Matrices and Determinants PYQs - Last 10 Years
JEE Advanced / Mathematics / Algebra / 29 recent questions
MathematicsAlgebra2017-2026
Practice 29 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.
29
PYQs on Page
Mathematics / Algebra
2017-2026
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Based on indexed question metadata
13
Last 5 Years
2022-2026
29
Last 10 Years
2017-2026
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29PYQs
MCQM41.4%
INTEGER31%
MCQ27.6%
Difficulty Mix
#1 Medium16
#2 Hard12
#3 Easy1
13 in last 5 years29 in last 10 years
Last 10 Years Matrices and Determinants Questions
Showing 29 of 29 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
14Matrices And Determinants
For any 3 \(\times\) 3 matrix M, let |M| denote the determinant of M. Let I be the 3 \(\times\) 3 identity matrix. Let E and F be two 3 \(\times\) 3 matrices such that (I \(-\) EF) is invertible. If G = (I \(-\) EF)\(-\)1, then which of the...
MCQM+4 / -22021
15Matrices And Determinants
For any 3 \(\times\) 3 matrix M, let | M | denote the determinant of M. Let\(E = \left[ {\matrix{
1 & 2 & 3 \cr
2 & 3 & 4 \cr
8 & {13} & {18} \cr
} } \right]\), $$P = \left[ {\matrix{
1 & 0 & 0 \cr
0 & 0 & 1 \cr
...
1 & 0 & 0 \cr
0 & 0 & 1 \cr
...
MCQM+4 / -22021
16Matrices And Determinants
Let \(\alpha\), \(\beta\) and \(\gamma\) be real numbers such that the system of linear equationsx + 2y + 3z = \(\alpha\)4x + 5y + 6z = \(\beta\)7x + 8y + 9z = \(\gamma\) \(-\) 1is consistent. Let | M | represent the determinant of the mat...
INTEGER+2 / -02021
17Matrices And Determinants
Let \(\alpha\), \(\beta\) and \(\gamma\) be real numbers such that the system of linear equationsx + 2y + 3z = \(\alpha\)4x + 5y + 6z = \(\beta\)7x + 8y + 9z = \(\gamma\) \(-\) 1is consistent. Let | M | represent the determinant of the mat...
INTEGER+2 / -02021
18Matrices And Determinants
The trace of a square matrix is defined to be the sum of its diagonal entries. If A is a 2 \(\times\) 2 matrix such that the trace of A is 3 and the trace of A3 is \(-\)18, then the value of the determinant of A is .............
INTEGER+3 / -12020
19Matrices And Determinants
Let M be a 3 \(\times\) 3 invertible matrix with real entries and let I denote the 3 \(\times\) 3 identity matrix. If M\(-\)1 = adj(adj M), then which of the following statements is/are ALWAYS TRUE?
MCQM+4 / -22020
20Matrices And Determinants
$${P_1} = I = \left[ {\matrix{
1 & 0 & 0 \cr
0 & 1 & 0 \cr
0 & 0 & 1 \cr
} } \right],\,{P_2} = \left[ {\matrix{
1 & 0 & 0 \cr
0 & 0 & 1 \cr
0 & 1 & 0 \cr
} } \right],\,{P_3} = \left[ {\matrix{
0 & 1 & 0 ...
1 & 0 & 0 \cr
0 & 1 & 0 \cr
0 & 0 & 1 \cr
} } \right],\,{P_2} = \left[ {\matrix{
1 & 0 & 0 \cr
0 & 0 & 1 \cr
0 & 1 & 0 \cr
} } \right],\,{P_3} = \left[ {\matrix{
0 & 1 & 0 ...
MCQM+4 / -12019
21Matrices And Determinants
Suppose
det\(\left| {\matrix{ {\sum\limits_{k = 0}^n k } & {\sum\limits_{k = 0}^n {{}^n{C_k}{k^2}} } \cr {\sum\limits_{k = 0}^n {{}^n{C_k}.k} } & {\sum\limits_{k = 0}^n {{}^n{C_k}{3^k}} } \cr } } \right| = 0\)
holds for some p...
det\(\left| {\matrix{ {\sum\limits_{k = 0}^n k } & {\sum\limits_{k = 0}^n {{}^n{C_k}{k^2}} } \cr {\sum\limits_{k = 0}^n {{}^n{C_k}.k} } & {\sum\limits_{k = 0}^n {{}^n{C_k}{3^k}} } \cr } } \right| = 0\)
holds for some p...
INTEGER+3 / -02019
22Matrices And Determinants
Let x \(\in\) R and let \(P = \left[ {\matrix{
1 & 1 & 1 \cr
0 & 2 & 2 \cr
0 & 0 & 3 \cr
} } \right]\), \(Q = \left[ {\matrix{
2 & x & x \cr
0 & 4 & 0 \cr
x & x & 6 \cr
} } \right]\) and R = PQP\(-\)1, w...
MCQM+4 / -12019
23Matrices And Determinants
Let \(M = \left[ {\matrix{
0 & 1 & a \cr
1 & 2 & 3 \cr
3 & b & 1 \cr
} } \right]\) andadj \(M = \left[ {\matrix{
{ - 1} & 1 & { - 1} \cr
8 & { - 6} & 2 \cr
{ - 5} & 3 & { - 1} \cr
} } \right]\)where a and b...
MCQM+4 / -12019
24Matrices And Determinants
Let \(M = \left[ {\matrix{
{{{\sin }^4}\theta } \cr
{1 + {{\cos }^2}\theta } \cr
} \matrix{
{ - 1 - {{\sin }^2}\theta } \cr
{{{\cos }^4}\theta } \cr
} } \right] = \alpha I + \beta {M^{ - 1}}\),where \(\alpha\) = $$\...
MCQ+3 / -12019
25Matrices And Determinants
Let P be a matrix of order 3 \(\times\) 3 such that all the entries in P are from the set {\(-\)1, 0, 1}. Then, the maximum possible value of the determinant of P is ............ .
INTEGER+3 / -02018
26Matrices And Determinants
Let S be the set of all column matrices \(\left[ {\matrix{
{{b_1}} \cr
{{b_2}} \cr
{{b_3}} \cr
} } \right]\) such that \({b_1},{b_2},{b_3} \in R\) and the system of equations (in real variables)$$\eqalign{
& - x + 2y + 5...
& - x + 2y + 5...
MCQM+4 / -12018
27Matrices And Determinants
How many 3 \(\times\) 3 matrices M with entries from {0, 1, 2} are there, for which the sum of the diagonal entries of MTM is 5?
MCQ+3 / -12017
28Matrices And Determinants
For a real number \(\alpha\), if the system$$\left[ {\matrix{
1 & \alpha & {{\alpha ^2}} \cr
\alpha & 1 & \alpha \cr
{{\alpha ^2}} & \alpha & 1 \cr
} } \right]\left[ {\matrix{
x \cr
y \cr
z \cr
} } \ri...
1 & \alpha & {{\alpha ^2}} \cr
\alpha & 1 & \alpha \cr
{{\alpha ^2}} & \alpha & 1 \cr
} } \right]\left[ {\matrix{
x \cr
y \cr
z \cr
} } \ri...
INTEGER+3 / -02017
29Matrices And Determinants
Which of the following is(are) NOT the square of a 3 \(\times\) 3 matrix with real entries?
MCQM+4 / -12017