Which one of the following does NOT equal \left|\begin{array}{ccc}1 & x & x^{2\end{array} ; 1 , y , y^{2} ; 1 , z , z^{2} ; |}?

Correct Answer is : |1x(x+1)x+11y(y+1)y+11z(z+1)z+1|

\left|\begin{array}{ccc}1 & x (x + 1) & x + 1 \ 1 & y (y + 1) & y + 1 \ 1 & z (z + 1) & z + 1 \ |\end{array}

\left|\begin{array}{ccc}1 & x + 1 & x^{2\end{array} + 1 ; 1 , y + 1 , y^{2} + 1 ; 1 , z + 1 , z^{2} + 1 ; |}

\left|\begin{array}{ccc}0 & x−y & x^{2\end{array}−y^{2} ; 0 , y−z , y^{2}−z^{2} ; 1 , z , z^{2} ; |}

\left|\begin{array}{ccc}2 & x + y & x^{2\end{array} + y^{2} ; 2 , y + z , y^{2} + z^{2} ; 1 , z , z^{2} ; |}

GATE Computer Science (CS) 2013 Solved Paper

Question : 13 of 65

Marks: +1, -0

Which one of the following does NOT equal

{|\table 1 , x , x^{2} ; 1 , y , y^{2} ; 1 , z , z^{2} ; |}

${|\table 1 , x (x + 1) , x + 1 ; 1 , y (y + 1) , y + 1 ; 1 , z (z + 1) , z + 1 ; |}$
${|\table 1 , x + 1 , x^{2} + 1 ; 1 , y + 1 , y^{2} + 1 ; 1 , z + 1 , z^{2} + 1 ; |}$
${|\table 0 , x−y , x^{2}−y^{2} ; 0 , y−z , y^{2}−z^{2} ; 1 , z , z^{2} ; |}$
${|\table 2 , x + y , x^{2} + y^{2} ; 2 , y + z , y^{2} + z^{2} ; 1 , z , z^{2} ; |}$

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