Matrices and Determinants PYQs - Last 10 Years
WB JEE / Mathematics / Algebra / 59 recent questions
MathematicsAlgebra2017-2026
Practice 59 WB JEE 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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2017-2026
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Last 10 Years Matrices and Determinants Questions
Showing 50 of 59 filtered questions.
1Matrices And Determinants
Let $\operatorname{det} A=\left|\begin{array}{ccc}\mathrm{l} & \mathrm{m} & \mathrm{n} \\ \mathrm{p} & \mathrm{q} & \mathrm{r} \\ \mathrm{l} & \mathrm{l} & \mathrm{l}\end{array}\right|$ If $(I-m)^2+(p-q)^2=9,(m-n)^2+(q-r)^2=16,(n-I)^2+(r-p)...
MCQ+1 / -0.252026
2Matrices And Determinants
Let us define the power of a matrix $A$ as the maximum $m \in Z^{+}$such that $A^m=I$. For two matrices $A$ and $B$ if $A^5=I$ and $A B A^{-1}=B^2$, then the power of the matrix $B$ is between
MCQ+1 / -0.252026
3Matrices And Determinants
If $f(x)=\frac{1+x}{1-x}$ and $A$ is a matrix such that $A^3=0$, then $f(A)=$
MCQ+1 / -0.252026
4Matrices And Determinants
If $\operatorname{adj} B=A,|P|=|Q|=1$, then $\operatorname{adj}\left(Q^{-1} B P^{-1}\right)=$
MCQ+1 / -0.252025
5Matrices And Determinants
Let $A=\left[\begin{array}{ccc}5 & 5 \alpha & \alpha \\ 0 & \alpha & 5 \alpha \\ 0 & 0 & 5\end{array}\right]$. If $|A|^2=25$, then $|\alpha|$ equals to
MCQ+1 / -0.252025
6Matrices And Determinants
If $a, b, c$ are positive real numbers each distinct from unity, then the value of the determinant $\left|\begin{array}{ccc}1 & \log _a b & \log _a c \\ \log _b a & 1 & \log _b c \\ \log _c a & \log _c b & 1\end{array}\right|$ is
MCQ+1 / -0.252025
7Matrices And Determinants
An $n \times n$ matrix is formed using 0, 1 and $-$1 as its elements. The number of such matrices which are skew symmetric is
MCQ+1 / -0.252025
8Matrices And Determinants
Suppose $\alpha, \beta, \gamma$ are the roots of the equation $x^3+q x+r=0($ with $r \neq 0)$ and they are in A.P. Then the rank of the matrix $\left(\begin{array}{lll}\alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & ...
MCQ+1 / -0.252025
9Matrices And Determinants
If the matrix $\left(\begin{array}{ccc}0 & a & a \\ 2 b & b & -b \\ c & -c & c\end{array}\right)$ is orthogonal, then the values of $a, b, c$ are
MCQ+1 / -0.252025
10Matrices And Determinants
If for a matrix $A,|A|=6$ and adj $A=\left[\begin{array}{ccc}1 & -2 & 4 \\ 4 & 1 & 1 \\ -1 & k & 0\end{array}\right]$, then $k$ is equal to
MCQ+1 / -0.252025
11Matrices And Determinants
If $P$ is a non-singular matrix of order $5 \times 5$ and the sum of the elements of each row is 1 , then the sum of the elements of each row in $P^{-1}$ is
MCQM+2 / -02025
12Matrices And Determinants
If \(\mathrm{a}_{\mathrm{i}}, \mathrm{b}_{\mathrm{i}}, \mathrm{c}_{\mathrm{i}} \in \mathbb{R}(\mathrm{i}=1,2,3)\) and \(x \in \mathbb{R}\) and $$\left|\begin{array}{lll}\mathrm{a}_1+b_1 x & a_1 x+b_1 & c_1 \\ \mathrm{a}_2+b_2 x & a_2 x+b_2 ...
MCQM+2 / -02024
13Matrices And Determinants
Let $$A=\left[\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right]$$, then
MCQ+2 / -0.52024
14Matrices And Determinants
Let $$A=\left(\begin{array}{ccc}1 & -1 & 0 \\ 0 & 1 & -1 \\ 1 & 1 & 1\end{array}\right), B=\left(\begin{array}{l}2 \\ 1 \\ 7\end{array}\right)$$
Then for the validity of the result \(\mathrm{AX}=\mathrm{B}, \mathrm{X}\) is
Then for the validity of the result \(\mathrm{AX}=\mathrm{B}, \mathrm{X}\) is
MCQ+2 / -0.52024
15Matrices And Determinants
If $$\left[\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right] \cdot A \cdot\left[\begin{array}{cc}-3 & 2 \\ 5 & -3\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$$, then \(A=\)
MCQ+1 / -0.252024
16Matrices And Determinants
$$
\text { If }\left|\begin{array}{lll}
x^k & x^{k+2} & x^{k+3} \\
y^k & y^{k+2} & y^{k+3} \\
z^k & z^{k+2} & z^{k+3}
\end{array}\right|=(x-y)(y-z)(z-x)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right) \text {, then }
$$
MCQ+1 / -0.252024
17Matrices And Determinants
If $$A=\left(\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right)$$ and \(\theta=\frac{2 \pi}{7}\), then \(A^{100}=A \times A \times \ldots .(100\) times) is equal to
MCQ+1 / -0.252024
18Matrices And Determinants
Let \(A = \left( {\matrix{
0 & 0 & 1 \cr
1 & 0 & 0 \cr
0 & 0 & 0 \cr
} } \right),B = \left( {\matrix{
0 & 1 & 0 \cr
0 & 0 & 1 \cr
0 & 0 & 0 \cr
} } \right)\) and $$P\left( {\matrix{
0 & 1 & 0 \cr
x ...
0 & 1 & 0 \cr
x ...
MCQ+2 / -0.52023
19Matrices And Determinants
Let \(\alpha,\beta\) be the roots of the equation \(a{x^2} + bx + c = 0,a,b,c\) real and \({s_n} = {\alpha ^n} + {\beta ^n}\) and $$\left| {\matrix{
3 & {1 + {s_1}} & {1 + {s_2}} \cr
{1 + {s_1}} & {1 + {s_2}} & {1 + {s_3}} \cr
...
3 & {1 + {s_1}} & {1 + {s_2}} \cr
{1 + {s_1}} & {1 + {s_2}} & {1 + {s_3}} \cr
...
MCQ+1 / -0.252023
20Matrices And Determinants
If the matrix Mr is given by \({M_r} = \left( {\matrix{
r & {r - 1} \cr
{r - 1} & r \cr
} } \right)\) for r = 1, 2, 3, ... then det (M1) + det (M2) + ... + det (M2008) =
MCQ+1 / -0.252023
21Matrices And Determinants
Let \(A = \left( {\matrix{
2 & 0 & 3 \cr
4 & 7 & {11} \cr
5 & 4 & 8 \cr
} } \right)\). Then
MCQ+1 / -0.252023
22Matrices And Determinants
Let A and B are orthogonal matrices and det A + det B = 0. Then
MCQ+1 / -0.252023
23Matrices And Determinants
Let $$\Delta = \left| {\matrix{
{\sin \theta \cos \phi } & {\sin \theta \sin \phi } & {\cos \theta } \cr
{\cos \theta \cos \phi } & {\cos \theta \sin \phi } & { - \sin \theta } \cr
{ - \sin \theta \sin \phi } & {\sin \theta \c...
{\sin \theta \cos \phi } & {\sin \theta \sin \phi } & {\cos \theta } \cr
{\cos \theta \cos \phi } & {\cos \theta \sin \phi } & { - \sin \theta } \cr
{ - \sin \theta \sin \phi } & {\sin \theta \c...
MCQM+2 / -02022
24Matrices And Determinants
The solution of \(\det (A - \lambda {I_2}) = 0\) be 4 and 8 and \(A = \left( {\matrix{
2 & 2 \cr
x & y \cr
} } \right)\). Then
(I2 is identity matrix of order 2)
(I2 is identity matrix of order 2)
MCQ+2 / -0.52022
25Matrices And Determinants
If \(A = \left( {\matrix{
1 & 1 \cr
0 & i \cr
} } \right)\) and \({A^{2018}} = \left( {\matrix{
a & b \cr
c & d \cr
} } \right)\), then \((a + d)\) equals
MCQ+1 / -0.252022
26Matrices And Determinants
If \(p = \left[ {\matrix{
1 & \alpha & 3 \cr
1 & 3 & 3 \cr
2 & 4 & 4 \cr
} } \right]\) is the adjoint of the \(3 \times 3\) matrix A and det A = 4, then \(\alpha\) is equal to
MCQ+1 / -0.252022
27Matrices And Determinants
If \(\Delta (x) = \left| {\matrix{
{x - 2} & {{{(x - 1)}^2}} & {{x^3}} \cr
{x - 1} & {{x^2}} & {{{(x + 1)}^3}} \cr
x & {{{(x + 1)}^2}} & {{{(x + 2)}^3}} \cr
} } \right|\), then coefficient of x in \(\Delta\)x is
MCQ+1 / -0.252022
28Matrices And Determinants
Under which of the following condition(s) does(do) the system of equations $$\left( {\matrix{
1 & 2 & 4 \cr
2 & 1 & 2 \cr
1 & 2 & {(a - 4)} \cr
} } \right)\left( {\matrix{
x \cr
y \cr
z \cr
} } \right) = \l...
1 & 2 & 4 \cr
2 & 1 & 2 \cr
1 & 2 & {(a - 4)} \cr
} } \right)\left( {\matrix{
x \cr
y \cr
z \cr
} } \right) = \l...
MCQ+1 / -0.252022
29Matrices And Determinants
\(\left| {\matrix{
x & {3x + 2} & {2x - 1} \cr
{2x - 1} & {4x} & {3x + 1} \cr
{7x - 2} & {17x + 6} & {12x - 1} \cr
} } \right| = 0\) is true for
MCQM+2 / -02021
30Matrices And Determinants
The determinant \(\left| {\matrix{
{{a^2} + 10} & {ab} & {ac} \cr
{ab} & {{b^2} + 10} & {bc} \cr
{ac} & {bc} & {{c^2} + 10} \cr
} } \right|\) is
MCQ+2 / -0.52021
31Matrices And Determinants
Let T and U be the set of all orthogonal matrices of order 3 over R and the set of all non-singular matrices of order 3 over R respectively. Let A = {\(-\)1, 0, 1}, then
MCQ+1 / -0.252021
32Matrices And Determinants
If an (> 0) be the nth term of a G.P. then$$\left| {\matrix{
{\log {a_n}} & {\log {a_{n + 1}}} & {\log {a_{n + 2}}} \cr
{\log {a_{n + 3}}} & {\log {a_{n + 4}}} & {\log {a_{n + 5}}} \cr
{\log {a_{n + 6}}} & {\log {a_{n + 7}}} & ...
{\log {a_n}} & {\log {a_{n + 1}}} & {\log {a_{n + 2}}} \cr
{\log {a_{n + 3}}} & {\log {a_{n + 4}}} & {\log {a_{n + 5}}} \cr
{\log {a_{n + 6}}} & {\log {a_{n + 7}}} & ...
MCQ+1 / -0.252021
33Matrices And Determinants
Let A and B two non singular skew symmetric matrices such that AB = BA, then A2B2(ATB)\(-\)1(AB\(-\)1)T is equal to
MCQ+1 / -0.252021
34Matrices And Determinants
Let \(A = \left( {\matrix{
1 & 0 & 0 \cr
0 & {\cos t} & {\sin t} \cr
0 & { - \sin t} & {\cos t} \cr
} } \right)\)Let \(\lambda\)1, \(\lambda\)2, \(\lambda\)3 be the roots of \(\det (A - \lambda {I_3}) = 0\), where I3 denote...
MCQ+1 / -0.252021
35Matrices And Determinants
If M is a 3 \(\times\) 3 matrix such that (0, 1, 2) M = (1 0 0), (3, 4 5) M = (0, 1, 0), then (6 7 8) M is equal to
MCQ+1 / -0.252021
36Matrices And Determinants
If the vectors \(\alpha = \widehat i + a\widehat j + {a^2}\widehat k,\,\beta = \widehat i + b\widehat j + {b^2}\widehat k\) and \(\,\gamma = \widehat i + c\widehat j + {c^2}\widehat k\) are three non-coplanarvectors and $$\left| {\matrix...
MCQ+2 / -0.52020
37Matrices And Determinants
Let A = $$\left( {\matrix{
{3 - t} \cr
{ - 1} \cr
0 \cr
} \matrix{
{} \cr
{} \cr
{} \cr
} \,\matrix{
1 \cr
{3 - t} \cr
{ - 1} \cr
} \matrix{
{} \cr
{} \cr
{} \cr
} \matrix{...
{3 - t} \cr
{ - 1} \cr
0 \cr
} \matrix{
{} \cr
{} \cr
{} \cr
} \,\matrix{
1 \cr
{3 - t} \cr
{ - 1} \cr
} \matrix{
{} \cr
{} \cr
{} \cr
} \matrix{...
MCQ+1 / -0.252020
38Matrices And Determinants
If f : S \(\to\) R, where S is the set of all non-singular matrices of order 2 over R and \(f\left[ {\left( {\matrix{
a & b \cr
c & d \cr
} } \right)} \right] = ad - bc\), then
MCQ+1 / -0.252020
39Matrices And Determinants
If \(\left| {\matrix{
{{a^2}} & {bc} & {{c^2} + ac} \cr
{{a^2} + ab} & {{b^2}} & {ca} \cr
{ab} & {{b^2} + bc} & {{c^2}} \cr
} } \right| = k{a^2}{b^2}{c^2}\),then K =
MCQ+1 / -0.252020
40Matrices And Determinants
Let \(A = \left[ {\matrix{
{12} & {24} & 5 \cr
x & 6 & 2 \cr
{ - 1} & { - 2} & 3 \cr
} } \right]\). The value of x for which the matrix A is not invertible is
MCQ+1 / -0.252020
41Matrices And Determinants
Let \(A = \left( {\matrix{
a & b \cr
c & d \cr
} } \right)\) be a 2 \(\times\) 2 real matrix with det A = 1. If the equation det (A \(-\) \(\lambda\)I2) = 0 has imaginary roots (I2 be the identity matrix of order 2), then
MCQ+1 / -0.252020
42Matrices And Determinants
The system of equations\(\eqalign{
& \lambda x + y + 3z = 0 \cr
& 2x + \mu y - z = 0 \cr
& 5x + 7y + z = 0 \cr}\)has infinitely many solutions in R. Then,
MCQ+2 / -0.52019
43Matrices And Determinants
Let A be a square matrix of order 3 whose all entries are 1 and let I3 be the identity matrix of order 3. Then, the matrix \(A - 3{I_3}\) is
MCQ+1 / -0.252019
44Matrices And Determinants
Let \(A = \left[ {\matrix{
3 & 0 & 3 \cr
0 & 3 & 0 \cr
3 & 0 & 3 \cr
} } \right]\). Then, the roots of the equation det \((A - \lambda {I_3})\) = 0 (where I3 is the identity matrix of order 3) are
MCQM+2 / -02019
45Matrices And Determinants
If \(A = \left( {\matrix{
5 & {5x} & x \cr
0 & x & {5x} \cr
0 & 0 & 5 \cr
} } \right)\) and \(|A{|^2} = 25\), then | x | is equal to
MCQ+1 / -0.252019
46Matrices And Determinants
If M is any square matrix of order 3 over R and if M' be the transpose of M, then adj(M') \(-\) (adj M)' is equal to
MCQ+1 / -0.252019
47Matrices And Determinants
Let A and B be two square matrices of order 3 and AB = O3, where O3 denotes the null matrix of order 3. Then,
MCQ+1 / -0.252019
48Matrices And Determinants
If the polynomial \(f(x) = \left| {\matrix{
{{{(1 + x)}^a}} & {{{(2 + x)}^b}} & 1 \cr
1 & {{{(1 + x)}^a}} & {{{(2 + x)}^b}} \cr
{{{(2 + x)}^b}} & 1 & {{{(1 + x)}^a}} \cr
} } \right|\), then the constant term of f(x) is
MCQ+2 / -0.52018
49Matrices And Determinants
If \(\left| {\matrix{
{ - 1} & 7 & 0 \cr
2 & 1 & { - 3} \cr
3 & 4 & 1 \cr
} } \right| = A\), then $$\left| {\matrix{
{13} & { - 11} & 5 \cr
{ - 7} & { - 1} & {25} \cr
{ - 21} & { - 3} & { - 15} \cr
} } \rig...
{13} & { - 11} & 5 \cr
{ - 7} & { - 1} & {25} \cr
{ - 21} & { - 3} & { - 15} \cr
} } \rig...
MCQ+1 / -0.252018
50Matrices And Determinants
The least positive integer n such that \({\left( {\matrix{
{\cos \pi /4} & {\sin \pi /4} \cr
{ - \sin {\pi \over 4}} & {\cos {\pi \over 4}} \cr
} } \right)^n}\) is an identity matrix of order 2 is
MCQ+2 / -0.52018