Available Questions 601 found Page 22 of 31
Standalone Questions
#760
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2025
KNOWLEDGE
1 Marks
If A and B are square matrices of order m such that \(A^{2}-B^{2}=(A-B)(A+B),\) then which of the following is always correct?
(A) \(A=B\)
(B) \(AB=BA\)
(C) \(A=0\) or \(B=0\)
(D) \(A=I\) or \(B=I\)
Key: B
Sol:
Sol:
The identity $A^2 - B^2 = (A - B)(A + B)$ holds for square matrices $A$ and $B$ only if they commute, i.e., $AB = BA$. This is because matrix multiplication is not generally commutative.
#759
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2025
KNOWLEDGE
1 Marks
If M and N are square matrices of order 3 such that det \((M)=m\) and \(MN=mI,\) then det (N) is equal to:
(A) -1
(B) 1
(C) \(-m^{2}\)
(D) \(m^{2}\)
Key: D
Sol:
Sol:
We use two key properties of determinants:
- Product Rule: \(\text{det}(AB) = \text{det}(A) \cdot \text{det}(B)\)
- Scalar Multiplication Rule: \(\text{det}(c A) = c^n \cdot \text{det}(A)\) (where \(n\) is the order of the matrix)
We take the determinant of both sides of the equation \(MN = mI\):
\[\text{det}(MN) = \text{det}(mI)\]Since the order \(n=3\) and \(\text{det}(I) = 1\), the right side simplifies to \(\text{det}(mI) = m^3 \cdot 1 = m^3\).
Substitute \(\text{det}(M) = m\) and \(\text{det}(mI) = m^3\) we get :
\[m \cdot \text{det}(N) = m^3\] \[\mathbf{\text{det}(N) = m^2}\]
#758
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2025
KNOWLEDGE
1 Marks
If \(A=\begin{bmatrix}1&2&3\\ -4&3&7\end{bmatrix}\) and \(B=\begin{bmatrix}4&3\\ -1&2\\ 0&5\end{bmatrix},\) then the correct statement is:
(A) Only AB is defined.
(B) Only BA is defined.
(C) AB and BA, both are defined.
(D) AB and BA, both are not defined.
Key:
Sol:
Sol:
#757
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2025
KNOWLEDGE
1 Marks
If \(\begin{vmatrix}2x&5\\ 12&x\end{vmatrix}=\begin{vmatrix}6&-5\\ 4&3\end{vmatrix}\) then the value of x is:
(A) 3
(B) 7
(C) \(\pm7\)
(D) \(\pm3\)
Key:
Sol:
Sol:
#756
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2025
KNOWLEDGE
1 Marks
If \(A=[a_{ij}]\) is a \(3\times3\) diagonal matrix such that \(a_{11}=1\), \(a_{22}=5\) and \(a_{33}=-2\), then \(|A|\) is:
(A) 0
(B) -10
(C) 10
(D) 1
Key:
Sol:
Sol:
#755
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2025
KNOWLEDGE
1 Marks
If \(\begin{bmatrix}4+x&x-1\\ -2&3\end{bmatrix}\) is a singular matrix, then the value of x is:
(A) 0
(B) 1
(C) -2
(D) 4
Key:
Sol:
Sol:
#754
Mathematics
Matrices and Determinants
MCQ_SINGLE
UNDERSTAND
2025
KNOWLEDGE
1 Marks
Let both \(AB^{\prime}\) and \(B^{\prime}A\) be defined for matrices A and B. If order of A is \(n\times m\), then the order of B is:
(A) \(n\times n\)
(B) \(n\times m\)
(C) \(m\times m\)
(D) \(m\times n\)
Key:
Sol:
Sol:
#753
Mathematics
Matrices and Determinants
MCQ_SINGLE
REMEMBER
2025
KNOWLEDGE
1 Marks
If \(A=\begin{bmatrix}-1&0&0\\ 0&3&0\\ 0&0&5\end{bmatrix},\) then A is a/an:
(A) scalar matrix
(B) identity matrix
(C) symmetric matrix
(D) skew-symmetric matrix
Key:
Sol:
Sol:
#752
Mathematics
Matrices and Determinants
MCQ_SINGLE
UNDERSTAND
2025
KNOWLEDGE
1 Marks
Sum of two skew-symmetric matrices of same order is always a/an:
(A) skew-symmetric matrix
(B) symmetric matrix
(C) null matrix
(D) identity matrix
Key:
Sol:
Sol:
#751
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2025
KNOWLEDGE
1 Marks
What is the total number of possible matrices of order \(3\times3\) with each entry as \(\sqrt{2}\) or \(\sqrt{3}\)?
(A) 9
(B) 512
(C) 615
(D) 64
Key:
Sol:
Sol:
#750
Mathematics
Matrices and Determinants
MCQ_SINGLE
REMEMBER
2025
KNOWLEDGE
1 Marks
The matrix \(A=\begin{bmatrix}\sqrt{3}&0&0\\ 0&\sqrt{2}&0\\ 0&0&\sqrt{5}\end{bmatrix}\) is a/an:
(A) scalar matrix
(B) identity matrix
(C) null matrix
(D) symmetric matrix
Key:
Sol:
Sol:
#749
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2025
KNOWLEDGE
1 Marks
If A and B are two square matrices each of order 3 with \(|A|=3\) and \(|B|=5\), then \(|2AB|\) is:
(A) 30
(B) 120
(C) 15
(D) 225
Key:
Sol:
Sol:
#748
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2025
KNOWLEDGE
1 Marks
Let A be a square matrix of order 3. If \(|A|=5\), then \(|\operatorname{adj} A|\) is:
(A) 5
(B) 125
(C) 25
(D) -5
Key:
Sol:
Sol:
#747
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2025
KNOWLEDGE
1 Marks
If \(\begin{bmatrix}2x-1&3x\\ 0&y^{2}-1\end{bmatrix}=\begin{bmatrix}x+3&12\\ 0&35\end{bmatrix},\) then the value of \((x-y)\) is :
(A) 2 or 10
(B) 2 or 10
(C) 2 or - 10
(D) -2 or - 10
Key:
Sol:
Sol:
#746
Mathematics
Matrices and Determinants
MCQ_SINGLE
REMEMBER
2024
KNOWLEDGE
1 Marks
If a matrix has 36 elements, the number of possible orders it can have, is:
(A) 13
(B) 3
(C) 5
(D) 9
Key: D
Sol:
Sol:
#745
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2024
KNOWLEDGE
1 Marks
If \(\begin{bmatrix}x+y&2\\ 5&xy\end{bmatrix}=\begin{bmatrix}6&2\\ 5&8\end{bmatrix},\) then the value of \((\frac{24}{x}+\frac{24}{y})\) is:
(A) 7
(B) 6
(C) 8
(D) 18
Key:
Sol:
Sol:
#744
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2024
KNOWLEDGE
1 Marks
\(\begin{vmatrix}x+1&x-1\\ x^{2}+x+1&x^{2}-x+1\end{vmatrix}\) is equal to:
(A) \(2x^{3}\)
(B) 2
(C) 0
(D) \(2x^{3}-2\)
Key:
Sol:
Sol:
#743
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2024
KNOWLEDGE
1 Marks
If A and B are two non-zero square matrices of same order such that \((A+B)^{2}=A^{2}+B^{2}\) then :
(A) \(AB=O\)
(B) \(AB=-BA\)
(C) \(BA=O\)
(D) \(AB=BA\)
Key:
Sol:
Sol:
#742
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2024
KNOWLEDGE
1 Marks
If the sum of all the elements of a \(3\times3\) scalar matrix is 9, then the product of all its elements is:
(A) 0
(B) 9
(C) 27
(D) 729
Key:
Sol:
Sol:
#741
Mathematics
Matrices and Determinants
MCQ_SINGLE
APPLY
2024
KNOWLEDGE
1 Marks
If \(\begin{vmatrix}-a&b&c\\ a&-b&c\\ a&b&-c\end{vmatrix}= kabc,\) then the value of k is:
(A) 0
(B) 1
(C) 2
(D) 4
Key:
Sol:
Sol: