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

JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Expansion of determinants, Solution of equation in the form of determinants and properties of determinants

  • question_answer
    If \[{{D}_{p}}=\left| \,\begin{matrix}    p & 15 & 8  \\    {{p}^{2}} & 35 & 9  \\    {{p}^{3}} & 25 & 10  \\ \end{matrix}\, \right|\], then \[{{D}_{1}}+{{D}_{2}}+{{D}_{3}}+{{D}_{4}}+{{D}_{5}}=\] [Kurukshetra CEE 1998]

    A) 0

    B) 25

    C) 625

    D) None of these

    Correct Answer: D

    Solution :

    \[{{D}_{1}}=\left| \,\begin{matrix}    1 & 15 & 8  \\    1 & 35 & 9  \\    1 & 25 & 10  \\ \end{matrix}\, \right|,{{D}_{2}}=\left| \,\begin{matrix}    2 & 15 & 8  \\    4 & 35 & 9  \\    8 & 25 & 10  \\ \end{matrix}\, \right|\] \[{{D}_{3}}=\left| \,\begin{matrix}    3 & 15 & 8  \\    9 & 35 & 9  \\    27 & 25 & 10  \\ \end{matrix}\, \right|,{{D}_{4}}=\left| \,\begin{matrix}    4 & 15 & 8  \\    16 & 35 & 9  \\    64 & 25 & 10  \\ \end{matrix}\, \right|\] \[{{D}_{5}}=\left| \,\begin{matrix}    5 & 15 & 8  \\    25 & 35 & 9  \\    125 & 25 & 10  \\ \end{matrix}\, \right|\] Þ \[{{D}_{1}}+{{D}_{2}}+{{D}_{3}}+{{D}_{4}}+{{D}_{5}}=\left| \,\begin{matrix}    15 & 75 & 40  \\    55 & 175 & 45  \\    225 & 125 & 50  \\ \end{matrix}\, \right|\] \[=15(3125)-75(-7375)+40(-32500)\] \[=46875+553125-1300000=-700000\] .


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