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Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2023
Let $A$ be a $2 \times 2$ matrix with real entries such that $A^{\prime}=\alpha A+I$, where $\alpha \in \mathbb{R}-\{-1,1\}$. If $\operatorname{det}\left(A^2-A\right)=4$, then the sum of...
JEE Main Mathematics Hard
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Q JEE MAIN 2023
Let $A=\left[\begin{array}{cc}1 & \frac{1}{51} \\ 0 & 1\end{array}\right]$. If $B=\left[\begin{array}{cc}1 & 2 \\ -1 & -1\end{array}\right] A\left[\begin{array}{cc}-1 & -2 \\ 1 & 1\end{array}\right]$, then the...
JEE Main Physics Hard
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Q JEE MAIN 2023
Let $f(x)=\frac{\sin x+\cos x-\sqrt{2}}{\sin x-\cos x}, x \in[0, \pi]-\left\{\frac{\pi}{4}\right\}$. Then $f\left(\frac{7 \pi}{12}\right) f^{\prime \prime}\left(\frac{7 \pi}{12}\right)$ is equal to -
JEE Main Mathematics Medium
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Q JEE MAIN 2023
Let $P=\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right], A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]$ and $Q=P Q P^{\top}$. If $...
JEE Main Mathematics Medium
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Q JEE MAIN 2023
If $A$ is a $3 \times 3$ matrix and $|A|=2$, then $\left|3 \operatorname{adj}\left(|3 A| A^2\right)\right|$ is equal to
JEE Main Mathematics Easy
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Q JEE-Main 2023
Let $\mathrm{A}=\left[a_{i j}\right]_{2 \times 2}$ where $a_{i j} \neq 0$ for all $\mathrm{j}_i \mathrm{j}$ and $\mathrm{A}^2=\mathrm{I}$. Let a be the sum of all diagonal elements...
JEE Main Mathematics Medium
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Q JEE MAIN
Let A be a non-singular matrix of order 3. If $\operatorname{det}(3 \operatorname{adj}(2 \operatorname{adj}((\operatorname{det} A) A)))=3^{-13} \cdot 2^{-10}$ and det $(3 \operatorname{adj}(2 A))=2^m \cdot 3^n$, then...
JEE Main Mathematics Easy
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Q JEE MAIN 2024
Let $A$ be a $3 \times 3$ matrix of non-negative real elements such that $A\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]=3\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$. Then the...
JEE Main Mathematics Hard
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Q JEE MAIN 2024
Let $A=\left[\begin{array}{cc}2 & -1 \\ 1 & 1\end{array}\right]$. If the sum of the diagonal elements of $A^{13}$ is $3^n$, then $n$ is equal to
JEE Main Mathematics Medium
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Q JEE MAIN 2024
Let $\alpha \in(0, \infty)$ and $A=\left[\begin{array}{lll}1 & 2 & \alpha \\ 1 & 0 & 1 \\ 0 & 1 & 2\end{array}\right]$. If $...
JEE Main Mathematics Hard
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