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2024 
Q1 - 2024 (01 Feb Shift 1) 
If the system of equations 
2 ?? + 3 ?? - ?? = 5 
?? + ???? + 3 ?? = - 4 
3 ?? - ?? + ???? = 7 
has infinitely many solutions, then 13 ???? is equal to 
(1) 1110 
(2) 1120 
(3) 1210 
(4) 1220 
Q2 - 2024 (01 Feb Shift 2) 
Let the system of equations ?? + 2 ?? + 3 ?? = 5 , 2 ?? + 3 ?? + ?? = 9 , 4 ?? + 3 ?? + ???? = ?? have 
infinite number of solutions. Then ?? + 2 ?? is equal to : 
(1) 28 
(2) 17 
(3) 22 
(4) 15 
Q3 - 2024 (27 Jan Shift 1) 
Let ?? = [
2 0 1
1 1 0
1 0 1
] , ?? = [ ?? 1
, ?? 2
, ?? 3
], where ?? 1
, ?? 2
, ?? 3
 are column matrices, and ?? 1
= [
1
0
0
], 
AB
2
= [
2
3
0
] , AB
3
= [
3
2
1
] 
Page 2


 
2024 
Q1 - 2024 (01 Feb Shift 1) 
If the system of equations 
2 ?? + 3 ?? - ?? = 5 
?? + ???? + 3 ?? = - 4 
3 ?? - ?? + ???? = 7 
has infinitely many solutions, then 13 ???? is equal to 
(1) 1110 
(2) 1120 
(3) 1210 
(4) 1220 
Q2 - 2024 (01 Feb Shift 2) 
Let the system of equations ?? + 2 ?? + 3 ?? = 5 , 2 ?? + 3 ?? + ?? = 9 , 4 ?? + 3 ?? + ???? = ?? have 
infinite number of solutions. Then ?? + 2 ?? is equal to : 
(1) 28 
(2) 17 
(3) 22 
(4) 15 
Q3 - 2024 (27 Jan Shift 1) 
Let ?? = [
2 0 1
1 1 0
1 0 1
] , ?? = [ ?? 1
, ?? 2
, ?? 3
], where ?? 1
, ?? 2
, ?? 3
 are column matrices, and ?? 1
= [
1
0
0
], 
AB
2
= [
2
3
0
] , AB
3
= [
3
2
1
] 
If ?? = | ?? | and ?? is the sum of all the diagonal elements of B, then ?? 3
+ ?? 3
 is equal to 
Q4 - 2024 (27 Jan Shift 2) 
The values of ?? , for which 
|
1
3
2
?? +
3
2
1
1
3
?? +
1
3
2 ?? + 3 3 ?? + 1 0
| = 0, 
lie in the interval 
(1) ( - 2 , 1 ) 
(2) ( - 3 , 0 ) 
(3) ( -
3
2
,
3
2
) 
(4) ( 0 , 3 ) 
Q5 - 2024 (29 Jan Shift 2) 
Let for any three distinct consecutive terms a , b , c of an A.P, the lines ???? + ???? + ?? = 0 be 
concurrent at the point P and Q ( ?? , ?? ) be a point such that the system of equations 
?? + ?? + ?? = 6, 
2 ?? + 5 ?? + ???? = ?? and 
?? + 2 ?? + 3 ?? = 4, has infinitely many solutions. Then ( PQ )
2
 is equal to 
Q6 - 2024 (30 Jan Shift 1) 
Consider the system of linear equation x + y + z = 4 ?? , ?? + 2 ?? + 2 ???? = 10 ?? , ?? + 3 ?? +
4 ?? 2
?? = ?? 2
+ 15, where ?? , ?? ? R. Which one of the following statements is NOT correct? 
(1) The system has unique solution if ?? ?
1
2
 and ?? ? 1 , 15 
(2) The system is inconsistent if ?? =
1
2
 and ?? ? 1 
(3) The system has infinite number of solutions if ?? =
1
2
 and ?? = 15 
(4) The system is consistent if ?? ?
1
2
 
Q7 - 2024 (30 Jan Shift 1) 
Page 3


 
2024 
Q1 - 2024 (01 Feb Shift 1) 
If the system of equations 
2 ?? + 3 ?? - ?? = 5 
?? + ???? + 3 ?? = - 4 
3 ?? - ?? + ???? = 7 
has infinitely many solutions, then 13 ???? is equal to 
(1) 1110 
(2) 1120 
(3) 1210 
(4) 1220 
Q2 - 2024 (01 Feb Shift 2) 
Let the system of equations ?? + 2 ?? + 3 ?? = 5 , 2 ?? + 3 ?? + ?? = 9 , 4 ?? + 3 ?? + ???? = ?? have 
infinite number of solutions. Then ?? + 2 ?? is equal to : 
(1) 28 
(2) 17 
(3) 22 
(4) 15 
Q3 - 2024 (27 Jan Shift 1) 
Let ?? = [
2 0 1
1 1 0
1 0 1
] , ?? = [ ?? 1
, ?? 2
, ?? 3
], where ?? 1
, ?? 2
, ?? 3
 are column matrices, and ?? 1
= [
1
0
0
], 
AB
2
= [
2
3
0
] , AB
3
= [
3
2
1
] 
If ?? = | ?? | and ?? is the sum of all the diagonal elements of B, then ?? 3
+ ?? 3
 is equal to 
Q4 - 2024 (27 Jan Shift 2) 
The values of ?? , for which 
|
1
3
2
?? +
3
2
1
1
3
?? +
1
3
2 ?? + 3 3 ?? + 1 0
| = 0, 
lie in the interval 
(1) ( - 2 , 1 ) 
(2) ( - 3 , 0 ) 
(3) ( -
3
2
,
3
2
) 
(4) ( 0 , 3 ) 
Q5 - 2024 (29 Jan Shift 2) 
Let for any three distinct consecutive terms a , b , c of an A.P, the lines ???? + ???? + ?? = 0 be 
concurrent at the point P and Q ( ?? , ?? ) be a point such that the system of equations 
?? + ?? + ?? = 6, 
2 ?? + 5 ?? + ???? = ?? and 
?? + 2 ?? + 3 ?? = 4, has infinitely many solutions. Then ( PQ )
2
 is equal to 
Q6 - 2024 (30 Jan Shift 1) 
Consider the system of linear equation x + y + z = 4 ?? , ?? + 2 ?? + 2 ???? = 10 ?? , ?? + 3 ?? +
4 ?? 2
?? = ?? 2
+ 15, where ?? , ?? ? R. Which one of the following statements is NOT correct? 
(1) The system has unique solution if ?? ?
1
2
 and ?? ? 1 , 15 
(2) The system is inconsistent if ?? =
1
2
 and ?? ? 1 
(3) The system has infinite number of solutions if ?? =
1
2
 and ?? = 15 
(4) The system is consistent if ?? ?
1
2
 
Q7 - 2024 (30 Jan Shift 1) 
If ?? ( ?? ) = |
2 c o s
4
? ?? 2 sin
4
? ?? 3 + sin
2
? 2 ?? 3 + 2 c o s
4
? ?? 2 sin
4
? ?? sin
2
? 2 ?? 2 c o s
4
? ?? 3 + 2 sin
4
? ?? sin
2
? 2 ?? | then 
1
5
?? '
( 0 ) is equal to 
(1) 0 
(2) 1 
(3) 2 
(4) 6 
Q8 - 2024 (30 Jan Shift 2) 
Consider the system of linear equations 
?? + ?? + ?? = 5 , ?? + 2 ?? + ?? 2
?? = 9 
?? + 3 ?? + ???? = ?? , where ?? , ?? ? ?? . Then, which of the following statement is NOT correct? 
(1) System has infinite number of solution if ?? = 1 and ?? = 13 
(2) System is inconsistent if ?? = 1 and ?? ? 13 
(3) System is consistent if ?? ? 1 and ?? = 13 
(4) System has unique solution if ?? ? 1 and ?? ? 13 
Q9 - 2024 (31 Jan Shift 1) 
If the system of linear equations 
?? - 2 ?? + ?? = - 4 
2 ?? + ???? + 3 ?? = 5 
3 ?? - ?? + ???? = 3 
has infinitely many solutions, then 12 ?? + 13 ?? is equal to 
(1) 60 
(2) 64 
(3) 54 
(4) 58 
Q10 - 2024 (31 Jan Shift 1) 
Page 4


 
2024 
Q1 - 2024 (01 Feb Shift 1) 
If the system of equations 
2 ?? + 3 ?? - ?? = 5 
?? + ???? + 3 ?? = - 4 
3 ?? - ?? + ???? = 7 
has infinitely many solutions, then 13 ???? is equal to 
(1) 1110 
(2) 1120 
(3) 1210 
(4) 1220 
Q2 - 2024 (01 Feb Shift 2) 
Let the system of equations ?? + 2 ?? + 3 ?? = 5 , 2 ?? + 3 ?? + ?? = 9 , 4 ?? + 3 ?? + ???? = ?? have 
infinite number of solutions. Then ?? + 2 ?? is equal to : 
(1) 28 
(2) 17 
(3) 22 
(4) 15 
Q3 - 2024 (27 Jan Shift 1) 
Let ?? = [
2 0 1
1 1 0
1 0 1
] , ?? = [ ?? 1
, ?? 2
, ?? 3
], where ?? 1
, ?? 2
, ?? 3
 are column matrices, and ?? 1
= [
1
0
0
], 
AB
2
= [
2
3
0
] , AB
3
= [
3
2
1
] 
If ?? = | ?? | and ?? is the sum of all the diagonal elements of B, then ?? 3
+ ?? 3
 is equal to 
Q4 - 2024 (27 Jan Shift 2) 
The values of ?? , for which 
|
1
3
2
?? +
3
2
1
1
3
?? +
1
3
2 ?? + 3 3 ?? + 1 0
| = 0, 
lie in the interval 
(1) ( - 2 , 1 ) 
(2) ( - 3 , 0 ) 
(3) ( -
3
2
,
3
2
) 
(4) ( 0 , 3 ) 
Q5 - 2024 (29 Jan Shift 2) 
Let for any three distinct consecutive terms a , b , c of an A.P, the lines ???? + ???? + ?? = 0 be 
concurrent at the point P and Q ( ?? , ?? ) be a point such that the system of equations 
?? + ?? + ?? = 6, 
2 ?? + 5 ?? + ???? = ?? and 
?? + 2 ?? + 3 ?? = 4, has infinitely many solutions. Then ( PQ )
2
 is equal to 
Q6 - 2024 (30 Jan Shift 1) 
Consider the system of linear equation x + y + z = 4 ?? , ?? + 2 ?? + 2 ???? = 10 ?? , ?? + 3 ?? +
4 ?? 2
?? = ?? 2
+ 15, where ?? , ?? ? R. Which one of the following statements is NOT correct? 
(1) The system has unique solution if ?? ?
1
2
 and ?? ? 1 , 15 
(2) The system is inconsistent if ?? =
1
2
 and ?? ? 1 
(3) The system has infinite number of solutions if ?? =
1
2
 and ?? = 15 
(4) The system is consistent if ?? ?
1
2
 
Q7 - 2024 (30 Jan Shift 1) 
If ?? ( ?? ) = |
2 c o s
4
? ?? 2 sin
4
? ?? 3 + sin
2
? 2 ?? 3 + 2 c o s
4
? ?? 2 sin
4
? ?? sin
2
? 2 ?? 2 c o s
4
? ?? 3 + 2 sin
4
? ?? sin
2
? 2 ?? | then 
1
5
?? '
( 0 ) is equal to 
(1) 0 
(2) 1 
(3) 2 
(4) 6 
Q8 - 2024 (30 Jan Shift 2) 
Consider the system of linear equations 
?? + ?? + ?? = 5 , ?? + 2 ?? + ?? 2
?? = 9 
?? + 3 ?? + ???? = ?? , where ?? , ?? ? ?? . Then, which of the following statement is NOT correct? 
(1) System has infinite number of solution if ?? = 1 and ?? = 13 
(2) System is inconsistent if ?? = 1 and ?? ? 13 
(3) System is consistent if ?? ? 1 and ?? = 13 
(4) System has unique solution if ?? ? 1 and ?? ? 13 
Q9 - 2024 (31 Jan Shift 1) 
If the system of linear equations 
?? - 2 ?? + ?? = - 4 
2 ?? + ???? + 3 ?? = 5 
3 ?? - ?? + ???? = 3 
has infinitely many solutions, then 12 ?? + 13 ?? is equal to 
(1) 60 
(2) 64 
(3) 54 
(4) 58 
Q10 - 2024 (31 Jan Shift 1) 
If ?? ( ?? ) = |
?? 3
2 ?? 2
+ 1 1 + 3 ?? 3 ?? 2
+ 2 2 ?? ?? 3
+ 6
?? 3
- ?? 4 ?? 2
- 2
| for all ?? ? R, then 2 ?? ( 0 ) + ?? '
( 0 ) is equal to 
(1) 48 
(2) 24 
(3) 42 
(4) 18 
Q11 - 2024 (31 Jan Shift 2) 
Let ?? be a 3 × 3 real matrix such that 
A (
1
0
1
) = 2 (
1
0
1
) , A (
- 1
0
1
) = 4 (
- 1
0
1
) , A (
0
1
0
) = 2 (
0
1
0
). 
Then, the system ( ?? - 3 ?? ) (
?? ?? ?? ) = (
1
2
3
) has 
(1) unique solution 
(2) exactly two solutions 
(3) no solution 
(4) infinitely many solutions 
Answer Key 
Q1 (2)  ???? (2) Q3 (28)  Q4 (2) 
Q5 (113)  Q6 (2) Q7 (1)  Q8 (4) 
Q9 (4) ?? ?? ?? ( ?? ) Q11 (1)  
 
Solutions 
Q1 
Using family of planes 
2x + 3y - z - 5 = k
1
( x + ?? y + 3z + 4 ) + k
2
( 3x - y 
Page 5


 
2024 
Q1 - 2024 (01 Feb Shift 1) 
If the system of equations 
2 ?? + 3 ?? - ?? = 5 
?? + ???? + 3 ?? = - 4 
3 ?? - ?? + ???? = 7 
has infinitely many solutions, then 13 ???? is equal to 
(1) 1110 
(2) 1120 
(3) 1210 
(4) 1220 
Q2 - 2024 (01 Feb Shift 2) 
Let the system of equations ?? + 2 ?? + 3 ?? = 5 , 2 ?? + 3 ?? + ?? = 9 , 4 ?? + 3 ?? + ???? = ?? have 
infinite number of solutions. Then ?? + 2 ?? is equal to : 
(1) 28 
(2) 17 
(3) 22 
(4) 15 
Q3 - 2024 (27 Jan Shift 1) 
Let ?? = [
2 0 1
1 1 0
1 0 1
] , ?? = [ ?? 1
, ?? 2
, ?? 3
], where ?? 1
, ?? 2
, ?? 3
 are column matrices, and ?? 1
= [
1
0
0
], 
AB
2
= [
2
3
0
] , AB
3
= [
3
2
1
] 
If ?? = | ?? | and ?? is the sum of all the diagonal elements of B, then ?? 3
+ ?? 3
 is equal to 
Q4 - 2024 (27 Jan Shift 2) 
The values of ?? , for which 
|
1
3
2
?? +
3
2
1
1
3
?? +
1
3
2 ?? + 3 3 ?? + 1 0
| = 0, 
lie in the interval 
(1) ( - 2 , 1 ) 
(2) ( - 3 , 0 ) 
(3) ( -
3
2
,
3
2
) 
(4) ( 0 , 3 ) 
Q5 - 2024 (29 Jan Shift 2) 
Let for any three distinct consecutive terms a , b , c of an A.P, the lines ???? + ???? + ?? = 0 be 
concurrent at the point P and Q ( ?? , ?? ) be a point such that the system of equations 
?? + ?? + ?? = 6, 
2 ?? + 5 ?? + ???? = ?? and 
?? + 2 ?? + 3 ?? = 4, has infinitely many solutions. Then ( PQ )
2
 is equal to 
Q6 - 2024 (30 Jan Shift 1) 
Consider the system of linear equation x + y + z = 4 ?? , ?? + 2 ?? + 2 ???? = 10 ?? , ?? + 3 ?? +
4 ?? 2
?? = ?? 2
+ 15, where ?? , ?? ? R. Which one of the following statements is NOT correct? 
(1) The system has unique solution if ?? ?
1
2
 and ?? ? 1 , 15 
(2) The system is inconsistent if ?? =
1
2
 and ?? ? 1 
(3) The system has infinite number of solutions if ?? =
1
2
 and ?? = 15 
(4) The system is consistent if ?? ?
1
2
 
Q7 - 2024 (30 Jan Shift 1) 
If ?? ( ?? ) = |
2 c o s
4
? ?? 2 sin
4
? ?? 3 + sin
2
? 2 ?? 3 + 2 c o s
4
? ?? 2 sin
4
? ?? sin
2
? 2 ?? 2 c o s
4
? ?? 3 + 2 sin
4
? ?? sin
2
? 2 ?? | then 
1
5
?? '
( 0 ) is equal to 
(1) 0 
(2) 1 
(3) 2 
(4) 6 
Q8 - 2024 (30 Jan Shift 2) 
Consider the system of linear equations 
?? + ?? + ?? = 5 , ?? + 2 ?? + ?? 2
?? = 9 
?? + 3 ?? + ???? = ?? , where ?? , ?? ? ?? . Then, which of the following statement is NOT correct? 
(1) System has infinite number of solution if ?? = 1 and ?? = 13 
(2) System is inconsistent if ?? = 1 and ?? ? 13 
(3) System is consistent if ?? ? 1 and ?? = 13 
(4) System has unique solution if ?? ? 1 and ?? ? 13 
Q9 - 2024 (31 Jan Shift 1) 
If the system of linear equations 
?? - 2 ?? + ?? = - 4 
2 ?? + ???? + 3 ?? = 5 
3 ?? - ?? + ???? = 3 
has infinitely many solutions, then 12 ?? + 13 ?? is equal to 
(1) 60 
(2) 64 
(3) 54 
(4) 58 
Q10 - 2024 (31 Jan Shift 1) 
If ?? ( ?? ) = |
?? 3
2 ?? 2
+ 1 1 + 3 ?? 3 ?? 2
+ 2 2 ?? ?? 3
+ 6
?? 3
- ?? 4 ?? 2
- 2
| for all ?? ? R, then 2 ?? ( 0 ) + ?? '
( 0 ) is equal to 
(1) 48 
(2) 24 
(3) 42 
(4) 18 
Q11 - 2024 (31 Jan Shift 2) 
Let ?? be a 3 × 3 real matrix such that 
A (
1
0
1
) = 2 (
1
0
1
) , A (
- 1
0
1
) = 4 (
- 1
0
1
) , A (
0
1
0
) = 2 (
0
1
0
). 
Then, the system ( ?? - 3 ?? ) (
?? ?? ?? ) = (
1
2
3
) has 
(1) unique solution 
(2) exactly two solutions 
(3) no solution 
(4) infinitely many solutions 
Answer Key 
Q1 (2)  ???? (2) Q3 (28)  Q4 (2) 
Q5 (113)  Q6 (2) Q7 (1)  Q8 (4) 
Q9 (4) ?? ?? ?? ( ?? ) Q11 (1)  
 
Solutions 
Q1 
Using family of planes 
2x + 3y - z - 5 = k
1
( x + ?? y + 3z + 4 ) + k
2
( 3x - y 
+ ?? ?? - 7 ) 
2 = k
1
+ 3 k
2
, 3 = k
1
?? - k
2
, - 1 = 3 k
1
+ ?? k
2
, - 5 = 
4 k
1
- 7 k
2
 
On solving we get 
?? 2
=
13
19
, ?? 1
=
- 1
19
, ?? = - 70 , ?? =
- 16
13
13 ???? = 13 ( - 70 ) (
- 16
13
)
= 1 1 2 0
 
Q2 
?? + 2 ?? + 3 ?? = 5 
2 ?? + 3 ?? + ?? = 9 
4 ?? + 3 ?? + ???? = ?? 
for infinite following ? = ?
1
= ?
2
= ?
3
= 0 
? = |
1 2 3
2 3 1
4 3 ?? | = 0 ? ?? = - 13 
?
1
= |
5 2 3
9 3 1
?? 3 -13
| = 0 ? ?? = 15 
?
2
= |
1 5 3
2 9 1
4 15 -13
| = 0 
?
3
= |
1 2 5
2 3 9
4 3 15
| = 0 
for ?? = - 13 , ?? = 15 system of equation has infinite solution hence ?? + 2 ?? = 17 
Q3 
?? = [
2 0 1
1 1 0
1 0 1
] ? B = [ B
1
, B
2
, B
3
] 
B
1
= [
x
1
y
1
z
1
] , ? B
2
= [
x
2
y
2
z
2
] , ? B
3
= [
x
3
y
3
z
3
]
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FAQs on JEE Mains Previous Year Questions (2021-2024): Matrices and Determinants - Mathematics (Maths) for JEE Main & Advanced

1. What are the basic concepts of matrices and determinants in JEE Mains?
Ans. Matrices and determinants are fundamental topics in mathematics that involve arrays of numbers and their properties. Matrices are used to represent data or systems of equations, while determinants are used to calculate the volume scaling factor of a matrix.
2. How are matrices and determinants applied in solving JEE Mains problems?
Ans. Matrices and determinants are commonly used in JEE Mains problems to solve systems of linear equations, find inverses of matrices, calculate areas and volumes, and perform transformations in geometry.
3. What are the key properties of matrices and determinants that are important for JEE Mains preparation?
Ans. Some important properties of matrices and determinants include the commutative property of addition, distributive property, scalar multiplication, determinant of a product of matrices, and the properties of determinants such as linearity and alternating property.
4. How can one improve their skills in solving matrices and determinants problems for JEE Mains?
Ans. Practice is key to improving skills in solving matrices and determinants problems. Students can solve a variety of problems, practice using different properties and theorems, and review past JEE Mains questions related to matrices and determinants.
5. Are there any specific tips or strategies for mastering matrices and determinants for JEE Mains?
Ans. Some tips for mastering matrices and determinants include understanding the basic concepts thoroughly, memorizing important formulas and properties, practicing regularly, and seeking help from teachers or online resources for clarification on difficult topics.
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JEE Mains Previous Year Questions (2021-2024): Matrices and Determinants JEE

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