Matrices & Determinants · JEE Main previous year questions

2004 3 questions

1. Q242004 · 24 Apr 2004 · Shift 1

   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

   1. A.$A^2=I$
   2. B.$A=(-1)I$, where $I$ is a unit matrix
   3. C.$A^{-1}$ does not exist
   4. D.$A$ is a zero matrix
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   Answer: A

2. Q252004 · 24 Apr 2004 · Shift 1

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

   1. A.$5$
   2. B.$-1$
   3. C.$2$
   4. D.$-2$
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   Answer: A

3. Q262004 · 24 Apr 2004 · Shift 1

   If $a_1,a_2,a_3,\dots \dots \dots ,a_n,\dots \dots$ 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

   1. A.$-2$
   2. B.$1$
   3. C.$2$
   4. D.$0$
   Show answer

   Answer: D