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JEE Main & Advanced JEE Main Paper (Held On 26 May 2012)

  • question_answer
    Statement 1: If the system of equations\[x+ky+3z=0,\]\[3x+ky-2z=0,\]\[2x+3y-4z=0\]has anon- trivial 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.   JEE Main Online Paper (Held On 26-May-2012)  

    A) Statement 1 is false, Statement 2 is true.

    B)                        Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.

    C)                        Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.

    D)                         Statement 1 is true, Statement 2 is false.

    Correct Answer: A

    Solution :

                    Given system of equations is \[x+ky+3z=0\] \[3x+ky-2z=0\] \[2x+3y-4z=0\] Since, system has non-trivial solution \[\therefore \]\[\left| \begin{matrix}    1 & k & 3  \\    3 & k & -2  \\    2 & 3 & -4  \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[1(-4k+6)-k(-12+4)+3(9-2k)=0\] \[\Rightarrow \]\[4k+33-6k=0\Rightarrow k=\frac{33}{2}\] Hence, statement -1 is, false. Statement-2 is the property. It is a true statement.


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