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JEE Main & Advanced Sample Paper JEE Main Sample Paper-24

  • question_answer
    Let \[a+b+c=s\] and \[\left| \begin{matrix}    s+c & a & b  \\    c & s+a & b  \\    c & a & s+b  \\ \end{matrix} \right|\] is equal to 54, then the value of s is

    A)  2                                

    B)  3

    C)  4                                

    D)  5

    Correct Answer: B

    Solution :

    \[{{C}_{1}}\to {{C}_{1}}+{{C}_{2}}\,+{{C}_{3}};\] we get \[=(a+b+c+s)\,\left| \begin{matrix}    1 & a & b  \\    1 & s+a & b  \\    1 & a & s+b  \\ \end{matrix} \right|\] \[=2s\,\left| \begin{matrix}    0 & -s & 0  \\    0 & s & -s  \\    1 & a & s+b  \\ \end{matrix} \right|\,=2{{s}^{3}}=54\] \[\therefore \,\,{{s}^{3}}=27\] \[s=3\]


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