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Manipal Engineering Manipal Engineering Solved Paper-2010

  • question_answer
    The number of values of the triplet\[(a,\,\,b,\,\,c)\]for  which\[a\cos 2x+b{{\sin }^{2}}x+c=0\]is satisfied by all real\[x\], is

    A)  0                                            

    B)  2

    C)  3                            

    D)         infinite

    Correct Answer: D

    Solution :

    \[a\cos 2x+b{{\sin }^{2}}x+c=0\] \[\Rightarrow \]               \[a(1-2{{\sin }^{2}}x)b{{\sin }^{2}}x+c=0\] \[ie\],    \[(b-2a){{\sin }^{2}}x+(a+c)=0\] It is an identity, if\[b-2a=0,\,\,a+c=0\], so                 \[\frac{a}{1}=\frac{b}{2}=\frac{c}{-1}\] Thus, number of triplet\[(a,\,\,b,\,\,c)\]are infinite.


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