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JEE Main & Advanced JEE Main Paper (Held on 10-4-2019 Morning)

  • question_answer
    If the system of linear equations
    \[x+y+z=5\]
    \[x+2y+2z=6\]
    \[x+3y+\lambda z=\mu ,\]\[(\lambda ,\mu \in R),\]has infinitely many solutions, then the value of \[\lambda +\mu \] is :
    [JEE Main 10-4-2019 Morning]

    A) 12                               

    B) 10

    C) 9                                 

    D) 7

    Correct Answer: B

    Solution :

    \[x+3y+\lambda z-\mu =p(x+y+z-5)+\]           \[q(x+2y+2z-6)\] on comparing the coefficient; \[p+q=1\]and \[p+2q=3\] \[\Rightarrow (p,q)=(-1,2)\] Hence \[x+3y+\lambda z-\mu =x+3y+3z-7\] \[\Rightarrow \lambda =3,\mu =7\]


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