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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2001

  • question_answer
    The function \[f(x)=sin\left( \frac{\pi x}{2} \right)+2cos\left( \frac{\pi x}{3} \right)-\tan \left( \frac{\pi x}{4} \right)\]is a periodic function. It's period is

    A)  6                 

    B)  3

    C)  4                 

    D)  12

    Correct Answer: D

    Solution :

     Period of\[\sin \frac{\pi x}{2}=\frac{2\pi }{\pi /2}=4\] Period of\[\cos \frac{\pi x}{3}=\frac{2\pi }{\pi /3}=6\] and period of\[\tan \frac{\pi x}{4}=\frac{\pi }{\pi /4}=4\] \[\therefore \]Period of the given function \[f(x)\] = LCM of 4, 6 and 4 \[=12\]


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