If $[x]$ denotes the greatest integer $\leq x$, then the range of the real valued function $f(x)=\frac{1}{\sqrt{x-[x]}}$ is

If $A$ is a $2 \times 2$ matrix such that $\operatorname{det} A=-21$ and trace of $A^3$ is 2024 , then the trace of $A$ is

If $\left[\begin{array}{lll}a & b & c \\ d & e & f \\ g & h & i\end{array}\right]$ is a skew-symmetric matrix and $b, c$ and $f$ are non-zero real numbers, then $\frac{b}{c}=$

In the matrix $\left[\begin{array}{ccc}-1 & x & 3 \\ -4 & -5 & -6 \\ -7 & y & 9\end{array}\right]$, if the cofactors of -6 and -7 are respectively 22 and 27 , then $5 x+y=$