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KVPY Sample Paper KVPY Stream-SX Model Paper-16

  • question_answer
    Let \[{{n}_{1}}=\sin 7+cos7,\] \[{{n}_{2}}=\sqrt{\sin 7}+\sqrt{\cos 7,}\]\[{{n}_{3}}=\sqrt{1+\sin 14,}\] \[{{n}_{4}}=1,\] then-

    A) \[{{n}_{2}}>{{n}_{3}}>{{n}_{4}}>{{n}_{1}}\]

    B) \[{{n}_{3}}>{{n}_{4}}>{{n}_{2}}>{{n}_{1}}\]

    C) \[{{n}_{3}}={{n}_{1}}>{{n}_{4}}>{{n}_{2}}\]

    D) \[{{n}_{2}}>{{n}_{1}}={{n}_{3}}>{{n}_{4}}\]

    Correct Answer: D

    Solution :

    \[\because \sqrt{1+\sin 14}>1\Rightarrow {{n}_{3}}>{{n}_{4}}\] \[\sqrt{1+\sin 14}=\sqrt{{{(\sin 7+\cos 7)}^{2}}}\]\[=\sin 7+\cos 7\And \sqrt{\sin 7}>\sin 7\] \[\sqrt{\cos 7}>\cos 7\] \[\therefore {{n}_{2}}>{{n}_{1}}={{n}_{3}}>{{n}_{4}}\]


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