MCQOPTIONS
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MCQOPTIONS
This section includes 110 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. |
Let I₃ be the Identity matrix of order 3 then (I₃)⁻¹ is equal to _________ |
| A. | 0 |
| B. | 3I₃ |
| C. | I₃ |
| D. | None of the mentioned |
| Answer» D. None of the mentioned | |
| 2. |
If A is an invertible square matrix then _________ |
| A. | (Aᵀ)⁻¹ = (A⁻¹)ᵀ |
| B. | (Aᵀ)ᵀ = (A⁻¹)ᵀ |
| C. | (Aᵀ)⁻¹ = (A⁻¹)⁻¹ |
| D. | None of the mentioned |
| Answer» B. (Aᵀ)ᵀ = (A⁻¹)ᵀ | |
| 3. |
If A is non singular matrix then AB = AC implies B = C. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» B. False | |
| 4. |
If for a square matrix A(non-singular) and B, null matrix O, AB = O then? |
| A. | B is a null matrix |
| B. | B is a non singular matrix |
| C. | B is a identity matrix |
| D. | All of the mentioned |
| Answer» B. B is a non singular matrix | |
| 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 |
| Answer» B. {n(n-1)/2}² | |
| 6. |
If for a square matrix A and B,null matrix O, (AB)ᵀ = O implies Aᵀ = O and Bᵀ = O. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» C. May be True or False | |
| 7. |
If A is a lower triangular matrix then Aᵀ is a _________ |
| A. | Lower triangular matrix |
| B. | Upper triangular matrix |
| C. | Null matrix |
| D. | None of the mentioned |
| Answer» C. Null matrix | |
| 8. |
If matrix A, B and C are invertible matrix of same order then (ABC)⁻¹ = _________ |
| A. | CBA |
| B. | C⁻¹ B⁻¹ A⁻¹ |
| C. | Cᵀ B⁻¹ Aᵀ |
| D. | None of the mentioned |
| Answer» C. Cᵀ B⁻¹ Aᵀ | |
| 9. |
If for a square matrix A, A² = A then such a matrix is known as _________ |
| A. | Idempotent matrix |
| B. | Orthagonal matrix |
| C. | Null matrix |
| D. | None of the mentioned |
| Answer» B. Orthagonal matrix | |
| 10. |
A square matrix A = [aᵢⱼ ]ₙₓₙ, if aᵢⱼ = 0 for i > j then that matrix is known as _______ |
| A. | Upper triangular matrix |
| B. | Lower triangular matrix |
| C. | Unit matrix |
| D. | Null matrix |
| Answer» B. Lower triangular matrix | |
| 11. |
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. | n²(n+1)(2n+1)/6 |
| D. | None of the mentioned |
| Answer» B. n(n-1)/2(2n+1) | |
| 12. |
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 |
| Answer» C. 1, 6, 12, 18, 24….. | |
| 13. |
Let A = [aᵢⱼ] given by abᵢⱼ = (i-j)³ is a _________ |
| A. | Symmetric matrix |
| B. | Anti-Symmetric matrix |
| C. | Identity matrix |
| D. | None of the mentioned |
| Answer» C. Identity matrix | |
| 14. |
The Inverse exist only for non-singular matrices. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» B. False | |
| 15. |
The series 1, 1, 1, 1, 1…….. is not an AGP. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» C. May be True or False | |
| 16. |
If for a square matrix A and B,null matrix O, AB = O implies A=O and B=O. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» C. May be True or False | |
| 17. |
The series a,(a+b)/2, b is in _______ |
| A. | AP |
| B. | GP |
| C. | HP |
| D. | None of the mentioned |
| Answer» B. GP | |
| 18. |
If a₁, a₂, a₃ are in airthemetic as well as geometric progression then which of the following is/are correct? |
| A. | 2a₂ = a₁ + a₃ |
| B. | a₂ = (a₁a₃)½ |
| C. | a₂ – a₁ = a₃ -a₂ |
| D. | All of the mentioned are correct |
| Answer» E. | |
| 19. |
Let A₁, A₂, be two AM’s and G₁, G₂ be two GM’s between a and b,then (A₁ + A₂) / G₁G₂ is equal to _______ |
| A. | (a+b) / 2ab |
| B. | 2ab/(a+b) |
| C. | (a+b)/(ab) |
| D. | None of the mentioned |
| Answer» D. None of the mentioned | |
| 20. |
A square matrix A = [aᵢⱼ ]ₙₓₙ, if aᵢⱼ = 0 for i < j then that matrix is known as _______ |
| A. | Upper triangular matrix |
| B. | Lower triangular matrix |
| C. | Unit matrix |
| D. | Null matrix |
| Answer» C. Unit matrix | |
| 21. |
Let A = [0 1 0 0 ], A⁻¹ is equal to _________ |
| A. | Null matrix |
| B. | Identity matrix |
| C. | Does not exist |
| D. | None of the mentioned |
| Answer» D. None of the mentioned | |
| 22. |
If a₁, a₂, a₃…….. are in AP then if a₇ = 15, then the value of common difference that would make a₂ a₇ a₁₂ greatest is? |
| A. | 2 |
| B. | 0 |
| C. | 4 |
| D. | 9 |
| Answer» C. 4 | |
| 23. |
For a skew symmetric odd ordered matrix A of integers, which of the following will hold true? |
| A. | det(A) = 9 |
| B. | det(A) = 81 |
| C. | det(A) = 0 |
| D. | det(A) = 4 |
| Answer» D. det(A) = 4 | |
| 24. |
If one geometric mean G and two airthmetic mean A₁, A₂ are inserted between two numbers, then (2A₁ – A₂) (2A₂ – A₁) is equal to _______ |
| A. | 2G |
| B. | G |
| C. | G² |
| D. | None of the mentioned |
| Answer» D. None of the mentioned | |
| 25. |
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» D. None of the mentioned | |
| 26. |
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 than that 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» D. None of the mentioned | |
| 27. |
If for sets A and B there exists an injective function but not bijective function from A to B then? |
| A. | Cardinality of A is strictly 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» C. Cardinality of B is equal to A | |
| 28. |
For a non-singular matrix A, A⁻¹ is equal to _________ |
| A. | (adj(A))/det(A) |
| B. | det(A)*(adj(A)) |
| C. | det(A)*A |
| D. | none of the mentioned |
| Answer» B. det(A)*(adj(A)) | |
| 29. |
If matrix A and B are symmetric and AB = BA iff _________ |
| A. | AB is symmetric matrix |
| B. | AB is an anti-symmetric matrix |
| C. | AB is a null matrix |
| D. | None of the mentioned |
| Answer» B. AB is an anti-symmetric matrix | |
| 30. |
A symmetric matrix is a one in which? |
| A. | All diagonal elements are zero |
| B. | All diagonal elements are 1 |
| C. | A = Aᵀ |
| D. | A = -Aᵀ |
| Answer» D. A = -Aᵀ | |
| 31. |
For a matrix A of order n, the det(adj(A)) = (det(A))ⁿ, where adj() is adjoint of matrix. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» C. May be True or False | |
| 32. |
For matrix A, (A₃) = I, A⁻¹ is equals to _________ |
| A. | A² |
| B. | A⁻² |
| C. | Can’t say |
| D. | None of the mentioned |
| Answer» B. A⁻² | |
| 33. |
The ninth term of 1⁄3, 1⁄7, 1⁄11, 1⁄15, 1⁄19,……… is given by? |
| A. | 1⁄35 |
| B. | 1⁄36 |
| C. | 1⁄39 |
| D. | None of the mentioned |
| Answer» B. 1⁄36 | |
| 34. |
If a, b, c are in hp then a⁻¹, b⁻¹, c⁻¹ are in _________ |
| A. | GP |
| B. | HP |
| C. | AP |
| D. | None of the mentioned |
| Answer» D. None of the mentioned | |
| 35. |
For number A, C if H is harmonic mean, G is geometric mean then H>=G. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» C. May be True or False | |
| 36. |
If a matrix A = [A₁₁ A₁₂ ⋯ A₁ₙ A₂₁ A₂ₙ ⋮ ⋮ Aₙ₁ Aₙ₂ ⋯ Aₙₙ], order(nxn) Aᵢᵢ = 1, Aᵢⱼ = 0 for i ≠ j. Then that matrix is known as ________ |
| A. | Identity matrix |
| B. | Null matrix |
| C. | Singular matrix |
| D. | None of the mentioned |
| Answer» B. Null matrix | |
| 37. |
If A is a subset of B and B is a subset of C, then cardinality 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» B. Cardinality of B | |
| 38. |
If between two numbers which are root of given equation. x² – 18x + 16 = 0, a GM is inserted then the value of that GM is? |
| A. | 4 |
| B. | 5 |
| C. | 6 |
| D. | 16 |
| Answer» B. 5 | |
| 39. |
If a, b, c are in hp, then b is related with a and c as _________ |
| A. | 2(1⁄b) = (1⁄a + 1⁄c) |
| B. | 2(1⁄c) = (1⁄b + 1⁄c) |
| C. | 2(1⁄a) = (1⁄a + 1⁄b) |
| D. | None of the mentioned |
| Answer» B. 2(1⁄c) = (1⁄b + 1⁄c) | |
| 40. |
For a matrix A, B and identity matrix I, if a matrix AB=I=BA then? |
| A. | B is inverse of A |
| B. | A is inverse of B |
| C. | A⁻¹ = B, B⁻¹ = A |
| D. | All of the mentioned |
| Answer» E. | |
| 41. |
Which of the following property of matrix multiplication is correct? |
| A. | Multiplication is not commutative in general |
| B. | Multiplication is associative |
| C. | Multiplication is distributive over addition |
| D. | All of the mentioned |
| Answer» E. | |
| 42. |
For matrix A if AAᵀ = I, I is identity matrix then A is? |
| A. | Orthagonal matrix |
| B. | Nilpotent matrix |
| C. | Idempotent matrix |
| D. | None of the mentioned |
| Answer» B. Nilpotent matrix | |
| 43. |
For matrix A and a scalar k, (kA)ᵀ is equal to _________ |
| A. | k(A) |
| B. | k(A)ᵀ |
| C. | k²(A) |
| D. | k²(A)ᵀ |
| Answer» C. k²(A) | |
| 44. |
For matrix A, (Aᵀ)ᵀ is equals to ___________ |
| A. | A |
| B. | Aᵀ |
| C. | Can’t say |
| D. | None of the mentioned |
| Answer» B. Aᵀ | |
| 45. |
Let A order(axb) and B order(cxd) be two matrices, then for AB to exist, correct relation is given by? |
| A. | a = d |
| B. | b = c |
| C. | a = b |
| D. | c = d |
| Answer» C. a = b | |
| 46. |
If in an AGP the common ratio of GP is 1 then that sequence becomes an AP sequence. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» B. False | |
| 47. |
For two number a,b HM between them is given by? |
| A. | (2b+2a )/3b |
| B. | 2ab/(a+b) |
| C. | (a+b)/2ab |
| D. | 2b/(a+b) |
| Answer» C. (a+b)/2ab | |
| 48. |
If A is a subset of B then _______ |
| A. | The cardinality of A is greater than B |
| B. | The cardinality of B is greater than A |
| C. | Can’t say |
| D. | None of the mentioned |
| Answer» C. Can’t say | |
| 49. |
For matrix A, B if A – B = O, where O is a null matrix then? |
| A. | A = O |
| B. | B = O |
| C. | A = B |
| D. | None of the mentioned |
| Answer» D. None of the mentioned | |
| 50. |
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 |
| Answer» D. number of rows of first matrix should be equal to number of column of second | |