JEE Main & Advanced Sample Paper JEE Main Sample Paper-4

  • question_answer
    If z is a complex number & minimum value of \[|z|+|z-1|+|2z-3|\]is K & if\[y=2[x]+3=3[x-k],\]then value of \[[x+y]=\] (where [.] is GIF)

    A)  15                         

    B)  9      

    C)  30                         

    D)  21

    Correct Answer: C

    Solution :

    \[|z|+|z-1|+|2z-3|=|z|+|z-1|+|3-2|\ge \] \[|z+z-1+3-2z|\] \[\therefore \]\[|z|+|z-1|2z-3|\ge 2\Rightarrow \lambda =2\] \[y=2[x]+3=3[x-2]\Rightarrow [x]=9\] \[y=2\times 9+3=21\] \[\Rightarrow \]\[[x+y]=[x+21]=[x]+21=30\]

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