JEE Advanced · 2018 · 20 May 2018 · Paper 2 · Determinants

More JEE Advanced questions on Determinants

1. 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 …
   JEE Advanced 2024 Copy linkView solution →
2. 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
   

   $$g(\theta )=\sqrt{f(\theta )-1}+\sqrt{f\left(\frac{\pi }{2}-\theta \right)-1}$$

   
   where …
   JEE Advanced 2022 Copy linkView solution →
3. 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 …
   JEE Advanced 2021 Copy linkView solution →
4. 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 …
   JEE Advanced 2021 Copy linkView solution →
5. 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
   JEE Advanced 2017 Copy linkView solution →
6. 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
   JEE Advanced 2016 Copy linkView solution →