2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Determinants & Matrices

JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Self Evaluation Test - Determinats

  • question_answer
    Matrix \[{{M}_{r}}\] is defined as \[{{M}_{r}}=\left( \begin{matrix}    r & r-1  \\    r-1 & r  \\ \end{matrix} \right),\]\[r\in N\].  The value of  \[det({{M}_{1}})+\det \,({{M}_{2}})+\det \,({{M}_{3}})+....+\det \,({{M}_{2014}})\] is

    A) \[2013\]

    B) \[2014\]

    C) \[{{(2013)}^{2}}\]

    D) \[{{(2014)}^{2}}\]

    Correct Answer: D

    Solution :

    [d] det \[(Mr)=\left| \begin{matrix}    r & r-1  \\    r-1 & r  \\ \end{matrix} \right|=2r-1\] \[\sum\limits_{r=1}^{2014}{\det ({{M}_{r}})=2\sum\limits_{r=1}^{2014}{r-2014}}\] \[=2\times \frac{2014\times 2015}{2}-2014={{(2014)}^{2}}\]


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