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#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) \(m\times n\)

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#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

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#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

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#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

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#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

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#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

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#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

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#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

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#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

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#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

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#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) \(2x^{3}-2\)

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#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) \(AB=BA\)

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#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

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#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

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#740 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2024

KNOWLEDGE 1 Marks

If \(A=[a_{ij}]\) be a \(3\times3\) matrix, where \(a_{ij}=i-3j\), then which of the following is false ?

(A) \(a_{11}\lt0\)

(B) \(a_{12}+a_{21}=-6\)

(C) \(a_{13}\gt a_{31}\)

(D) \(a_{31}=0\)

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#739 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2024

KNOWLEDGE 1 Marks

If \(F(x)=\begin{bmatrix}\cos~x&-\sin~x&0\\ \sin~x&\cos~x&0\\ 0&0&1\end{bmatrix}\) and \([F(x)]^{2}=F(kx)\), then the value of k is :

(A) 1

(B) 2

(C) 0

(D) -2

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#738 Mathematics Matrices and Determinants

MCQ_SINGLE UNDERSTAND 2024

KNOWLEDGE 1 Marks

If \(A=[a_{ij}]\) is an identity matrix, then which of the following is true ?

(A) \(a_{ij}=\begin{cases}0,&if~i=j\\ 1,&if~i\ne j\end{cases}\)

(B) \(a_{ij}=1,\forall i,j\)

(C) \(a_{ij}=0,\forall i,j\)

(D) \(a_{ij}=\begin{cases}0,&if~i\ne j\\ 1,&if~i=j\end{cases}\)

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#737 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2024

KNOWLEDGE 1 Marks

Let \(A=\begin{bmatrix}a&b\\ c&d\end{bmatrix}\) be a square matrix such that adj \(A=A\) Then, \((a+b+c+d)\) is equal to :

(A) 2a

(B) 2b

(C) 2c

(D) 0

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#736 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2024

KNOWLEDGE 1 Marks

If A and B are two skew symmetric matrices, then \((AB+BA)\) is :

(A) a skew symmetric matrix

(B) a symmetric matrix

(C) a null matrix

(D) an identity matrix

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#735 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2024

KNOWLEDGE 1 Marks

If \(A=\begin{bmatrix}2&0&0\\ 0&3&0\\ 0&0&5\end{bmatrix},\) then \(A^{-1}\) is:

(A) \([\begin{matrix}\frac{1}{2}&0&0\\ 0&3&0\\ 0&0&\frac{1}{5}\end{matrix}]\)

(B) \(30[\begin{matrix}\frac{1}{2}&0&0\\ 0&\frac{1}{3}&0\\ 0&0&\frac{1}{5}\end{matrix}]\)

(C) \(\frac{1}{30}[\begin{matrix}2&0&0\\ 0&3&0\\ 0&0&5\end{matrix}]\)

(D) \(\frac{1}{30}[\begin{matrix}\frac{1}{2}&0&0\\ 0&\frac{1}{3}&0\\ 0&0&\frac{1}{5}\end{matrix}]\)

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