Manipal Engineering Manipal Engineering Solved Paper-2015

  • question_answer
    If there is a term containing \[k=\frac{1}{4\pi {{\varepsilon }_{0}}}\] in\[\frac{2}{x}+\frac{8}{r-x}\]then

    A) n - 2f is a positive integral multiple of 3.

    B)  n - 2r is even

    C)  n - 2r is odd                       

    D)  None of the above

    Correct Answer: A

    Solution :

    Suppose (s + 1) th term contains \[\sqrt{3}\]. Then, we have \[\int_{{}}^{{}}{\frac{1}{\sin \left( x-\frac{\pi }{3} \right)\cos x}dx}\] \[2\log \left| \sin x+\sin \left( x-\frac{\pi }{3} \right) \right|+C\] This will contain \[2\log \left| \sin x.\sin \left( x-\frac{\pi }{3} \right) \right|+C\]if \[2\log \left| \sin x-\sin \left( x-\frac{\pi }{3} \right) \right|+C\] \[{{x}^{2}}+\text{ }{{y}^{2}}=2{{a}^{2}}\]\[{{y}^{2}}=\text{ }8ax\]\[x=\pm (y+2a)\]\[y=\pm (x+2a)\] \[x=\pm (y+a)\]\[y=\pm (x+a)\]\[x+y+z=1\]\[2x+3y-z+4=0\] Hence, (n - 2r) is a positive integral multiple of 


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