Matrices and Determinants PYQs - Last 5 Years
JEE Advanced / Mathematics / Algebra / 13 recent questions
MathematicsAlgebra2022-2026
Practice 13 JEE Advanced 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.
13
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Mathematics / Algebra
2022-2026
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13
Last 5 Years
2022-2026
13
Last 10 Years
2017-2026
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13PYQs
MCQ46.2%
MCQM30.8%
INTEGER23.1%
Difficulty Mix
#1 Hard8
#2 Medium4
#3 Easy1
13 in last 5 years13 in last 10 years
Last 5 Years Matrices and Determinants Questions
Showing 13 of 13 filtered questions.
1Matrices And Determinants
Consider the matrix $$ M = \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix}. $$ Let $p, q, r, s, a, b, c$ and $d$ be integers such that $$ M^{26} = \begin{bmatrix} p & q \\ r & s \end{bmatrix} \quad \text{and} \quad \sum\limits_{k=1}^{26} M^k ...
MCQM+4 / -12026
2Matrices And Determinants
Which one of the following matrices can be obtained by performing elementary row transformations on the $3 \times 3$ identity matrix?
MCQ+3 / -12026
3Matrices And Determinants
Let $I=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)$ and $P=\left(\begin{array}{ll}2 & 0 \\ 0 & 3\end{array}\right)$. Let $Q=\left(\begin{array}{ll}x & y \\ z & 4\end{array}\right)$ for some non-zero real numbers $x, y$, and $z$,...
MCQM+4 / -22025
4Matrices And Determinants
Consider the matrix$$ P = \begin{pmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{pmatrix}. $$Let the transpose of a matrix $X$ be denoted by $X^T$. Then the number of $3 \times 3$ invertible matrices $Q$ with integer entries, such that$$ ...
MCQ+3 / -12025
5Matrices And Determinants
Let $\alpha$ and $\beta$ be the distinct roots of the equation $x^2+x-1=0$. Consider the set $T=\{1, \alpha, \beta\}$. For a $3 \times 3$ matrix $M=\left(a_{i j}\right)_{3 \times 3}$, define $R_i=a_{i 1}+a_{i 2}+a_{i 3}$ and $C_j=a_{1 j}+a_...
MCQ+3 / -12024
6Matrices And Determinants
Let $S=\left\{A=\left(\begin{array}{lll}0 & 1 & c \\ 1 & a & d \\ 1 & b & e\end{array}\right): a, b, c, d, e \in\{0,1\}\right.$ and $\left.|A| \in\{-1,1\}\right\}$, where $|A|$ denotes the determinant of $A$. Then the number of elements in ...
INTEGER+4 / -02024
7Matrices And Determinants
Let $\mathbb{R}^2$ denote $\mathbb{R} \times \mathbb{R}$. Let
\(S=\left\{(a, b, c): a, b, c \in \mathbb{R} \text { and } a x^2+2 b x y+c y^2>0 \text { for all }(x, y) \in \mathbb{R}^2-\{(0,0)\}\right\} .\)
Then which of the following st...
\(S=\left\{(a, b, c): a, b, c \in \mathbb{R} \text { and } a x^2+2 b x y+c y^2>0 \text { for all }(x, y) \in \mathbb{R}^2-\{(0,0)\}\right\} .\)
Then which of the following st...
MCQM+4 / -22024
8Matrices And Determinants
Let $R=\left\{\left(\begin{array}{lll}a & 3 & b \\ c & 2 & d \\ 0 & 5 & 0\end{array}\right): a, b, c, d \in\{0,3,5,7,11,13,17,19\}\right\}$.
Then the number of invertible matrices in $R$ is :
Then the number of invertible matrices in $R$ is :
INTEGER+4 / -02023
9Matrices And Determinants
Let $M=\left(a_{i j}\right), i, j \in\{1,2,3\}$, be the $3 \times 3$ matrix such that $a_{i j}=1$ if $j+1$ is divisible by $i$, otherwise $a_{i j}=0$. Then which of the following statements is(are) true?
MCQM+4 / -22023
10Matrices And Determinants
Let $\alpha, \beta$ and $\gamma$ be real numbers. Consider the following system of linear equations
$$ \begin{aligned} & x+2 y+z=7 \\\\ & x+\alpha z=11 \\\\ & 2 x-3 y+\beta z=\gamma \end{aligned} $$
Match each entry in List-I to the correct...
$$ \begin{aligned} & x+2 y+z=7 \\\\ & x+\alpha z=11 \\\\ & 2 x-3 y+\beta z=\gamma \end{aligned} $$
Match each entry in List-I to the correct...
MCQ+3 / -12023
11Matrices And Determinants
If $M=\left(\begin{array}{rr}\frac{5}{2} & \frac{3}{2} \\ -\frac{3}{2} & -\frac{1}{2}\end{array}\right)$, then which of the following matrices is equal to $M^{2022} ?$
MCQ+3 / -12022
12Matrices And Determinants
Let $\beta$ be a real number. Consider the matrix
$$ A=\left(\begin{array}{ccc} \beta & 0 & 1 \\ 2 & 1 & -2 \\ 3 & 1 & -2 \end{array}\right) $$
If $A^{7}-(\beta-1) A^{6}-\beta A^{5}$ is a singular matrix, then the value of $9 \beta$ is __...
$$ A=\left(\begin{array}{ccc} \beta & 0 & 1 \\ 2 & 1 & -2 \\ 3 & 1 & -2 \end{array}\right) $$
If $A^{7}-(\beta-1) A^{6}-\beta A^{5}$ is a singular matrix, then the value of $9 \beta$ is __...
INTEGER+3 / -12022
13Matrices And Determinants
Let \(p, q, r\) be nonzero real numbers that are, respectively, the \(10^{\text {th }}, 100^{\text {th }}\) and \(1000^{\text {th }}\) terms of a harmonic progression. Consider the system of linear equations
$$$
\begin{gathered}
x+y+z=1 \\...
$$$
\begin{gathered}
x+y+z=1 \\...
MCQ+3 / -12022