Matrices & Determinants · JEE Main previous year questions

2012 3 questions

1. Q112012 · 26 May 2012 · Shift 1

   Statement 1: If the system of equations $x+ky+3z=0,3x+ky-2z=0,2x+3y-4z=0$ has a nontrivial solution, then the value of $k$ is $\frac{31}{2}$. Statement 2: A system of three homogeneous equations in three variables has a non trivial solution if the determinant of the coefficient matrix is zero.

   1. A.Statement 1 is false, Statement 2 is true.
   2. B.Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
   3. C.Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
   4. D.Statement 1 is true, Statement 2 is false.
   Show answer

   Answer: A

2. Q102012 · 12 May 2012 · Shift 1

   Let $A$ and $B$ be real matrices of the form $\left[\begin{array}{cc}\alpha & 0\\ 0& \beta \end{array}\right]$ and $\left[\begin{array}{cc}0& \gamma \\ \delta & 0\end{array}\right]$, respectively. Statement 1: $AB-BA$ is always an invertible matrix. Statement 2: $AB-BA$ is never an identity matrix.

   1. A.Statement 1 is true, Statement 2 is false.
   2. B.Statement 1 is false, Statement 2 is true.
   3. C.Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.
   4. D.Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation of Statement 1.
   Show answer

   Answer: B

3. Q112012 · 7 May 2012 · Shift 1

   If $A=\left(\begin{array}{c}\alpha -1\\ 0\\ 0\end{array}\right),B=\left(\begin{array}{c}\alpha +1\\ 0\\ 0\end{array}\right)$ be two matrices, then $A{B}^T$ is a non-zero matrix for $|\alpha |$ not equal to

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

   Answer: C