Determinants JEE Main PYQs PDF, 2020–2026

Determinants questions per year

Topic-wise weightage by year

How many Determinants questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Swipe the table sideways for older years.

Newest questions (2026)

The 12 newest of the 20 JEE Main 2026 Determinants questions in the free PDF, latest shift first.

1. JEE Main 2026 · 8 Apr · Shift 2 · Consistency of Linear Equations

   If the system of linear equations :

   $\begin{array}{cc} & x+y+z=6 \\ & x+2y+5z=10 \\ & 2x+3y+\lambda z=\mu\end{array}$

   has infinitely many solutions, then the value of $\lambda+\mu$ equals:

   Solve it online →

2. JEE Main 2026 · 8 Apr · Shift 2 · Adjoint and Inverse

   Let $A=\left[\begin{array}{ccc}\alpha & 1 & 2 \\ 2 & 3 & 0 \\ 0 & 4 & 5\end{array}\right]$ and $B=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & -5\alpha & 0 \\ 0 & 4\alpha & -2\alpha\end{array}\right]+\mathrm{adj}(A)$. If $\det (B)=66$, then $\det (\mathrm{adj}(A))$ equals :

   Solve it online →

3. JEE Main 2026 · 6 Apr · Shift 1 · Adjoint and Inverse

   Let $A=\left[\begin{array}{ccc}-1 & 1 & -1 \\ 1 & 0 & 1 \\ 0 & 0 & 1\end{array}\right]$ satisfy

   ${\mathrm{A}}^{2}+\alpha(\mathrm{adj}(\mathrm{adj}({\mathrm{A}})))+\beta(\mathrm{adj}({\mathrm{A}})(\mathrm{adj}(\mathrm{adj}({\mathrm{A}}))))=\left[\begin{array}{ccc}2 & -2 & 2 \\ -2 & 0 & -1 \\ 0 & 0 & -1\end{array}\right]$ for some $\alpha,\beta\in {\mathbb{R}}$.

   Then $(\alpha-\beta)^{2}$ is equal to $\_\_\_\_$

   Solve it online →

4. JEE Main 2026 · 6 Apr · Shift 2 · Consistency of Linear Equations

   The sum of all possible values of $\theta\in [0,2\pi]$, for which the system of equations :

   $\begin{array}{cc} & x\cos 3\theta-8y-12z=0 \\ & x\cos 2\theta+3y+3z=0 \\ & x+y+3z=0\end{array}$

   has a non-trivial solution, is equal to :

   Solve it online →

5. JEE Main 2026 · 5 Apr · Shift 2 · Properties of Determinants

   If $f:{\mathbf{N}}\rightarrow {\mathbf{Z}}$ is defined by

   $f(n)=\left|\begin{array}{ccc}n & -1 & -5 \\ -2n^{2} & 3(2k+1) & 2k+1 \\ -3n^{3} & 3k(2k+1) & 3k(k+2)+1\end{array}\right|,k\in N,$

   and $\sum_{{n=1}}^{k}f(n)=98$, then $k$ is equal to :

   Solve it online →

6. JEE Main 2026 · 5 Apr · Shift 1 · Consistency of Linear Equations

   Consider the system of linear equations in $x,y,z$ :

   $\begin{array}{cc} & x+2y+tz=0 \\ & 6x+y+5tz=0 \\ & 3x+t^{2}y+f(t)z=0\end{array}$

   where $f:{\mathbb{R}}\rightarrow {\mathbb{R}}$ is a differentiable function. If this system has infinitely many solutions for all $t\in {\mathbb{R}}$, then $f$

   Solve it online →

7. JEE Main 2026 · 4 Apr · Shift 2 · Consistency of Linear Equations

   If the system of equations :

   $\begin{array}{cc} & x+y+z=5 \\ & x+2y+3z=9 \\ & x+3y+\lambda z=\mu\end{array}$

   has infinitely many solutions, then the value of $\lambda+\mu$ is :

   Solve it online →

8. JEE Main 2026 · 4 Apr · Shift 1 · Adjoint and Inverse

   Let $A=\left[\begin{array}{ccc}1 & 1 & 2 \\ -2 & 0 & 1 \\ 1 & 3 & 5\end{array}\right]$. Then the sum of all elements of the matrix $\mathrm{adj}\left(\mathrm{adj}\left(2(\mathrm{adj}{\ \mathrm{A}})^{{-1}}\right)\right)$ is equal to:

   Solve it online →

9. JEE Main 2026 · 4 Apr · Shift 2 · Properties of Determinants

   Let $A=\left[\begin{array}{ccc}1 & 2 & 7 \\ 4 & -2 & 8 \\ 3 & 8 & -7\end{array}\right]$ and $\det (A-\alpha I)=0$, where $\alpha$ is a real number. If the largest possible value of $\alpha$ is $p$, then the circle $(x-p)^{2}+(y-2p)^{2}=320$, intersects the co-ordinate axes at

   Solve it online →

10. JEE Main 2026 · 2 Apr · Shift 1 · Consistency of Linear Equations

    Let $\alpha,\beta\in {\mathbb{R}}$ be such that the system of linear equations

    $\begin{array}{cc}x+2y+z & =5 \\ 2x+y+\alpha z & =5 \\ 8x+4y+\beta z & =18\end{array}$

    has no solution. Then $\frac{\beta}{\alpha}$ is equal to :

    Solve it online →

11. JEE Main 2026 · 2 Apr · Shift 2 · Consistency of Linear Equations

    If the system of equations

    $x+5y+6z=4$

    $2x+3y+4z=7$

    $x+6y+az=b$

    has infinitely many solutions, then the point $(a,b)$ lies on the line

    Solve it online →

12. JEE Main 2026 · 24 Jan · Shift 2 · Adjoint and Inverse

    Let $P=[p_{{ij}}]$ and $Q=[q_{{ij}}]$ be two square matrices of order 3 such that $q_{{{\mathrm{ij}}}}=2^{{({\mathrm{i}}+{\mathrm{j}}-1)}}{\mathrm{p}}_{{{\mathrm{ij}}}}$ and $\det ({\mathrm{Q}})=2^{{10}}$. Then the value of $\det (\mathrm{adj}(\mathrm{adj}{\mathrm{P}}))$ is:

    Solve it online →

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