Matrices and Determinants PYQs - Last 5 Years
AP EAPCET / Mathematics / Algebra / 96 recent questions
MathematicsAlgebra2021-2025
Practice 96 AP EAPCET 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.
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Last 5 Years Matrices and Determinants Questions
Showing 50 of 96 filtered questions.
1Matrices And Determinants
If $x^a y^b=e^m, x^c y^d=e^n, \Delta_1=\left|\begin{array}{ll}m & b \\ n & d\end{array}\right|$, $\Delta_2=\left|\begin{array}{cc}a & m \\ c & n\end{array}\right|, \Delta_3=\left|\begin{array}{cc}a & b \\ c & d\end{array}\right|$, then the ...
MCQ+1 / -02025
2Matrices And Determinants
If the system of equations $2 x+p y+6 z=8$, $x+2 y+q z=5$ and $x+y+3 z=4$ has infinitely many solutions, then $p=$
MCQ+1 / -02025
3Matrices And Determinants
A value of $\theta$ lying between 0 and $\pi / 2$ and satisfying $\left|\begin{array}{ccc}1+\sin ^2 \theta & \cos ^2 \theta & 4 \sin 4 \theta \\ \sin ^2 \theta & 1+\cos ^2 \theta & 4 \sin 4 \theta \\ \sin ^2 \theta & \cos ^2 \theta & 1+4 \s...
MCQ+1 / -02025
4Matrices And Determinants
If the system of equations $2 x+3 y-3 z=3, x+2 y+0 z=1 2 x-y+z=\beta$ has infinitely many solutions, then $\frac{\alpha}{\beta}-\frac{\beta}{\alpha}=$
MCQ+1 / -02025
5Matrices And Determinants
If the inverse of $\left[\begin{array}{ccc}-x & 14 x & 7 x \\ 0 & 1 & 0 \\ x & -4 x & -2 x\end{array}\right]$ is $\left[\begin{array}{ccc}2 & 0 & 7 \\ 0 & 1 & 0 \\ 1 & -2 & 1\end{array}\right]$, then $\left|\begin{array}{ccc}x & x+1 & x+2 \...
MCQ+1 / -02025
6Matrices And Determinants
If $A=\left[\begin{array}{ccc}-1 & x & -3 \\ 2 & 4 & z \\ y & 5 & -6\end{array}\right]$ is a symmetric matrix and $B=\left[\begin{array}{ccc}0 & 2 & q \\ p & 0 & -4 \\ -3 & r & s\end{array}\right]$ is a skew-symmetric matrix, then $|A|+|B|...
MCQ+1 / -02025
7Matrices And Determinants
If the values of $x, y$ and $z$ which satisfy the equations $2 x-3 y+2 z+15=0,3 x+y-z+2=0$ and $x-3 y-3 z+8=0$ simultaneously are $\alpha, \beta$ and $\gamma$ respectively, then
MCQ+1 / -02025
8Matrices And Determinants
If $B$ is the inverse of a third order matrix $A$ and det $B=k$, then $(\operatorname{adj}(\operatorname{adj} \mathrm{A}))^{-1}=$
MCQ+1 / -02025
9Matrices And Determinants
If $A=\left[\begin{array}{lll}2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2\end{array}\right]$ and $\alpha, \beta, \gamma$ are the roots of the equation represented by $|A-x I|=0$, then $\alpha^2+\beta^2+\gamma^2=$
MCQ+1 / -02025
10Matrices And Determinants
$f(x)$ is an $n$th degree polynomial satisfying $f(x)=\frac{1}{2}\left|\begin{array}{cc}f(x) & f\left(\frac{1}{x}\right)-f(x) \\ 1 & f\left(\frac{1}{x}\right)\end{array}\right|$. If $f(2)=33$, then the value of $f(3)$ is
MCQ+1 / -02025
11Matrices And Determinants
Consider two systems of 3 linear equations in 3 unknowns $A X=B$ and $C X=D$. If $A X=B$ has unique solution $D$ and $C X=D$ has unique solution $B$, then the solution of $\left(A-C^{-1}\right) X=0$ is
MCQ+1 / -02025
12Matrices And Determinants
If $a$ is the determinant of the adjoint of the matrix $\left[\begin{array}{lll}1 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 3\end{array}\right]$ and $b$ is the determinant of the inverse of the matrix $\left[\begin{array}{ccc}1 & 2 & 3 \\ 4 & -3 & -1...
MCQ+1 / -02025
13Matrices And Determinants
If $A=\left[\begin{array}{ccc}1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6\end{array}\right]$ and the rank of $A$ is 2 , then the value of $x$ is equal to
MCQ+1 / -02025
14Matrices And Determinants
$$ \left|\begin{array}{ll} 2 & 1 \\ 3 & 1 \end{array}\right|+\left|\begin{array}{cc} 1 & \frac{1}{3} \\ 3 & 1 \end{array}\right|+\left|\begin{array}{cc} \frac{1}{2} & \frac{1}{9} \\ 3 & 1 \end{array}\right|+\left|\begin{array}{cc} \frac{1}{...
MCQ+1 / -02025
15Matrices And Determinants
$A=\left[\begin{array}{ccc}0 & k & k \\ k & -4 & -6 \\ k & -3 & -5\end{array}\right]$ is a singular matrix for
MCQ+1 / -02025
16Matrices And Determinants
If $P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$ is the adjoint of a matrix $A$ and det $A=4$, then the value of $\alpha$ is
MCQ+1 / -02025
17Matrices And Determinants
The rank of the matrix $\left[\begin{array}{cccc}2 & -3 & 4 & 0 \\ 5 & -4 & 2 & 1 \\ 1 & -3 & 5 & -4\end{array}\right]$ is
MCQ+1 / -02025
18Matrices And Determinants
If $\alpha$ is a real root of the equation $x^3+6 x^2+5 x-42=0$, then the determinant of the matrix
$\left[\begin{array}{lll}\alpha-1 & \alpha+1 & \alpha+2 \\ \alpha-2 & \alpha+3 & \alpha-3 \\ \alpha+4 & \alpha-4 & \alpha+5\end{array}\right...
$\left[\begin{array}{lll}\alpha-1 & \alpha+1 & \alpha+2 \\ \alpha-2 & \alpha+3 & \alpha-3 \\ \alpha+4 & \alpha-4 & \alpha+5\end{array}\right...
MCQ+1 / -02025
19Matrices And Determinants
$A$ is the set of all matrices of order 3 with entries 0 or 1 only. $B$ is the subset of $A$ consisting of all matrices with determinant value 1 . If $C$ is the subset of $A$ consisting of all matrices with determinant value -1 , then
MCQ+1 / -02025
20Matrices And Determinants
The value of $p$ and $q$ is that system of equations $2 x+p y+6 z=8, x+2 y+q z=5$ and $x+y+3 z=4$ may have no solution are
MCQ+1 / -02025
21Matrices And Determinants
Consider the matrices $A=\left[\begin{array}{ccc}x & y & 0 \\ -3 & 1 & 2 \\ 1 & -2 & z\end{array}\right]$ and $B=\left[\begin{array}{ccc}1 & -2 & -2 \\ 2 & 0 & 1 \\ 2 & 1 & 0\end{array}\right]$
If the cofactors of the elements $z, 1$ in 3rd...
If the cofactors of the elements $z, 1$ in 3rd...
MCQ+1 / -02025
22Matrices And Determinants
The number of solutions of the system of equations $2 x+y-z=7, x-3 y+2 z=1, x+4 y-3 z=5$ is
MCQ+1 / -02025
23Matrices And Determinants
If the values $x=\alpha, y=\beta, z=\gamma$ satisfy all the 3 equations $x+2 y+3 z=4,3 x+y+z=3$ and $x+3 y+3 z=2$, then $3 \alpha+\gamma=$
MCQ+1 / -02025
24Matrices And Determinants
If $A=\left[\begin{array}{lll}1 & 2 & 3 \\ 1 & 3 & 5 \\ 2 & 1 & 6\end{array}\right]$ and $|\operatorname{adj}(\operatorname{adj} A)|(\operatorname{adj} A)^{-1}=k A$, then $k=$
MCQ+1 / -02025
25Matrices And Determinants
In solving a system of linear equations $A X=B$ by Cramer's rule, in the usual notation, if $\Delta_1=\left|\begin{array}{ccc}-11 & 1 & -7 \\ -4 & 1 & -2 \\ 5 & 1 & 1\end{array}\right|$ and $\Delta_3=\left|\begin{array}{ccc}4 & 1 & -11 \\ 1...
MCQ+1 / -02025
26Matrices And Determinants
If $A=\left[\begin{array}{ccc}a & b & c \\ d & e & f \\ l & m & n\end{array}\right]$ is a matrix such that $|A|>0$ and $\operatorname{adj}(A)=\left[\begin{array}{ccc}0 & 4 & -6 \\ 10 & 8 & 0 \\ 2 & 4 & -4\end{array}\right]$, then $\frac{c d...
MCQ+1 / -02025
27Matrices And Determinants
If $A=\left[\begin{array}{ccc}1 & 2 & -2 \\ 2 & -1 & 2 \\ -1 & 1 & -2\end{array}\right]$, then $A+2 A^{-1}=$
MCQ+1 / -02025
28Matrices And Determinants
$A=\left[\begin{array}{ccc}1 & -1 & 2 \\ -2 & 3 & -3\end{array}\right]$ is the given matrix and $A^T$ represents the transpose of $A$, then $A A^T-A-A^T=$
MCQ+1 / -02025
29Matrices And Determinants
If $A$ and $B$ are both $3 \times 3$ matrices, then which of the following statements are true?
(i) $A B=0 \Rightarrow A=0$ or $B=0$
(ii) $A B=I_3 \Rightarrow A^{-1}=B$
(iii) $(A-B)^2=A^2-2 A B+B^2$
(i) $A B=0 \Rightarrow A=0$ or $B=0$
(ii) $A B=I_3 \Rightarrow A^{-1}=B$
(iii) $(A-B)^2=A^2-2 A B+B^2$
MCQ+1 / -02025
30Matrices And Determinants
If $A=\left[\begin{array}{ccc}x & 2 & 1 \\ -2 & y & 0 \\ 2 & 0 & -1\end{array}\right], x$ and $y$ are non-zero numbers, trace of $A=0$ and determinant of $A=-6$, then the minor of the elements 1 of $A$ is
MCQ+1 / -02025
31Matrices And Determinants
If the system of equations $a_1 x+b_1 y+c_1 z=0, a_2 x+b_2 y+c_2 z=0$ and $a_3 x+b_3 y+c_3 z=0$ has only trivial solution, then the rank of $\left[\begin{array}{lll}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{array}\right]$ i...
MCQ+1 / -02024
32Matrices And Determinants
4. If $A=\left[\begin{array}{lll}83 & 74 & 41 \\ 93 & 96 & 31 \\ 24 & 15 & 79\end{array}\right]$, then $\operatorname{det}\left(A-A^T\right)$ is equal to
MCQ+1 / -02024
33Matrices And Determinants
If $\left|\begin{array}{lll}a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c\end{array}\right|>0$, then $a b c>$
MCQ+1 / -02024
34Matrices And Determinants
If $A=\left[\begin{array}{lll}a & 1 & 2 \\ 1 & 2 & b \\ c & 1 & 3\end{array}\right]$ and $\operatorname{adj} A=\left[\begin{array}{ccc}7 & -1 & -5 \\ -3 & 9 & 5 \\ 1 & -3 & 5\end{array}\right]$, then $a^2+b^2+c^2=$
MCQ+1 / -02024
35Matrices And Determinants
If $P$ and $Q$ are two $3 \times 3$ matrices such that $|P Q|=1$ and $|P|=9$, then the determinant of adjoint of the matrix $P$. $\operatorname{adj} 3 Q$ is
MCQ+1 / -02024
36Matrices And Determinants
If the set of equations $x+2 y+3 z=6, x+3 y+5 z=9$, $2 x+5 y+a z=b$ has unique solution, then
MCQ+1 / -02024
37Matrices And Determinants
The system of linear equations $x+2 y+z=-3$, $3 x+3 y-2 z=-1$ and $2 x+7 y+7 z=-4$ has
MCQ+1 / -02024
38Matrices And Determinants
$A=\left[\begin{array}{lll}0 & 1 & 2 \\ 2 & 3 & 0 \\ 4 & 0 & 3\end{array}\right]$ and $B$ is a matrix such that $A B=B A$.If $A B$ is not an identity matrix, then the matrix that can be taken as $B$ is
MCQ+1 / -02024
39Matrices And Determinants
If $\alpha, \beta$ and $\gamma(\alpha<\beta<\gamma)$ are the values of $x$ such that $\left[\begin{array}{ccc}x-2 & 0 & 1 \\ 1 & x+3 & 2 \\ 2 & 0 & 2 x-1\end{array}\right]$ is a singular matrix, then $2 \alpha+3 \beta+4 \gamma$ is equal to
MCQ+1 / -02024
40Matrices And Determinants
Let $A$ be a $4 \times 4$ matrix and $P$ be is adjoint matrix, If $|P|=\left|\frac{A}{2}\right|$ then $\left|A^{-1}\right|$
MCQ+1 / -02024
41Matrices And Determinants
If $A=\left|\begin{array}{lll}2 & 3 & 4 \\ 1 & k & 2 \\ 4 & 1 & 5\end{array}\right|$ is singular matrix, then the quadratic equation having the roots $k$ an $\frac{1}{k}$ is
MCQ+1 / -02024
42Matrices And Determinants
The system $x+2 y+3 z=4,4 x+5 y+3 z=5,3 x+4 y+3 z=\lambda$ is consistent and $3 \lambda=n+100$, then $n=$
MCQ+1 / -02024
43Matrices And Determinants
Assertion (A) : If $B$ is a $3 \times 3$ matrix and $|B|=6$, then $|\operatorname{adj}(B)|=36$
Reason (R) : If $B$ is a square matrix of order $n$, then $|\operatorname{adj}(B)|=|B|^n$
Reason (R) : If $B$ is a square matrix of order $n$, then $|\operatorname{adj}(B)|=|B|^n$
MCQ+1 / -02024
44Matrices And Determinants
$\left|\begin{array}{ccc}a+b+2 c & a & b \\ c & b+c+2 a & b \\ c & a & c+a+2 b\end{array}\right|=$
MCQ+1 / -02024
45Matrices And Determinants
If $3 A=\left[\begin{array}{ccc}1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b\end{array}\right]$ and $A A^T=I$, then $\frac{a}{b}+\frac{b}{a}=$
MCQ+1 / -02024
46Matrices And Determinants
$$
\text { If } A=\left[\begin{array}{lll}
1 & 0 & 2 \\
2 & 1 & 3 \\
3 & 2 & 4
\end{array}\right] \text {, then } A^2-5 A+6 I=
$$
MCQ+1 / -02024
47Matrices And Determinants
Sum of the positive roots of the equation
$$ \left|\begin{array}{ccc} x^2+2 x & x+2 & 1 \\ 2 x+1 & x-1 & 1 \\ x+2 & -1 & 1 \end{array}\right|=0 \text { is } $$
$$ \left|\begin{array}{ccc} x^2+2 x & x+2 & 1 \\ 2 x+1 & x-1 & 1 \\ x+2 & -1 & 1 \end{array}\right|=0 \text { is } $$
MCQ+1 / -02024
48Matrices And Determinants
If the solution of the system of simultaneous linear equations $x+y-z=6,3 x+2 y-z=5$ and $2 x-y-2 z+3=0$ is $x=\alpha, y=\beta, z=y$, then $\alpha+\beta=$
MCQ+1 / -02024
49Matrices And Determinants
If $A=\left[a_{i j}\right], 1 \leq i, j \leq n$ with $n \geq 2$ and $a_{i j}=i+j$ is a matrix, then the rank of $A$ is
MCQ+1 / -02024
50Matrices And Determinants
Let $A, B, C, D$ and $E$ be $n \times n$ matrices each with non-zero determinant. If $A B C D E=I$, then $C^{-1}=$
MCQ+1 / -02024