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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 34

  • question_answer
    \[x+y+z=15\] if 9, x, y, z, a are in A.P. while \[\frac{1}{X}+\frac{1}{Y}+\frac{1}{Z}=\frac{5}{3}\] if 9, X, Y, Z, a are in H.P., then the value of a will be-

    A) 1     

    B)        2     

    C) 3                     

    D)        9

    Correct Answer: A

    Solution :

    [a] 9, x, y, z, a are in A.P. \[x+y+z=15\Rightarrow 3\left[ \frac{9+a}{2} \right]=15\] \[a=1\] 9, X, Y, Z, a are in H.P. \[\frac{1}{9},\frac{1}{X},\frac{1}{Y},\frac{1}{Z},\frac{1}{a}\] are in A.P. \[\frac{1}{X}+\frac{1}{Y}+\frac{1}{Z}=\frac{5}{3}\Rightarrow 3\frac{\left[ \frac{1}{9}+\frac{1}{a} \right]}{2}=\frac{5}{3}\Rightarrow a=1\]


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