Solved papers for JEE Main & Advanced AIEEE Solved Paper-2003

done AIEEE Solved Paper-2003 Total Questions - 3

• question_answer1) If \[\left| \begin{matrix}    a & {{a}^{2}} & 1+{{a}^{3}}  \\  b & {{b}^{2}} & 1+{{b}^{3}}  \\   c & {{c}^{2}} & 1+{{c}^{3}}  \\ \end{matrix} \right|=0\] and vectors \[(1,\,\,a,\,\,{{a}^{2}})\], \[(1,\,\,a,\,\,{{a}^{2}})\] and \[(1,\,\,c,\,\,{{c}^{2}})\] are non-coplanar, then the product abc equals     AIEEE  Solved  Paper-2003
  A)
  2                             
  done clear
  B)
  -1                           
  done clear
  C)
  1                             
  done clear
  D)
  0
  done clear
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• question_answer2) If the system of linear equations                 \[x+2\] ay \[+\,az=0\]                 \[x+3\] by \[+\,bz=0\] and        \[x+4\] cy \[+cz=0\] has a non-zero solution, then a, b, c     AIEEE  Solved  Paper-2003
  A)
                          are in AP                             
  done clear
  B)
  are in GP                             
  done clear
  C)
  are in HP                             
  done clear
  D)
  satisfy a+2b+3c=0
  done clear
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• question_answer3) If \[1,\,\omega ,\,{{\omega }^{2}}\]are the cube roots of unity, then                 \[\Delta =\left| \begin{matrix}    1 & {{\omega }^{n}} & {{\omega }^{2n}}  \\    {{\omega }^{n}} & {{\omega }^{2n}} & 1  \\    {{\omega }^{2n}} & 1 & {{\omega }^{n}}  \\ \end{matrix} \right|\] is equal to     AIEEE  Solved  Paper-2003
  A)
                          0                             
  done clear
  B)
  1                             
  done clear
  C)
  \[\omega \]                       
  done clear
  D)
        \[{{\omega }^{2}}\]
  done clear
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