Matrices

JEE Main · Mathematics · 11 past questions

These are the board's own papers. 108 more board questions reprinted in the books we use in class are for signed-in students: sign in.

1. Q1 2026 2 Apr Shift 1

   Let $A=\begin{bmatrix}1&2\\1&\alpha\end{bmatrix}$ and $B=\begin{bmatrix}3&3\\\beta&2\end{bmatrix}$. If…

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2. Q2 2026 2 Apr Shift 2

   Consider the matrices $A=\begin{bmatrix}2&-2\\4&-2\end{bmatrix}$ and…

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3. Q3 2026 4 Apr Shift 1

   Let $S=\left\{A=\begin{bmatrix}a&b\\c&d\end{bmatrix}: a,b,c,d\in\{0,1,2,3,4\}\text{ and }A^2-4A+3I=0\right\}$…

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4. Q4 2026 4 Apr Shift 1

   Let $A = \begin{bmatrix} 1 & 1 & 2 \\ -2 & 0 & 1 \\ 1 & 3 & 5 \end{bmatrix}$. Then the sum of all elements of…

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5. Q5 2026 4 Apr Shift 2

   If the system of equations…

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6. Q6 2026 5 Apr Shift 1

   Let A be a $3\times 3$ matrix such that…

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7. Q7 2026 5 Apr Shift 2

   Let M be a $3\times 3$ matrix such that…

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8. Q8 2026 6 Apr Shift 1

   Let $A=\begin{bmatrix}-1&1&-1\\1&0&1\\0&0&1\end{bmatrix}$ satisfy…

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9. Q9 2026 6 Apr Shift 2

   Let $A = \begin{bmatrix}1&0&0\\3&1&0\\9&3&1\end{bmatrix}$ and $B=[b_{ij}],\ 1\le i,j\le 3$. If $B=A^{99}-I$…

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10. Q10 2026 6 Apr Shift 2

    Let $A = \begin{bmatrix} 1 & 3 & -1 \\ 2 & 1 & \alpha \\ 0 & 1 & -1 \end{bmatrix}$ be a singular matrix. Let…

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11. Q11 2026 8 Apr Shift 2

    Let A = [[α,1,2],[2,3,0],[0,4,5]] and B = [[1,0,0],[0,-5α,0],[0,4α,-2α]] + adj(A). If det(B) = 66, then…

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