Matrices and Determinants · Mathematics · KCET

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MCQ (Single Correct Answer)

1

If $A$ is a square matrix such that $A^2=A$, then $(I-A)^3$ is

KCET 2025
2

If $A$ and $B$ are two matrices such that $A B$ is an identity matrix and the order of matrix $B$ is $3 \times 4$, then the order of matrix $A$ is

KCET 2025
3
Which of the following statements is not correct?
KCET 2025
4
If a matrix $A=\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]$ satisfies $A^6=k A^{\prime}$, then the value of $k$ is
KCET 2025
5

If $A=\left[\begin{array}{ll}k & 2 \\ 2 & k\end{array}\right]$ and $\left|A^3\right|=125$, then the value of $k$ is

KCET 2025
6

If $A$ is a square matrix satisfying the equation $A^2-5 A+7 I=0$, where $I$ is the $I$ dentity matrix and 0 is null matrix of same order, then $A^{-1}=$

KCET 2025
7
If $A$ is a square matrix of order $3 \times 3, \operatorname{det} A=3$, then the value of $\operatorname{det}\left(3 A^{-1}\right)$ is
KCET 2025
8
If $B=\left[\begin{array}{ll}1 & 3 \\ 1 & \alpha\end{array}\right]$ be the adjoint of a matrix $A$ and $|A|=2$, then the value of $\alpha$ is
KCET 2025
9

If $A$ is a square matrix, such that $A^2=A$, then $(I+A)^3$ is equal to

KCET 2024
10

If $A=\left(\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right)$, then $A^{10}$ is equal to

KCET 2024
11

If $f(x)=\left|\begin{array}{ccc}x-3 & 2 x^2-18 & 2 x^3-81 \\ x-5 & 2 x^2-50 & 4 x^3-500 \\ 1 & 2 & 3\end{array}\right|$, then $f(\mathrm{l}) \cdot f(3)+f(3) \cdot f(5)+f(5) \cdot f(\mathrm{l})$ is

KCET 2024
12

If $P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$ is the adjoint of a $3 \times 3$ $\operatorname{matrix} A$ and $|A|=4$, then $\alpha$ is equal to

KCET 2024
13

If $A=\left|\begin{array}{cc}x & 1 \\ 1 & x\end{array}\right|$ and $B=\left|\begin{array}{ccc}x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x\end{array}\right|$, then $\frac{d B}{d x}$ is

KCET 2024
14

$$\text { The value of }\left|\begin{array}{ccc} \sin ^2 14^{\circ} & \sin ^2 66^{\circ} & \tan 135^{\circ} \\ \sin ^2 66^{\circ} & \tan 135^{\circ} & \sin ^2 14^{\circ} \\ \tan 135^{\circ} & \sin ^2 14^{\circ} & \sin ^2 66^{\circ} \end{array}\right|$$ is

KCET 2023
15

If $$x\left[\begin{array}{l}3 \\ 2\end{array}\right]+y\left[\begin{array}{r}1 \\ -1\end{array}\right]=\left[\begin{array}{l}15 \\ 5\end{array}\right]$$, then the value of $$x$$ and $$y$$ are

KCET 2023
16

If $$A$$ and $$B$$ are two matrices, such that $$A B=B$$ and $$B A=A$$, then $$A^2+B^2$$ equals to

KCET 2023
17

If $$A=\left[\begin{array}{cc}2-k & 2 \\ 1 & 3-k\end{array}\right]$$ is singular matrix, then the value of $$5 k-k^2$$ is equal to

KCET 2023
18

If $$\Delta=\left|\begin{array}{ccc}1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2\end{array}\right|$$ and $$\Delta_1=\left|\begin{array}{ccc}1 & 1 & 1 \\ b c & c a & a b \\ a & b & c\end{array}\right|$$, then

KCET 2023
19

If $$A=\left[\begin{array}{cc}1 & \tan \alpha / 2 \\ -\tan \alpha / 2 & 1\end{array}\right]$$ and $$A B=I$$, then $$B$$ is equal to

KCET 2023
20

If $$A$$ is a matrix of order $$3 \times 3$$, then $$\left(A^2\right)^{-1}$$ is equal to

KCET 2022
21

If $$A=\left[\begin{array}{ll}2 & -1 \\ 3 & -2\end{array}\right]$$, then the inverse of the matrix $$A^3$$ is

KCET 2022
22

If $$A$$ is a skew symmetric matrix, then A$$^{2021}$$ is

KCET 2022
23

If $$A=\left[\begin{array}{ll}0 & 1 \\ 0 & 0\end{array}\right]$$, then $$(a I+b A)^n$$ is (where $$I$$ is the identify matrix of order 2)

KCET 2022
24

If $$A$$ is a $$3 \times 3$$ matrix such that $$|5 \cdot \operatorname{adj} A|=5$$, then $$|A|$$ is equal to

KCET 2022
25

If there are two values of '$$a$$' which makes determinant

$$\Delta=\left|\begin{array}{ccc} 1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2 a \end{array}\right|=86$$

Then, the sum of these number is

KCET 2022
26

If $$A_n=\left[\begin{array}{cc}1-n & n \\ n & 1-n\end{array}\right]$$, then $$\left|A_1\right|+\left|A_2\right|+\ldots .\left|A_{2021}\right|=$$

KCET 2022
27

If $$A=\left[\begin{array}{ccc}1 & -2 & 1 \\ 2 & 1 & 3\end{array}\right]$$

$$ B=\left[\begin{array}{ll}2 & 1 \\ 3 & 2 \\ 1 & 1\end{array}\right]$$, then $$(A B)^{\prime}$$ is equal to

KCET 2021
28

Let $$M$$ be $$2 \times 2$$ symmetric matrix with integer entries, then $$M$$ is invertible if

KCET 2021
29

If $$A$$ and $$B$$ are matrices of order 3 and $$|A|=5,|B|=3$$, then $$|3 A B|$$ is

KCET 2021
30

If $$A$$ and $$B$$ are invertible matrices then which of the following is not correct?

KCET 2021
31

If $$x^3-2 x^2-9 x+18=0$$ and $$A=\left|\begin{array}{lll}1 & 2 & 3 \\ 4 & x & 6 \\ 7 & 8 & 9\end{array}\right|$$ then the maximum value of $$A$$ is

KCET 2021
32

If $$A=\left(\begin{array}{lll}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right)$$ then $$A^4$$ is equal to

KCET 2020
33

If $$\left(\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right) A=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)$$ then the matrix $$a$$ is

KCET 2020
34

If $$f(x)=\left|\begin{array}{ccc}x^3-x & a+x & b+x \\ x-a & x^2-x & c+x \\ x-b & x-c & 0\end{array}\right|$$, then

KCET 2020
35

If $$A$$ and $$B$$ are square matrices of same order and $$B$$ is a skew symmetric matrix, then $$A^{\prime} B A$$ is

KCET 2020
36

If $$A$$ is a square matrix of order 3 and $$|A|=5$$, then $$\mid A$$ adj. $$A \mid$$ is

KCET 2020
37

If $$a_1 a_2 a_3 \ldots a_9$$ are in AP, then the value of $$\left|\begin{array}{lll}a_1 & a_2 & a_3 \\ a_4 & a_5 & a_6 \\ a_7 & a_8 & a_9\end{array}\right|$$ is

KCET 2020
38

The inverse of the matrix $$\left[\begin{array}{ccc}2 & 5 & 0 \\ 0 & 1 & 1 \\ -1 & 0 & 3\end{array}\right]$$ is

KCET 2019
39

If $$P$$ and $$Q$$ are symmetric matrices of the same order then $$P Q-Q P$$ is

KCET 2019
40

If $$3 A+4 B^{\prime}=\left[\begin{array}{ccc}7 & -10 & 17 \\ 0 & 6 & 31\end{array}\right]$$ and $$2 B+3 A^{\prime}\left[\begin{array}{cc}-1 & 18 \\ 4 & 0 \\ -5 & -7\end{array}\right]$$ then $$B=$$

KCET 2019
41

If $$A=\left[\begin{array}{ll}1 & 3 \\ 4 & 2\end{array}\right], B=\left[\begin{array}{cc}2 & -1 \\ -1 & 2\end{array}\right]$$, Then $$\left|A B B^{\prime}\right|=$$

KCET 2019
42

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

KCET 2019
43

The constant term in the expansion of $$\left|\begin{array}{ccc}3 x+1 & 2 x-1 & x+2 \\ 5 x-1 & 3 x+2 & x+1 \\ 7 x-2 & 3 x+1 & 4 x-1\end{array}\right|$$ is

KCET 2019
44
If $A=\left[\begin{array}{cc}2 & -2 \\ -2 & 2\end{array}\right]$, then $A^n=2^k A$, where $k$ is equal to
KCET 2018
45
If $\left[\begin{array}{cc}1 & 1 \\ -1 & 1\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{l}2 \\ 4\end{array}\right]$, then the values of $x$ and $y$ respectively are
KCET 2018
46
If $A=\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right]$, then $A A^{\prime}$ is equal to
KCET 2018
47
If $x, y, z \in R$, then the value of determinant $\left|\begin{array}{lll}\left(5^x+5^{-x}\right)^2 & \left(5^x-5^{-x}\right)^2 & 1 \\ \left(6^x+6^{-x}\right)^2 & \left(6^x-6^{-x}\right)^2 & 1 \\ \left(7^x+7^{-x}\right)^2 & \left(7^x-7^{-x}\right)^2 & 1\end{array}\right|$ is
KCET 2018
48
The value of determinant $\left|\begin{array}{lll}a-b & b+c & a \\ b-a & c+a & b \\ c-a & a+b & c\end{array}\right|$ is
KCET 2018
49
If $\left(x_1, y_1\right),\left(x_2, y_2\right)$ and $\left(x_3, y_3\right)$ are the vertices of a triangle whose are is ' $k$ ' square units, then $\left|\begin{array}{lll}x_1 & y_1 & 4 \\ x_2 & y_2 & 4 \\ x_3 & y_3 & 4\end{array}\right|^2$ is
KCET 2018
50
Let $A$ be a square matrix of order $3 \times 3$, then $|5 A|$ is equal to
KCET 2018
51
$$ \text { } \begin{aligned} Let\,\,\,\Delta & =\left|\begin{array}{lll} A x & x^2 & 1 \\ B y & y^2 & 1 \\ C z & z^2 & 1 \end{array}\right| \text { and } \Delta_1 =\left|\begin{array}{ccc} A & B & C \\ x & y & z \\ z y & z x & x y \end{array}\right| \text {, then }\left|\begin{array}{ccc} A x & B y & C y \\ x^2 & y^2 & z^2 \\ 1 & 1 & 1 \end{array}\right| \end{aligned} $$
KCET 2017
52
If $\left|\begin{array}{ll}3 & x \\ x & 1\end{array}\right|=\left|\begin{array}{ll}3 & 2 \\ 4 & 1\end{array}\right|$, then $x$ is equal to
KCET 2017
53
If $2\left|\begin{array}{ll}1 & 3 \\ 0 & x\end{array}\right|+\left|\begin{array}{ll}y & 0 \\ 1 & 2\end{array}\right|=\left|\begin{array}{ll}5 & 6 \\ 1 & 8\end{array}\right|$, then the value of $x$ and $y$ are
KCET 2017
54
If $A$ is a square matrix of order $3 \times 3$, then $|K A|$ is equal to
KCET 2017
55

If $A=\frac{1}{\pi}\left|\begin{array}{ll}\sin ^{-1}(\pi x) & \tan ^{-1}\left(\frac{x}{\pi}\right) \\ \sin ^{-1}\left(\frac{x}{\pi}\right) & \cot ^{-1}(\pi x)\end{array}\right|$

$B=\left|\begin{array}{cc}-\cos ^{-1}(\pi x) & \tan ^{-1}\left(\frac{x}{\pi}\right) \\ \sin ^{-1}\left(\frac{x}{\pi}\right) & -\tan ^{-1}(\pi x)\end{array}\right|$,

then $A-B$ is :

KCET 2017
56
If a matrix $A$ is both symmetric and skew symmetric, then
KCET 2017
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