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  3. RAJASTHAN ­ PET

RAJASTHAN ­ PET Rajasthan PET Solved Paper-2003

  • question_answer
    \[\left| \begin{matrix}    {{1}^{2}} & {{2}^{2}} & {{3}^{2}}  \\    {{2}^{2}} & {{3}^{2}} & {{4}^{2}}  \\    {{3}^{2}} & {{4}^{2}} & {{5}^{2}}  \\ \end{matrix} \right|\]is equal to

    A)  8                 

    B)  \[-8\]

    C)  400               

    D)  1

    Correct Answer: B

    Solution :

     \[\left| \begin{matrix}    {{1}^{2}} & {{2}^{2}} & {{3}^{2}}  \\    {{2}^{2}} & {{3}^{2}} & {{4}^{2}}  \\    {{3}^{2}} & {{4}^{2}} & {{5}^{5}}  \\ \end{matrix} \right|=\left| \begin{matrix}    1 & 4 & 9  \\    4 & 9 & 16  \\    9 & 16 & 25  \\ \end{matrix} \right|\] \[=\left| \begin{matrix}    1 & 4 & 9  \\    3 & 5 & 7  \\    5 & 7 & 9  \\ \end{matrix} \right|[{{R}_{3}}\to {{R}_{3}}-{{R}_{2}},{{R}_{2}}\to {{R}_{2}}-{{R}_{1}}]\] \[=1(45-49)-4(27-35)+9(21-25)\] \[=-4-4(-8)+9(-4)\] \[=-4+32-36=-8\]


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