MCQOPTIONS
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MCQOPTIONS
This section includes 111 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. |
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 | |
| 2. |
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 | |
| 3. |
For a non-singular matrix A, A-1 is equal to _________a) (adj(A))/det(A)b) det(A)*(adj(A))c) det( |
| 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)) | |
| 4. |
For a matrix A of order n, the det(adj(A)) = (det(A))n, where adj() is adjoint of matrix. |
| A. | True |
| B. | False |
| Answer» C. | |
| 5. |
If A is non singular matrix then AB = AC implies B = C. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 6. |
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 | |
| 7. |
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 | |
| 8. |
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 | |
| 9. |
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 | |
| 10. |
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. | |
| 11. |
If \({\rm{A}} = \left[ {\begin{array}{*{20}{c}} 0&1\\ 1&0 \end{array}} \right]\), then the value of A4 is |
| A. | \(\left[ {\begin{array}{*{20}{c}} 1&0\\ 0&1 \end{array}} \right]\) |
| B. | \(\left[ {\begin{array}{*{20}{c}} 1&1\\ 0&0 \end{array}} \right]\) |
| C. | \(\left[ {\begin{array}{*{20}{c}} 0&0\\ 1&1 \end{array}} \right]\) |
| D. | \(\left[ {\begin{array}{*{20}{c}} 0&1\\ 1&0 \end{array}} \right]\) |
| Answer» B. \(\left[ {\begin{array}{*{20}{c}} 1&1\\ 0&0 \end{array}} \right]\) | |
| 12. |
Consider the following in respect of the matrix \({\rm{A}} = \left( {\begin{array}{*{20}{c}} { - 1}&1\\ 1&{ - 1} \end{array}} \right):\)1. A2 = -A2. A3 = 4AWhich of the above is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» C. Both 1 and 2 | |
| 13. |
If \({\rm{A}} = \left[ {\begin{array}{*{20}{c}} 1&1&{ - 1}\\ 2&{ - 3}&4\\ 3&{ - 2}&3 \end{array}} \right]{\rm{\;and\;\;B}} = \left[ {\begin{array}{*{20}{c}} { - 1}&{ - 2}&{ - 1}\\ 6&{12}&6\\ 5&{10}&5 \end{array}} \right]\) then which of the following is/are correct?1. A and B commute.2. AB is a null matrix.Select the correct answer using the code given below: |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» C. Both 1 and 2 | |
| 14. |
Let \(\rm A = \left[ {\begin{array}{*{20}{c}} {\rm{a}}&{\rm{h}}&{\rm{g}}\\ {\rm{h}}&{\rm{b}}&{\rm{f}}\\ {\rm{g}}&{\rm{f}}&{\rm{c}} \end{array}} \right]\) and \({\rm{B}} = \left[ {\begin{array}{*{20}{c}} {\rm{x}}\\ {\rm{y}}\\ {\rm{z}} \end{array}} \right],\) then what is AB equal to? |
| A. | \(\left[ {\begin{array}{*{20}{c}} {{\rm{ax}} + {\rm{hy}} + {\rm{gz}}}\\ {\rm{y}}\\ {\rm{z}} \end{array}} \right]\) |
| B. | \(\left[ {\begin{array}{*{20}{c}} {{\rm{ax}} + {\rm{hy}} + {\rm{gz}}}\\ {{\rm{hx}} + {\rm{by}} + {\rm{fz}}}\\ {\rm{z}} \end{array}} \right]\) |
| C. | \(\left[ {\begin{array}{*{20}{c}} {{\rm{ax}} + {\rm{hy}} + {\rm{gz}}}\\ {{\rm{hx}} + {\rm{by}} + {\rm{fz}}}\\ {{\rm{gx}} + {\rm{fy}} + {\rm{cz}}} \end{array}} \right]\) |
| D. | \(\left[ {\begin{array}{*{20}{c}} {{\rm{ax}} + {\rm{hy}} + {\rm{gz}}}&{{\rm{hx}} + {\rm{by}} + {\rm{fz}}}&{{\rm{gx}} + {\rm{fy}} + {\rm{cz}}} \end{array}} \right]\) |
| Answer» D. \(\left[ {\begin{array}{*{20}{c}} {{\rm{ax}} + {\rm{hy}} + {\rm{gz}}}&{{\rm{hx}} + {\rm{by}} + {\rm{fz}}}&{{\rm{gx}} + {\rm{fy}} + {\rm{cz}}} \end{array}} \right]\) | |
| 15. |
If \(A = \left[ {\begin{array}{*{20}{c}} {4i - 6}&{10i}\\ {14i}&{6 + 4i} \end{array}} \right]\) and \(k = \frac{1}{{2i}}\), where \(i = \sqrt { - 1}\), then kA is equal to |
| A. | \(\left[ {\begin{array}{*{20}{c}} {2 + 3i}&5\\ 7&{2 - 3i} \end{array}} \right]\) |
| B. | \(\left[ {\begin{array}{*{20}{c}} {2 - 3i}&5\\ 7&{2 + 3i} \end{array}} \right]\) |
| C. | \(\left[ {\begin{array}{*{20}{c}} {2 - 3i}&7\\ 5&{2 + 3i} \end{array}} \right]\) |
| D. | \(\left[ {\begin{array}{*{20}{c}} {2 + 3i}&5\\ 7&{2 + 3i} \end{array}} \right]\) |
| Answer» B. \(\left[ {\begin{array}{*{20}{c}} {2 - 3i}&5\\ 7&{2 + 3i} \end{array}} \right]\) | |
| 16. |
If \(m = \left[ {\begin{array}{*{20}{c}} 1&0\\ 0&1 \end{array}} \right]\) and \(n = \left[ {\begin{array}{*{20}{c}} 0&1\\ { - 1}&0 \end{array}} \right]\), then what is the value of the determinant of m cos θ – n sin θ? |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 17. |
Let \(d \in R\), and \(A = \left[ {\begin{array}{*{20}{c}}{ - 2}&{4 + d}&{\left( {{\rm{sin}}\theta } \right) - 2}\\1&{\left( {{\rm{sin}}\theta } \right) + 2}&d\\5&{\left( {2{\rm{sin}}\theta } \right) - d}&{\left( { - {\rm{sin}}\theta } \right) + 2 + 2d}\end{array}} \right]\), θ ∈ [0, 2π]. If the minimum value of det (A) is 8, then a value of d is: |
| A. | -5 |
| B. | -7 |
| C. | 2(√2 + 1) |
| D. | 2(√2 + 2) |
| Answer» B. -7 | |
| 18. |
If \(\left[ {\begin{array}{*{20}{c}} 1&1\\ 0&1 \end{array}} \right]\cdot\left[ {\begin{array}{*{20}{c}} 1&2\\ 0&1 \end{array}} \right]\cdot\left[ {\begin{array}{*{20}{c}} 1&3\\ 0&1 \end{array}} \right] \ldots \ldots \ldots \left[ {\begin{array}{*{20}{c}} 1&{{\rm{n}} - 1}\\ 0&1 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1&{78}\\ 0&1 \end{array}} \right],\;\)then the inverse of \(\left[ {\begin{array}{*{20}{c}} 1&{\rm{n}}\\ 0&1 \end{array}} \right]\) is: |
| A. | \(\left[ {\begin{array}{*{20}{c}} 1&0\\ {12}&1 \end{array}} \right]\) |
| B. | \(\left[ {\begin{array}{*{20}{c}} 1&{ - 13}\\ 0&1 \end{array}} \right]\) |
| C. | \(\left[ {\begin{array}{*{20}{c}} 1&{ - 12}\\ 0&1 \end{array}} \right]\) |
| D. | \(\left[ {\begin{array}{*{20}{c}} 1&0\\ {13}&1 \end{array}} \right]\) |
| Answer» C. \(\left[ {\begin{array}{*{20}{c}} 1&{ - 12}\\ 0&1 \end{array}} \right]\) | |
| 19. |
\(A = \left[ {\begin{array}{*{20}{c}} 2&3\\ 1&2 \end{array}} \right]\), \(B = \left[ {\begin{array}{*{20}{c}} x&4\\ y&-2 \end{array}} \right]\), \(A B= \left[ {\begin{array}{*{20}{c}} 3&2\\ 1&0 \end{array}} \right]\)What is the value of x and y? |
| A. | 3, 1 |
| B. | -3, 1 |
| C. | 3, -1 |
| D. | -3, -1 |
| Answer» D. -3, -1 | |
| 20. |
A is a 3 × 4 real matrix and Ax = b is an inconsistent system of equations. The highest possible rank of A is |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 21. |
Let A be a non-singular diagonalisable matrix of order 3 with eignvalues λ1, λ2, λ3. A-1 is diagonalisable if: |
| A. | λ1 = 2,λ2 = 0, λ3 = -1 |
| B. | λ1 = 0, λ2 = 3, λ3 = -2 |
| C. | λ1 = -1, λ2 = 2,λ3 = -3 |
| D. | λ1 = -3, λ2 = 1, λ3 = 0 |
| Answer» D. λ1 = -3, λ2 = 1, λ3 = 0 | |
| 22. |
Consider the following in respect of matrices A, B and C of same order:1) (A + B + C)' = A' + B’ + C’2) (AB)’ = A’B’3) (ABC)’ = C’B’A’Where A’ is the transpose of the matrix A.Which of the above are correct? |
| A. | 1 and 2 only |
| B. | 2 and 3 only |
| C. | 1 and 3 only |
| D. | 1, 2, and e |
| Answer» D. 1, 2, and e | |
| 23. |
If \({\rm{A}} = \left| {\begin{array}{*{20}{c}}2&0&0\\0&2&0\\0&0&2\end{array}} \right|\) and \({\rm{B}} = \left| {\begin{array}{*{20}{c}}1&2&3\\0&1&3\\0&0&2\end{array}} \right|\). Then the determinant AB has the value |
| A. | 4 |
| B. | 8 |
| C. | 16 |
| D. | 32 |
| Answer» D. 32 | |
| 24. |
Find the value of x - y, if \(\begin{bmatrix} \rm 2 & \rm3x\\ 8 & \rm 2y \end{bmatrix} = \begin{bmatrix} 2 & 9\\8 & 4 \end{bmatrix}\) |
| A. | 3 |
| B. | 2 |
| C. | 1 |
| D. | 0 |
| Answer» D. 0 | |
| 25. |
If the system of linear equationsx + y + z = 5x + 2y + 2z = 6x + 3y + λz = μ(λ, μ ∈ R), has infinitely many solutions, then the value of λ + μ is: |
| A. | 12 |
| B. | 9 |
| C. | 7 |
| D. | 10 |
| Answer» E. | |
| 26. |
If a matrix A is Symmetric as well as Skew-Symmetric, then: |
| A. | A is a diagonal matrix |
| B. | A is a unit matirx |
| C. | A is a triangular matirx |
| D. | A is a null matrix |
| Answer» E. | |
| 27. |
Let \(\alpha {\rm{\;and\;}}\beta\) be the roots of the equationx2 + x +1 = 0. Then for y ≠ 0 in R,\(\left| {\begin{array}{*{20}{c}} {y + 1}&\alpha &\beta \\ \alpha &{y + \beta }&1\\ \beta &1&{y + \alpha } \end{array}} \right|\) is equal to: |
| A. | y(y2 – 1) |
| B. | y(y2 – 3) |
| C. | y3 |
| D. | y3 – 1 |
| Answer» D. y3 – 1 | |
| 28. |
If \({\rm{A}} = \left[ {\begin{array}{*{20}{c}} 1&0&{ - 2}\\ 2&{ - 3}&4 \end{array}} \right]\), then the matrix X for which 2X + 3A = 0 holds true is |
| A. | \(\left[ {\begin{array}{*{20}{c}} { - \frac{3}{2}}&0&{ - 3}\\ { - 3}&{ - \frac{9}{2}}&{ - 6} \end{array}} \right]\) |
| B. | \(\left[ {\begin{array}{*{20}{c}} {\frac{3}{2}}&0&{ - 3}\\ 3&{ - \frac{9}{2}}&{ - 6} \end{array}} \right]\) |
| C. | \(\left[ {\begin{array}{*{20}{c}} {\frac{3}{2}}&0&3\\ 3&{\frac{9}{2}}&6 \end{array}} \right]\) |
| D. | \(\left[ {\begin{array}{*{20}{c}} { - \frac{3}{2}}&0&3\\ { - 3}&{\frac{9}{2}}&{ - 6} \end{array}} \right]\) |
| Answer» E. | |
| 29. |
If \(A = \left[ {\begin{array}{*{20}{c}} {coshx}&{sinhx}\\ { - sinhx}&{coshx} \end{array}} \right]\), then trace (A2) is equal to |
| A. | 2 |
| B. | -2 |
| C. | cosh 2x |
| D. | sinh 2x |
| Answer» B. -2 | |
| 30. |
If A is an orthogonal matrix of order 3 and \({\rm{B}} = \left[ {\begin{array}{*{20}{c}} 1&2&3\\ { - 3}&0&2\\ 2&5&0 \end{array}} \right]\), then which of the following is/are correct?1. |AB| = ± 472. AB = BASelect the correct answer using the code given below: |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» B. 2 only | |
| 31. |
For which value of x, will the matrix \(\left[ {\begin{array}{*{20}{c}} 8&x&0\\ 4&0&2\\ {12}&6&0 \end{array}} \right]\) become singular. |
| A. | 4 |
| B. | 6 |
| C. | 8 |
| D. | 12 |
| Answer» B. 6 | |
| 32. |
For a square matrix A, which of the following properties hold?1) (A - 1) - 1 = A2) \(\det \left( {{A^{ - 1}}} \right) = \frac{1}{{detA}}\)3) (λA) - 1 = λA - 1 where λ is a scalarSelect the correct answer using the code given below: |
| A. | 1 and 2 only |
| B. | 2 and 3 only |
| C. | 1 and 3 only |
| D. | 1, 2 and 3 |
| Answer» B. 2 and 3 only | |
| 33. |
Let S = {(-1, 0, 1), (2, 1, 4)}. The value of k for which the vector (3k + 2, 3,10) belongs to the linear span of S is: |
| A. | 3 |
| B. | -2 |
| C. | 2 |
| D. | 8 |
| Answer» D. 8 | |
| 34. |
Let λ be a real number for which the system of linear equationsx + y + z = 64x + λy - λz = λ - 23x + 2y - 4z = - 5has infinitely many solutions. Then λ is a root of the quadratic equation: |
| A. | λ2 + 3λ - 4 = 0 |
| B. | λ2 - 3λ - 4 = 0 |
| C. | λ2 + λ - 6 = 0 |
| D. | λ2 - λ - 6 = 0 |
| Answer» E. | |
| 35. |
If the value of a third order determinant is 16, then the value of the determinant formed by replacing each of its elements by its cofactor is |
| A. | 96 |
| B. | 48 |
| C. | 256 |
| D. | 16 |
| Answer» D. 16 | |
| 36. |
If \({\rm{X}} = \left[ {\begin{array}{*{20}{c}} 3&{ - 4}\\ 1&{ - 1} \end{array}} \right],{\rm{\;B}} = \left[ {\begin{array}{*{20}{c}} 5&2\\ { - 2}&1 \end{array}} \right]{\rm{\;and\;A}} = \left[ {\begin{array}{*{20}{c}} {\rm{p}}&{\rm{q}}\\ {\rm{r}}&{\rm{s}} \end{array}} \right]\)Satisfy the equation AX = B, then the matrix A is equal to |
| A. | \(\left[ {\begin{array}{*{20}{c}} { - 7}&{26}\\ 1&{ - 5} \end{array}} \right]\) |
| B. | \(\left[ {\begin{array}{*{20}{c}} 7&{26}\\ 4&{17} \end{array}} \right]\) |
| C. | \(\left[ {\begin{array}{*{20}{c}} { - 7}&{ - 4}\\ {26}&{13} \end{array}} \right]\) |
| D. | \(\left[ {\begin{array}{*{20}{c}} { - 7}&{26}\\ { - 6}&{23} \end{array}} \right]\) |
| Answer» B. \(\left[ {\begin{array}{*{20}{c}} 7&{26}\\ 4&{17} \end{array}} \right]\) | |
| 37. |
If V is the real vector space of all mapping from R to R.V1 = {f ∈ V: f(-x) = f(x)} and V2 = {f ∈ V: f(-x) = -f(x)}, then which one of the following is correct. |
| A. | Neither V1 nor V2 are subspaces of V |
| B. | V1 is a subspace of V, but V2 is not a subspace of V |
| C. | both V1 and V2 are subspaces of V |
| D. | V1 is not a subspace of V, but V2 is a subspace of V |
| Answer» D. V1 is not a subspace of V, but V2 is a subspace of V | |
| 38. |
If \({\rm{A}} = \left[ {\begin{array}{*{20}{c}} {\cos {\rm{\alpha }}}&{\sin {\rm{\alpha }}}\\ { - \sin {\rm{\alpha }}}&{\cos {\rm{\alpha }}} \end{array}} \right]\) then what is AAT equal to (where AT is the transpose of A)? |
| A. | Null matrix |
| B. | Identify matrix |
| C. | A |
| D. | -A |
| Answer» C. A | |
| 39. |
If \({\rm{A}} = \left[ {\begin{array}{*{20}{c}} {\cos {\rm{\theta }}}&{\sin {\rm{\theta }}}\\ { - \sin {\rm{\theta }}}&{\cos {\rm{\theta }}} \end{array}} \right]\), then what is A3 equal to? |
| A. | \(\left[ {\begin{array}{*{20}{c}} {\cos 3{\rm{\theta }}}&{\sin 3{\rm{\theta }}}\\ { - \sin 3{\rm{\theta }}}&{\cos 3{\rm{\theta }}} \end{array}} \right]\) |
| B. | \(\left[ {\begin{array}{*{20}{c}} {{{\cos }^3}{\rm{\theta \;}}}&{{{\sin }^3}{\rm{\theta }}}\\ { - {{\sin }^3}{\rm{\theta }}}&{{{\cos }^3}{\rm{\theta }}} \end{array}} \right]\) |
| C. | \(\left[ {\begin{array}{*{20}{c}} {\cos 3{\rm{\theta }}}&{ - \sin 3{\rm{\theta }}}\\ {\sin 3{\rm{\theta }}}&{\cos 3{\rm{\theta }}} \end{array}} \right]\) |
| D. | \(\left[ {\begin{array}{*{20}{c}} {{{\cos }^3}{\rm{\theta }}}&{ - {{\sin }^3}{\rm{\theta }}}\\ {{{\sin }^3}{\rm{\theta }}}&{{{\cos }^3}{\rm{\theta }}} \end{array}} \right]\) |
| Answer» B. \(\left[ {\begin{array}{*{20}{c}} {{{\cos }^3}{\rm{\theta \;}}}&{{{\sin }^3}{\rm{\theta }}}\\ { - {{\sin }^3}{\rm{\theta }}}&{{{\cos }^3}{\rm{\theta }}} \end{array}} \right]\) | |
| 40. |
If \({\rm{A}} = \left[ {\begin{array}{*{20}{c}} 1&{{\rm{sin\theta }}}&1\\ { - {\rm{sin\theta }}}&1&{{\rm{sin\theta }}}\\ { - 1}&{ - {\rm{sin\theta }}}&1 \end{array}} \right]{\rm{\;}}\) then for all \(\rm \theta \in ( \frac {3_\pi}{4}, \ \frac {5\pi}{4})\) lies in the interval |
| A. | \(\left( {\frac{3}{2},3} \right.]\) |
| B. | \(\left[ {\frac{5}{2},4} \right)\) |
| C. | \(\left( {0,\frac{3}{2}} \right]\) |
| D. | \(\left( {1,\frac{5}{2}} \right)\) |
| Answer» B. \(\left[ {\frac{5}{2},4} \right)\) | |
| 41. |
If A and B are two invertible square matrices of same order, then what is (AB) - 1 equal to? |
| A. | B - 1A - 1 |
| B. | A - 1B - 1 |
| C. | B - 1A |
| D. | A - 1B |
| Answer» B. A - 1B - 1 | |
| 42. |
If each element of a 3 × 3 matrix is multiplied by 3, then the determinant of the newly formed matrix is |
| A. | 3 (det A) |
| B. | 9 (det A) |
| C. | 27 (det A) |
| D. | (det A)3 |
| Answer» D. (det A)3 | |
| 43. |
If matrix \({\rm{A}} = \left[ {\begin{array}{*{20}{c}} {1 - {\rm{i}}}&{\rm{i}}\\ { - {\rm{i}}}&{1 - {\rm{i}}} \end{array}} \right]\) where \(\rm i = \sqrt {-1},\) then which one of the following is correct? |
| A. | A is hermitian |
| B. | A is skew-hermitian |
| C. | (A̅)T + A is hermitian |
| D. | (A̅)T + A is skew-hermitian |
| Answer» D. (A̅)T + A is skew-hermitian | |
| 44. |
If A is an identity matrix of order 3, then its inverse (A-1) |
| A. | is equal to null matrix |
| B. | is equal to A |
| C. | is equal to 3A |
| D. | does not exist |
| Answer» C. is equal to 3A | |
| 45. |
If \({\rm{A}} = \left( {\begin{array}{*{20}{c}} { - 2}&2\\ 2&{ - 2} \end{array}} \right)\), then which one of the following is correct? |
| A. | A2 = -2A |
| B. | A2 = -4A |
| C. | A2 = -3A |
| D. | A2 = 4A |
| Answer» C. A2 = -3A | |
| 46. |
Let \(\Delta = \begin{vmatrix} Ax & x^2 & 1 \\\ By & y^2 & 1 \\\ Cz & z^2 & 1 \end{vmatrix}\) and \(\Delta_1 = \begin{vmatrix} A & B & C \\\ x & y & z \\\ zy & zx & xy \end{vmatrix}\), then |
| A. | Δ1 = -Δ |
| B. | Δ1 ≠ Δ |
| C. | Δ1 - Δ = 0 |
| D. | Δ1 = Δ = 0 |
| Answer» D. Δ1 = Δ = 0 | |
| 47. |
If A is a matrix of order 3 × 5 and B is a matrix of order 5 × 3, then the order of AB and BA will respectively be |
| A. | 3 × 3 and 3 × 3 |
| B. | 3 × 5 and 5 × 3 |
| C. | 3 × 3 and 5 × 5 |
| D. | 5 × 3 and 3 × 5 |
| Answer» D. 5 × 3 and 3 × 5 | |
| 48. |
If A and B are two matrices such than AB is of order n × n, then which one of the following is correct? |
| A. | A and B should be square matrices of same order. |
| B. | Either A or B should be a square matrix. |
| C. | Both A and B should be of same order |
| D. | Orders of A and B need not be the same. |
| Answer» B. Either A or B should be a square matrix. | |
| 49. |
A linear transformation T : R2 → R2 first reflects points through the vertical axis (y-axis) and then reflects points through the line x = y. The standard matrix of T is: |
| A. | \(\left[ {\begin{array}{*{20}{c}} 0&{ - 1}\\ 1&0 \end{array}} \right]\) |
| B. | \(\left[ {\begin{array}{*{20}{c}} { - 1}&0\\ 0&{ - 1} \end{array}} \right]\) |
| C. | \(\left[ {\begin{array}{*{20}{c}} 0&1\\ { - 1}&0 \end{array}} \right]\) |
| D. | \(\left[ {\begin{array}{*{20}{c}} 1&0\\ 0&1 \end{array}} \right]\) |
| Answer» D. \(\left[ {\begin{array}{*{20}{c}} 1&0\\ 0&1 \end{array}} \right]\) | |
| 50. |
A matrix is represented as A = \(\begin{bmatrix} -4 &1 &-1 \\ -1 &-1 &-1 \\ 7 &-3 &1 \end{bmatrix}\). The rank of the matrix is: |
| A. | 2 |
| B. | 4 |
| C. | 3 |
| D. | 1 |
| Answer» B. 4 | |