AIEEE 2004 (Maths) Mock Test

Let $A=\left(\begin{array}{ccc}0& 0& -1\\ 0& -1& 0\\ -1& 0& 0\end{array}\right).$ The only correct statement about the matrix $A$ is

Let $A=\left(\begin{array}{ccc}1& -1& 1\\ 2& 1& -3\\ 1& 1& 1\end{array}\right)$ and $10B=\left(\begin{array}{ccc}4& 2& 2\\ -5& 0& a\\ 1& -2& 3\end{array}\right).$ If $B$ is the inverse of matrix $A,$ then $a$ is

If $a_1,a_2,a_3,....,a_n,....$ are in G.P., then the value of the determinant
$$\left|\begin{array}{ccc}\log a_n& \log a_{n+1}& \log a_{n+2}\\ \log a_{n+3}& \log a_{n+4}& \log a_{n+5}\\ \log a_{n+6}& \log a_{n+7}& \log a_{n+8}\end{array}\right|$$
is

Let two numbers have arithmetic mean $9$ and geometric mean $4.$ Then these numbers are the roots of the quadratic equation

If $(1-p)$ is a root of quadratic equation $x^2+px+(1-p)=0,$ then its roots are