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Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2024
Let $A$ and $B$ be two square matrices of order 3 such that $|A|=3$ and $|B|=2$. Then $\left|A^T A(\operatorname{adj}(2 A))^{-1}(\operatorname{adj}(4 B))(\operatorname{adj}(A B))^{-1} A A^T\right|$ is...
JEE Main Mathematics Easy
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Q JEE MAIN 2024
Let $A=\left[\begin{array}{lll}2 & a & 0 \\ 1 & 3 & 1 \\ 0 & 5 & b\end{array}\right]$. If $A^3=4 A^2-A-21 I$, where 1 is...
JEE Main Mathematics Hard
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Q JEE MAIN
Let A be a square matrix such that $A A^T=I$. Then $\frac{1}{2} A\left[\left(A+A^T\right)^2+\left(A-A^T\right)^2\right]$ is equal to
JEE Main Mathematics Medium
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Q JEE MAIN
Let $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha\end{array}\right]$ and $|2 A|^3=2^{21}$ where $...
JEE Main Mathematics Easy
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Q JEE-Main 2024
If $\mathrm{A}=\left[\begin{array}{cc}\sqrt{2} & 1 \\ -1 & \sqrt{2}\end{array}\right], \mathrm{B}=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right], \mathrm{C}=\mathrm{ABA}^{\mathrm{T}}$ and $\mathrm{X}=\mathrm{A}^{\mathrm{T}} \mathrm{C}^2 \mathrm{~A}$, then $\operatorname{det} \mathrm{X}$ is equal...
JEE Main Mathematics Easy
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Q JEE MAIN 2024
Let $A=\left[\begin{array}{lll}2 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 1\end{array}\right], B=\left[B_1, B_2, B_3\right]$, where $B_1, \mathrm{~B}_2, \mathrm{~B}_3$...
JEE Main Mathematics Hard
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Q JEE MAIN 2025
Let $\alpha, \beta(\alpha \neq \beta)$ be the values of $m$, for which the equations $x+y+z=1 ; x+2 y+4 z=m$ and $x+4 y+10 z=m^{2}$ have infinitely...
JEE Main Mathematics Easy
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Q JEE MAIN 2025
Let $A=\left[\begin{array}{cc}\frac{1}{\sqrt{2}} & -2 0 & 1\end{array}\right]$ and $\mathrm{P}=\left[\begin{array}{cc}\cos \theta & -\sin \theta \sin \theta & \cos \theta\end{array}\right], \theta>0$. If $\mathrm{B}=\mathrm{PAP}^{\mathrm{T}}, \mathrm{C}=\mathrm{P}^{\mathrm{T}} \mathrm{B}^{10} \mathrm{P}$ and...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
The number of singular matrices of order 2, whose elements are from the set {2,3,6,9}, is ______.
JEE Main Mathematics Hard
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Q JEE MAIN 2025
Let A be a $3 \times 3$ matrix such that $|{\mathop{\rm adj}\nolimits} ({\mathop{\rm adj}\nolimits} ({\mathop{\rm adj}\nolimits} {\rm{A}}))| = 81$.
If $...
JEE Main Mathematics Medium
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