KVPY Sample Paper KVPY Stream-SX Model Paper-9

  • question_answer
    Let P=\[\left\{ \theta :\sin \theta -\cos \,\theta \sqrt{2}\cos \theta  \right\}\]and \[\left\{ \theta :\sin \theta +\cos \,\theta \sqrt{2}\sin \theta  \right\}\]be two sets. Then

    A) \[P\subset Q\,and\,Q-P\ne \phi \]

    B) \[Q\subset P\]

    C) \[P\subset Q\]

    D) \[P=Q\]

    Correct Answer: D

    Solution :

    \[P=\{\theta :\sin \theta -\cos \theta =\sqrt{2}\cos \theta \}\]
    \[\sin \theta =\left( \sqrt{2}+1 \right)\cos \theta \Rightarrow \tan \theta =\sqrt{2}+1\]
    \[Q=\{\theta :\sin \theta +\cos \theta =\sqrt{2}\sin \theta \}\]
    \[\cos \theta =\left( \sqrt{2}-1 \right)\sin \theta \Rightarrow \tan \theta =\sqrt{2}+1\]
    \[\therefore P=Q\]


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