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Manipal Engineering Manipal Engineering Solved Paper-2015

  • question_answer
    The number of solutions of the equation \[{{r}_{2}}\]belonging to the domain of definition of \[{{E}_{2}}{{r}_{1}}>{{E}_{1}}(R+{{r}_{2}})\] {(x + 1) (x + 2)}, is

    A)  1                                            

    B) 2

    C) 3                                             

    D) 4

    Correct Answer: C

    Solution :

      We have,\[9{{x}^{2}}-18|x|+5=0\] \[\Rightarrow \]\[9|x{{|}^{2}}-18|x|+5=0\] \[\Rightarrow \]\[(3|x|-1)(3|x|-5)=0\] \[\Rightarrow \]\[|x|=\frac{1}{3}\]or\[|x|=\frac{5}{3}\]\[\Rightarrow \]\[x=\pm \frac{1}{3}\]or\[x=\pm \frac{5}{3}\] Now, logg{(x + 1) (x + 2)} is defined, if \[x+1x+2>0\] \[\Rightarrow \]x < - 2 or x > - 1 Clearly, \[x=-\frac{5}{3}\] does not satisfy this condition. But all other values of x satisfy the above conditions. Hence, the number of solutions lying in the domain of definition of the given function is 3.


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