Matrices and Determinants PYQs - Last 10 Years
JEE Main / Mathematics / Algebra / 336 recent questions
MathematicsAlgebra2017-2026
Practice 336 JEE Main 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 36 of 336 filtered questions.
1Matrices And Determinants
The greatest value of c \(\in\) R for which the system
of linear equations
x – cy – cz = 0
cx – y + cz = 0
cx + cy – z = 0
has a non-trivial solution, is :
of linear equations
x – cy – cz = 0
cx – y + cz = 0
cx + cy – z = 0
has a non-trivial solution, is :
MCQ+4 / -12019
2Matrices And Determinants
Let \(A = \left( {\matrix{
{\cos \alpha } & { - \sin \alpha } \cr
{\sin \alpha } & {\cos \alpha } \cr
} } \right)\), (\(\alpha\) \(\in\) R) such that $${A^{32}} = \left( {\matrix{
0 & { - 1} \cr
1 & 0 \cr
} } \rig...
0 & { - 1} \cr
1 & 0 \cr
} } \rig...
MCQ+4 / -12019
3Matrices And Determinants
Let the number 2,b,c be in an A.P. and
A = \(\left[ {\matrix{ 1 & 1 & 1 \cr 2 & b & c \cr 4 & {{b^2}} & {{c^2}} \cr } } \right]\). If det(A) \(\in\) [2, 16], then c
lies in the interval :
A = \(\left[ {\matrix{ 1 & 1 & 1 \cr 2 & b & c \cr 4 & {{b^2}} & {{c^2}} \cr } } \right]\). If det(A) \(\in\) [2, 16], then c
lies in the interval :
MCQ+4 / -12019
4Matrices And Determinants
Let P = \(\left[ {\matrix{
1 & 0 & 0 \cr
3 & 1 & 0 \cr
9 & 3 & 1 \cr
} } \right]\) and Q = [qij] be two 3 \(\times\) 3 matrices such that Q – P5 = I3.
Then \({{{q_{21}} + {q_{31}}} \over {{q_{32}}}}\) is equal to :
Then \({{{q_{21}} + {q_{31}}} \over {{q_{32}}}}\) is equal to :
MCQ+4 / -12019
5Matrices And Determinants
An ordered pair (\(\alpha\), \(\beta\)) for which the system of linear equations
(1 + \(\alpha\)) x + \(\beta\)y + z = 2
\(\alpha\)x + (1 + \(\beta\))y + z = 3
\(\alpha\)x + \(\beta\)y + 2z = 2
has a unique solution, is :
(1 + \(\alpha\)) x + \(\beta\)y + z = 2
\(\alpha\)x + (1 + \(\beta\))y + z = 3
\(\alpha\)x + \(\beta\)y + 2z = 2
has a unique solution, is :
MCQ+4 / -12019
6Matrices And Determinants
The set of all values of \(\lambda\) for which the system of linear equations
x – 2y – 2z = \(\lambda\)x
x + 2y + z = \(\lambda\)y
– x – y = \(\lambda\)z
has a non-trivial solutions :
x – 2y – 2z = \(\lambda\)x
x + 2y + z = \(\lambda\)y
– x – y = \(\lambda\)z
has a non-trivial solutions :
MCQ+4 / -12019
7Matrices And Determinants
If A = \(\left[ {\matrix{
1 & {\sin \theta } & 1 \cr
{ - \sin \theta } & 1 & {\sin \theta } \cr
{ - 1} & { - \sin \theta } & 1 \cr
} } \right]\);
then for all \(\theta\) \(\in\) $$\left( {{{3\pi } \over 4},{{5\pi } \o...
then for all \(\theta\) \(\in\) $$\left( {{{3\pi } \over 4},{{5\pi } \o...
MCQ+4 / -12019
8Matrices And Determinants
If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = \(\left[ {\matrix{
2 & 3 \cr
5 & { - 1} \cr
} } \right]\), then AB is equal
to :
to :
MCQ+4 / -12019
9Matrices And Determinants
If \(B = \left[ {\matrix{
5 & {2\alpha } & 1 \cr
0 & 2 & 1 \cr
\alpha & 3 & { - 1} \cr
} } \right]\) is the inverse of a 3 × 3 matrix A, then the sum of all values of \(\alpha\) for which
det(A) + 1 = 0, is :
det(A) + 1 = 0, is :
MCQ+4 / -12019
10Matrices And Determinants
A value of \(\theta \in \left( {0,{\pi \over 3}} \right)\), for which
$$\left| {\matrix{
{1 + {{\cos }^2}\theta } & {{{\sin }^2}\theta } & {4\cos 6\theta } \cr
{{{\cos }^2}\theta } & {1 + {{\sin }^2}\theta } & {4\cos 6\theta } \c...
$$\left| {\matrix{
{1 + {{\cos }^2}\theta } & {{{\sin }^2}\theta } & {4\cos 6\theta } \cr
{{{\cos }^2}\theta } & {1 + {{\sin }^2}\theta } & {4\cos 6\theta } \c...
MCQ+4 / -12019
11Matrices And Determinants
Let A = \(\left( {\matrix{
0 & {2q} & r \cr
p & q & { - r} \cr
p & { - q} & r \cr
} } \right).\) If AAT = I3, then \(\left| p \right|\) is :
MCQ+4 / -12019
12Matrices And Determinants
If the system of linear equations
2x + 2y + 3z = a
3x – y + 5z = b
x – 3y + 2z = c
where a, b, c are non zero real numbers, has more one solution, then :
2x + 2y + 3z = a
3x – y + 5z = b
x – 3y + 2z = c
where a, b, c are non zero real numbers, has more one solution, then :
MCQ+4 / -12019
13Matrices And Determinants
If \(\left| {\matrix{
{a - b - c} & {2a} & {2a} \cr
{2b} & {b - c - a} & {2b} \cr
{2c} & {2c} & {c - a - b} \cr
} } \right|\)
= (a + b + c) (x + a + b + c)2, x \(\ne\) 0,
then x is equal to :
= (a + b + c) (x + a + b + c)2, x \(\ne\) 0,
then x is equal to :
MCQ+4 / -12019
14Matrices And Determinants
Let A and B be two invertible matrices of order 3 \(\times\) 3. If det(ABAT) = 8 and det(AB–1) = 8,
then det (BA–1 BT) is equal to :
then det (BA–1 BT) is equal to :
MCQ+4 / -12019
15Matrices And Determinants
If the system of equations
x + y + z = 5
x + 2y + 3z = 9
x + 3y + az = \(\beta\)
has infinitely many solutions, then \(\beta\) \(-\) \(\alpha\) equals -
x + y + z = 5
x + 2y + 3z = 9
x + 3y + az = \(\beta\)
has infinitely many solutions, then \(\beta\) \(-\) \(\alpha\) equals -
MCQ+4 / -12019
16Matrices And Determinants
Let d \(\in\) R, and
$$A = \left[ {\matrix{
{ - 2} & {4 + d} & {\left( {\sin \theta } \right) - 2} \cr
1 & {\left( {\sin \theta } \right) + 2} & d \cr
5 & {\left( {2\sin \theta } \right) - d} & {\left( { - \sin \theta } \ri...
$$A = \left[ {\matrix{
{ - 2} & {4 + d} & {\left( {\sin \theta } \right) - 2} \cr
1 & {\left( {\sin \theta } \right) + 2} & d \cr
5 & {\left( {2\sin \theta } \right) - d} & {\left( { - \sin \theta } \ri...
MCQ+4 / -12019
17Matrices And Determinants
Let A = \(\left[ {\matrix{
2 & b & 1 \cr
b & {{b^2} + 1} & b \cr
1 & b & 2 \cr
} } \right]\) where b > 0.
Then the minimum value of \({{\det \left( A \right)} \over b}\) is -
Then the minimum value of \({{\det \left( A \right)} \over b}\) is -
MCQ+4 / -12019
18Matrices And Determinants
The number of values of \(\theta\) \(\in\) (0, \(\pi\)) for which the system of linear equations
x + 3y + 7z = 0
\(-\) x + 4y + 7z = 0
(sin3\(\theta\))x + (cos2\(\theta\))y + 2z = 0.
has a non-trival solution, is -
x + 3y + 7z = 0
\(-\) x + 4y + 7z = 0
(sin3\(\theta\))x + (cos2\(\theta\))y + 2z = 0.
has a non-trival solution, is -
MCQ+4 / -12019
19Matrices And Determinants
If the system of linear equations
x + y + z = 5
x + 2y + 2z = 6
x + 3y + \(\lambda\)z = \(\mu\), (\(\lambda\), \(\mu\) \(\in\) R), has infinitely many solutions, then the value of \(\lambda\) + \(\mu\) is :
x + y + z = 5
x + 2y + 2z = 6
x + 3y + \(\lambda\)z = \(\mu\), (\(\lambda\), \(\mu\) \(\in\) R), has infinitely many solutions, then the value of \(\lambda\) + \(\mu\) is :
MCQ+4 / -12019
20Matrices And Determinants
If \({\Delta _1} = \left| {\matrix{
x & {\sin \theta } & {\cos \theta } \cr
{ - \sin \theta } & { - x} & 1 \cr
{\cos \theta } & 1 & x \cr
} } \right|\) and
$${\Delta _2} = \left| {\matrix{
x & {\sin 2\theta } & {\cos 2\...
$${\Delta _2} = \left| {\matrix{
x & {\sin 2\theta } & {\cos 2\...
MCQ+4 / -12019
21Matrices And Determinants
Let \(\lambda\) be a real number for which the system of linear equations x + y + z = 6, 4x + \(\lambda\)y – \(\lambda\)z = \(\lambda\) – 2,
3x + 2y – 4z = – 5 has infinitely many solutions. Then \(\lambda\) is a root of the quadratic ...
3x + 2y – 4z = – 5 has infinitely many solutions. Then \(\lambda\) is a root of the quadratic ...
MCQ+4 / -12019
22Matrices And Determinants
The sum of the real roots of the equation
\(\left| {\matrix{ x & { - 6} & { - 1} \cr 2 & { - 3x} & {x - 3} \cr { - 3} & {2x} & {x + 2} \cr } } \right| = 0\), is equal to :
\(\left| {\matrix{ x & { - 6} & { - 1} \cr 2 & { - 3x} & {x - 3} \cr { - 3} & {2x} & {x + 2} \cr } } \right| = 0\), is equal to :
MCQ+4 / -12019
23Matrices And Determinants
The number of values of k for which the system of linear equations,
(k + 2)x + 10y = k
kx + (k +3)y = k -1
has no solution, is :
(k + 2)x + 10y = k
kx + (k +3)y = k -1
has no solution, is :
MCQ+4 / -12018
24Matrices And Determinants
Let A = \(\left[ {\matrix{
1 & 0 & 0 \cr
1 & 1 & 0 \cr
1 & 1 & 1 \cr
} } \right]\) and B = A20. Then the sum of the elements of the first column of B is :
MCQ+4 / -12018
25Matrices And Determinants
Let \(A\) be a matrix such that \(A.\left[ {\matrix{
1 & 2 \cr
0 & 3 \cr
} } \right]\) is a scalar matrix and |3A| = 108.
Then A2 equals :
Then A2 equals :
MCQ+4 / -12018
26Matrices And Determinants
Let S be the set of all real values of k for which the systemof linear equations
x + y + z = 2
2x + y \(-\) z = 3
3x + 2y + kz = 4
has a unique solution. Then S is :
x + y + z = 2
2x + y \(-\) z = 3
3x + 2y + kz = 4
has a unique solution. Then S is :
MCQ+4 / -12018
27Matrices And Determinants
If the system of linear equations
x + ay + z = 3
x + 2y + 2z = 6
x + 5y + 3z = b
has no solution, then :
x + ay + z = 3
x + 2y + 2z = 6
x + 5y + 3z = b
has no solution, then :
MCQ+4 / -12018
28Matrices And Determinants
Suppose A is any 3\(\times\) 3 non-singular matrix and ( A \(-\) 3I) (A \(-\) 5I) = O where I = I3 and O = O3. If \(\alpha\)A + \(\beta\)A-1 = 4I, then \(\alpha\) + \(\beta\) is equal to :
MCQ+4 / -12018
29Matrices And Determinants
If the system of linear equations
x + ky + 3z = 0
3x + ky - 2z = 0
2x + 4y - 3z = 0
has a non-zero solution (x, y, z), then \({{xz} \over {{y^2}}}\) is equal to
x + ky + 3z = 0
3x + ky - 2z = 0
2x + 4y - 3z = 0
has a non-zero solution (x, y, z), then \({{xz} \over {{y^2}}}\) is equal to
MCQ+4 / -12018
30Matrices And Determinants
If \(\left| {\matrix{
{x - 4} & {2x} & {2x} \cr
{2x} & {x - 4} & {2x} \cr
{2x} & {2x} & {x - 4} \cr
} } \right| = \left( {A + Bx} \right){\left( {x - A} \right)^2}\)
then the ordered pair (A, B) is equal to :
then the ordered pair (A, B) is equal to :
MCQ+4 / -12018
31Matrices And Determinants
For two 3 × 3 matrices A and B, let A + B = 2BT and 3A + 2B = I3, where BT is
the transpose of B and I3 is 3 × 3 identity matrix. Then :
the transpose of B and I3 is 3 × 3 identity matrix. Then :
MCQ+4 / -12017
32Matrices And Determinants
The number of real values of \(\lambda\) for which the system of linear equations
2x + 4y \(-\) \(\lambda\)z = 0
4x + \(\lambda\)y + 2z = 0
\(\lambda\)x + 2y + 2z = 0
has infinitely many solutions, is :
2x + 4y \(-\) \(\lambda\)z = 0
4x + \(\lambda\)y + 2z = 0
\(\lambda\)x + 2y + 2z = 0
has infinitely many solutions, is :
MCQ+4 / -12017
33Matrices And Determinants
If
\(S = \left\{ {x \in \left[ {0,2\pi } \right]:\left| {\matrix{ 0 & {\cos x} & { - \sin x} \cr {\sin x} & 0 & {\cos x} \cr {\cos x} & {\sin x} & 0 \cr } } \right| = 0} \right\},\)
then $$\sum\limits_{x \in S} {\tan \left...
\(S = \left\{ {x \in \left[ {0,2\pi } \right]:\left| {\matrix{ 0 & {\cos x} & { - \sin x} \cr {\sin x} & 0 & {\cos x} \cr {\cos x} & {\sin x} & 0 \cr } } \right| = 0} \right\},\)
then $$\sum\limits_{x \in S} {\tan \left...
MCQ+4 / -12017
34Matrices And Determinants
Let A be any 3 \(\times\) 3 invertible matrix. Then which one of the following is not always true ?
MCQ+4 / -12017
35Matrices And Determinants
If \(A = \left[ {\matrix{
2 & { - 3} \cr
{ - 4} & 1 \cr
} } \right]\),
then adj(3A2 + 12A) is equal to
then adj(3A2 + 12A) is equal to
MCQ+4 / -12017
36Matrices And Determinants
If S is the set of distinct values of 'b' for which the following system of linear equations
x + y + z = 1
x + ay + z = 1
ax + by + z = 0
has no solution, then S is :
x + y + z = 1
x + ay + z = 1
ax + by + z = 0
has no solution, then S is :
MCQ+4 / -12017