Matrices and Determinants PYQs - Last 10 Years

TS EAMCET / Mathematics / Algebra / 115 recent questions

MathematicsAlgebra2016-2025

All Matrices and Determinants PYQs Last 5 Years Create chapter test

Practice 115 TS EAMCET Mathematics questions from Matrices and Determinants. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

115

PYQs on Page

Mathematics / Algebra

2020-2025

Year Range

Based on indexed question metadata

97

Last 5 Years

2021-2025

115

Last 10 Years

2016-2025

Recent Year Trend

2020

2022

2023

2024

2025

202027 max PYQs/year2025

Question Types

115PYQs

MCQ100%

Difficulty Mix

#1 Unknown115

97 in last 5 years115 in last 10 years

Last 10 Years Matrices and Determinants Questions

Showing 50 of 115 filtered questions.

1Matrices And Determinants

The positive value of ' $a$ ' for which the system of linear homogeneous equations $x+a y+z=0, a x+2 y-z=0$, $2 x+3 y+z=0$ has non-trivial solution is

2Matrices And Determinants

If $x=\alpha, y=\beta, z=\gamma$ is the solution of the system of equations $2 x+3 y+z=-1,3 x+y+z=4$, $x-3 y-2 z=1$, then the value of $\beta$ is

3Matrices And Determinants

If $A=\left[\begin{array}{lll}1 & 2 & 2 \\ 2 & 1 & 1 \\ 1 & 2 & 1\end{array}\right]$ then $|\operatorname{adj}|\left(A^2\right) \mid=$

4Matrices And Determinants

Consider a homogeneous system of three linear equations in three unknowns represented by $A X=0$.
If $X=\left[\begin{array}{c}l \\ m \\ 0\end{array}\right], l \neq 0, m \neq 0, l, m \in R$ represents an infinite number of solutions of this ...

5Matrices And Determinants

The number of real values of ' $a$ ' for which the system of equations $2 x+3 y+a z=0, x+a y-2 z=0$ and $3 x+y+3 z=0$ has non-trivial solution is

6Matrices And Determinants

A is a $3 \times 3$ matrix satisfying $A^3-5 A^2+7 A+I=0$ If $A^5-6 A^4+12 A^3-6 A^2+2 A+2 I=l A+m I$, then $l+m=$

7Matrices And Determinants

If $A=\left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & x & 1\end{array}\right], A^{-1}=\frac{1}{2}\left[\begin{array}{ccc}1 & -1 & 1 \\ -8 & 6 & 2 y \\ 5 & -3 & 1\end{array}\right]$, then the point $(x, y)$ lies on the curve represente...

8Matrices And Determinants

If the system of simultaneous linear equations $x+\lambda y-2 z=1, x-y+\lambda z=2$ and $x-2 y+3 z=3$ is inconsistent for $\lambda=\lambda_1$ and $\lambda_2$, then $\lambda_1+\lambda_2=$

9Matrices And Determinants

The sum of all the roots of the equation
$\left|\begin{array}{ccc}x & -3 & 2 \\ -1 & -2 & (x-1) \\ 1 & (x-2) & 3\end{array}\right|=0$ is

10Matrices And Determinants

If $A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$, then $\operatorname{adj}(\operatorname{adj}(\operatorname{adj} A))$

11Matrices And Determinants

The system of linear equation $(\sin \theta) x+y-2 z=0$, $2 x-y+(\cos \theta) z=0$ and $-3 x+(\sec \theta) y+3 z=0$, where $\theta \neq(2 n+1) \frac{\pi}{2}$, has non-trivial solution for

12Matrices And Determinants

If the system of simultaneous linear equations $x-2 y+z=0,2 x+3 y+z=6$ and $x+2 y+p z=q$ has infinitely many solutions, then

13Matrices And Determinants

If the system of linear equations $(\sin \theta) x-y+z=0$, $x-(\cos \theta) y+z=0, x+y+(\sin \theta) z=0$ has non-trivial solution, then the least positive value of $\theta$ is

14Matrices And Determinants

If $A=\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 1 & 1 \\ 1 & 3 & 1\end{array}\right]$ and $B=\left[\begin{array}{lll}2 & 3 & 4 \\ 3 & 2 & 2 \\ 2 & 4 & 2\end{array}\right]$, then $\sqrt{|\operatorname{adj}(A B)|}=$

15Matrices And Determinants

If $A=\left[\begin{array}{lll}1 & 5 & 2 \\ 4 & 1 & 3 \\ 2 & 6 & 3\end{array}\right]$, then $\left|(\operatorname{adj} A)^{-1}\right|=$

16Matrices And Determinants

If $\Delta_r=\left|\begin{array}{cc}\frac{1}{3 r-2} & \frac{2}{3 r-5} \\ 0 & \frac{3}{3 r+1}\end{array}\right|$ then $\sum\limits_{r=1}^{33} \Delta_r=$

17Matrices And Determinants

$A=\left[\begin{array}{ccc}1 & -3 & -5 \\ -2 & 4 & -6 \\ 7 & -11 & 13\end{array}\right]$, then $\sqrt{|\operatorname{adj} A|}=$

18Matrices And Determinants

If $\left|\begin{array}{ccc}9 & 25 & 16 \\ 16 & 36 & 25 \\ 25 & 49 & 36\end{array}\right|=K$, then $K, K+1$ are the roots of the equation

19Matrices And Determinants

If the augmented matrix corresponding to the system of equations $x+y-z=1,2 x+4 y-z=0$ and $3 x+4 y+5 z=18$ is transformed to $\left[\begin{array}{cccc}1 & a & 0 & -1 \\ 0 & 2 & 1 & b \\ 0 & 0 & c & 32\end{array}\right]$ then $\sqrt{a+b+c}=...

20Matrices And Determinants

If $A+2 B=\left[\begin{array}{ccc}1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1\end{array}\right]$ and $2 A-B=\left[\begin{array}{ccc}2 & -1 & 5 \\ 2 & -1 & 6 \\ 0 & 1 & 2\end{array}\right]$, then $\operatorname{tr}(A)-\operatorname{tr}(B)=$

21Matrices And Determinants

If $\left|\begin{array}{ccc}1 & 2 & 3-\lambda \\ 0 & -1-\lambda & 2 \\ 1-\lambda & 1 & 3\end{array}\right|=A \lambda^3+B \lambda^2+C \lambda+D$, then $D+A=$

22Matrices And Determinants

$A$ and $B$ are two non-square matrices. If $P=A+B, Q=A^T B, R=A B^T$, then the matrices whose order is equal to the order of $A$ are

23Matrices And Determinants

$A, C$ are $3 \times 3$ matrices $B, D$ are $3 \times 1$ matrices. If $A X=B$ has unique solution and $C X=D$ has infinite number of solutions, then

24Matrices And Determinants

$A, B, C$ and $D$ are square matrices such that $A+B$ is symmetric, $A-B$ is skew-symmetric and $D$ is the transpose of $C$.
If $A=\left[\begin{array}{ccc}-1 & 2 & 3 \\\\ 4 & 3 & -2 \\\\ 3 & -4 & 5\end{array}\right]$ and
$C=\left[\begin{arr...

25Matrices And Determinants

$\operatorname{det}\left[\begin{array}{ccc}\frac{a^2+b^2}{c} & c & c \\\\ a & \frac{b^2+c^2}{a} & a \\\ b & b & \frac{c^2+a^2}{b}\end{array}\right]=$

26Matrices And Determinants

If $A$ is square matrix and $A^2+I=2 A$, then $A^9=$

27Matrices And Determinants

The system of simultaneous linear equations
$$ \begin{aligned} & x-2 y+3 z=4,3 x+y-2 z=7 \\ & 2 x+3 y+z=6 \text { has } \end{aligned} $$

28Matrices And Determinants

If $A X=D$ represents the system of linear equations $3 x-4 y+7 z+6=0,5 x+2 y-4 z+9=0$ and $8 x-6 y-z+5=0$, then

29Matrices And Determinants

If $\mathrm{A}=\left[\begin{array}{lll}1 & 2 & 2 \\ 3 & 2 & 3 \\ 1 & 1 & 2\end{array}\right]$ and $\mathrm{A}^{-1}=\left[\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right]$, ...

30Matrices And Determinants

If $\alpha, \beta, \gamma$ are the roots of the equation $2 x^3-5 x^2+4 x-3=0$, then $\Sigma \alpha \beta(\alpha+\beta)=$

31Matrices And Determinants

If $(x, y, z)=(\alpha, \beta, \gamma)$ is the unique solution of the system of simultaneous linear equations $3 x-4 y+z+7=0$, $2 x+3 y-z=10$ and $x-2 y-3 z=3$, then $\alpha=$

32Matrices And Determinants

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $\left|\begin{array}{lll}x & 2 & 2 \\ 2 & x & 2 \\ 2 & 2 & x\end{array}\right|=0$ and $\min (\alpha, \beta, \gamma)=\alpha$, then $2 \alpha+3 \beta+4 \gamma$ is equal to

33Matrices And Determinants

$A=\left[\begin{array}{ll}1 & 2 \\\\ 2 & 1\end{array}\right]$ and $B=\left[\begin{array}{ll}x & y \\\\ 1 & 2\end{array}\right]$ are two matrices such that $(A+B)(A-B)=A^{2}-B^{2}$ If $C=\left[\begin{array}{ll}x & 2 \\\\ 1 & y\end{array}\rig...

34Matrices And Determinants

If $x=k$ satisfies the equation $\left|\begin{array}{ccc}x-2 & 3 x-3 & 5 x-5 \\\\ x-4 & 3 x-9 & 5 x-25 \\\\ x-8 & 3 x-27 & 5 x-125\end{array}\right|=0$, then $x=k$ also satisfies the equation

35Matrices And Determinants

If $\frac{x^{2}}{2 x^{4}+7 x^{2}+6}=\frac{A x+B}{x^{2}+a}+\frac{C x+D}{a x^{2}+3}$, then $A+B+C-2 D=$

36Matrices And Determinants

If the homogeneous system of linear equations $x-2 y+3 z=0,2 x+4 y-5 z=0,3 x+\lambda y+\mu z=0$ has non-trivial solution, then $8 \mu+11 \lambda=$

37Matrices And Determinants

If $A$ is a non-singular matrix, then $\operatorname{adj}\left(A^{-1}\right)=$

38Matrices And Determinants

The system of equations $x+3 y+7=0$, $3 x+10 y-3 z+18=0$ and $3 y-9 z+2=0$ has

39Matrices And Determinants

If $A=\left[\begin{array}{lll}x & y & y \\ y & x & y \\ y & y & x\end{array}\right]$ is a matrix such that $5 A^{-1}=\left[\begin{array}{ccc}-3 & 2 & 2 \\ 2 & -3 & 2 \\ 2 & 2 & -3\end{array}\right]$, then $A^2-4 A=$

40Matrices And Determinants

If $a \neq b \neq c, \Delta_1=\left[\begin{array}{lll}1 & a^2 & b c \\ 1 & b^2 & c a \\ 1 & c^2 & a b\end{array}\right]$, $\Delta_2=\left[\begin{array}{ccc}1 & 1 & 1 \\ a^2 & b^2 & c^2 \\ a^3 & b^3 & c^3\end{array}\right]$ and $\frac{\Delta...

41Matrices And Determinants

If $A=\left[\begin{array}{lll}9 & 3 & 0 \\ 1 & 5 & 8 \\ 7 & 6 & 2\end{array}\right]$ and $A A^T-A^2=\left[\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right]$, then $\sum\limi...

42Matrices And Determinants

$A=\left[a_{i j}\right]$ is a $3 \times 3$ matrix with positive integers as its elements. Elements of $A$ are such that the sum of all elements of each row is equal to 6 and $a_{22}=2$.If $\mathrm{a}_{i j}=\left\{\begin{array}{cl}\mathrm{a}...

43Matrices And Determinants

If $|\operatorname{adj} A|=x$ and $|\operatorname{adj} B|=y$, then $\left|(\operatorname{adj}(A B))^{-1}\right|=$

44Matrices And Determinants

$\left|\begin{array}{ccc}\frac{-b c}{a^{2}} & \frac{c}{a} & \frac{b}{a} \\ \frac{c}{b} & -\frac{a c}{b^{2}} & \frac{a}{b} \\ \frac{b}{c} & \frac{a}{c} & -\frac{a b}{c^{2}}\end{array}\right|=$

45Matrices And Determinants

The system of equations $x+3 b y+b z=0, x+2 a y+a z=0$ and $x+4 c y+c z=0$ has

46Matrices And Determinants

If $\operatorname{adj}\left[\begin{array}{ccc}1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1\end{array}\right]=\left[\begin{array}{ccc}5 & m & -2 \\ 1 & 1 & 0 \\ -2 & -2 & n\end{array}\right]$, then $m+n=$

47Matrices And Determinants

If $A$ and $B$ are two square matrices of the same order and $(A B+B A)^T+(A B-B A)^T=2 B A$, then

48Matrices And Determinants

If $A$ is a square matrix of order $3, \operatorname{then}\left|\operatorname{Adj}\left(\operatorname{Adj} A^2\right)\right|=$

49Matrices And Determinants

If $A=\left[\begin{array}{ll}0 & 3 \\ 0 & 0\end{array}\right]$ and $f(x)=x+x^2+x^3+\ldots \ldots+x^{2023}$, then $f(A)+I=$

50Matrices And Determinants

If $\left|\begin{array}{ccc}(1+\alpha)^2 & (1+2 \alpha)^2 & (1+3 \alpha)^2 \\ (2+\alpha)^2 & (2+2 \alpha)^2 & (2+3 \alpha)^2 \\ (3+\alpha)^2 & (3+2 \alpha)^2 & (3+3 \alpha)^2\end{array}\right|=k$ and $\alpha=-2$, then $k=$