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JEE Main & Advanced Sample Paper JEE Main Sample Paper-14

  • question_answer
    The number of solutions of the system of equations \[\{x\}+y+[z]=2.3,\] \[x+[y]+\{z\}=4.5\] and \[[x]+\{y\}+z=6.2,\] where \[\{\cdot \}\] and \[[\cdot ]\] denote fractional part and greatest integer function respectively

    A)  0                                            

    B)  1                 

    C)  2                                            

    D)  3

    Correct Answer: B

    Solution :

     On adding giving equations, we get \[x+\{x\}\,=[x\}+y+[y]\,+\{y\}+z+[z]\] \[+[z]=13\] \[\Rightarrow \]               \[2x+2y+2z=13\]  \[(\because \,x=[x]+\{x\})\] \[\Rightarrow \]               \[x+y+z=6.5\] Also, \[(x-\{x\})+(z-[z])=6.5-2.3\] \[\Rightarrow \]               \[[x]+[z]=4.2\] \[\Rightarrow \]               \[[x]=4,\,\,\{z\}=0.2\] Similarly, \[\{y\}+[z]=2\,\,\,\Rightarrow \,\,\,\{y\}=0,\,\,[z]=2\] Also, \[\{x\}+[y]=0.3\] \[\Rightarrow \]               \[\{x\}=0.3\] and \[[y]=0\] \[\therefore \] \[x=[x]+[x]\,=4+0.3=4.3\] \[x=[y]\,+\{y\}\,=0+0=0\] \[z=[z]+\{z\}=2\,+0.2\,=2.2\] Hence, (4, 3, 0, 2, 2) is the only solution.


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