List of top Mathematics Questions on Applications of Determinants and Matrices asked in LPUNEST

If the cost price of an article is 500 and it is sold at a profit of $10%$, what is the selling price?
If \(P = \{1, 2\}\), then \(P \times P \times P = \{(1,1,1), (1,1,2), (1,2,1), (2,1,2), (2,2,1), (2,2,2)\}\). The ordered triplet missing in \(P \times P \times P\) are:
If \(x,y,z\) are in A.P. with common difference \(d\) and the rank of the matrix \[ \begin{pmatrix} 4 & 5 & x \\ 5 & 6 & y\\ 6 & k & z \end{pmatrix} \] is \(2\), then the values of \(k,d\) are:
If \[ \left| \begin{array}{ccc} x^{n} & x^{n+2} & x^{n+3} \\ y^{n} & y^{n+2} & y^{n+3} \\ z^{n} & z^{n+2} & z^{n+3} \end{array} \right| =(x-y)(y-z)(z-x)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right) \] then \(n\) is equal to:
If \(A=(a_{ij})_{4\times 4}\) such that \[ a_{ij}= \begin{cases} 2 & \text{if } i=j\\ 0 & \text{if } i\neq j \end{cases} \] then \[ \left\{\dfrac{\det(\operatorname{adj}(\operatorname{adj}A))}{7}\right\} \] is (where \(\{\ \}\) represents fractional part function)
If \(x\neq 0,\; y\neq 0,\; z\neq 0\) and \[ \left| \begin{array}{ccc} 1+x & 1 & 1 \\ 1+y & 1+2y & 1 \\ 1+z & 1+z & 1+3z \end{array} \right|=0, \] then \(x^{-1}+y^{-1}+z^{-1}=\)