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JEE Main & Advanced Sample Paper JEE Main Sample Paper-8

  • question_answer
    If a is real and \[\sqrt{2}ax+\sin \text{ }By+\cos \text{ }Bz=0,\] \[x+\cos \text{ }By+\sin \text{ }Bz=0,-x+\sin \text{ }By-\cos \]\[Bz=0,\]then the set of all values of a for which the system of linear equations has a non-trivial solution, is -

    A)  [1, 2]                    

    B)  [-1, 1]

    C)   \[[1,\infty ]\]                                  

    D)  \[[{{2}^{-1/2}},{{2}^{1/2}}]\]

    Correct Answer: B

    Solution :

     For non-trivial solution, \[\Delta =\left| \begin{matrix}    \sqrt{2}a & \sin B & \cos B  \\    1 & \cos B & \sin B  \\    -1 & \sin B & -\cos B  \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[a\sqrt{2}[-{{\cos }^{2}}B-{{\sin }^{2}}B]-\sin B[-\cos B+\sin B]\] \[+\cos B[\sin B+\cos B]=0\] \[\Rightarrow \]\[-a\sqrt{2}+\sin 2B+\cos 2B=0\Rightarrow a\in [-1,1]\]


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