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#853 Mathematics Matrices and Determinants

MCQ_SINGLE UNDERSTAND 2023

KNOWLEDGE 1 Marks

Let A be the area of a triangle having vertices $(x_1, y_1), (x_2, y_2)$ and $(x_3, y_3)$. Which of the following is correct?

(A) $|\begin{matrix}x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\\ x_{3}&y_{3}&1\end{matrix}|=\pm A$

(B) $|\begin{matrix}x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\\ x_{3}&y_{3}&1\end{matrix}|=\pm2A$

(C) $|\begin{matrix}x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\\ x_{3}&y_{3}&1\end{matrix}|=\pm\frac{A}{2}$

(D) $|\begin{matrix}x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\\ x_{3}&y_{3}&1\end{matrix}|^{2}=A^{2}$

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#852 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2023 AISSCE(Board Exam)

KNOWLEDGE 1 Marks

The value $|\begin{bmatrix}x+y & y+z & z+x\\ z & x & y\\ 1 & 1 & 1\end{bmatrix}|$ is :

(A) 0

(B) 1

(C) $x+y+z$

(D) $2(x+y+z)$

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#851 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2023 AISSCE(Board Exam)

KNOWLEDGE 1 Marks

Let A be a $3\times3$ matrix such that | adj A|=64. Then |A| is equal to:

(A) 8 only

(B) \- 8 only

(C) 64

(D) 8 or-8

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#850 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2023 AISSCE(Board Exam)

KNOWLEDGE 1 Marks

If |A|=2, where A is a $2\times2$ matrix, then |4$A^{-1}$| equals :

(A) 4

(B) 2

(C) 8

(D) \frac{1}{32}

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#849 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

If |(a, 3, 4), (1, 2, 1), (1, 4, 1)| = 0, then the value of a is

(A) 1

(B) 2

(C) 3

(D) 4

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#848 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

For what value of $x\in[0,\frac{\pi}{2}]$, is $A+A'=\sqrt{3}I$, where $A=\begin{bmatrix}\cos x & \sin x\\ -\sin x & \cos x\end{bmatrix}$ ?

(A) $\frac{\pi}{3}$

(B) $\frac{\pi}{6}$

(C) $0$

(D) $\frac{\pi}{2}$

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#847 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

A and B are skew-symmetric matrices of same order. AB is symmetric, if:

(A) $AB=O$

(B) $AB=-BA$

(C) $AB=BA$

(D) $BA=O$

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#846 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2023 AISSCE(Board Exam)

KNOWLEDGE 1 Marks

If $A\cdot(\text{adj }A)=\begin{bmatrix}3&0&0\\ 0&3&0\\ 0&0&3\end{bmatrix}$, then the value of $|A|+| \text{adj }A|$ is equal to :

(A) 12

(B) 9

(C) 3

(D) 27

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#845 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

If $A=\begin{bmatrix}1&4&x\\ z&2&y\\ -3&-1&3\end{bmatrix}$ is a symmetric matrix, then the value of $x+y+z$ is :

(A) 10

(B) 6

(C) 8

(D) 0

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#844 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

4. If a matrix $A=\begin{bmatrix}1 & 2 & 3\end{bmatrix}$, then the matrix $AA'$ (where $A'$ is the transpose of A) is:

(A) 14

(B) $\begin{bmatrix}1 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 3\end{bmatrix}$

(C) $\begin{bmatrix}1 & 2 & 3\\ 2 & 3 & 1\\ 3 & 1 & 2\end{bmatrix}$

(D) $\begin{bmatrix}14\end{bmatrix}$

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#843 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

3. If A is a square matrix and $A^{2}=A$ then $(I+A)^{2}-3A$ is equal to :

(A) I

(B) A

(C) 2A

(D) 3I

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#842 Mathematics Matrices and Determinants

MCQ_SINGLE UNDERSTAND 2023

KNOWLEDGE 1 Marks

2. The product $\begin{bmatrix}a & b\\ -b & a\end{bmatrix}\begin{bmatrix}a & -b\\ b & a\end{bmatrix}$ is equal to :

(A) $\begin{bmatrix}a^{2}+b^{2} & 0\\ 0 & a^{2}+b^{2}\end{bmatrix}$

(B) $\begin{bmatrix}(a+b)^{2} & 0\\ (a+b)^{2} & 0\end{bmatrix}$

(C) $\begin{bmatrix}a^{2}+b^{2} & 0\\ a^{2}+b^{2} & 0\end{bmatrix}$

(D) $\begin{bmatrix}a & 0\\ 0 & b\end{bmatrix}$

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#841 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

1. If $x\begin{bmatrix}1\\ 2\end{bmatrix}+y\begin{bmatrix}2\\ 5\end{bmatrix}=\begin{bmatrix}4\\ 9\end{bmatrix}$, then

(A) $x=1, y=2$

(B) $x=2, y=1$

(C) $x=1, y=-1$

(D) $x=3, y=2$

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#840 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

If A=\begin{bmatrix}0&1\\ -1&0\end{bmatrix} and (3\~I+4\~A)(3\~I-4\~A)=x^{2}I, then the value(s) x is/are:

(A) \pm\sqrt{7}

(B) 0

(C) \pm5

(D) 25

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#839 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

If A=\begin{bmatrix}3&4\\ 5&2\end{bmatrix} and 2A+B is a null matrix, then B is equal to :

(A) \begin{bmatrix}6&8\\ 10&4\end{bmatrix}

(B) \begin{bmatrix}-6&-8\\ -10&-4\end{bmatrix}

(C) \begin{bmatrix}5&8\\ 10&3\end{bmatrix}

(D) \begin{bmatrix}-5&-8\\ -10&-3\end{bmatrix}

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#838 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

If for a square matrix A, A^{2}-3A+I=O and A^{-1}=xA+yI, then the value of x+y is:

(A) \-2

(B) 2

(C) 3

(D) -3

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#837 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

If A=[(1, 0), (2, 1)], B=[(x, 0), (1, 1)] and A=B², then x equals

(A) ±1

(B) -1

(C) 1

(D) 2

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#836 Mathematics Matrices and Determinants

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

If for a square matrix A, A² - A + I = O then A⁻¹ equals

(A) A

(B) A+I

(C) I-A

(D) A-I

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#834 Mathematics Linear Programming

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

The number of feasible solutions of the linear programming problem given as Maximize $z=15x+30y$ subject to constraints : $3x+y\le12, x+2y\le10, x\ge0, y\ge0$ is

(A) 1

(B) 2

(C) 3

(D) infinite

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#833 Mathematics Linear Programming

MCQ_SINGLE APPLY 2023

KNOWLEDGE 1 Marks

16. Which of the following points satisfies both the inequations $2x+y\le10$ and $x+2y\ge8$?

(A) $(-2,4)$

(B) $(3,2)$

(C) $(-5,6)$

(D) $(4, 2)$

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