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JEE Main & Advanced Sample Paper JEE Main Sample Paper-20

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


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