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Matrices and Determinants JEE Main PYQs (2002–2024) with Solutions — Mathematics | JEE Arc

Mathematics

Matrices and Determinants

Appeared 245 times across 23 years of JEE Main papers — about 10.7 questions a year. Every one of them is below, with a full worked solution.

Questions per year

1’02

3’03

3’04

4’05

2’06

2’07

3’08

2’09

3’10

2’11

2’12

2’13

2’14

2’15

6’16

6’17

8’18

30’19

25’20

37’21

31’22

41’23

28’24

364 questions in the bank

Practise this topic

Q01JEE Main 202431 Jan, Shift 1EasyMatrices and Determinants245× since 2002

A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix}

, then

\det(A)

equals

Q02JEE Main 2025April, Unspecified (session-level dataset)MediumMatrices and Determinants245× since 2002

If the system of equations \\

2x + \lambda y + 3z = 5

3x + 2y - z = 7

4x + 5y + \mu z = 9

\\ has infinitely many solutions, then

(\lambda^2 + \mu^2)

is equal to:

Q03JEE Main 2025April, Unspecified (session-level dataset)MediumMatrices and Determinants245× since 2002

Let

A

be a

3 \times 3

real matrix such that

A^2(A - 2I) - 4(A - I) = O

, where

I

and

O

are the identity and null matrices, respectively. If

A^5 = \alpha A^2 + \beta A + \gamma I

, where

\alpha

\beta

and

\gamma

are real constants, then

\alpha + \beta + \gamma

is equal to:

Q04JEE Main 2025April, Unspecified (session-level dataset)MediumMatrices and Determinants245× since 2002

If the system of linear equations

3x + y + \beta z = 3

2x + \alpha y - z = -3

x + 2y + z = 4

has infinitely many solutions, then the value of

22\beta - 9\alpha

is:

Q05JEE Main 2025April, Unspecified (session-level dataset)MediumMatrices and Determinants245× since 2002

Let

a\in\mathbb{R}

and

A

be a matrix of order

3\times3

such that

\det(A)=-4

and

A+I=\begin{pmatrix}1 & a & 1\\2 & 1 & 0\\a & 1 & 2\end{pmatrix},

where

I

is the

3\times3

identity. If

\det\bigl((a+1)\adj((a-1)A)\bigr)=2^m3^n,\quad m,n\in\{0,1,2,\dots,20\},

then

m+n

is equal to:

Q06JEE Main 2025April, Unspecified (session-level dataset)MediumMatrices and Determinants245× since 2002

Let

A

be a matrix of order

3\times3

with

\lvert A\rvert=5

. If

\bigl\lvert 2\,\mathrm{adj}\bigl(3A\,\mathrm{adj}(2A)\bigr)\bigr\rvert=2^{\alpha}3^{\beta}5^{\gamma}

, where

\alpha,\beta,\gamma\in\mathbb{N}

, then

\alpha+\beta+\gamma

is equal to:

Q07JEE Main 2025April, Unspecified (session-level dataset)MediumMatrices and Determinants245× since 2002

y(x)=\begin{vmatrix} \sin x & \cos x & \sin x+\cos x+1 \\ 27 & 28 & 27 \\ 1 & 1 & 1 \end{vmatrix},\;x\in\mathbb{R},

then

\frac{d^2y}{dx^2}+y

is equal to:

Q08JEE Main 2025April, Unspecified (session-level dataset)MediumMatrices and Determinants245× since 2002

Let the matrix

A=\begin{pmatrix}1&0&0\\1&0&1\\0&1&0\end{pmatrix}

satisfy

A^n = A^{n-2} + A^2 - I

for

n\ge3

. Then the sum of all the elements of

A^{50}

is:

Q09JEE Main 2025April, Unspecified (session-level dataset)MediumMatrices and Determinants245× since 2002

Let the system of equations

x + 5y - z = 1

4x + 3y - 3z = 7

, and

24x + y + \lambda z = \mu

, with

\lambda,\mu \in \mathbb{R}

, have infinitely many solutions. Then the number of solutions of this system, if

x,y,z

are integers and satisfy

7 \le x+y+z \le 77

, is:

Q10JEE Main 2025April, Unspecified (session-level dataset)MediumMatrices and Determinants245× since 2002

Let

A

be a

3 \times 3

matrix such that

|\operatorname{adj} (\operatorname{adj}(\operatorname{adj} A))| = 81

. If

S = \left\{ n \in \mathbb{Z} : |\operatorname{adj}(\operatorname{adj} A)|^{\frac{(n-1)^2}{2}} = |A|^{3n^2 - 5n - 4} \right\},

then

\sum_{n \in S} \left| A^{n^2 + n} \right|

is equal to:

Showing the first 10 of 364. Practise this topic or open any question from the full list below.

All 364 Matrices and Determinants questions by year

JEE Main 2026 · 31

JEE Main 2025 · 24

JEE Main 2024 · 41

JEE Main 2023 · 47

JEE Main 2022 · 46

JEE Main 2021 · 61

JEE Main 2020 · 31

JEE Main 2019 · 30

JEE Main 2018 · 8

JEE Main 2017 · 6

JEE Main 2016 · 6

JEE Main 2015 · 2

JEE Main 2014 · 2

JEE Main 2013 · 2

JEE Main 2012 · 2

JEE Main 2011 · 2

JEE Main 2010 · 3

JEE Main 2009 · 2

JEE Main 2008 · 3

JEE Main 2007 · 2

JEE Main 2006 · 2

JEE Main 2005 · 4

JEE Main 2004 · 3

JEE Main 2003 · 3

JEE Main 2002 · 1

Annual Paper 1 · Q4433: If a>0 and discriminant of a x² + 2bx + c is -ve, then | a b ax + b b c bx + c ax + b bx + c 0 | is equal to