2. Solved Papers
  3. JAMIA MILLIA ISLAMIA

JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2009

  • question_answer
        If \[f(x)=\]\[\left| \begin{matrix}    1 & x & x+1  \\    2x & x(x-1) & (x+1)x  \\    3x(x-1) & x(x-1)(x-2) & (x+1)x(x-1)  \\ \end{matrix} \right|\]then\[f(100)\]is equal to

    A)  0                                            

    B)  1

    C)  100                                       

    D)  \[-100\]

    Correct Answer: A

    Solution :

                    \[f(x)=\] \[\left| \begin{matrix}    1 & x & x+1  \\    2x & x(x-1) & (x+1)x  \\    3x(x-1) & x(x-1)(x-2) & (x+1)x(x-1)  \\ \end{matrix} \right|\] Applying\[{{R}_{3}}\to {{R}_{3}}-({{R}_{1}}+{{R}_{2}})\] \[=\left| \begin{matrix}    1 & x & 0  \\    2x & x(x-1) & 0  \\    3x(x-1) & x(x-1)(x-2) & 0  \\ \end{matrix} \right|=0\] \[\therefore \]  \[f(x)=0\Rightarrow f(100)=0\]


You need to login to perform this action.
You will be redirected in 3 sec spinner