∨ ¬q

c) ¬p ∨ q

d) ¬p ∧ q

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3. p ∨ q is logically equivalent to:

a) ¬q → ¬p

b) q → p

c) ¬p → ¬q

d) ¬p → q

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4. ¬ (p ↔ q) is logically equivalent to:

a) q↔p

b) p↔¬q

c) ¬p↔¬q

d) ¬q↔¬p

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5. p ∧ q is logically equivalent to:

a) ¬ (p → ¬q)

b) (p → ¬q)

c) (¬p → ¬q)

d) (¬p → q)

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6. Which of the following statement is correct?

a) p ∨ q ≡ q ∨ p

b) ¬(p ∧ q) ≡ ¬p ∨ ¬q

c) (p ∨ q) ∨ r ≡ p ∨ (q ∨ r)

d) All of mentioned

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7. p ↔ q is logically equivalent to:

a) (p → q) → (q → p)

b) (p → q) ∨ (q → p)

c) (p → q) ∧ (q → p)

d) (p ∧ q) → (q ∧ p)

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8. (p → q) ∧ (p → r) is logically equivalent to:

a) p → (q ∧ r)

b) p → (q ∨ r)

c) p ∧ (q ∨ r)

d) p ∨ (q ∧ r)

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9. (p → r) ∨ (q → r) is logically equivalent to:

a) (p ∧ q) ∨ r

b) (p ∨ q) → r

c) (p ∧ q) → r

d) (p → q) → r

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10. ¬ (p ↔ q) is logically equivalent to:

a) p ↔ ¬q

b) ¬p ↔ q

c) ¬p ↔ ¬q

d) ¬q ↔ ¬p

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## Discrete Mathematics MCQ Set 4

1. If a matrix A = [A_{11} A_{12} ⋯ A_{1n} A_{21} A_{2n} ⋮ ⋮ A_{n1} A_{n2} ⋯ A_{nn} ], order(nxn) A_{ii} = 1, A_{ij} = 0 for i ≠ j. Then that matrix is know as

a) Identity matrix

b) Null matrix

c) Singular matrix

d) None of the mentioned

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2. A symmetric matrix is a one in which

a) All diagonal elements are zero

b) All diagonal elements are 1

c) A = A^{T}

d) A = -A^{T}

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3. An anti-symmetric matrix is a one in which

a) All diagonal elements are zero

b) All diagonal elements are 1

c) A = A^{T}

d) A = -A^{T}

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4. A matrix having one row and many columns is known as?

a) Row matrix

b) Column matrix

c) Diagonal matrix

4) None of the mentioned

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5. A matrix having many rows and one column is known as?

a) Row matrix

b) Column matrix

c) Diagonal matrix

4) None of the mentioned

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6. The trace of the matrix is defined as:

a) Sum of all the elements of the matrix

b) Sum of all the elements of leading diagonal of matrix

c) Sum of all non-zero elements of matrix

d) None of the mentioned

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7. A square matrix A = [a_{ij} ]_{nxn}, if a_{ij} = 0 for i > j then that matrix is known as:

a) Upper triangular matrix

b) Lower triangular matrix

c) Unit matrix

d) Null matrix

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_{ij}]

_{nxn}, if a

_{ij}= 0 for i > j.

8. A square matrix A = [a_{ij} ]_{nxn}, if a_{ij} = 0 for i < j then that matrix is known as:

a) Upper triangular matrix

b) Lower triangular matrix

c) Unit matrix

d) Null matrix

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_{ij}]

_{nxn}, if a

_{ij}= 0 for i < j.

9. Two matrix can be added if:

a) rows of both the matrices are same

b) columns of both the matrices are same

c) both rows and columns of both the matrices are same

d) number of rows of first matrix should be equal to number of column of second

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10. For matrix A if AA^{T} = I, I is identity matrix then A is :

a) Orthagonal matrix

b) Nilpotent matrix

c) Idempotent matrix

d) None of the mentioned

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^{T}= I = A

^{T}A.

## Discrete Mathematics MCQ Set 5

1. Domain of a function is :

a) the maximal set of numbers for which a function is defined

b) the maximal set of numbers which a function can take values

c) it is set of natural numbers for which a function is defined

d) none of the mentioned

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2. What is domain of function f(x)= x^{1/2} ?

a) (2, ∞)

b) (-∞, 1)

c) [0, ∞)

d) None of the mentioned

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3. Range of a function is :

a) the maximal set of numbers for which a function is defined

b) the maximal set of numbers which a function can take values

c) it is set of natural numbers for which a function is defined

d) none of the mentioned

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4. What is domain of function f(x) = x^{-1} for it to be defined everywhere on domain?

a) (2, ∞)

b) (-∞, ∞) – {0}

c) [0, ∞)

d) None of the mentioned

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^{-1}is not defined for x=0,otherwise it defined for every real number.

5. State whether the given statement is true or false

The range of function f(x) = sin(x) is (-∞, ∞).

a) True

b) False

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6. State whether the given statement is true or false

Codomain is the subset of range.

a) True

b) False

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7. What is range of function f(x) = x^{-1} which is defined everywhere on its domain?

a) (-∞, ∞)

b) (-∞, ∞) – {0}

c) [0, ∞)

d) None of the mentioned

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^{-1}may take any real number hence it’s range is all real numbers.

8. If f(x) = 2^{x} then range of the function is :

a) (-∞, ∞)

b) (-∞, ∞) – {0}

c) (0, ∞)

d) None of the mentioned

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9. If f(x) = x^{2} + 4 then range of f(x) is given by

a) [4, ∞)

b) (-∞, ∞) – {0}

c) (0, ∞)

d) None of the mentioned

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^{2}is 0,thus x

^{2}+4 may take any value between [4,∞).

10. State True or False.

Let f(x)=sin^{2}(x) + log(x) then domain of f(x) is (-∞, ∞).

a) True

b) False