List of top Mathematics Questions on Properties of Determinants asked in BITSAT

If beginvmatrix p & q-y & r-z
p-x & q & r-z
p-x & q-y & r endvmatrix=0, then the value of (p)/(x)+(q)/(y)+(r)/(z) is
If the matrix beginbmatrix 1 & 3 & λ+2
2 & 4 & 8
3 & 5 & 10 endbmatrix is singular, then λ=
If [x] denotes the greatest integer ≤ x and -1≤ x<0, 0≤ y<1, 1≤ z<2, then the value of the determinant beginvmatrix [x]+1 & [y] & [z]
[x] & [y]+1 & [z]
[x] & [y] & [z]+1 endvmatrix is
Let M be a 3×3 non-singular matrix with det(M)=α. If |M⁴operatornameadj(M)|=K, then the value of K is
If \(x, y, z\) are complex numbers, and
\[ \Delta = \begin{vmatrix} 0 & -y & -z \\ \overline{y} & 0 & -x \\ \overline{z} & \overline{x} & 0 \end{vmatrix}, \]
then \(\Delta\) is:

If

\( \begin{vmatrix} p & q - y & r - z \\ p - x & q & r - z \\ p - x & q - y & r \end{vmatrix} = 0 \),


then the value of \( \dfrac{p}{x} + \dfrac{q}{y} + \dfrac{r}{z} \) is

If \( [x] \) denotes the greatest integer less than or equal to \( x \), and \( -1 < x < 0 < y < 1 < z < 2 \), then the value of the determinant

\( \begin{vmatrix} [x] + 1 & [y] & [z] \\ [x] & [y] + 1 & [z] \\ [x] & [y] & [z] + 1 \end{vmatrix} \)
is
If the matrix beginpmatrix 1 & 3 & λ+2
2 & 4 & 8
3 & 5 & 10 endpmatrix is singular, then λ=
Let \(M\) be a \(3\times3\) non-singular matrix with \(\det(M)=\alpha\). If \(|M^{-1}\operatorname{adj}(M)|=K\), then the value of \(K\) is
If \[ \begin{vmatrix} p & q - y & r - z \\ p - x & q & r - z \\ p - x & q - y & r \end{vmatrix} = 0, \] then the value of \(\dfrac{p}{x} + \dfrac{q}{y} + \dfrac{r}{z}\) is
The determinant \[ \left| \begin{matrix} 1 & x & x^2 \\ 1 & x^3 & x^4 \\ 1 & x^5 & x^6 \end{matrix} \right| \] vanishes for
The value of the determinant \[ \begin{vmatrix} 265 & 240 & 219 \\ 240 & 225 & 198 \\ 191 & 198 & 181 \end{vmatrix} \] is:
If A=bmatrix2&0&0
2&2&0
2&2&2bmatrix, then det(adj A) is equal to:
The value of vmatrix 1 & 2 & 3
-4 & 3 & 6
2 & -7 & 9 vmatrix is