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JEE Main & Advanced Sample Paper JEE Main Sample Paper-11

  • question_answer
    If a is real and \[\sqrt{2ax}+\sin \]By\[+\cos Bz=0\],\[x+\cos \]By\[+\sin \]\[Bz=0,-x+\sin By-\]\[\cos Bz=0,\]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. \[\Delta =\left| \begin{matrix}    \sqrt{2a} & \sin B & \cos B  \\    1 & \cos B & \sin B  \\    -1 & \sin B & -\cos B  \\ \end{matrix} \right|-\] \[\Rightarrow \]\[a\sqrt{2}[-{{\cos }^{2}}B-{{\sin }^{2}}B]-\sin B[-\cos B+\sin B]\] \[+\cos B[\sin B+\cos B]=0\] \[\Rightarrow \]\[-a\sqrt{2}+\sin 2B+\cos 2B=0\Rightarrow a\in [-1,1]\]


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