KVPY Sample Paper KVPY Stream-SX Model Paper-5

  • question_answer
    The number of integral values of k for which the equation \[7\cos x+5\sin x=2k+1\] has a solution is

    A) 4                                 

    B) 8       

    C) 10                                

    D) 12

    Correct Answer: B

    Solution :

    We have, \[7\cos x+5\sin x=2k+1\]
    The minimum and maximum value of \[7\cos x+5\sin x\] is \[-\sqrt{{{7}^{2}}+{{5}^{2}}},\sqrt{{{7}^{2}}+{{5}^{2}}}\],\[-\sqrt{74},\sqrt{74}\]
    \[\therefore \]\[-\sqrt{74}<2k+1<\sqrt{74}\]
    \[\Rightarrow \]\[-\,8<2k+1<8\]
    \[\Rightarrow \]\[-\,4\le k\le 3\]
    Total 8 integral value.

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