MCQOPTIONS
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MCQOPTIONS
This section includes 70 Mcqs, each offering curated multiple-choice questions to sharpen your Discrete Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
A _________ is a Boolean variable. |
| A. | Literal |
| B. | String |
| C. | Keyword |
| D. | Identifier |
| Answer» B. String | |
| 2. |
Simplify the expression using K-maps: F(A,B,C,D)=Σ (1,3,5,6,7,11,13,14). |
| A. | AB+BC’D+A’B’C |
| B. | BCD’+A’C’D+BD’ |
| C. | A’D+BCD+A’BC+AB’C’ |
| D. | AC’D’+BC+A’BD+C’D’ |
| Answer» D. AC’D’+BC+A’BD+C’D’ | |
| 3. |
Inversion of single bit input to a single bit output using _________ |
| A. | NOT gate |
| B. | NOR gate |
| C. | AND gate |
| D. | NAND gate |
| Answer» B. NOR gate | |
| 4. |
How many minimal forms are there in the function F(A, B, C) = ∑(1, 3, 2, 5, 6, 7) if it is having cyclic prime implicants k-map? |
| A. | 216 |
| B. | 2 |
| C. | 14 |
| D. | 82 |
| Answer» C. 14 | |
| 5. |
What is the maximum number of prime implicants with 34-variable minimized expression? |
| A. | 34 |
| B. | 764 |
| C. | 2³³ |
| D. | 2³¹ |
| Answer» D. 2³¹ | |
| 6. |
How many cells are there for an 8-variable K-Map? |
| A. | 421 |
| B. | 1048 |
| C. | 256 |
| D. | 375 |
| Answer» D. 375 | |
| 7. |
Simplify the expression: XY’ + X’ + Y’X’. |
| A. | X’ + Y |
| B. | XY’ |
| C. | (XY)’ |
| D. | Y’ + X |
| Answer» D. Y’ + X | |
| 8. |
a ⊕ b = ________ |
| A. | (a+b)(a`+b`) |
| B. | (a+b`) |
| C. | b` |
| D. | a` + b` |
| Answer» B. (a+b`) | |
| 9. |
In Boolean algebra, the data is a bit-representation of information consists of _________ |
| A. | 0 and 1 |
| B. | 2 and 5 |
| C. | 1 and 15 |
| D. | 4 and 8 |
| Answer» B. 2 and 5 | |
| 10. |
Use Karnaugh map to find the simplified expression of the function: F = x’yz + xy + xy’z’. |
| A. | xz’+y’z’ |
| B. | xy’z+xy |
| C. | y’z+x’y+z |
| D. | yz+xy+xy’z |
| Answer» E. | |
| 11. |
Minimize the following Boolean expression using Boolean identities. |
| A. | A + B + C’ |
| B. | AC’ + B |
| C. | B + AC |
| D. | A(B’ + C) |
| Answer» E. | |
| 12. |
Addition of two or more bits produces how many bits to construct a logic gate? |
| A. | 108 |
| B. | 2 |
| C. | 32 |
| D. | 64 |
| Answer» C. 32 | |
| 13. |
In OR gate for 13 numbers of inputs what are the stages possible for it? |
| A. | 1239 |
| B. | 213 |
| C. | 13 |
| D. | 1387 |
| Answer» C. 13 | |
| 14. |
(X+Y`)(X+Z) can be represented by _____ |
| A. | (X+Y`Z) |
| B. | (Y+X`) |
| C. | XY` |
| D. | (X+Z`) |
| Answer» B. (Y+X`) | |
| 15. |
For an 18-variable k-map determine the number of prime implicants? |
| A. | 2¹⁸ |
| B. | 35 |
| C. | 253 |
| D. | 721 |
| Answer» B. 35 | |
| 16. |
How many false essential prime implicants for the given Boolean functions f(A, B, C) = ∑m(2, 5, 6)? |
| A. | 1024 |
| B. | 2 |
| C. | 16 |
| D. | 435 |
| Answer» C. 16 | |
| 17. |
Evaluate the expression: (X + Z)(X + XZ’) + XY + Y. |
| A. | XY+Z’ |
| B. | Y+XZ’+Y’Z |
| C. | X’Z+Y |
| D. | X+Y |
| Answer» E. | |
| 18. |
In Gray coding, the adjacent code values differ by _______ |
| A. | single bit |
| B. | 3 bits |
| C. | 10 bits |
| D. | 0 bit |
| Answer» B. 3 bits | |
| 19. |
Who has invented K-map? |
| A. | Maurice Karnaugh |
| B. | Edward Veitch |
| C. | George Boole |
| D. | Adam Smith |
| Answer» B. Edward Veitch | |
| 20. |
What is the simplification value of MN(M + N’) + M(N + N’)? |
| A. | M |
| B. | MN+M’N’ |
| C. | (1+M) |
| D. | M+N’ |
| Answer» C. (1+M) | |
| 21. |
In Multiplexer gate, for selecting the inputs, two bits named _____ and _____ are required generally. |
| A. | selector bit, data bit |
| B. | parity bit. Generator bit |
| C. | input bit, inverted bit |
| D. | raising bit, sinking bit |
| Answer» B. parity bit. Generator bit | |
| 22. |
In which logic gate the output state is usually the complement of the input state? |
| A. | NOT gate |
| B. | NOR gate |
| C. | X-NOR gate |
| D. | OR gate |
| Answer» B. NOR gate | |
| 23. |
If an expression is given that x+x’y’z=x+y’z, find the minimal expression of the function F(x,y,z) = x+x’y’z+yz? |
| A. | y’ + z |
| B. | xz + y’ |
| C. | x + z |
| D. | x’ + y |
| Answer» D. x’ + y | |
| 24. |
Determine the number of essential prime implicants of the function f(a, b, c, d) = Σm(1, 3, 4, 8, 10, 13) + d(2, 5, 7, 12), where m denote the minterm and d denotes the don’t care condition. |
| A. | 2³ |
| B. | 3 |
| C. | 643 |
| D. | 128 |
| Answer» C. 643 | |
| 25. |
How many NAND gates are required to make an XOR gate? |
| A. | 7 |
| B. | 12 |
| C. | 4 |
| D. | 8 |
| Answer» D. 8 | |
| 26. |
K-map is used for _______ |
| A. | logic minimization |
| B. | expression maximization |
| C. | summing of parity bits |
| D. | logic gate creation |
| Answer» B. expression maximization | |
| 27. |
The set for which the Boolean function is functionally complete is __________ |
| A. | {*, %, /} |
| B. | {., +, -} |
| C. | {^, +, -} |
| D. | {%, +, *} |
| Answer» C. {^, +, -} | |
| 28. |
In order to make a luggage security alarm, a single _____ is used. |
| A. | NOR gate |
| B. | NAND gate |
| C. | X-NOR gate |
| D. | XOR gate |
| Answer» C. X-NOR gate | |
| 29. |
How many essential prime implicants are there in the K-Map of the function F = Σ(0, 1, 2, 4, 7, 11, 12, 13, 15)? |
| A. | 4 |
| B. | 1 |
| C. | 3 |
| D. | 7 |
| Answer» C. 3 | |
| 30. |
_________ is used to implement the Boolean functions. |
| A. | Logical notations |
| B. | Arithmetic logics |
| C. | Logic gates |
| D. | Expressions |
| Answer» D. Expressions | |
| 31. |
Find the simplified expression A’BC’+AC’. |
| A. | B |
| B. | A+C |
| C. | (A+B)C’ |
| D. | B’C |
| Answer» D. B’C | |
| 32. |
Simplify the expression using K-maps: F(A,B,C) = Σ (1,3,5,6,7). |
| A. | AC’+B’ |
| B. | AB+C |
| C. | AB’+B’C’ |
| D. | A’BC+B’C+AC |
| Answer» C. AB’+B’C’ | |
| 33. |
A NOR gate can be derived from ______ |
| A. | NAND gate |
| B. | XOR gate |
| C. | AND gate |
| D. | OR gate |
| Answer» B. XOR gate | |
| 34. |
Find the simplified term Y’ (X’ + Y’) (X + X’Y)? |
| A. | XY’ |
| B. | X’Y |
| C. | X + Y |
| D. | X’Y’ |
| Answer» B. X’Y | |
| 35. |
Simplify the expression XZ’ + (Y + Y’Z) + XY. |
| A. | (1+XY’) |
| B. | YZ + XY’ + Z’ |
| C. | (X + Y +Z) |
| D. | XY’+ Z’ |
| Answer» D. XY’+ Z’ | |
| 36. |
There are _________ numbers of Boolean functions of degree n. |
| A. | n |
| B. | 2⁽²*ⁿ⁾ |
| C. | n³ |
| D. | n⁽ⁿ*²⁾ |
| Answer» C. n³ | |
| 37. |
Which of the following is built exclusively from NOR gate? |
| A. | Plant guard machine |
| B. | Apollo Guidance Computer |
| C. | Street market app |
| D. | Dish washer |
| Answer» C. Street market app | |
| 38. |
Which of the following algorithms transforms any NFA into its identical DFA? |
| A. | Minimal set construction |
| B. | Dynamic programming |
| C. | Powerset construction |
| D. | Huffman coding |
| Answer» C. Powerset construction | |
| 39. |
Optimisation of an FSM machine can be done by ________ |
| A. | Naive-bias algorithm |
| B. | Huffman encoding scheme |
| C. | Pirate-plot algorithm |
| D. | Hopcroft minimization algorithm |
| Answer» C. Pirate-plot algorithm | |
| 40. |
Which of the following techniques refer to the equivalence of DFA and N-DFA automata? |
| A. | subset construction |
| B. | superset construction |
| C. | powerset construction |
| D. | finite field construction |
| Answer» C. powerset construction | |
| 41. |
How many states are there in combinatorial FSM? |
| A. | 86 |
| B. | 2¹⁹ |
| C. | 1 |
| D. | 132 |
| Answer» D. 132 | |
| 42. |
Which of the following is not a member of the set of a deterministic finite state machine? |
| A. | state-transition function |
| B. | initial state |
| C. | input symbols |
| D. | stack |
| Answer» C. input symbols | |
| 43. |
In the operating system, newly started processes can have a start in the _________ |
| A. | Blocked state |
| B. | Running sate |
| C. | Ready state |
| D. | Exit state |
| Answer» D. Exit state | |
| 44. |
In lexical analysis of a compiler______ is used. |
| A. | DFA |
| B. | NDFA |
| C. | NFA |
| D. | Turing machine |
| Answer» B. NDFA | |
| 45. |
In system engineering which of the following methods bridges the gap between the two ends of system development? |
| A. | ASM method |
| B. | VSM method |
| C. | Factor method |
| D. | FSM method |
| Answer» B. VSM method | |
| 46. |
Which of the following gates is used to implement a logical conditional? |
| A. | OR gate |
| B. | Magnetic logic gate |
| C. | XOR gate |
| D. | IMPLY gate |
| Answer» E. | |
| 47. |
f(x, y, z) = xy’+yz’+xyz, what are essential prime implicants of this switching function? |
| A. | 8 |
| B. | 0 |
| C. | 4 |
| D. | 3 |
| Answer» C. 4 | |
| 48. |
Minimize the Boolean expression using Boolean identities: A′B+ABC′+BC’+AB′C′. |
| A. | B(AC)’ + AC’ |
| B. | AC’ + B’ |
| C. | ABC + B’ + C |
| D. | BC’ + A’B |
| Answer» B. AC’ + B’ | |
| 49. |
__________ is a disjunctive normal form. |
| A. | product-of-sums |
| B. | product-of-subtractions |
| C. | sum-of-products |
| D. | sum-of-subtractions |
| Answer» D. sum-of-subtractions | |
| 50. |
A deterministic automaton system can have ______ transition for a given state of an input symbol. |
| A. | exactly one |
| B. | more than one |
| C. | no transition |
| D. | 2n transition |
| Answer» B. more than one | |