Determinants — JEE Advanced PYQs

Let $\mathrm{S}=\{\mathrm{A}=\left(\begin{array}{lll}0& 1& \mathrm{c}\\ 1& \mathrm{a}& \mathrm{d}\\ 1& \mathrm{b}& \mathrm{e}\end{array}\right):\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d},\mathrm{e}\in \{0,1\}$ and …

Let $|M|$ denote the determinant of a square matrix $M$. Let $g:\left[0,\frac{\pi }{2}\right]\to \mathbb{R}$ be the function defined by

where …

Let $\alpha ,\beta$ and $\gamma$ be real numbers such that the system of linear equations
$x+2y+3z=\alpha$
$4x+5y+6z=\beta$
$7x+8y+9z=\gamma -1$
is consistent. Let $|M|$ represent the determinant of the matrix …

For any 3 × 3 matrix M, let $|M|$ denote the determinant of M. Let
$E=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 4\\ 8& 13& 18\end{array}\right],P=\left[\begin{array}{lll}1& 0& 0\\ 0& 0& 1\\ 0& 1& 0\end{array}\right]$ and …

Let $P$ be a matrix of order $3\times 3$ such that all the entries in $P$ are from the set $\{-1,0,1\}$. Then, the maximum possible value of the determinant of $P$ is ____.

If $f(x)=\left|\begin{array}{ccc}\cos (2x)& \cos (2x)& \sin (2x)\\ -\cos x& \cos x& -\sin x\\ \sin x& \sin x& \cos x\end{array}\right|$, then

The total number of distinct $x\in \mathbb{R}$ for which $\left|\begin{array}{ccc}x& x^2& 1+x^3\\ 2x& 4x^2& 1+8x^3\\ 3x& 9x^2& 1+27x^3\end{array}\right|=10$ is

Which of the following values of $\alpha$ satisfy the equation …

Let $P=\left[a_{ij}\right]$ be a $3\times 3$ matrix and let $Q=\left[b_{ij}\right]$, where $b_{ij}=2^{i+j}{a}_{ij}$ for $1\le i,j\le 3$. If the determinant of $P$ is 2 , then the determinant of the matrix $Q$ is

Let $\omega \ne 1$ be a cube root of unity and $S$ be the set of all non-singular matrices of the form

where each of $a$, $b$, and $c$ is either $\omega$ or …

Let p be an odd prime number and $T_p$ be the following set of $2\times 2$ matrices:


The number of A in $T_p$ such that $\det (A)$ is not divisible by p is

Consider the following linear equations

Match the conditions/expressions in Column I with statements in Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 m …