Q JEE Main 2024

Let 𝐴 be a 2 × 2 symmetric matrix such that $A\left[\begin{array}{l}1 \\ 1\end{array}\right]=\left[\begin{array}{l}3 \\ 7\end{array}\right]$ and the determinant of...

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Q JEE Main 2024

Let $A=\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right]$ and $B=I+\operatorname{adj}(A)+(\operatorname{adj} A)^2+\cdots+(\operatorname{adj} A)^{10}$. Then, the sum of all the elements of...

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Q JEE MAIN 2024

Let $A=I_2-2 M^{\mathrm{T}}$, where M is real matrix of order $2 \times 1$ such that the relation $\mathrm{M}^{\mathrm{T}} \mathrm{M}=\mathrm{I}_1$ holds....

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Q JEE MAIN 2024

Let $\mathrm{R}=\left(\begin{array}{lll}\mathrm{x} & 0 & 0 \\ 0 & \mathrm{y} & 0 \\ 0 & 0 & \mathrm{z}\end{array}\right)$ be a...

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Q Jee Main 2024

Let $A$ be a $3 \times 3$ matrix and $\operatorname{det}(A)=2$. If $\mathrm{n}=\operatorname{det}(\underbrace{\operatorname{adj}(\operatorname{adj}(\ldots \ldots}(\operatorname{adj} A))))$ Then the remainder when n is...

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Q JEE-Main 2024

Let A be a $2 \times 2$ real matrix and I be the identity matrix of order 2 . If...

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Q Jee Main 2024

Let A be a $3 \times 3$ real matrix such that $...

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Q Jee Main 2024

Let $A=\left[\begin{array}{ccc}2 & 1 & 2 \\ 6 & 2 & 11 \\ 3 & 3 & 2\end{array}\right]$ and $...

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Q JEE MAIN 2026

Let $A=\left[\begin{array}{ll}3 & -4 \\ 1 & -1\end{array}\right]$ and $B$ be two matrices such that $A^{100}=100 B+I$. Then the sum...

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Q JEE MAIN 2026

Let $\mathrm{A}_2 \mathrm{~B}$ and $C$ be three $2 \times 2$ matrices with real entries such that $B=(I+A)^{-1}$ and $\mathrm{A}+\mathrm{C}=\mathrm{I}$. If...

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Q JEE MAIN 2026

Let $A=\left[\begin{array}{ccc}0 & 2 & -3 \\ -2 & 0 & 1 \\ 3 & -1 & 0\end{array}\right]$ and $B$...

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Q JEE MAIN 2026

The system of linear equations $$ \begin{aligned} & x+y+z=6 \\ & 2 x+5 y+a z=36 \\ & x+2 y+3 z=b...

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Q JEE MAIN_2026_

Let $|\mathrm{A}|=6$, where A is a $3 \times 3$ matrix. If $...

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Q JEE MAIN_2026_

Among the statements :

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Q JEE MAIN 2026

If $X=\left[\begin{array}{c}x \\ y \\ z\end{array}\right]$ is a solution of the system of equations $A X=B$, where $...

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Q JEE MAIN_2026

Let $A$ be a $3 \times 3$ matrix such that $A+A^T=O$. If $...

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Q JEE MAIN_2026_

If $\mathrm{A}=\left[\begin{array}{ll}2 & 3 \\ 3 & 5\end{array}\right]$, then the determinant of the matrix $\left(\mathrm{A}^{2025}-3 \mathrm{~A}^{2024}+\mathrm{A}^{2023}\right)$ is

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Q JEE MAIN 2026

For the matrices $\mathrm{A}=\left[\begin{array}{ll}3 & -4 \\ 1 & -1\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{ll}-29 & 49 \\ -13 & 18\end{array}\right]$, if $...

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Q JEE MAIN 2026

For some $\quad \alpha, \beta \in \mathbf{R}, \quad$ let $\quad A=\left[\begin{array}{ll}\alpha & 2 \\ 1 & 2\end{array}\right] \quad$ and $...

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Q JEE MAIN_2019_

If the system of linear equations $$ \begin{aligned} & x+y+z=5 \\ & x+2 y+2 z=6 \\ & x+3 y+\lambda z=\mu,(\lambda,...

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Q JEE MAIN 2019

$...

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Q JEE MAIN 2019

If $B=\left[\begin{array}{ccc}5 & 2 \alpha & 1 \\ 0 & 2 & 1\end{array}\right]$ is the inverse of a $...

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Q JEE MAIN 2019

If $A$ is a symmetric matrix and $B$ is a skew-symmetric matrix such that $...

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Q JEE Main 2020

Let $A$ be a $2 \times 2$ real matrix with entries from $\{0,1\}$ and $|A| \neq 0$. Consider the following...

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Q JEE MAIN 2020

Let $A=\left\{X=(x, y, z)^{\top}: P X=0\right.$ and $\left.x^2+y^2+z^2=1\right\}$, where $...

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Q JEE MAIN 2020

Let $a, b, c \in R$ be all non-zero and satisfy $a^3+b^3+c^3=2$. If the matrix $$ A=\left(\begin{array}{lll} a & b...

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Q JEE MAIN 2019

If $...

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Q JEE MAIN 2019

If the system of linear equations x – 4y + 7z = g 3y – 5z = h – 2x...

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Q JEE MAIN 2019

The set of all values of $\lambda$ for which the system of linear equations $$ \begin{aligned} & x-2 y-2 z=\lambda...

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Q JEE MAIN 2019

The expression $\sim(\sim p \rightarrow q)$ is logically equivalent to

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Q JEE MAIN 2020

The negation of the Boolean expression $p \vee(\sim p \wedge q)$ is equivalent to

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Q JEE MAIN 2020

Let $\theta=\frac{\pi}{5}$ and $\mathrm{A}=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]$. If $\mathrm{B}=\mathrm{A}+\mathrm{A}^4$, then $\operatorname{det}(\mathrm{B})$ :

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Q JEE MAIN 2019

lf $$ A=\left[\begin{array}{ccc} e^t & e^{-t} & e^{-t} \sin t \\ e^t & -e^t \cos t-e^{-t} \sin t & -e^{-t}...

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Q JEE MAIN 2020

The numer of all $3 \times 3$ matrices A , with enteries from the set $\{-1,0,1)$ such that the sum...

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Q JEE MAIN 2019

Let $A=\left(\begin{array}{ccc}0 & 2 q & r \\ p & q & -r \\ p & -q & r\end{array}\right)$. If...

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Q JEE MAIN 2019

If the system of linear equations $$ \begin{aligned} & 2 x+2 y+3 z=a \\ & 3 x-y+5 z=b \\ &...

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Q JEE Main 2019

https://competishun.com/let-f-r-rightarrow-r-be-a-function-such-that-fxx3x2-fprime1x-fprime-prime2fprime-prime-prime3-x-in-r-then-f2-equals/ has infinitely many solutions, then $\beta-\alpha$ equals

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Q JEE MAIN 2020

$$ \text { If } A=\left[\begin{array}{cc} \cos \theta & i \sin \theta \\ i \sin \theta & \cos \theta \end{array}\right],\left(\theta=\frac{\pi}{24}\right)...

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Q JEE MAIN 2019

Contrapositive of the statement “If two numbers are not equal, then their squares are not equal.” is :

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Q JEE MAIN 2020

Which of the following statements is a tautology?

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Q JEE MAIN 2019

Let $A$ and $B$ be two invertible matrices of order $3 \times 3$. If $\operatorname{det}\left(A B A^{\top}\right)=8$ and $\operatorname{det}\left(A B^{-1}\right)=8$,...

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Q JEE MAIN 2019

The logical statement (MF ST-1) $[\sim(\sim p \vee q) \vee(p \wedge r)] \wedge(\sim q \wedge r)$ is equivalent to

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Q JEE MAIN 2019

If the system of linear equations $$ \begin{gathered} x-4 y+7 z=g \\ 3 y-5 z=h \\ -2 x+5 y-9 z=k...

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Q JEE MAIN 2020

If $\mathrm{A}=\left(\begin{array}{ll}2 & 2 \\ 9 & 4\end{array}\right)$ and $\mathrm{I}=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)$, then $10 \mathrm{~A}^{-1}$ is...

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Q JEE MAIN 2019

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Q JEE Main 2021

The number of elements in the set $\left\{A=\left(\begin{array}{ll}a & b \\ 0 & d\end{array}\right): a, b, d \in\{-1,0,1\}\right.$ and $\left.(I-A)^3=I-A^3\right\}$...

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Q JEE MAIN 2019

If the system of equations 2x+3y-z=0, x+ky-2z=0 and $2 x-y+z=0$ has a non-trivial solution $(x, y, z)$, then $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}+k$ is...

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Q JEE MAIN 2020

Let $\alpha$ be a root of the equation $x^2+x+1=0$ and the matrix $...

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Q JEE MAIN 2019

The number of values of $\theta \in(0, \pi)$ for which the system of linear equations $$ \begin{aligned} & x+3 y+7...

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Q JEE MAIN 2021

If the matrix $A=\left[\begin{array}{cc}0 & 2 \\ k & -1\end{array}\right]$ satisfies $A\left(A^3+3 I\right)=2 I$, then the value of $K$ is...

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Q JEE Main 2021

If $A=\left(\begin{array}{cc}\frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ \frac{-2}{\sqrt{5}} & \frac{1}{\sqrt{5}}\end{array}\right), B=\left(\begin{array}{ll}1 & 0 \\ i & 1\end{array}\right), i=\sqrt{-1}$, and $Q=A^{\top} B A$,...

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Q JEE MAIN_2021_

Let $A=\left(\begin{array}{ccc}{[x+1]} & {[x+2]} & {[x+3]} \\ {[x]} & {[x+3]} & {[x+3]} \\ {[x]} & {[x+2]} & {[x+4]}\end{array}\right)$, where $[t]$...

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Q JEE MAIN 2021

Let A be a $3 \times 3$ real matrix. If $\operatorname{det}(2 \operatorname{Adj}(2 \operatorname{Adj}(\operatorname{Adj}(2 A))))=2^{41}$, then the value of $\operatorname{det}\left(A^2\right)$ equal...

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Q JEE Main 2019

If $A=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]$, then the matrix $A^{-50}$ when $\theta=\frac{\pi}{12}$, is equal...

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Q JEE MAIN 2019

Let $\quad \mathrm{A}=\left(\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right),(\alpha \in \mathrm{R}) \quad$ such that $...

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Q JEE MAIN 2019

The greatest value of $c \in R$ for which the system of linear equations $$ \begin{aligned} & x-c y-c z=0...

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Q JEE Main 2019

The system of linear equations $$ \begin{aligned} & x+y+z=2 \\ & 2 x+3 y+2 z=5 \\ & 2 x+3 y+\left(a^2-1\right)...

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Q JEE MAIN 2021

Let $\mathrm{A}=\left(\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 0\end{array}\right)$. Then $\mathrm{A}^{2025}-\mathrm{A}^{2020}$...

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Q JEE MAIN_2021

Let $M=\left\{A=\left(\begin{array}{ll}a & b \\ c & d\end{array}\right): a, b, c, d \in\{ \pm 3, \pm 2, \pm 1,0\}\right\}$ Difine...

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Q JEE MAIN 2021 S2

If $A=\left[\begin{array}{lll}1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1\end{array}\right]$ and $...

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Q JEE MAIN 2021 S2

Let $A$ and $B$ be two $3 \times 3$ real matrices such that $\left(A^2-B^2\right)$ is invertible matrix. If $A^5=B^5$ and...

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Q JEE MAIN 2019

If the system of linear equations $$ \begin{aligned} & x-2 y+k z=1 \\ & 2 x+y+z=2 \\ & 3 x-y-k...

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Q JEE MAIN 2019

Let the numbers 2, $\mathrm{b}, \mathrm{c}$ be in an A.P. and $...

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Q JEE MAIN 2021

If the matrix $\mathrm{A}=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 2 & 0 \\ 3 & 0 & -1\end{array}\right]$...

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Q JEE MAIN 2021

Let $A=\left[\begin{array}{cc}1 & 2 \\ -1 & 4\end{array}\right]$. If $A^{-1}=\alpha I+\beta A, \alpha, \beta \in R, I$ is a $...

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Q JEE MAIN 2021

If $P=\left[\begin{array}{cc}1 & 0 \\ 1 / 2 & 1\end{array}\right]$, then $P^{50}$ is :

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Q JEE MAIN_22-

Let $A=\left[a_i\right]$ be a real matrix of order $3 \times 3$, such that $a_{i 1}+a_{i 2}+a_{i 3}=1$, for $i=1,2,3$. Then,...

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Q JEE MAIN 2021

let $A=\left(\begin{array}{ccc}1 & -1 & 0 \\ 0 & 1 & -1 \\ 0 & 0 & 1\end{array}\right)$ and $...

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Q JEE-MAIN 2021

Let $A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$ and $B=\left[\begin{array}{l}\alpha \\ \beta\end{array}\right] \neq\left[\begin{array}{l}0 \\ 0\end{array}\right]$ such that $A B=B$ and...

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Q JEE MAIN 2021

Let $A=\left[\begin{array}{ll}2 & 3 \\ a & 0\end{array}\right], a \in R$ be written as $P+Q$ where $P$ is a symmetric...

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Q JEE MAIN 2021

Let $I$ be an identity matrix of order $2 \times 2$ and $P=\left[\begin{array}{ll}2 & -1 \\ 5 & -3\end{array}\right]$. Then...

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Q JEE MAIN 2021

If for the matrix, $A=\left[\begin{array}{cc}1 & -\alpha \\ \alpha & \beta\end{array}\right], A A^{\top}=I_2$, then the value of $\alpha^4+\beta^4$ is :

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Q JEE MAIN 2021

Let $P=\left[\begin{array}{ccc}3 & -1 & -2 \\ 2 & 0 & \alpha \\ 3 & -5 & 0\end{array}\right]$, where $...

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Q JEE MAIN 2021

Let $A=\left[\begin{array}{l}a_1 \\ a_2\end{array}\right]$ and $B=\left[\begin{array}{l}b_1 \\ b_2\end{array}\right]$ be two $2 \times 1$ matrices with real entries such that $\mathrm{A}=\mathrm{XB}$,...

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Q JEE MAIN 2021

Let $\mathrm{A}=\left\{\mathrm{a}_{\mathrm{ij}}\right\}$ be a $3 \times 3$ matrix, where $\mathrm{a}_{\mathrm{ij}}=\left\{\begin{array}{cll}(-1)^{\mathrm{j}-\mathrm{i}} & \text { if } & \mathrm{i}\mathrm{j},\end{array}\right.$, hen $...

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Q JEE MAIN 2021

Let M be any 3 × 3 matrix with entries from the set {0, 1, 2}. The maximum number of...

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Q JEE MAIN_2021_

If $A=\left(\begin{array}{cc}0 & \sin \alpha \\ \sin \alpha & 0\end{array}\right)$ and $\operatorname{det}=\left(A^2-\frac{1}{2} I\right)=0$ then a possible value of $\alpha$ is

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Q JEE MAIN 2021

For the system of linear equations : $$ x-2 y=I, x-y+k z=-2, k y+4 z=6, k \in R, $$ consider...

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Q JEE MAIN 2021

Let $A$ and $B$ be $3 \times 3$ real matrices such that $A$ is symmetric matrix and $B$ is skew-symmetric...

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Q JEE MAIN 2021

Let $A+2 B=\left[\begin{array}{ccc}1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1\end{array}\right]$ and...

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Q JEE-MAIN 2021

Let

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Q JEE-MAIN 2021

The total number of 3 × 3 matrices A having enteries from the set (0, 1, 2, 3) such that...

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Q JEE MAIN 2021

Let $A=\left[\begin{array}{cc}i & -i \\ -i & i\end{array}\right], i=\sqrt{-1}$ Then, the system of linear equation $A^8=\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}8 \\ 64\end{array}\right]$...

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Q JEE MAIN 2021

Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of...

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Q JEE MAIN 2021

If $A=\left[\begin{array}{cc}0 & -\tan \left(\frac{\theta}{2}\right) \\ \tan \left(\frac{\theta}{2}\right) & 0\end{array}\right]$ and $\left(I_2+A\right)\left(I_2-A\right)^{-1}= \left[\begin{array}{cc}a & -b \\ b & a\end{array}\right]$, then...

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Q JEE MAIN 2021

Let $A=\left[\begin{array}{lll}x & y & z \\ y & z & x \\ z & x & y\end{array}\right]$, where $...

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Q JEE MAIN_2022

Let A be a 2 × 2 matrix with det (A) = –1 and det ((A + I) (Adj (A)...

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Q JEE MAIN 2022

Let $A=\left[\begin{array}{ccc}2 & -1 & -1 \\ 1 & 0 & -1 \\ 1 & -1 & 0\end{array}\right]$ and $B=A-I$....

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Q MEMORY BASED QUESTION 2026

If $A=\left[\begin{array}{ll}\alpha & 2 \\ 1 & 2\end{array}\right], B=\left[\begin{array}{ll}1 & 1 \\ \beta & 1\end{array}\right]$ and $...

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Q JEE MAIN 2022

Let A be a matrix of order 2 × 2, whose entries are from the set {0, 1, 2, 3,...

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Q JEE MAIN 2022

Let $M=\left[\begin{array}{cc}0 & -\alpha \\ \alpha & 0\end{array}\right]$, where $\alpha$ is a non-zero real number an $N=\sum_{k=1}^{49} M^{2 k}$. If...

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Q JEE MAIN 2022

Let $A=\left(\begin{array}{cc}1+i & 1 \\ -i & 0\end{array}\right)$ where $i=\sqrt{-1}$. Then, the number of elements in the set $...

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Q JEE MAIN 2022

Let $...

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Q JEE MAIN 2022

Let $\mathrm{S}=\left\{\left(\begin{array}{cc}-1 & \mathrm{a} \\ 0 & \mathrm{~b}\end{array}\right) ; \mathrm{a}, \mathrm{b} \in\{1,2,3, \ldots 100\}\right\}$ and let $\mathrm{T}_{\mathrm{n}}=\left\{\mathrm{A} \in \mathrm{S}: \mathrm{A}^{\mathrm{n}(\mathrm{n}+1)}=\mathrm{I}\right\}$....

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Q JEE MAIN 2022

Let $A=\left(\begin{array}{ll}2 & -2 \\ 1 & -1\end{array}\right)$ and $B=\left(\begin{array}{ll}-1 & 2 \\ -1 & 2\end{array}\right)$. Then the number of...

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Q JEE MAIN 2022

Let $A$ and $B$ be two $3 \times 3$ matrices such that $A B=I$ and $|A|=\frac{1}{8}$ then $|\operatorname{adj}(\operatorname{Badj}(2 A))|$ is...

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Q JEE MAIN 2022

Let $\mathrm{A}=\left[a_{i j}\right]$ be a square matrix of order 3 such that $a_{i j}=2^{i-i}$, for all $\mathrm{i}_{\text {and }} \mathrm{j}=1,2,3$....

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Q JEE MAIN 2022

The positive value of the determinant of the matrix $A$, whose $...

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Q JEE MAIN 2022

If the system of linear equations $...

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Q JEE MAIN 2022

Let $A$ be a matrix of order $3 \times 3$ and $\operatorname{det}(A)=2$. Then $\operatorname{det}\left(\operatorname{det}(A)\right.$ adj $\left(5 \operatorname{adj}\left(A^3\right)\right)$ ) is equal...

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Q JEE MAIN 2022

Let $A=\left[\begin{array}{cc}0 & -2 \\ 2 & 0\end{array}\right]$. If $M$ and $N$ are two matrices given by $M=\sum_{k=1}^{10} A^{2 k}$...

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Q JEE MAIN 2024

Let $A$ be $a \times 3$ real matrix such that $...

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Q JEE MAIN 2022

Let $S=\{\sqrt{n}: 1 \leq n \leq 50$ and $n$ is odd $\}$ Let $a \in S$ and $...

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Q

If $\mathrm{A}=\left[\begin{array}{cc}1 & 5 \\ \lambda & 10\end{array}\right], \mathrm{A}^{-1}=\alpha \mathrm{A}+\beta \mathrm{I}$ and $\alpha+\beta=-2$, then $4 \alpha^2+\beta 2+\lambda^2$ is equal to...

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Q JEE MAIN 2023

Among the statements $(\mathrm{S} 1):(\mathrm{p} \Rightarrow \mathrm{q}) \vee((\sim \mathrm{p}) \wedge \mathrm{q})$ is a tautology $...

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Q JEE MAIN 2023

Let P be a square matrix such that $\mathrm{P}^2=\mathrm{I}-\mathrm{P}$. For $\alpha, \beta, \gamma, \delta \in \mathrm{N}$, if $\mathrm{P}^\alpha+\mathrm{P}^\beta=\gamma \mathrm{I}-29 \mathrm{P}$...

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Q JEE MAIN 2025

Let $I$ be the identity matrix of order $3 \times 3$ and for the matrix $...

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Q JEE MAIN 2025

Let $...

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Q JEE MAIN 2025

Let A be a $3 \times 3$ real matrix such that $A^2(A-2 I)-4(A-I)=O$, where I and O are the identity...

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Q JEE MAIN 2025

Let the matrix $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0\end{array}\right]$...

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Q JEE MAIN 2023

Negation of $p \wedge(q \wedge \sim(p \wedge q))$ is

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Q JEE MAIN 2023

Let $B=\left[\begin{array}{ccc}1 & 3 & \alpha \\ 1 & 2 & 3 \\ \alpha & \alpha & \alpha\end{array}\right], \alpha>2$ be...

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Q JEE MAIN 2023

Let the determinant of a square matrix A of order m be m – n, where m and n satisfy...

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Q JEE MAIN 2023

The number of symmetric matrices of order 3, with all the entries from the set {0, 1, 2, 3, 4,...

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Q JEE-Main 2023

Let $\mathrm{A}=\left[\mathrm{a}_{\mathrm{i}}\right] 2 \times 2$ where $\mathrm{a}_{\mathrm{i}} \neq 0$ for all $\mathrm{i}, \mathrm{j}$ and $\mathrm{A}^2=\mathrm{I}$. Let a be the sum...

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Q JEE MAIN 2023

Let $A=\left[\begin{array}{lll}0 & 1 & 2 \\ a & 0 & 3 \\ 1 & c & 0\end{array}\right]$, where $...

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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...

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Q JEE MAIN 2023

Let $A=\left[\begin{array}{cc}1 & \frac{1}{51} \\ 0 & 1\end{array}\right]$. If $...

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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 -

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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...

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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

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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...

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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 $...

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Q JEE MAIN 2024

Let $A$ be a $3 \times 3$ matrix of non-negative real elements such that $...

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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...

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Q JEE MAIN 2024

Let $\alpha \in(0, \infty)$ and $...

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Q JEE MAIN 2024

Let $A$ and $B$ be two square matrices of order 3 such that $|A|=3$ and $|B|=2$. Then $...

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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 $...

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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

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Let $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha\end{array}\right]$ and $...

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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 $\mathrm{X}=\mathrm{A}^{\mathrm{T}} \mathrm{C}^2 \mathrm{~A}$,...

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Q JEE MAIN 2024

Let $...

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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...

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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...

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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 ______.

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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...

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Q JEE MAIN 2025

Let $A = \left[ {\begin{array}{*{20}{c}} {\cos \theta }&0&{ - \sin \theta }\\ 0&1&0\\ {\sin \theta }&0&{\cos \theta } \end{array}} \right]$....

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Q JEE MAIN 2025

Let A be a matrix of order $3 \times 3$ and $|A| = 5$. If $...

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Q JEE MAIN 2025

For some a, b, let $$ f(x)=\left|\begin{array}{ccc} a+\frac{\sin x}{x} & 1 & \mathbf{b} \\ \mathbf{a} & 1+\frac{\sin x}{x} & \mathbf{b}...

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Q JEE MAIN 2025

If the system of equations $x+2 y-3 z=2$ $2 x+\lambda y+5 z=5$ $14 x+3 y+\mu z=33$ has infinitely many solutions,...

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Q JEE MAIN 2025

Let $a \in R$ and A be a matrix of order $3 \times 3$ such that $...

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Q JEE MAIN 2025

Let $A = \left[ {\begin{array}{*{20}{c}} \alpha &{ - 1}\\ 6&\beta \end{array}} \right],\alpha > 0$, such that $\det (A) = 0$...

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Q JEE MAIN 2025

The system of equations $x+y+z=6$, $x+2 y+5 z=9$, $x+5 y+\lambda z=\mu$, has no solution if

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Q JEE MAIN 2025

Let $\mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\right]$ be a $3 \times 3$ matrix such that $\mathrm{A}\left[\begin{array}{l}0 1 0\end{array}\right]=\left[\begin{array}{l}0 0 1\end{array}\right], \mathrm{A}\left[\begin{array}{l}4 1 3\end{array}\right]=\left[\begin{array}{l}0 1 0\end{array}\right]$...

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Q JEE MAIN 2025

Let $S=\left\{m \in \mathbf{Z}: A^{m^2}+A^m=3 I-A^{-6}\right\}$, where $A=\left[\begin{array}{cc}2 & -1 \\ 1 & 0\end{array}\right]$. Then $n(S)$ is equal to ______.

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Q JEE MAIN 2025

Let M and N respectively be the maximum and the minimum values of $...

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Q JEE MAIN 2025

Let M denote the set of all real matrices of order $3 \times 3$ and let $...

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Q JEE MAIN 2025

Let A be a $3 \times 3$ matrix such that ${X^T}AX = O$ for all nonzero $3 \times 1$ matrices...

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Q JEE MAIN 2025

If the system of equations $2x - y + z = 4$ $5x + \lambda y + 3z = 12$...

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Q JEE MAIN 2025

If A,B, and $\left( {{\mathop{\rm adj}\nolimits} \left( {{{\rm{A}}^{ - 1}}} \right) + {\mathop{\rm adj}\nolimits} \left( {{{\rm{B}}^{ - 1}}} \right)} \right)$...

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Q JEE MAIN 2025

If the system of equations $(\lambda -1)\text{x}+(\lambda -4)\text{y}+\lambda \text{z}=5$ $\lambda \text{x}+(\lambda -1)\text{y}+(\lambda -4)\text{z}=7$ $(\lambda +1)\text{x}+(\lambda +2)\text{y}-(\lambda +2)\text{z}=9$ has infinitely many...

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Q JEE MAIN 2025

If the system of linear equations : $$ \begin{aligned} & x+y+2 z=6 \\ & 2 x+3 y+a z=a+1 \\ &...

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Q JEE MAIN 2025

For a $3 \times 3$ matrix $M$, let trace $(M)$ denote the sum of all the diagonal elements of $M$....

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