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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2001

  • question_answer
    If the solutions for\[\theta \]of \[\cos p\theta +\cos q\theta =0,p>q>0\]are in AP, then the numerically smallest common difference of AP is:

    A)  \[-\frac{\pi }{p+q}\]                      

    B)  \[\frac{2\pi }{p+q}\]

    C)  \[\frac{\pi }{2(p+q)}\]  

    D)         \[\frac{1}{p+q}\]

    E)  \[\frac{1}{2(p+q)}\]

    Correct Answer: B

    Solution :

    The given equation can be rewritten as \[\cos p\theta =\cos (\pi -q\theta )\] \[\Rightarrow \] \[p\theta =2n\pi \pm (\pi -q\theta )\] Taking\[+\]sign                 \[(p+q)\theta =(2n+1)\pi \] \[\Rightarrow \]               \[\theta =\frac{(2n+1)\pi }{(p+q)}\] Thus, the solution are in AP with common difference\[\left( \frac{2\pi }{p+q} \right)\].


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